id	sid	tid	token	lemma	pos
asir-1804	1	1	applied	apply	VERB
asir-1804	1	2	science	science	NOUN
asir-1804	1	3	and	and	CCONJ
asir-1804	1	4	innovative	innovative	ADJ
asir-1804	1	5	research	research	NOUN
asir-1804	1	6	issn	issn	VERB
asir-1804	1	7	2474	2474	NUM
asir-1804	1	8	-	-	SYM
asir-1804	1	9	4972	4972	NUM
asir-1804	1	10	(	(	PUNCT
asir-1804	1	11	print	print	NOUN
asir-1804	1	12	)	)	PUNCT
asir-1804	1	13	issn	issn	VERB
asir-1804	1	14	2474	2474	NUM
asir-1804	1	15	-	-	SYM
asir-1804	1	16	4980	4980	NUM
asir-1804	1	17	(	(	PUNCT
asir-1804	1	18	online	online	ADJ
asir-1804	1	19	)	)	PUNCT
asir-1804	1	20	vol	vol	NOUN
asir-1804	1	21	.	.	PROPN
asir-1804	2	1	3	3	NUM
asir-1804	2	2	,	,	PUNCT
asir-1804	2	3	no	no	INTJ
asir-1804	2	4	.	.	NOUN
asir-1804	2	5	1	1	NUM
asir-1804	2	6	,	,	PUNCT
asir-1804	2	7	2019	2019	NUM
asir-1804	2	8	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1804	2	9	15	15	NUM
asir-1804	2	10	original	original	ADJ
asir-1804	2	11	paper	paper	NOUN
asir-1804	2	12	software	software	NOUN
asir-1804	2	13	for	for	ADP
asir-1804	2	14	teaching	teach	VERB
asir-1804	2	15	through	through	ADP
asir-1804	2	16	interactive	interactive	ADJ
asir-1804	2	17	demonstrations	demonstration	NOUN
asir-1804	2	18	about	about	ADP
asir-1804	2	19	converging	converge	VERB
asir-1804	2	20	lenses	lense	NOUN
asir-1804	2	21	pavlos	pavlos	PROPN
asir-1804	2	22	mihas1	mihas1	PROPN
asir-1804	2	23	*	*	PROPN
asir-1804	2	24	1	1	NUM
asir-1804	2	25	department	department	NOUN
asir-1804	2	26	of	of	ADP
asir-1804	2	27	primary	primary	ADJ
asir-1804	2	28	education	education	NOUN
asir-1804	2	29	,	,	PUNCT
asir-1804	2	30	democritus	democritus	PROPN
asir-1804	2	31	university	university	PROPN
asir-1804	2	32	of	of	ADP
asir-1804	2	33	thrace	thrace	NOUN
asir-1804	2	34	,	,	PUNCT
asir-1804	2	35	greece	greece	PROPN
asir-1804	2	36	received	receive	VERB
asir-1804	2	37	:	:	PUNCT
asir-1804	2	38	january	january	PROPN
asir-1804	2	39	9	9	NUM
asir-1804	2	40	,	,	PUNCT
asir-1804	2	41	2019	2019	NUM
asir-1804	2	42	accepted	accept	VERB
asir-1804	2	43	:	:	PUNCT
asir-1804	2	44	january	january	PROPN
asir-1804	2	45	27	27	NUM
asir-1804	2	46	,	,	PUNCT
asir-1804	2	47	2019	2019	NUM
asir-1804	2	48	online	online	ADV
asir-1804	2	49	published	publish	VERB
asir-1804	2	50	:	:	PUNCT
asir-1804	2	51	february	february	PROPN
asir-1804	2	52	1	1	NUM
asir-1804	2	53	,	,	PUNCT
asir-1804	2	54	2019	2019	NUM
asir-1804	2	55	doi:10.22158	doi:10.22158	NOUN
asir-1804	2	56	/	/	SYM
asir-1804	2	57	asir.v3n1p15	asir.v3n1p15	PROPN
asir-1804	2	58	url	url	PROPN
asir-1804	2	59	:	:	PUNCT
asir-1804	2	60	http://dx.doi.org/10.22158/asir.v3n1p15	http://dx.doi.org/10.22158/asir.v3n1p15	PROPN
asir-1804	2	61	abstract	abstract	NOUN
asir-1804	2	62	in	in	ADP
asir-1804	2	63	this	this	DET
asir-1804	2	64	paper	paper	NOUN
asir-1804	2	65	,	,	PUNCT
asir-1804	2	66	software	software	NOUN
asir-1804	2	67	is	be	AUX
asir-1804	2	68	presented	present	VERB
asir-1804	2	69	for	for	ADP
asir-1804	2	70	teaching	teach	VERB
asir-1804	2	71	through	through	ADP
asir-1804	2	72	interactive	interactive	ADJ
asir-1804	2	73	demonstrations	demonstration	NOUN
asir-1804	2	74	about	about	ADP
asir-1804	2	75	lenses	lense	NOUN
asir-1804	2	76	.	.	PUNCT
asir-1804	3	1	at	at	ADP
asir-1804	3	2	first	first	ADV
asir-1804	3	3	we	we	PRON
asir-1804	3	4	explore	explore	VERB
asir-1804	3	5	lenses	lense	NOUN
asir-1804	3	6	constructed	construct	VERB
asir-1804	3	7	by	by	ADP
asir-1804	3	8	two	two	NUM
asir-1804	3	9	spherical	spherical	ADJ
asir-1804	3	10	surfaces	surface	NOUN
asir-1804	3	11	.	.	PUNCT
asir-1804	4	1	we	we	PRON
asir-1804	4	2	explore	explore	VERB
asir-1804	4	3	the	the	DET
asir-1804	4	4	ray	ray	NOUN
asir-1804	4	5	diagrams	diagram	NOUN
asir-1804	4	6	and	and	CCONJ
asir-1804	4	7	wave	wave	NOUN
asir-1804	4	8	fronts	front	NOUN
asir-1804	4	9	.	.	PUNCT
asir-1804	5	1	then	then	ADV
asir-1804	5	2	there	there	PRON
asir-1804	5	3	is	be	VERB
asir-1804	5	4	a	a	DET
asir-1804	5	5	page	page	NOUN
asir-1804	5	6	for	for	ADP
asir-1804	5	7	understanding	understand	VERB
asir-1804	5	8	the	the	DET
asir-1804	5	9	thick	thick	ADJ
asir-1804	5	10	lens	lens	NOUN
asir-1804	5	11	model	model	NOUN
asir-1804	5	12	.	.	PUNCT
asir-1804	6	1	we	we	PRON
asir-1804	6	2	introduce	introduce	VERB
asir-1804	6	3	a	a	DET
asir-1804	6	4	step	step	NOUN
asir-1804	6	5	by	by	ADP
asir-1804	6	6	step	step	NOUN
asir-1804	6	7	procedure	procedure	NOUN
asir-1804	6	8	to	to	PART
asir-1804	6	9	find	find	VERB
asir-1804	6	10	the	the	DET
asir-1804	6	11	focal	focal	ADJ
asir-1804	6	12	length	length	NOUN
asir-1804	6	13	and	and	CCONJ
asir-1804	6	14	find	find	VERB
asir-1804	6	15	the	the	DET
asir-1804	6	16	principal	principal	ADJ
asir-1804	6	17	planes	plane	NOUN
asir-1804	6	18	and	and	CCONJ
asir-1804	6	19	finally	finally	ADV
asir-1804	6	20	the	the	DET
asir-1804	6	21	use	use	NOUN
asir-1804	6	22	of	of	ADP
asir-1804	6	23	the	the	DET
asir-1804	6	24	focal	focal	ADJ
asir-1804	6	25	length	length	NOUN
asir-1804	6	26	and	and	CCONJ
asir-1804	6	27	principal	principal	ADJ
asir-1804	6	28	points	point	NOUN
asir-1804	6	29	to	to	PART
asir-1804	6	30	construct	construct	VERB
asir-1804	6	31	the	the	DET
asir-1804	6	32	image	image	NOUN
asir-1804	6	33	.	.	PUNCT
asir-1804	7	1	there	there	PRON
asir-1804	7	2	is	be	VERB
asir-1804	7	3	a	a	DET
asir-1804	7	4	page	page	NOUN
asir-1804	7	5	for	for	ADP
asir-1804	7	6	finding	find	VERB
asir-1804	7	7	the	the	DET
asir-1804	7	8	position	position	NOUN
asir-1804	7	9	of	of	ADP
asir-1804	7	10	the	the	DET
asir-1804	7	11	image	image	NOUN
asir-1804	7	12	not	not	PART
asir-1804	7	13	by	by	ADP
asir-1804	7	14	the	the	DET
asir-1804	7	15	formula	formula	NOUN
asir-1804	7	16	but	but	CCONJ
asir-1804	7	17	by	by	ADP
asir-1804	7	18	the	the	DET
asir-1804	7	19	method	method	NOUN
asir-1804	7	20	we	we	PRON
asir-1804	7	21	use	use	VERB
asir-1804	7	22	on	on	ADP
asir-1804	7	23	an	an	DET
asir-1804	7	24	actual	actual	ADJ
asir-1804	7	25	experiment	experiment	NOUN
asir-1804	7	26	:	:	PUNCT
asir-1804	7	27	we	we	PRON
asir-1804	7	28	move	move	VERB
asir-1804	7	29	the	the	DET
asir-1804	7	30	screen	screen	NOUN
asir-1804	7	31	back	back	ADV
asir-1804	7	32	and	and	CCONJ
asir-1804	7	33	forth	forth	ADV
asir-1804	7	34	until	until	SCONJ
asir-1804	7	35	we	we	PRON
asir-1804	7	36	can	can	AUX
asir-1804	7	37	get	get	VERB
asir-1804	7	38	the	the	DET
asir-1804	7	39	sharpest	sharp	ADJ
asir-1804	7	40	possible	possible	ADJ
asir-1804	7	41	image	image	NOUN
asir-1804	7	42	.	.	PUNCT
asir-1804	8	1	this	this	PRON
asir-1804	8	2	is	be	AUX
asir-1804	8	3	done	do	VERB
asir-1804	8	4	by	by	ADP
asir-1804	8	5	finding	find	VERB
asir-1804	8	6	the	the	DET
asir-1804	8	7	minimum	minimum	NOUN
asir-1804	8	8	of	of	ADP
asir-1804	8	9	a	a	DET
asir-1804	8	10	standard	standard	ADJ
asir-1804	8	11	deviation	deviation	NOUN
asir-1804	8	12	of	of	ADP
asir-1804	8	13	the	the	DET
asir-1804	8	14	position	position	NOUN
asir-1804	8	15	of	of	ADP
asir-1804	8	16	the	the	DET
asir-1804	8	17	rays	ray	NOUN
asir-1804	8	18	for	for	ADP
asir-1804	8	19	a	a	DET
asir-1804	8	20	given	give	VERB
asir-1804	8	21	position	position	NOUN
asir-1804	8	22	of	of	ADP
asir-1804	8	23	the	the	DET
asir-1804	8	24	screen	screen	NOUN
asir-1804	8	25	.	.	PUNCT
asir-1804	9	1	then	then	ADV
asir-1804	9	2	there	there	PRON
asir-1804	9	3	is	be	VERB
asir-1804	9	4	a	a	DET
asir-1804	9	5	simulation	simulation	NOUN
asir-1804	9	6	of	of	ADP
asir-1804	9	7	an	an	DET
asir-1804	9	8	experiment	experiment	NOUN
asir-1804	9	9	for	for	ADP
asir-1804	9	10	finding	find	VERB
asir-1804	9	11	the	the	DET
asir-1804	9	12	focal	focal	ADJ
asir-1804	9	13	length	length	NOUN
asir-1804	9	14	.	.	PUNCT
asir-1804	10	1	this	this	PRON
asir-1804	10	2	uses	use	VERB
asir-1804	10	3	a	a	DET
asir-1804	10	4	macro	macro	NOUN
asir-1804	10	5	to	to	PART
asir-1804	10	6	simulate	simulate	VERB
asir-1804	10	7	the	the	DET
asir-1804	10	8	finding	finding	NOUN
asir-1804	10	9	of	of	ADP
asir-1804	10	10	several	several	ADJ
asir-1804	10	11	image	image	NOUN
asir-1804	10	12	points	point	NOUN
asir-1804	10	13	b	b	NOUN
asir-1804	10	14	for	for	ADP
asir-1804	10	15	several	several	ADJ
asir-1804	10	16	object	object	NOUN
asir-1804	10	17	points	point	NOUN
asir-1804	10	18	a.	a.	NOUN
asir-1804	10	19	these	these	DET
asir-1804	10	20	values	value	NOUN
asir-1804	10	21	are	be	AUX
asir-1804	10	22	used	use	VERB
asir-1804	10	23	first	first	ADV
asir-1804	10	24	in	in	ADP
asir-1804	10	25	the	the	DET
asir-1804	10	26	graphical	graphical	ADJ
asir-1804	10	27	representation	representation	NOUN
asir-1804	10	28	of	of	ADP
asir-1804	10	29	the	the	DET
asir-1804	10	30	image	image	NOUN
asir-1804	10	31	point	point	NOUN
asir-1804	10	32	as	as	ADP
asir-1804	10	33	a	a	DET
asir-1804	10	34	function	function	NOUN
asir-1804	10	35	of	of	ADP
asir-1804	10	36	b	b	NOUN
asir-1804	10	37	and	and	CCONJ
asir-1804	10	38	the	the	DET
asir-1804	10	39	image	image	NOUN
asir-1804	10	40	points	point	VERB
asir-1804	10	41	as	as	ADP
asir-1804	10	42	a	a	DET
asir-1804	10	43	function	function	NOUN
asir-1804	10	44	of	of	ADP
asir-1804	10	45	a.	a.	NOUN
asir-1804	10	46	with	with	ADP
asir-1804	10	47	suitable	suitable	ADJ
asir-1804	10	48	least	least	ADJ
asir-1804	10	49	square	square	ADJ
asir-1804	10	50	fits	fit	NOUN
asir-1804	10	51	we	we	PRON
asir-1804	10	52	get	get	VERB
asir-1804	10	53	two	two	NUM
asir-1804	10	54	lines	line	NOUN
asir-1804	10	55	with	with	ADP
asir-1804	10	56	parameters	parameter	NOUN
asir-1804	10	57	that	that	PRON
asir-1804	10	58	give	give	VERB
asir-1804	10	59	values	value	NOUN
asir-1804	10	60	for	for	ADP
asir-1804	10	61	the	the	DET
asir-1804	10	62	focal	focal	ADJ
asir-1804	10	63	length	length	NOUN
asir-1804	10	64	and	and	CCONJ
asir-1804	10	65	principal	principal	ADJ
asir-1804	10	66	plane	plane	NOUN
asir-1804	10	67	.	.	PUNCT
asir-1804	11	1	then	then	ADV
asir-1804	11	2	there	there	PRON
asir-1804	11	3	is	be	VERB
asir-1804	11	4	a	a	DET
asir-1804	11	5	simulation	simulation	NOUN
asir-1804	11	6	of	of	ADP
asir-1804	11	7	two	two	NUM
asir-1804	11	8	experiments	experiment	NOUN
asir-1804	11	9	of	of	ADP
asir-1804	11	10	finding	find	VERB
asir-1804	11	11	the	the	DET
asir-1804	11	12	focal	focal	ADJ
asir-1804	11	13	length	length	NOUN
asir-1804	11	14	of	of	ADP
asir-1804	11	15	a	a	DET
asir-1804	11	16	lens	len	NOUN
asir-1804	11	17	.	.	PUNCT
asir-1804	12	1	the	the	DET
asir-1804	12	2	spreadsheet	spreadsheet	NOUN
asir-1804	12	3	calculates	calculate	VERB
asir-1804	12	4	the	the	DET
asir-1804	12	5	distance	distance	NOUN
asir-1804	12	6	b	b	PROPN
asir-1804	12	7	vs	vs	ADP
asir-1804	12	8	a	a	PRON
asir-1804	12	9	,	,	PUNCT
asir-1804	12	10	the	the	DET
asir-1804	12	11	image	image	NOUN
asir-1804	12	12	y	y	PROPN
asir-1804	12	13	,	,	PUNCT
asir-1804	12	14	and	and	CCONJ
asir-1804	12	15	there	there	PRON
asir-1804	12	16	ar	ar	VERB
asir-1804	12	17	graphs	graph	NOUN
asir-1804	12	18	of	of	ADP
asir-1804	12	19	y	y	PROPN
asir-1804	12	20	as	as	ADP
asir-1804	12	21	a	a	DET
asir-1804	12	22	function	function	NOUN
asir-1804	12	23	of	of	ADP
asir-1804	12	24	a	a	PRON
asir-1804	12	25	and	and	CCONJ
asir-1804	12	26	y	y	PROPN
asir-1804	12	27	as	as	ADP
asir-1804	12	28	a	a	DET
asir-1804	12	29	function	function	NOUN
asir-1804	12	30	of	of	ADP
asir-1804	12	31	b	b	NOUN
asir-1804	12	32	from	from	ADP
asir-1804	12	33	which	which	PRON
asir-1804	12	34	we	we	PRON
asir-1804	12	35	find	find	VERB
asir-1804	12	36	1	1	NUM
asir-1804	12	37	)	)	PUNCT
asir-1804	12	38	a	a	DET
asir-1804	12	39	hyperbolic	hyperbolic	ADJ
asir-1804	12	40	fit	fit	NOUN
asir-1804	12	41	for	for	ADP
asir-1804	12	42	y	y	PROPN
asir-1804	12	43	vs	vs	ADP
asir-1804	12	44	a	a	PRON
asir-1804	12	45	and	and	CCONJ
asir-1804	12	46	a	a	DET
asir-1804	12	47	linear	linear	ADJ
asir-1804	12	48	fit	fit	NOUN
asir-1804	12	49	for	for	ADP
asir-1804	12	50	y	y	PROPN
asir-1804	12	51	vs	vs	ADP
asir-1804	12	52	b	b	PROPN
asir-1804	12	53	from	from	ADP
asir-1804	12	54	which	which	PRON
asir-1804	12	55	we	we	PRON
asir-1804	12	56	calculate	calculate	VERB
asir-1804	12	57	the	the	DET
asir-1804	12	58	focal	focal	ADJ
asir-1804	12	59	distance	distance	NOUN
asir-1804	12	60	,	,	PUNCT
asir-1804	12	61	2	2	X
asir-1804	12	62	)	)	PUNCT
asir-1804	12	63	it	it	PRON
asir-1804	12	64	calculates	calculate	VERB
asir-1804	12	65	1	1	NUM
asir-1804	12	66	/	/	SYM
asir-1804	12	67	a	a	PRON
asir-1804	12	68	and	and	CCONJ
asir-1804	12	69	1	1	NUM
asir-1804	12	70	/	/	SYM
asir-1804	12	71	b	b	NOUN
asir-1804	12	72	and	and	CCONJ
asir-1804	12	73	then	then	ADV
asir-1804	12	74	finds	find	VERB
asir-1804	12	75	a	a	DET
asir-1804	12	76	linear	linear	ADJ
asir-1804	12	77	fit	fit	NOUN
asir-1804	12	78	and	and	CCONJ
asir-1804	12	79	a	a	DET
asir-1804	12	80	parabolic	parabolic	ADJ
asir-1804	12	81	fit	fit	NOUN
asir-1804	12	82	for	for	ADP
asir-1804	12	83	the	the	DET
asir-1804	12	84	data	datum	NOUN
asir-1804	12	85	.	.	PUNCT
asir-1804	13	1	also	also	ADV
asir-1804	13	2	we	we	PRON
asir-1804	13	3	get	get	VERB
asir-1804	13	4	the	the	DET
asir-1804	13	5	same	same	ADJ
asir-1804	13	6	parameters	parameter	NOUN
asir-1804	13	7	by	by	ADP
asir-1804	13	8	finding	find	VERB
asir-1804	13	9	the	the	DET
asir-1804	13	10	cuts	cut	NOUN
asir-1804	13	11	of	of	ADP
asir-1804	13	12	lines	line	NOUN
asir-1804	13	13	uniting	unite	VERB
asir-1804	13	14	the	the	DET
asir-1804	13	15	point	point	NOUN
asir-1804	13	16	(	(	PUNCT
asir-1804	13	17	a,0	a,0	NOUN
asir-1804	13	18	)	)	PUNCT
asir-1804	13	19	and	and	CCONJ
asir-1804	13	20	(	(	PUNCT
asir-1804	13	21	0,b	0,b	PROPN
asir-1804	13	22	)	)	PUNCT
asir-1804	13	23	..	..	PUNCT
asir-1804	14	1	3	3	X
asir-1804	14	2	)	)	PUNCT
asir-1804	14	3	there	there	PRON
asir-1804	14	4	is	be	VERB
asir-1804	14	5	a	a	DET
asir-1804	14	6	plot	plot	NOUN
asir-1804	14	7	of	of	ADP
asir-1804	14	8	a+b	a+b	NUM
asir-1804	14	9	vs	vs	ADP
asir-1804	14	10	a	a	PRON
asir-1804	14	11	and	and	CCONJ
asir-1804	14	12	then	then	ADV
asir-1804	14	13	the	the	DET
asir-1804	14	14	points	point	NOUN
asir-1804	14	15	are	be	AUX
asir-1804	14	16	fitted	fit	VERB
asir-1804	14	17	with	with	ADP
asir-1804	14	18	a	a	DET
asir-1804	14	19	hyperbola	hyperbola	PROPN
asir-1804	14	20	whose	whose	DET
asir-1804	14	21	asymptotes	asymptote	NOUN
asir-1804	14	22	give	give	VERB
asir-1804	14	23	the	the	DET
asir-1804	14	24	sum	sum	NOUN
asir-1804	14	25	of	of	ADP
asir-1804	14	26	focal	focal	ADJ
asir-1804	14	27	length	length	NOUN
asir-1804	14	28	and	and	CCONJ
asir-1804	14	29	principal	principal	ADJ
asir-1804	14	30	planes	plane	NOUN
asir-1804	14	31	.	.	PUNCT
asir-1804	15	1	then	then	ADV
asir-1804	15	2	there	there	PRON
asir-1804	15	3	is	be	VERB
asir-1804	15	4	a	a	DET
asir-1804	15	5	page	page	NOUN
asir-1804	15	6	where	where	SCONJ
asir-1804	15	7	we	we	PRON
asir-1804	15	8	can	can	AUX
asir-1804	15	9	see	see	VERB
asir-1804	15	10	two	two	NUM
asir-1804	15	11	lenses	lense	NOUN
asir-1804	15	12	for	for	ADP
asir-1804	15	13	which	which	PRON
asir-1804	15	14	the	the	DET
asir-1804	15	15	shape	shape	NOUN
asir-1804	15	16	can	can	AUX
asir-1804	15	17	change	change	VERB
asir-1804	15	18	to	to	PART
asir-1804	15	19	have	have	VERB
asir-1804	15	20	a	a	DET
asir-1804	15	21	perfect	perfect	ADJ
asir-1804	15	22	focusing	focus	VERB
asir-1804	15	23	at	at	ADP
asir-1804	15	24	a	a	DET
asir-1804	15	25	given	give	VERB
asir-1804	15	26	distance	distance	NOUN
asir-1804	15	27	.	.	PUNCT
asir-1804	16	1	these	these	DET
asir-1804	16	2	two	two	NUM
asir-1804	16	3	lenses	lense	NOUN
asir-1804	16	4	are	be	AUX
asir-1804	16	5	based	base	VERB
asir-1804	16	6	on	on	ADP
asir-1804	16	7	huygens	huygen	NOUN
asir-1804	16	8	’	’	PART
asir-1804	16	9	ideas	idea	NOUN
asir-1804	16	10	,	,	PUNCT
asir-1804	16	11	spherical	spherical	ADJ
asir-1804	16	12	and	and	CCONJ
asir-1804	16	13	huygen	huygen	PROPN
asir-1804	16	14	lenses	lense	NOUN
asir-1804	16	15	.	.	PUNCT
asir-1804	17	1	keywords	keyword	NOUN
asir-1804	17	2	ray	ray	VERB
asir-1804	17	3	diagrams	diagram	NOUN
asir-1804	17	4	,	,	PUNCT
asir-1804	17	5	wave	wave	NOUN
asir-1804	17	6	fronts	front	NOUN
asir-1804	17	7	,	,	PUNCT
asir-1804	17	8	minimum	minimum	ADJ
asir-1804	17	9	deviation	deviation	NOUN
asir-1804	17	10	,	,	PUNCT
asir-1804	17	11	focal	focal	ADJ
asir-1804	17	12	length	length	NOUN
asir-1804	17	13	,	,	PUNCT
asir-1804	17	14	fermat	fermat	PROPN
asir-1804	17	15	’s	’s	PART
asir-1804	17	16	principle	principle	NOUN
asir-1804	17	17	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1804	17	18	applied	apply	VERB
asir-1804	17	19	science	science	NOUN
asir-1804	17	20	and	and	CCONJ
asir-1804	17	21	innovative	innovative	ADJ
asir-1804	17	22	research	research	NOUN
asir-1804	17	23	vol	vol	NOUN
asir-1804	17	24	.	.	PUNCT
asir-1804	18	1	3	3	NUM
asir-1804	18	2	,	,	PUNCT
asir-1804	18	3	no	no	INTJ
asir-1804	18	4	.	.	NOUN
asir-1804	18	5	1	1	NUM
asir-1804	18	6	,	,	PUNCT
asir-1804	18	7	2019	2019	NUM
asir-1804	18	8	16	16	NUM
asir-1804	18	9	published	publish	VERB
asir-1804	18	10	by	by	ADP
asir-1804	18	11	scholink	scholink	PROPN
asir-1804	18	12	inc	inc	PROPN
asir-1804	18	13	.	.	PROPN
asir-1804	18	14	1	1	NUM
asir-1804	18	15	.	.	X
asir-1804	19	1	introduction	introduction	NOUN
asir-1804	19	2	the	the	DET
asir-1804	19	3	teaching	teaching	NOUN
asir-1804	19	4	of	of	ADP
asir-1804	19	5	lenses	lense	NOUN
asir-1804	19	6	can	can	AUX
asir-1804	19	7	be	be	AUX
asir-1804	19	8	facilitated	facilitate	VERB
asir-1804	19	9	when	when	SCONJ
asir-1804	19	10	the	the	DET
asir-1804	19	11	student	student	NOUN
asir-1804	19	12	is	be	AUX
asir-1804	19	13	having	have	VERB
asir-1804	19	14	an	an	DET
asir-1804	19	15	image	image	NOUN
asir-1804	19	16	of	of	ADP
asir-1804	19	17	what	what	PRON
asir-1804	19	18	is	be	AUX
asir-1804	19	19	being	be	AUX
asir-1804	19	20	taught	teach	VERB
asir-1804	19	21	.	.	PUNCT
asir-1804	20	1	the	the	DET
asir-1804	20	2	teaching	teaching	NOUN
asir-1804	20	3	of	of	ADP
asir-1804	20	4	the	the	DET
asir-1804	20	5	theory	theory	NOUN
asir-1804	20	6	of	of	ADP
asir-1804	20	7	real	real	ADJ
asir-1804	20	8	lenses	lense	NOUN
asir-1804	20	9	is	be	AUX
asir-1804	20	10	not	not	PART
asir-1804	20	11	so	so	ADV
asir-1804	20	12	easy	easy	ADJ
asir-1804	20	13	to	to	PART
asir-1804	20	14	follow	follow	VERB
asir-1804	20	15	(	(	PUNCT
asir-1804	20	16	walther	walther	NOUN
asir-1804	20	17	,	,	PUNCT
asir-1804	20	18	1996	1996	NUM
asir-1804	20	19	)	)	PUNCT
asir-1804	20	20	.	.	PUNCT
asir-1804	21	1	students	student	NOUN
asir-1804	21	2	can	can	AUX
asir-1804	21	3	see	see	VERB
asir-1804	21	4	the	the	DET
asir-1804	21	5	limitations	limitation	NOUN
asir-1804	21	6	of	of	ADP
asir-1804	21	7	paraxial	paraxial	ADJ
asir-1804	21	8	optics	optic	NOUN
asir-1804	21	9	and	and	CCONJ
asir-1804	21	10	very	very	ADV
asir-1804	21	11	thin	thin	ADJ
asir-1804	21	12	lenses	lense	NOUN
asir-1804	21	13	.	.	PUNCT
asir-1804	22	1	this	this	DET
asir-1804	22	2	spreadsheet	spreadsheet	NOUN
asir-1804	22	3	permits	permit	VERB
asir-1804	22	4	to	to	ADP
asir-1804	22	5	the	the	DET
asir-1804	22	6	student	student	NOUN
asir-1804	22	7	to	to	PART
asir-1804	22	8	use	use	VERB
asir-1804	22	9	5	5	NUM
asir-1804	22	10	kinds	kind	NOUN
asir-1804	22	11	of	of	ADP
asir-1804	22	12	simulation	simulation	NOUN
asir-1804	22	13	:	:	PUNCT
asir-1804	22	14	a	a	X
asir-1804	22	15	)	)	PUNCT
asir-1804	22	16	choose	choose	NOUN
asir-1804	22	17	of	of	ADP
asir-1804	22	18	radii	radius	NOUN
asir-1804	22	19	and	and	CCONJ
asir-1804	22	20	center	center	NOUN
asir-1804	22	21	of	of	ADP
asir-1804	22	22	the	the	DET
asir-1804	22	23	circle	circle	NOUN
asir-1804	22	24	on	on	ADP
asir-1804	22	25	right	right	ADV
asir-1804	22	26	.	.	PUNCT
asir-1804	23	1	the	the	DET
asir-1804	23	2	program	program	NOUN
asir-1804	23	3	does	do	AUX
asir-1804	23	4	ray	ray	VERB
asir-1804	23	5	tracing	tracing	NOUN
asir-1804	23	6	of	of	ADP
asir-1804	23	7	the	the	DET
asir-1804	23	8	constructed	construct	VERB
asir-1804	23	9	lens	len	NOUN
asir-1804	23	10	.	.	PUNCT
asir-1804	24	1	except	except	SCONJ
asir-1804	24	2	of	of	ADP
asir-1804	24	3	the	the	DET
asir-1804	24	4	ray	ray	NOUN
asir-1804	24	5	tracing	tracing	PROPN
asir-1804	24	6	,	,	PUNCT
asir-1804	24	7	the	the	DET
asir-1804	24	8	student	student	NOUN
asir-1804	24	9	can	can	AUX
asir-1804	24	10	observe	observe	VERB
asir-1804	24	11	the	the	DET
asir-1804	24	12	wave	wave	NOUN
asir-1804	24	13	fronts	front	NOUN
asir-1804	24	14	.	.	PUNCT
asir-1804	25	1	b	b	X
asir-1804	25	2	)	)	PUNCT
asir-1804	25	3	paraxial	paraxial	ADJ
asir-1804	25	4	theory	theory	NOUN
asir-1804	25	5	of	of	ADP
asir-1804	25	6	lenses	lense	NOUN
asir-1804	25	7	.	.	PUNCT
asir-1804	26	1	c	c	X
asir-1804	26	2	)	)	PUNCT
asir-1804	26	3	finding	find	VERB
asir-1804	26	4	the	the	DET
asir-1804	26	5	image	image	NOUN
asir-1804	26	6	at	at	ADP
asir-1804	26	7	the	the	DET
asir-1804	26	8	point	point	NOUN
asir-1804	26	9	of	of	ADP
asir-1804	26	10	the	the	DET
asir-1804	26	11	maximum	maximum	ADJ
asir-1804	26	12	concentration	concentration	NOUN
asir-1804	26	13	of	of	ADP
asir-1804	26	14	rays	ray	NOUN
asir-1804	26	15	.	.	PUNCT
asir-1804	27	1	d	d	X
asir-1804	27	2	)	)	PUNCT
asir-1804	27	3	experiments	experiment	NOUN
asir-1804	27	4	for	for	ADP
asir-1804	27	5	finding	find	VERB
asir-1804	27	6	the	the	DET
asir-1804	27	7	focal	focal	ADJ
asir-1804	27	8	length	length	NOUN
asir-1804	27	9	of	of	ADP
asir-1804	27	10	a	a	DET
asir-1804	27	11	lens	len	NOUN
asir-1804	27	12	.	.	PUNCT
asir-1804	28	1	e	e	X
asir-1804	28	2	)	)	PUNCT
asir-1804	28	3	lenses	lense	NOUN
asir-1804	28	4	that	that	PRON
asir-1804	28	5	change	change	VERB
asir-1804	28	6	shape	shape	NOUN
asir-1804	28	7	when	when	SCONJ
asir-1804	28	8	we	we	PRON
asir-1804	28	9	change	change	VERB
asir-1804	28	10	the	the	DET
asir-1804	28	11	position	position	NOUN
asir-1804	28	12	of	of	ADP
asir-1804	28	13	the	the	DET
asir-1804	28	14	source	source	NOUN
asir-1804	28	15	or	or	CCONJ
asir-1804	28	16	of	of	ADP
asir-1804	28	17	the	the	DET
asir-1804	28	18	image	image	NOUN
asir-1804	28	19	.	.	PUNCT
asir-1804	29	1	2	2	X
asir-1804	29	2	.	.	X
asir-1804	29	3	use	use	NOUN
asir-1804	29	4	of	of	ADP
asir-1804	29	5	the	the	DET
asir-1804	29	6	spreadsheet	spreadsheet	NOUN
asir-1804	29	7	in	in	ADP
asir-1804	29	8	the	the	DET
asir-1804	29	9	introductory	introductory	ADJ
asir-1804	29	10	page	page	NOUN
asir-1804	29	11	of	of	ADP
asir-1804	29	12	the	the	DET
asir-1804	29	13	spreadsheet	spreadsheet	NOUN
asir-1804	29	14	there	there	PRON
asir-1804	29	15	are	be	VERB
asir-1804	29	16	several	several	ADJ
asir-1804	29	17	command	command	NOUN
asir-1804	29	18	buttons	button	NOUN
asir-1804	29	19	that	that	PRON
asir-1804	29	20	are	be	AUX
asir-1804	29	21	shortcuts	shortcut	NOUN
asir-1804	29	22	to	to	ADP
asir-1804	29	23	different	different	ADJ
asir-1804	29	24	pages	page	NOUN
asir-1804	29	25	.	.	PUNCT
asir-1804	30	1	a	a	DET
asir-1804	30	2	)	)	PUNCT
asir-1804	30	3	spherical	spherical	ADJ
asir-1804	30	4	lenses	lense	NOUN
asir-1804	30	5	.	.	PUNCT
asir-1804	31	1	figure	figure	NOUN
asir-1804	31	2	1	1	NUM
asir-1804	31	3	.	.	PUNCT
asir-1804	32	1	the	the	DET
asir-1804	32	2	screen	screen	NOUN
asir-1804	32	3	for	for	ADP
asir-1804	32	4	spherical	spherical	ADJ
asir-1804	32	5	waves	wave	NOUN
asir-1804	32	6	for	for	ADP
asir-1804	32	7	a	a	DET
asir-1804	32	8	thick	thick	ADJ
asir-1804	32	9	lens	lens	NOUN
asir-1804	32	10	as	as	SCONJ
asir-1804	32	11	it	it	PRON
asir-1804	32	12	can	can	AUX
asir-1804	32	13	be	be	AUX
asir-1804	32	14	seen	see	VERB
asir-1804	32	15	from	from	ADP
asir-1804	32	16	figure	figure	NOUN
asir-1804	32	17	1	1	NUM
asir-1804	32	18	,	,	PUNCT
asir-1804	32	19	there	there	PRON
asir-1804	32	20	are	be	VERB
asir-1804	32	21	two	two	NUM
asir-1804	32	22	buttons	button	NOUN
asir-1804	32	23	and	and	CCONJ
asir-1804	32	24	a	a	DET
asir-1804	32	25	form	form	NOUN
asir-1804	32	26	:	:	PUNCT
asir-1804	32	27	the	the	DET
asir-1804	32	28	2	2	NUM
asir-1804	32	29	buttons	button	NOUN
asir-1804	32	30	.	.	PUNCT
asir-1804	33	1	the	the	DET
asir-1804	33	2	button	button	NOUN
asir-1804	33	3	“	"	PUNCT
asir-1804	33	4	find	find	VERB
asir-1804	33	5	location	location	NOUN
asir-1804	33	6	of	of	ADP
asir-1804	33	7	the	the	DET
asir-1804	33	8	sharpest	sharp	ADJ
asir-1804	33	9	image	image	NOUN
asir-1804	33	10	”	"	PUNCT
asir-1804	33	11	activates	activate	VERB
asir-1804	33	12	the	the	DET
asir-1804	33	13	sheet	sheet	NOUN
asir-1804	33	14	“	"	PUNCT
asir-1804	33	15	standard	standard	ADJ
asir-1804	33	16	deviation	deviation	NOUN
asir-1804	33	17	of	of	ADP
asir-1804	33	18	y	y	PROPN
asir-1804	33	19	vs	vs	ADP
asir-1804	33	20	x	x	PROPN
asir-1804	33	21	”	"	PUNCT
asir-1804	33	22	where	where	SCONJ
asir-1804	33	23	the	the	DET
asir-1804	33	24	position	position	NOUN
asir-1804	33	25	of	of	ADP
asir-1804	33	26	the	the	DET
asir-1804	33	27	minimum	minimum	NOUN
asir-1804	33	28	of	of	ADP
asir-1804	33	29	the	the	DET
asir-1804	33	30	standard	standard	ADJ
asir-1804	33	31	deviation	deviation	NOUN
asir-1804	33	32	of	of	ADP
asir-1804	33	33	the	the	DET
asir-1804	33	34	emerging	emerge	VERB
asir-1804	33	35	rays	ray	NOUN
asir-1804	33	36	(	(	PUNCT
asir-1804	33	37	or	or	CCONJ
asir-1804	33	38	in	in	ADP
asir-1804	33	39	case	case	NOUN
asir-1804	33	40	of	of	ADP
asir-1804	33	41	imaginary	imaginary	ADJ
asir-1804	33	42	image	image	NOUN
asir-1804	33	43	their	their	PRON
asir-1804	33	44	backward	backward	ADJ
asir-1804	33	45	extrapolation	extrapolation	NOUN
asir-1804	33	46	)	)	PUNCT
asir-1804	33	47	is	be	AUX
asir-1804	33	48	found	find	VERB
asir-1804	33	49	.	.	PUNCT
asir-1804	34	1	the	the	DET
asir-1804	34	2	form	form	NOUN
asir-1804	34	3	appears	appear	VERB
asir-1804	34	4	after	after	SCONJ
asir-1804	34	5	we	we	PRON
asir-1804	34	6	press	press	VERB
asir-1804	34	7	the	the	DET
asir-1804	34	8	button	button	NOUN
asir-1804	34	9	“	"	PUNCT
asir-1804	34	10	show	show	VERB
asir-1804	34	11	form	form	NOUN
asir-1804	34	12	for	for	ADP
asir-1804	34	13	parameters	parameter	NOUN
asir-1804	34	14	”	"	PUNCT
asir-1804	34	15	.	.	PUNCT
asir-1804	35	1	on	on	ADP
asir-1804	35	2	the	the	DET
asir-1804	35	3	form	form	NOUN
asir-1804	35	4	“	"	PUNCT
asir-1804	35	5	biconvex	biconvex	NOUN
asir-1804	35	6	”	"	PUNCT
asir-1804	35	7	there	there	PRON
asir-1804	35	8	are	be	VERB
asir-1804	35	9	scroll	scroll	NOUN
asir-1804	35	10	bars	bar	NOUN
asir-1804	35	11	for	for	ADP
asir-1804	35	12	changing	change	VERB
asir-1804	35	13	the	the	DET
asir-1804	35	14	radii	radius	NOUN
asir-1804	35	15	,	,	PUNCT
asir-1804	35	16	the	the	DET
asir-1804	35	17	position	position	NOUN
asir-1804	35	18	of	of	ADP
asir-1804	35	19	the	the	DET
asir-1804	35	20	centers	center	NOUN
asir-1804	35	21	the	the	DET
asir-1804	35	22	index	index	NOUN
asir-1804	35	23	of	of	ADP
asir-1804	35	24	refraction	refraction	NOUN
asir-1804	35	25	of	of	ADP
asir-1804	35	26	the	the	DET
asir-1804	35	27	lens	len	NOUN
asir-1804	35	28	and	and	CCONJ
asir-1804	35	29	the	the	DET
asir-1804	35	30	index	index	NOUN
asir-1804	35	31	of	of	ADP
asir-1804	35	32	refraction	refraction	NOUN
asir-1804	35	33	of	of	ADP
asir-1804	35	34	the	the	DET
asir-1804	35	35	medium	medium	NOUN
asir-1804	35	36	on	on	ADP
asir-1804	35	37	the	the	DET
asir-1804	35	38	right	right	ADJ
asir-1804	35	39	side	side	NOUN
asir-1804	35	40	of	of	ADP
asir-1804	35	41	the	the	DET
asir-1804	35	42	lens	len	NOUN
asir-1804	35	43	,	,	PUNCT
asir-1804	35	44	also	also	ADV
asir-1804	35	45	there	there	PRON
asir-1804	35	46	are	be	VERB
asir-1804	35	47	buttons	button	NOUN
asir-1804	35	48	for	for	ADP
asir-1804	35	49	starting	starting	NOUN
asir-1804	35	50	,	,	PUNCT
asir-1804	35	51	stopping	stop	VERB
asir-1804	35	52	and	and	CCONJ
asir-1804	35	53	continuing	continue	VERB
asir-1804	35	54	the	the	DET
asir-1804	35	55	movement	movement	NOUN
asir-1804	35	56	of	of	ADP
asir-1804	35	57	wave	wave	NOUN
asir-1804	35	58	fronts	front	NOUN
asir-1804	35	59	.	.	PUNCT
asir-1804	36	1	when	when	SCONJ
asir-1804	36	2	the	the	DET
asir-1804	36	3	wave	wave	NOUN
asir-1804	36	4	fronts	front	NOUN
asir-1804	36	5	are	be	AUX
asir-1804	36	6	stopped	stop	VERB
asir-1804	36	7	the	the	DET
asir-1804	36	8	user	user	NOUN
asir-1804	36	9	can	can	AUX
asir-1804	36	10	move	move	VERB
asir-1804	36	11	them	they	PRON
asir-1804	36	12	manually	manually	ADV
asir-1804	36	13	by	by	ADP
asir-1804	36	14	a	a	DET
asir-1804	36	15	scroll	scroll	NOUN
asir-1804	36	16	bar	bar	NOUN
asir-1804	36	17	.	.	PUNCT
asir-1804	37	1	there	there	PRON
asir-1804	37	2	are	be	VERB
asir-1804	37	3	also	also	ADV
asir-1804	37	4	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1804	37	5	applied	apply	VERB
asir-1804	37	6	science	science	NOUN
asir-1804	37	7	and	and	CCONJ
asir-1804	37	8	innovative	innovative	ADJ
asir-1804	37	9	research	research	NOUN
asir-1804	37	10	vol	vol	NOUN
asir-1804	37	11	.	.	PUNCT
asir-1804	38	1	3	3	NUM
asir-1804	38	2	,	,	PUNCT
asir-1804	38	3	no	no	INTJ
asir-1804	38	4	.	.	NOUN
asir-1804	38	5	1	1	NUM
asir-1804	38	6	,	,	PUNCT
asir-1804	38	7	2019	2019	NUM
asir-1804	38	8	17	17	NUM
asir-1804	38	9	published	publish	VERB
asir-1804	38	10	by	by	ADP
asir-1804	38	11	scholink	scholink	PROPN
asir-1804	38	12	inc	inc	PROPN
asir-1804	38	13	.	.	PROPN
asir-1804	38	14	buttons	button	NOUN
asir-1804	38	15	for	for	ADP
asir-1804	38	16	moving	move	VERB
asir-1804	38	17	to	to	ADP
asir-1804	38	18	other	other	ADJ
asir-1804	38	19	parts	part	NOUN
asir-1804	38	20	of	of	ADP
asir-1804	38	21	the	the	DET
asir-1804	38	22	worksheet	worksheet	NOUN
asir-1804	38	23	related	relate	VERB
asir-1804	38	24	to	to	ADP
asir-1804	38	25	biconvex	biconvex	ADJ
asir-1804	38	26	lenses	lense	NOUN
asir-1804	38	27	.	.	PUNCT
asir-1804	39	1	there	there	PRON
asir-1804	39	2	is	be	VERB
asir-1804	39	3	a	a	DET
asir-1804	39	4	scroll	scroll	NOUN
asir-1804	39	5	bar	bar	NOUN
asir-1804	39	6	that	that	PRON
asir-1804	39	7	changes	change	VERB
asir-1804	39	8	the	the	DET
asir-1804	39	9	scale	scale	NOUN
asir-1804	39	10	of	of	ADP
asir-1804	39	11	the	the	DET
asir-1804	39	12	graph	graph	NOUN
asir-1804	39	13	.	.	PUNCT
asir-1804	40	1	the	the	DET
asir-1804	40	2	user	user	NOUN
asir-1804	40	3	can	can	AUX
asir-1804	40	4	change	change	VERB
asir-1804	40	5	the	the	DET
asir-1804	40	6	scale	scale	NOUN
asir-1804	40	7	to	to	PART
asir-1804	40	8	see	see	VERB
asir-1804	40	9	more	more	ADJ
asir-1804	40	10	details	detail	NOUN
asir-1804	40	11	or	or	CCONJ
asir-1804	40	12	less	less	ADJ
asir-1804	40	13	.	.	PUNCT
asir-1804	41	1	this	this	PRON
asir-1804	41	2	is	be	AUX
asir-1804	41	3	seen	see	VERB
asir-1804	41	4	in	in	ADP
asir-1804	41	5	figure	figure	NOUN
asir-1804	41	6	2	2	NUM
asir-1804	41	7	is	be	AUX
asir-1804	41	8	shown	show	VERB
asir-1804	41	9	a	a	DET
asir-1804	41	10	case	case	NOUN
asir-1804	41	11	of	of	ADP
asir-1804	41	12	virtual	virtual	ADJ
asir-1804	41	13	image	image	NOUN
asir-1804	41	14	.	.	PUNCT
asir-1804	42	1	the	the	DET
asir-1804	42	2	scale	scale	NOUN
asir-1804	42	3	was	be	AUX
asir-1804	42	4	changed	change	VERB
asir-1804	42	5	to	to	ADP
asir-1804	42	6	a	a	DET
asir-1804	42	7	smaller	small	ADJ
asir-1804	42	8	value	value	NOUN
asir-1804	42	9	than	than	ADP
asir-1804	42	10	in	in	ADP
asir-1804	42	11	figure	figure	NOUN
asir-1804	42	12	1	1	NUM
asir-1804	42	13	.	.	PUNCT
asir-1804	43	1	figure	figure	NOUN
asir-1804	43	2	2	2	NUM
asir-1804	43	3	.	.	PUNCT
asir-1804	44	1	a	a	DET
asir-1804	44	2	case	case	NOUN
asir-1804	44	3	of	of	ADP
asir-1804	44	4	imaginary	imaginary	ADJ
asir-1804	44	5	image	image	NOUN
asir-1804	44	6	.	.	PUNCT
asir-1804	45	1	the	the	DET
asir-1804	45	2	form	form	NOUN
asir-1804	45	3	appears	appear	VERB
asir-1804	45	4	when	when	SCONJ
asir-1804	45	5	the	the	DET
asir-1804	45	6	user	user	NOUN
asir-1804	45	7	presses	press	VERB
asir-1804	45	8	“	"	PUNCT
asir-1804	45	9	parameters	parameter	NOUN
asir-1804	45	10	”	"	PUNCT
asir-1804	45	11	the	the	DET
asir-1804	45	12	radius	radius	NOUN
asir-1804	45	13	of	of	ADP
asir-1804	45	14	the	the	DET
asir-1804	45	15	circle	circle	NOUN
asir-1804	45	16	on	on	ADP
asir-1804	45	17	the	the	DET
asir-1804	45	18	right	right	ADJ
asir-1804	45	19	side	side	NOUN
asir-1804	45	20	,	,	PUNCT
asir-1804	45	21	the	the	DET
asir-1804	45	22	radius	radius	NOUN
asir-1804	45	23	of	of	ADP
asir-1804	45	24	the	the	DET
asir-1804	45	25	circle	circle	NOUN
asir-1804	45	26	on	on	ADP
asir-1804	45	27	the	the	DET
asir-1804	45	28	left	left	NOUN
asir-1804	45	29	,	,	PUNCT
asir-1804	45	30	the	the	DET
asir-1804	45	31	center	center	NOUN
asir-1804	45	32	of	of	ADP
asir-1804	45	33	the	the	DET
asir-1804	45	34	circle	circle	NOUN
asir-1804	45	35	on	on	ADP
asir-1804	45	36	the	the	DET
asir-1804	45	37	right	right	ADJ
asir-1804	45	38	side	side	NOUN
asir-1804	45	39	are	be	AUX
asir-1804	45	40	determined	determine	VERB
asir-1804	45	41	by	by	ADP
asir-1804	45	42	moving	move	VERB
asir-1804	45	43	the	the	DET
asir-1804	45	44	corresponding	corresponding	ADJ
asir-1804	45	45	scroll	scroll	NOUN
asir-1804	45	46	bars	bar	NOUN
asir-1804	45	47	.	.	PUNCT
asir-1804	46	1	the	the	DET
asir-1804	46	2	program	program	NOUN
asir-1804	46	3	calculates	calculate	VERB
asir-1804	46	4	the	the	DET
asir-1804	46	5	position	position	NOUN
asir-1804	46	6	of	of	ADP
asir-1804	46	7	the	the	DET
asir-1804	46	8	center	center	NOUN
asir-1804	46	9	of	of	ADP
asir-1804	46	10	the	the	DET
asir-1804	46	11	left	left	ADJ
asir-1804	46	12	side	side	NOUN
asir-1804	46	13	so	so	SCONJ
asir-1804	46	14	that	that	SCONJ
asir-1804	46	15	both	both	DET
asir-1804	46	16	circles	circle	NOUN
asir-1804	46	17	cut	cut	VERB
asir-1804	46	18	each	each	DET
asir-1804	46	19	other	other	ADJ
asir-1804	46	20	at	at	ADP
asir-1804	46	21	x	x	X
asir-1804	46	22	=	=	NOUN
asir-1804	46	23	0	0	NUM
asir-1804	46	24	.	.	PUNCT
asir-1804	47	1	there	there	PRON
asir-1804	47	2	is	be	VERB
asir-1804	47	3	a	a	DET
asir-1804	47	4	limit	limit	NOUN
asir-1804	47	5	on	on	ADP
asir-1804	47	6	the	the	DET
asir-1804	47	7	changes	change	NOUN
asir-1804	47	8	of	of	ADP
asir-1804	47	9	the	the	DET
asir-1804	47	10	position	position	NOUN
asir-1804	47	11	of	of	ADP
asir-1804	47	12	the	the	DET
asir-1804	47	13	right	right	ADJ
asir-1804	47	14	circle	circle	NOUN
asir-1804	47	15	so	so	SCONJ
asir-1804	47	16	that	that	SCONJ
asir-1804	47	17	the	the	DET
asir-1804	47	18	right	right	ADJ
asir-1804	47	19	circle	circle	NOUN
asir-1804	47	20	remains	remain	VERB
asir-1804	47	21	on	on	ADP
asir-1804	47	22	the	the	DET
asir-1804	47	23	right	right	ADJ
asir-1804	47	24	side	side	NOUN
asir-1804	47	25	.	.	PUNCT
asir-1804	48	1	figure	figure	NOUN
asir-1804	48	2	3	3	NUM
asir-1804	48	3	.	.	PUNCT
asir-1804	49	1	the	the	DET
asir-1804	49	2	use	use	NOUN
asir-1804	49	3	of	of	ADP
asir-1804	49	4	the	the	DET
asir-1804	49	5	minimum	minimum	ADJ
asir-1804	49	6	deviation	deviation	NOUN
asir-1804	49	7	to	to	PART
asir-1804	49	8	find	find	VERB
asir-1804	49	9	the	the	DET
asir-1804	49	10	position	position	NOUN
asir-1804	49	11	of	of	ADP
asir-1804	49	12	the	the	DET
asir-1804	49	13	image	image	NOUN
asir-1804	49	14	with	with	ADP
asir-1804	49	15	a	a	DET
asir-1804	49	16	simultaneous	simultaneous	ADJ
asir-1804	49	17	representation	representation	NOUN
asir-1804	49	18	of	of	ADP
asir-1804	49	19	the	the	DET
asir-1804	49	20	spot	spot	NOUN
asir-1804	49	21	on	on	ADP
asir-1804	49	22	the	the	DET
asir-1804	49	23	screen	screen	NOUN
asir-1804	49	24	which	which	PRON
asir-1804	49	25	we	we	PRON
asir-1804	49	26	move	move	VERB
asir-1804	49	27	back	back	ADV
asir-1804	49	28	and	and	CCONJ
asir-1804	49	29	forth	forth	ADV
asir-1804	49	30	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1804	49	31	applied	apply	VERB
asir-1804	49	32	science	science	NOUN
asir-1804	49	33	and	and	CCONJ
asir-1804	49	34	innovative	innovative	ADJ
asir-1804	49	35	research	research	NOUN
asir-1804	49	36	vol	vol	NOUN
asir-1804	49	37	.	.	PUNCT
asir-1804	50	1	3	3	NUM
asir-1804	50	2	,	,	PUNCT
asir-1804	50	3	no	no	INTJ
asir-1804	50	4	.	.	NOUN
asir-1804	50	5	1	1	NUM
asir-1804	50	6	,	,	PUNCT
asir-1804	50	7	2019	2019	NUM
asir-1804	50	8	18	18	NUM
asir-1804	50	9	published	publish	VERB
asir-1804	50	10	by	by	ADP
asir-1804	50	11	scholink	scholink	PROPN
asir-1804	50	12	inc	inc	PROPN
asir-1804	50	13	.	.	PUNCT
asir-1804	51	1	there	there	PRON
asir-1804	51	2	are	be	VERB
asir-1804	51	3	scroll	scroll	NOUN
asir-1804	51	4	bars	bar	NOUN
asir-1804	51	5	for	for	ADP
asir-1804	51	6	the	the	DET
asir-1804	51	7	position	position	NOUN
asir-1804	51	8	of	of	ADP
asir-1804	51	9	the	the	DET
asir-1804	51	10	source	source	NOUN
asir-1804	51	11	.	.	PUNCT
asir-1804	52	1	the	the	DET
asir-1804	52	2	values	value	NOUN
asir-1804	52	3	are	be	AUX
asir-1804	52	4	shown	show	VERB
asir-1804	52	5	on	on	ADP
asir-1804	52	6	the	the	DET
asir-1804	52	7	corresponding	corresponding	ADJ
asir-1804	52	8	labels	label	NOUN
asir-1804	52	9	.	.	PUNCT
asir-1804	53	1	also	also	ADV
asir-1804	53	2	there	there	PRON
asir-1804	53	3	is	be	VERB
asir-1804	53	4	a	a	DET
asir-1804	53	5	scroll	scroll	NOUN
asir-1804	53	6	bar	bar	NOUN
asir-1804	53	7	for	for	ADP
asir-1804	53	8	changing	change	VERB
asir-1804	53	9	the	the	DET
asir-1804	53	10	width	width	NOUN
asir-1804	53	11	of	of	ADP
asir-1804	53	12	the	the	DET
asir-1804	53	13	bundle	bundle	NOUN
asir-1804	53	14	of	of	ADP
asir-1804	53	15	rays	ray	NOUN
asir-1804	53	16	that	that	PRON
asir-1804	53	17	is	be	AUX
asir-1804	53	18	incident	incident	NOUN
asir-1804	53	19	on	on	ADP
asir-1804	53	20	the	the	DET
asir-1804	53	21	lens	len	NOUN
asir-1804	53	22	.	.	PUNCT
asir-1804	54	1	the	the	DET
asir-1804	54	2	option	option	NOUN
asir-1804	54	3	buttons	button	NOUN
asir-1804	54	4	“	"	PUNCT
asir-1804	54	5	point	point	NOUN
asir-1804	54	6	source	source	NOUN
asir-1804	54	7	”	"	PUNCT
asir-1804	54	8	,	,	PUNCT
asir-1804	54	9	“	"	PUNCT
asir-1804	54	10	parallel	parallel	ADJ
asir-1804	54	11	bundle	bundle	NOUN
asir-1804	54	12	”	"	PUNCT
asir-1804	54	13	are	be	AUX
asir-1804	54	14	for	for	ADP
asir-1804	54	15	the	the	DET
asir-1804	54	16	option	option	NOUN
asir-1804	54	17	of	of	ADP
asir-1804	54	18	a	a	DET
asir-1804	54	19	point	point	NOUN
asir-1804	54	20	source	source	NOUN
asir-1804	54	21	or	or	CCONJ
asir-1804	54	22	a	a	DET
asir-1804	54	23	parallel	parallel	ADJ
asir-1804	54	24	bundle	bundle	NOUN
asir-1804	54	25	of	of	ADP
asir-1804	54	26	rays	ray	NOUN
asir-1804	54	27	from	from	ADP
asir-1804	54	28	the	the	DET
asir-1804	54	29	left	left	NOUN
asir-1804	54	30	.	.	PUNCT
asir-1804	55	1	the	the	DET
asir-1804	55	2	form	form	NOUN
asir-1804	55	3	contains	contain	VERB
asir-1804	55	4	a	a	DET
asir-1804	55	5	button	button	NOUN
asir-1804	55	6	for	for	ADP
asir-1804	55	7	finding	find	VERB
asir-1804	55	8	the	the	DET
asir-1804	55	9	position	position	NOUN
asir-1804	55	10	of	of	ADP
asir-1804	55	11	the	the	DET
asir-1804	55	12	sharpest	sharp	ADJ
asir-1804	55	13	image	image	NOUN
asir-1804	55	14	which	which	PRON
asir-1804	55	15	has	have	VERB
asir-1804	55	16	the	the	DET
asir-1804	55	17	same	same	ADJ
asir-1804	55	18	function	function	NOUN
asir-1804	55	19	as	as	SCONJ
asir-1804	55	20	the	the	DET
asir-1804	55	21	button	button	NOUN
asir-1804	55	22	mentioned	mention	VERB
asir-1804	55	23	earlier	early	ADV
asir-1804	55	24	.	.	PUNCT
asir-1804	56	1	in	in	ADP
asir-1804	56	2	the	the	DET
asir-1804	56	3	case	case	NOUN
asir-1804	56	4	of	of	ADP
asir-1804	56	5	virtual	virtual	ADJ
asir-1804	56	6	image	image	NOUN
asir-1804	56	7	the	the	DET
asir-1804	56	8	position	position	NOUN
asir-1804	56	9	of	of	ADP
asir-1804	56	10	the	the	DET
asir-1804	56	11	image	image	NOUN
asir-1804	56	12	can	can	AUX
asir-1804	56	13	be	be	AUX
asir-1804	56	14	found	find	VERB
asir-1804	56	15	also	also	ADV
asir-1804	56	16	by	by	ADP
asir-1804	56	17	extrapolating	extrapolate	VERB
asir-1804	56	18	the	the	DET
asir-1804	56	19	refracted	refract	VERB
asir-1804	56	20	rays	ray	NOUN
asir-1804	56	21	to	to	ADP
asir-1804	56	22	the	the	DET
asir-1804	56	23	back	back	NOUN
asir-1804	56	24	.	.	PUNCT
asir-1804	57	1	there	there	PRON
asir-1804	57	2	is	be	VERB
asir-1804	57	3	a	a	DET
asir-1804	57	4	macro	macro	NOUN
asir-1804	57	5	in	in	ADP
asir-1804	57	6	this	this	DET
asir-1804	57	7	worksheet	worksheet	NOUN
asir-1804	57	8	which	which	PRON
asir-1804	57	9	permits	permit	VERB
asir-1804	57	10	the	the	DET
asir-1804	57	11	calculation	calculation	NOUN
asir-1804	57	12	of	of	ADP
asir-1804	57	13	the	the	DET
asir-1804	57	14	image	image	NOUN
asir-1804	57	15	by	by	ADP
asir-1804	57	16	finding	find	VERB
asir-1804	57	17	for	for	SCONJ
asir-1804	57	18	each	each	PRON
asir-1804	57	19	x	x	PUNCT
asir-1804	57	20	position	position	VERB
asir-1804	57	21	the	the	DET
asir-1804	57	22	corresponding	correspond	VERB
asir-1804	57	23	y	y	PROPN
asir-1804	57	24	position	position	NOUN
asir-1804	57	25	of	of	ADP
asir-1804	57	26	the	the	DET
asir-1804	57	27	ray	ray	NOUN
asir-1804	57	28	.	.	PUNCT
asir-1804	58	1	for	for	ADP
asir-1804	58	2	each	each	DET
asir-1804	58	3	point	point	NOUN
asir-1804	58	4	x	x	PUNCT
asir-1804	58	5	the	the	DET
asir-1804	58	6	program	program	NOUN
asir-1804	58	7	finds	find	VERB
asir-1804	58	8	the	the	DET
asir-1804	58	9	average	average	NOUN
asir-1804	58	10	of	of	ADP
asir-1804	58	11	yposition	yposition	NOUN
asir-1804	58	12	for	for	ADP
asir-1804	58	13	each	each	DET
asir-1804	58	14	ray	ray	NOUN
asir-1804	58	15	.	.	PUNCT
asir-1804	59	1	then	then	ADV
asir-1804	59	2	it	it	PRON
asir-1804	59	3	calculates	calculate	VERB
asir-1804	59	4	the	the	DET
asir-1804	59	5	standard	standard	ADJ
asir-1804	59	6	deviation	deviation	NOUN
asir-1804	59	7	for	for	ADP
asir-1804	59	8	all	all	DET
asir-1804	59	9	rays	ray	NOUN
asir-1804	59	10	.	.	PUNCT
asir-1804	60	1	the	the	DET
asir-1804	60	2	graph	graph	NOUN
asir-1804	60	3	shows	show	VERB
asir-1804	60	4	that	that	SCONJ
asir-1804	60	5	there	there	PRON
asir-1804	60	6	is	be	VERB
asir-1804	60	7	a	a	DET
asir-1804	60	8	minimum	minimum	NOUN
asir-1804	60	9	of	of	ADP
asir-1804	60	10	the	the	DET
asir-1804	60	11	standard	standard	ADJ
asir-1804	60	12	deviation	deviation	NOUN
asir-1804	60	13	.	.	PUNCT
asir-1804	61	1	this	this	PRON
asir-1804	61	2	will	will	AUX
asir-1804	61	3	be	be	AUX
asir-1804	61	4	the	the	DET
asir-1804	61	5	position	position	NOUN
asir-1804	61	6	where	where	SCONJ
asir-1804	61	7	the	the	DET
asir-1804	61	8	image	image	NOUN
asir-1804	61	9	is	be	AUX
asir-1804	61	10	the	the	DET
asir-1804	61	11	most	most	ADV
asir-1804	61	12	clear	clear	ADJ
asir-1804	61	13	.	.	PUNCT
asir-1804	62	1	for	for	ADP
asir-1804	62	2	non	non	ADJ
asir-1804	62	3	-	-	ADJ
asir-1804	62	4	paraxial	paraxial	ADJ
asir-1804	62	5	rays	ray	NOUN
asir-1804	62	6	this	this	DET
asir-1804	62	7	position	position	NOUN
asir-1804	62	8	does	do	AUX
asir-1804	62	9	not	not	PART
asir-1804	62	10	coincide	coincide	VERB
asir-1804	62	11	with	with	ADP
asir-1804	62	12	the	the	DET
asir-1804	62	13	one	one	NOUN
asir-1804	62	14	given	give	VERB
asir-1804	62	15	by	by	ADP
asir-1804	62	16	the	the	DET
asir-1804	62	17	paraxial	paraxial	ADJ
asir-1804	62	18	theory	theory	NOUN
asir-1804	62	19	.	.	PUNCT
asir-1804	63	1	on	on	ADP
asir-1804	63	2	the	the	DET
asir-1804	63	3	same	same	ADJ
asir-1804	63	4	graph	graph	NOUN
asir-1804	63	5	appears	appear	VERB
asir-1804	63	6	a	a	DET
asir-1804	63	7	“	"	PUNCT
asir-1804	63	8	spot	spot	NOUN
asir-1804	63	9	”	"	PUNCT
asir-1804	63	10	that	that	PRON
asir-1804	63	11	resembles	resemble	VERB
asir-1804	63	12	the	the	DET
asir-1804	63	13	spot	spot	NOUN
asir-1804	63	14	formed	form	VERB
asir-1804	63	15	on	on	ADP
asir-1804	63	16	a	a	DET
asir-1804	63	17	screen	screen	NOUN
asir-1804	63	18	from	from	ADP
asir-1804	63	19	a	a	DET
asir-1804	63	20	point	point	NOUN
asir-1804	63	21	source	source	NOUN
asir-1804	63	22	.	.	PUNCT
asir-1804	64	1	as	as	SCONJ
asir-1804	64	2	we	we	PRON
asir-1804	64	3	approach	approach	VERB
asir-1804	64	4	the	the	DET
asir-1804	64	5	position	position	NOUN
asir-1804	64	6	of	of	ADP
asir-1804	64	7	the	the	DET
asir-1804	64	8	least	least	ADJ
asir-1804	64	9	standard	standard	ADJ
asir-1804	64	10	deviation	deviation	NOUN
asir-1804	64	11	the	the	DET
asir-1804	64	12	spot	spot	NOUN
asir-1804	64	13	becomes	become	VERB
asir-1804	64	14	smaller	small	ADJ
asir-1804	64	15	.	.	PUNCT
asir-1804	65	1	the	the	DET
asir-1804	65	2	spot	spot	NOUN
asir-1804	65	3	does	do	AUX
asir-1804	65	4	not	not	PART
asir-1804	65	5	coincide	coincide	VERB
asir-1804	65	6	generally	generally	ADV
asir-1804	65	7	with	with	ADP
asir-1804	65	8	the	the	DET
asir-1804	65	9	position	position	NOUN
asir-1804	65	10	of	of	ADP
asir-1804	65	11	the	the	DET
asir-1804	65	12	image	image	NOUN
asir-1804	65	13	from	from	ADP
asir-1804	65	14	the	the	DET
asir-1804	65	15	paraxial	paraxial	ADJ
asir-1804	65	16	theory	theory	NOUN
asir-1804	65	17	.	.	PUNCT
asir-1804	66	1	the	the	DET
asir-1804	66	2	student	student	NOUN
asir-1804	66	3	can	can	AUX
asir-1804	66	4	study	study	VERB
asir-1804	66	5	the	the	DET
asir-1804	66	6	limitations	limitation	NOUN
asir-1804	66	7	of	of	ADP
asir-1804	66	8	the	the	DET
asir-1804	66	9	model	model	NOUN
asir-1804	66	10	of	of	ADP
asir-1804	66	11	paraxial	paraxial	ADJ
asir-1804	66	12	theory	theory	NOUN
asir-1804	66	13	by	by	ADP
asir-1804	66	14	moving	move	VERB
asir-1804	66	15	to	to	ADP
asir-1804	66	16	the	the	DET
asir-1804	66	17	sheet	sheet	NOUN
asir-1804	66	18	“	"	PUNCT
asir-1804	66	19	thick	thick	ADJ
asir-1804	66	20	lens	lens	NOUN
asir-1804	66	21	model	model	NOUN
asir-1804	66	22	”	"	PUNCT
asir-1804	66	23	.	.	PUNCT
asir-1804	67	1	b	b	X
asir-1804	67	2	)	)	PUNCT
asir-1804	67	3	paraxial	paraxial	ADJ
asir-1804	67	4	theory	theory	NOUN
asir-1804	67	5	the	the	DET
asir-1804	67	6	student	student	NOUN
asir-1804	67	7	can	can	AUX
asir-1804	67	8	study	study	VERB
asir-1804	67	9	the	the	DET
asir-1804	67	10	paraxial	paraxial	ADJ
asir-1804	67	11	theory	theory	NOUN
asir-1804	67	12	of	of	ADP
asir-1804	67	13	the	the	DET
asir-1804	67	14	lens	lens	NOUN
asir-1804	67	15	by	by	ADP
asir-1804	67	16	clicking	click	VERB
asir-1804	67	17	in	in	ADP
asir-1804	67	18	the	the	DET
asir-1804	67	19	introduction	introduction	NOUN
asir-1804	67	20	the	the	DET
asir-1804	67	21	button	button	NOUN
asir-1804	67	22	“	"	PUNCT
asir-1804	67	23	paraxial	paraxial	ADJ
asir-1804	67	24	theory	theory	NOUN
asir-1804	67	25	:	:	PUNCT
asir-1804	67	26	thick	thick	ADJ
asir-1804	67	27	lens	lens	PROPN
asir-1804	67	28	model	model	NOUN
asir-1804	67	29	”	"	PUNCT
asir-1804	67	30	.	.	PUNCT
asir-1804	68	1	when	when	SCONJ
asir-1804	68	2	the	the	DET
asir-1804	68	3	user	user	NOUN
asir-1804	68	4	presses	press	VERB
asir-1804	68	5	this	this	DET
asir-1804	68	6	button	button	NOUN
asir-1804	68	7	,	,	PUNCT
asir-1804	68	8	the	the	DET
asir-1804	68	9	sheet	sheet	NOUN
asir-1804	68	10	“	"	PUNCT
asir-1804	68	11	thick	thick	ADJ
asir-1804	68	12	lens	lens	NOUN
asir-1804	68	13	model	model	NOUN
asir-1804	68	14	”	"	PUNCT
asir-1804	68	15	appears	appear	VERB
asir-1804	68	16	(	(	PUNCT
asir-1804	68	17	figure	figure	NOUN
asir-1804	68	18	4	4	NUM
asir-1804	68	19	)	)	PUNCT
asir-1804	68	20	.	.	PUNCT
asir-1804	69	1	the	the	DET
asir-1804	69	2	user	user	NOUN
asir-1804	69	3	can	can	AUX
asir-1804	69	4	press	press	VERB
asir-1804	69	5	“	"	PUNCT
asir-1804	69	6	parameters	parameter	NOUN
asir-1804	69	7	”	"	PUNCT
asir-1804	69	8	follow	follow	VERB
asir-1804	69	9	a	a	DET
asir-1804	69	10	step	step	NOUN
asir-1804	69	11	by	by	ADP
asir-1804	69	12	step	step	NOUN
asir-1804	69	13	exposition	exposition	NOUN
asir-1804	69	14	of	of	ADP
asir-1804	69	15	the	the	DET
asir-1804	69	16	elements	element	NOUN
asir-1804	69	17	of	of	ADP
asir-1804	69	18	paraxial	paraxial	ADJ
asir-1804	69	19	theory	theory	NOUN
asir-1804	69	20	.	.	PUNCT
asir-1804	70	1	for	for	ADP
asir-1804	70	2	this	this	DET
asir-1804	70	3	purpose	purpose	NOUN
asir-1804	70	4	in	in	ADP
asir-1804	70	5	this	this	DET
asir-1804	70	6	form	form	NOUN
asir-1804	70	7	there	there	PRON
asir-1804	70	8	are	be	VERB
asir-1804	70	9	two	two	NUM
asir-1804	70	10	buttons	button	NOUN
asir-1804	70	11	:	:	PUNCT
asir-1804	70	12	increase	increase	VERB
asir-1804	70	13	number	number	NOUN
asir-1804	70	14	of	of	ADP
asir-1804	70	15	steps	step	NOUN
asir-1804	70	16	,	,	PUNCT
asir-1804	70	17	decrease	decrease	VERB
asir-1804	70	18	number	number	NOUN
asir-1804	70	19	of	of	ADP
asir-1804	70	20	steps	step	NOUN
asir-1804	70	21	.	.	PUNCT
asir-1804	71	1	left	leave	VERB
asir-1804	71	2	and	and	CCONJ
asir-1804	71	3	right	right	ADJ
asir-1804	71	4	foci	focus	NOUN
asir-1804	71	5	,	,	PUNCT
asir-1804	71	6	principal	principal	ADJ
asir-1804	71	7	planes	plane	NOUN
asir-1804	71	8	:	:	PUNCT
asir-1804	71	9	figure	figure	VERB
asir-1804	71	10	4	4	NUM
asir-1804	71	11	.	.	PUNCT
asir-1804	71	12	steps	step	NOUN
asir-1804	71	13	for	for	ADP
asir-1804	71	14	paraxial	paraxial	ADJ
asir-1804	71	15	theory	theory	NOUN
asir-1804	71	16	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1804	71	17	applied	apply	VERB
asir-1804	71	18	science	science	NOUN
asir-1804	71	19	and	and	CCONJ
asir-1804	71	20	innovative	innovative	ADJ
asir-1804	71	21	research	research	NOUN
asir-1804	71	22	vol	vol	NOUN
asir-1804	71	23	.	.	PUNCT
asir-1804	72	1	3	3	NUM
asir-1804	72	2	,	,	PUNCT
asir-1804	72	3	no	no	INTJ
asir-1804	72	4	.	.	NOUN
asir-1804	72	5	1	1	NUM
asir-1804	72	6	,	,	PUNCT
asir-1804	72	7	2019	2019	NUM
asir-1804	72	8	19	19	NUM
asir-1804	72	9	published	publish	VERB
asir-1804	72	10	by	by	ADP
asir-1804	72	11	scholink	scholink	PROPN
asir-1804	72	12	inc	inc	PROPN
asir-1804	72	13	.	.	PUNCT
asir-1804	73	1	if	if	SCONJ
asir-1804	73	2	the	the	DET
asir-1804	73	3	user	user	NOUN
asir-1804	73	4	chooses	choose	VERB
asir-1804	73	5	from	from	ADP
asir-1804	73	6	the	the	DET
asir-1804	73	7	introduction	introduction	NOUN
asir-1804	73	8	or	or	CCONJ
asir-1804	73	9	from	from	ADP
asir-1804	73	10	form	form	NOUN
asir-1804	73	11	“	"	PUNCT
asir-1804	73	12	biconvex	biconvex	NOUN
asir-1804	73	13	”	"	PUNCT
asir-1804	73	14	sheet	sheet	NOUN
asir-1804	73	15	,	,	PUNCT
asir-1804	73	16	the	the	DET
asir-1804	73	17	“	"	PUNCT
asir-1804	73	18	thick	thick	ADJ
asir-1804	73	19	lens	lens	NOUN
asir-1804	73	20	model	model	NOUN
asir-1804	73	21	”	"	PUNCT
asir-1804	73	22	a	a	DET
asir-1804	73	23	form	form	NOUN
asir-1804	73	24	appears	appear	VERB
asir-1804	73	25	as	as	ADP
asir-1804	73	26	in	in	ADP
asir-1804	73	27	figure	figure	NOUN
asir-1804	73	28	4	4	NUM
asir-1804	73	29	.	.	PUNCT
asir-1804	74	1	if	if	SCONJ
asir-1804	74	2	he	he	PRON
asir-1804	74	3	presses	press	VERB
asir-1804	74	4	the	the	DET
asir-1804	74	5	button	button	NOUN
asir-1804	74	6	increase	increase	NOUN
asir-1804	74	7	the	the	DET
asir-1804	74	8	number	number	NOUN
asir-1804	74	9	of	of	ADP
asir-1804	74	10	steps	step	NOUN
asir-1804	74	11	to	to	ADP
asir-1804	74	12	1	1	NUM
asir-1804	74	13	,	,	PUNCT
asir-1804	74	14	on	on	ADP
asir-1804	74	15	the	the	DET
asir-1804	74	16	screen	screen	NOUN
asir-1804	74	17	appears	appear	VERB
asir-1804	74	18	a	a	DET
asir-1804	74	19	ray	ray	NOUN
asir-1804	74	20	parallel	parallel	NOUN
asir-1804	74	21	to	to	ADP
asir-1804	74	22	the	the	DET
asir-1804	74	23	x	x	NOUN
asir-1804	74	24	-	-	NOUN
asir-1804	74	25	axis	axis	NOUN
asir-1804	74	26	from	from	ADP
asir-1804	74	27	the	the	DET
asir-1804	74	28	right	right	ADJ
asir-1804	74	29	side	side	NOUN
asir-1804	74	30	of	of	ADP
asir-1804	74	31	the	the	DET
asir-1804	74	32	lens	len	NOUN
asir-1804	74	33	.	.	PUNCT
asir-1804	75	1	as	as	SCONJ
asir-1804	75	2	the	the	DET
asir-1804	75	3	ray	ray	NOUN
asir-1804	75	4	passes	pass	VERB
asir-1804	75	5	through	through	ADP
asir-1804	75	6	the	the	DET
asir-1804	75	7	lens	lens	NOUN
asir-1804	75	8	it	it	PRON
asir-1804	75	9	undergoes	undergo	VERB
asir-1804	75	10	two	two	NUM
asir-1804	75	11	refractions	refraction	NOUN
asir-1804	75	12	.	.	PUNCT
asir-1804	76	1	on	on	ADP
asir-1804	76	2	emerging	emerge	VERB
asir-1804	76	3	from	from	ADP
asir-1804	76	4	the	the	DET
asir-1804	76	5	lens	lens	NOUN
asir-1804	76	6	crosses	cross	VERB
asir-1804	76	7	the	the	DET
asir-1804	76	8	x	x	NOUN
asir-1804	76	9	-	-	NOUN
asir-1804	76	10	axis	axis	NOUN
asir-1804	76	11	on	on	ADP
asir-1804	76	12	the	the	DET
asir-1804	76	13	left	left	ADJ
asir-1804	76	14	focus	focus	NOUN
asir-1804	76	15	of	of	ADP
asir-1804	76	16	the	the	DET
asir-1804	76	17	lens	len	NOUN
asir-1804	76	18	.	.	PUNCT
asir-1804	77	1	on	on	ADP
asir-1804	77	2	a	a	DET
asir-1804	77	3	textbox	textbox	NOUN
asir-1804	77	4	of	of	ADP
asir-1804	77	5	the	the	DET
asir-1804	77	6	form	form	NOUN
asir-1804	77	7	appear	appear	VERB
asir-1804	77	8	the	the	DET
asir-1804	77	9	value	value	NOUN
asir-1804	77	10	of	of	ADP
asir-1804	77	11	the	the	DET
asir-1804	77	12	point	point	NOUN
asir-1804	77	13	of	of	ADP
asir-1804	77	14	the	the	DET
asir-1804	77	15	left	left	ADJ
asir-1804	77	16	focus	focus	NOUN
asir-1804	77	17	and	and	CCONJ
asir-1804	77	18	the	the	DET
asir-1804	77	19	value	value	NOUN
asir-1804	77	20	of	of	ADP
asir-1804	77	21	the	the	DET
asir-1804	77	22	left	left	ADJ
asir-1804	77	23	focus	focus	NOUN
asir-1804	77	24	derived	derive	VERB
asir-1804	77	25	from	from	ADP
asir-1804	77	26	the	the	DET
asir-1804	77	27	paraxial	paraxial	ADJ
asir-1804	77	28	theory	theory	NOUN
asir-1804	77	29	.	.	PUNCT
asir-1804	78	1	the	the	DET
asir-1804	78	2	distance	distance	NOUN
asir-1804	78	3	y	y	PROPN
asir-1804	78	4	of	of	ADP
asir-1804	78	5	the	the	DET
asir-1804	78	6	initial	initial	ADJ
asir-1804	78	7	parallel	parallel	ADJ
asir-1804	78	8	ray	ray	NOUN
asir-1804	78	9	and	and	CCONJ
asir-1804	78	10	also	also	ADV
asir-1804	78	11	other	other	ADJ
asir-1804	78	12	parameters	parameter	NOUN
asir-1804	78	13	(	(	PUNCT
asir-1804	78	14	as	as	ADP
asir-1804	78	15	in	in	ADP
asir-1804	78	16	the	the	DET
asir-1804	78	17	previous	previous	ADJ
asir-1804	78	18	case	case	NOUN
asir-1804	78	19	)	)	PUNCT
asir-1804	78	20	can	can	AUX
asir-1804	78	21	be	be	AUX
asir-1804	78	22	changed	change	VERB
asir-1804	78	23	by	by	ADP
asir-1804	78	24	pressing	press	VERB
asir-1804	78	25	the	the	DET
asir-1804	78	26	button	button	NOUN
asir-1804	78	27	“	"	PUNCT
asir-1804	78	28	parameters	parameter	NOUN
asir-1804	78	29	”	"	PUNCT
asir-1804	78	30	which	which	PRON
asir-1804	78	31	is	be	AUX
asir-1804	78	32	similar	similar	ADJ
asir-1804	78	33	to	to	ADP
asir-1804	78	34	the	the	DET
asir-1804	78	35	one	one	NOUN
asir-1804	78	36	in	in	ADP
asir-1804	78	37	the	the	DET
asir-1804	78	38	previous	previous	ADJ
asir-1804	78	39	section	section	NOUN
asir-1804	78	40	.	.	PUNCT
asir-1804	79	1	if	if	SCONJ
asir-1804	79	2	the	the	DET
asir-1804	79	3	user	user	NOUN
asir-1804	79	4	wants	want	VERB
asir-1804	79	5	to	to	PART
asir-1804	79	6	change	change	VERB
asir-1804	79	7	the	the	DET
asir-1804	79	8	radii	radius	NOUN
asir-1804	79	9	or	or	CCONJ
asir-1804	79	10	the	the	DET
asir-1804	79	11	indexes	index	NOUN
asir-1804	79	12	of	of	ADP
asir-1804	79	13	refraction	refraction	NOUN
asir-1804	79	14	he	he	PRON
asir-1804	79	15	should	should	AUX
asir-1804	79	16	press	press	VERB
asir-1804	79	17	the	the	DET
asir-1804	79	18	button	button	NOUN
asir-1804	79	19	“	"	PUNCT
asir-1804	79	20	adjustment	adjustment	NOUN
asir-1804	79	21	of	of	ADP
asir-1804	79	22	geometrical	geometrical	ADJ
asir-1804	79	23	parameters	parameter	NOUN
asir-1804	79	24	and	and	CCONJ
asir-1804	79	25	indexes	index	NOUN
asir-1804	79	26	of	of	ADP
asir-1804	79	27	refraction	refraction	NOUN
asir-1804	79	28	”	"	PUNCT
asir-1804	79	29	.	.	PUNCT
asir-1804	80	1	for	for	ADP
asir-1804	80	2	the	the	DET
asir-1804	80	3	step	step	NOUN
asir-1804	80	4	1	1	NUM
asir-1804	80	5	,	,	PUNCT
asir-1804	80	6	the	the	DET
asir-1804	80	7	student	student	NOUN
asir-1804	80	8	can	can	AUX
asir-1804	80	9	see	see	VERB
asir-1804	80	10	that	that	PRON
asir-1804	80	11	by	by	ADP
asir-1804	80	12	decreasing	decrease	VERB
asir-1804	80	13	the	the	DET
asir-1804	80	14	value	value	NOUN
asir-1804	80	15	of	of	ADP
asir-1804	80	16	y	y	PROPN
asir-1804	80	17	for	for	ADP
asir-1804	80	18	the	the	DET
asir-1804	80	19	parallel	parallel	ADJ
asir-1804	80	20	ray	ray	NOUN
asir-1804	80	21	,	,	PUNCT
asir-1804	80	22	the	the	DET
asir-1804	80	23	point	point	NOUN
asir-1804	80	24	of	of	ADP
asir-1804	80	25	intersection	intersection	NOUN
asir-1804	80	26	of	of	ADP
asir-1804	80	27	the	the	DET
asir-1804	80	28	emerging	emerge	VERB
asir-1804	80	29	ray	ray	NOUN
asir-1804	80	30	with	with	ADP
asir-1804	80	31	the	the	DET
asir-1804	80	32	xaxis	xaxis	NOUN
asir-1804	80	33	is	be	AUX
asir-1804	80	34	very	very	ADV
asir-1804	80	35	near	near	ADP
asir-1804	80	36	the	the	DET
asir-1804	80	37	value	value	NOUN
asir-1804	80	38	of	of	ADP
asir-1804	80	39	the	the	DET
asir-1804	80	40	left	left	ADJ
asir-1804	80	41	focus	focus	NOUN
asir-1804	80	42	calculated	calculate	VERB
asir-1804	80	43	according	accord	VERB
asir-1804	80	44	to	to	ADP
asir-1804	80	45	the	the	DET
asir-1804	80	46	paraxial	paraxial	ADJ
asir-1804	80	47	model	model	NOUN
asir-1804	80	48	.	.	PUNCT
asir-1804	81	1	for	for	ADP
asir-1804	81	2	the	the	DET
asir-1804	81	3	next	next	ADJ
asir-1804	81	4	step	step	NOUN
asir-1804	81	5	2	2	NUM
asir-1804	81	6	there	there	PRON
asir-1804	81	7	is	be	VERB
asir-1804	81	8	an	an	DET
asir-1804	81	9	extrapolation	extrapolation	NOUN
asir-1804	81	10	of	of	ADP
asir-1804	81	11	the	the	DET
asir-1804	81	12	emerging	emerge	VERB
asir-1804	81	13	ray	ray	NOUN
asir-1804	81	14	to	to	ADP
asir-1804	81	15	the	the	DET
asir-1804	81	16	right	right	NOUN
asir-1804	81	17	.	.	PUNCT
asir-1804	82	1	on	on	ADP
asir-1804	82	2	the	the	DET
asir-1804	82	3	next	next	ADJ
asir-1804	82	4	step	step	NOUN
asir-1804	82	5	3	3	NUM
asir-1804	82	6	the	the	DET
asir-1804	82	7	incident	incident	NOUN
asir-1804	82	8	ray	ray	NOUN
asir-1804	82	9	-parallel	-parallel	PROPN
asir-1804	82	10	to	to	ADP
asir-1804	82	11	the	the	DET
asir-1804	82	12	x	x	PUNCT
asir-1804	82	13	axis	axis	NOUN
asir-1804	82	14	is	be	AUX
asir-1804	82	15	extrapolated	extrapolate	VERB
asir-1804	82	16	to	to	ADP
asir-1804	82	17	the	the	DET
asir-1804	82	18	left	left	NOUN
asir-1804	82	19	.	.	PUNCT
asir-1804	83	1	on	on	ADP
asir-1804	83	2	step	step	NOUN
asir-1804	83	3	4	4	NUM
asir-1804	83	4	,	,	PUNCT
asir-1804	83	5	the	the	DET
asir-1804	83	6	intersection	intersection	NOUN
asir-1804	83	7	h1	h1	NOUN
asir-1804	83	8	of	of	ADP
asir-1804	83	9	the	the	DET
asir-1804	83	10	2	2	NUM
asir-1804	83	11	rays	ray	NOUN
asir-1804	83	12	is	be	AUX
asir-1804	83	13	found	find	VERB
asir-1804	83	14	.	.	PUNCT
asir-1804	84	1	this	this	PRON
asir-1804	84	2	is	be	AUX
asir-1804	84	3	the	the	DET
asir-1804	84	4	first	first	ADJ
asir-1804	84	5	principal	principal	ADJ
asir-1804	84	6	point	point	NOUN
asir-1804	84	7	.	.	PUNCT
asir-1804	85	1	a	a	DET
asir-1804	85	2	line	line	NOUN
asir-1804	85	3	parallel	parallel	NOUN
asir-1804	85	4	to	to	ADP
asir-1804	85	5	the	the	DET
asir-1804	85	6	y	y	NOUN
asir-1804	85	7	-	-	PUNCT
asir-1804	85	8	axis	axis	NOUN
asir-1804	85	9	through	through	ADP
asir-1804	85	10	the	the	DET
asir-1804	85	11	first	first	ADJ
asir-1804	85	12	principal	principal	ADJ
asir-1804	85	13	point	point	NOUN
asir-1804	85	14	represents	represent	VERB
asir-1804	85	15	the	the	DET
asir-1804	85	16	first	first	ADJ
asir-1804	85	17	principal	principal	ADJ
asir-1804	85	18	plane	plane	NOUN
asir-1804	85	19	.	.	PUNCT
asir-1804	86	1	in	in	ADP
asir-1804	86	2	the	the	DET
asir-1804	86	3	4	4	NUM
asir-1804	86	4	next	next	ADJ
asir-1804	86	5	steps	step	NOUN
asir-1804	86	6	the	the	DET
asir-1804	86	7	procedure	procedure	NOUN
asir-1804	86	8	is	be	AUX
asir-1804	86	9	repeated	repeat	VERB
asir-1804	86	10	for	for	ADP
asir-1804	86	11	a	a	DET
asir-1804	86	12	ray	ray	NOUN
asir-1804	86	13	incident	incident	NOUN
asir-1804	86	14	parallel	parallel	NOUN
asir-1804	86	15	to	to	ADP
asir-1804	86	16	the	the	DET
asir-1804	86	17	x	x	NOUN
asir-1804	86	18	-	-	NOUN
asir-1804	86	19	axis	axis	NOUN
asir-1804	86	20	from	from	ADP
asir-1804	86	21	the	the	DET
asir-1804	86	22	left	left	NOUN
asir-1804	86	23	.	.	PUNCT
asir-1804	87	1	so	so	ADV
asir-1804	87	2	we	we	PRON
asir-1804	87	3	get	get	VERB
asir-1804	87	4	the	the	DET
asir-1804	87	5	two	two	NUM
asir-1804	87	6	principal	principal	ADJ
asir-1804	87	7	points	point	NOUN
asir-1804	87	8	and	and	CCONJ
asir-1804	87	9	the	the	DET
asir-1804	87	10	two	two	NUM
asir-1804	87	11	principal	principal	ADJ
asir-1804	87	12	planes	plane	NOUN
asir-1804	87	13	,	,	PUNCT
asir-1804	87	14	which	which	PRON
asir-1804	87	15	are	be	AUX
asir-1804	87	16	shown	show	VERB
asir-1804	87	17	without	without	ADP
asir-1804	87	18	the	the	DET
asir-1804	87	19	incident	incident	NOUN
asir-1804	87	20	rays	ray	NOUN
asir-1804	87	21	in	in	ADP
asir-1804	87	22	step	step	NOUN
asir-1804	87	23	9	9	NUM
asir-1804	87	24	.	.	PUNCT
asir-1804	88	1	on	on	ADP
asir-1804	88	2	step	step	NOUN
asir-1804	88	3	9	9	NUM
asir-1804	88	4	are	be	AUX
asir-1804	88	5	calculated	calculate	VERB
asir-1804	88	6	the	the	DET
asir-1804	88	7	2	2	NUM
asir-1804	88	8	nodal	nodal	NOUN
asir-1804	88	9	points	point	NOUN
asir-1804	88	10	.	.	PUNCT
asir-1804	89	1	for	for	ADP
asir-1804	89	2	a	a	DET
asir-1804	89	3	lens	lens	NOUN
asir-1804	89	4	in	in	ADP
asir-1804	89	5	the	the	DET
asir-1804	89	6	air	air	NOUN
asir-1804	89	7	the	the	DET
asir-1804	89	8	2	2	NUM
asir-1804	89	9	nodal	nodal	NOUN
asir-1804	89	10	points	point	NOUN
asir-1804	89	11	coincide	coincide	NOUN
asir-1804	89	12	with	with	ADP
asir-1804	89	13	the	the	DET
asir-1804	89	14	principal	principal	ADJ
asir-1804	89	15	points	point	NOUN
asir-1804	89	16	.	.	PUNCT
asir-1804	90	1	in	in	ADP
asir-1804	90	2	the	the	DET
asir-1804	90	3	case	case	NOUN
asir-1804	90	4	of	of	ADP
asir-1804	90	5	a	a	DET
asir-1804	90	6	lens	lens	NOUN
asir-1804	90	7	in	in	ADP
asir-1804	90	8	the	the	DET
asir-1804	90	9	air	air	NOUN
asir-1804	90	10	the	the	DET
asir-1804	90	11	focal	focal	ADJ
asir-1804	90	12	length	length	NOUN
asir-1804	90	13	of	of	ADP
asir-1804	90	14	the	the	DET
asir-1804	90	15	lens	lens	NOUN
asir-1804	90	16	is	be	AUX
asir-1804	90	17	found	find	VERB
asir-1804	90	18	by	by	ADP
asir-1804	90	19	f=	f=	NOUN
asir-1804	90	20	(	(	PUNCT
asir-1804	90	21	1	1	NUM
asir-1804	90	22	/	/	SYM
asir-1804	90	23	n-1	n-1	NUM
asir-1804	90	24	)	)	PUNCT
asir-1804	91	1	[	[	X
asir-1804	91	2	(	(	PUNCT
asir-1804	91	3	n	n	X
asir-1804	91	4	r1	r1	NOUN
asir-1804	91	5	r2)/	r2)/	NUM
asir-1804	91	6	(	(	PUNCT
asir-1804	91	7	n-1	n-1	NUM
asir-1804	91	8	)	)	PUNCT
asir-1804	92	1	d	d	NOUN
asir-1804	92	2	+	+	NOUN
asir-1804	92	3	n	n	PRON
asir-1804	92	4	(	(	PUNCT
asir-1804	92	5	r2	r2	PROPN
asir-1804	92	6	r1	r1	PROPN
asir-1804	92	7	)	)	PUNCT
asir-1804	92	8	]	]	PUNCT
asir-1804	93	1	(	(	PUNCT
asir-1804	93	2	reinhard	reinhard	PROPN
asir-1804	93	3	jenny	jenny	PROPN
asir-1804	93	4	,	,	PUNCT
asir-1804	93	5	p.	p.	NOUN
asir-1804	93	6	16	16	NUM
asir-1804	93	7	)	)	PUNCT
asir-1804	93	8	.	.	PUNCT
asir-1804	94	1	the	the	DET
asir-1804	94	2	above	above	ADJ
asir-1804	94	3	method	method	NOUN
asir-1804	94	4	is	be	AUX
asir-1804	94	5	depicted	depict	VERB
asir-1804	94	6	in	in	ADP
asir-1804	94	7	rowlands	rowlands	PROPN
asir-1804	94	8	(	(	PUNCT
asir-1804	94	9	pp	pp	ADJ
asir-1804	94	10	.	.	PUNCT
asir-1804	95	1	1	1	NUM
asir-1804	95	2	-	-	SYM
asir-1804	95	3	12	12	NUM
asir-1804	95	4	,	,	PUNCT
asir-1804	95	5	for	for	ADP
asir-1804	95	6	principal	principal	ADJ
asir-1804	95	7	planes	plane	NOUN
asir-1804	95	8	,	,	PUNCT
asir-1804	95	9	pp	pp	ADJ
asir-1804	95	10	.	.	PUNCT
asir-1804	96	1	1	1	NUM
asir-1804	96	2	-	-	SYM
asir-1804	96	3	18	18	NUM
asir-1804	96	4	for	for	ADP
asir-1804	96	5	cardinal	cardinal	ADJ
asir-1804	96	6	points	point	NOUN
asir-1804	96	7	)	)	PUNCT
asir-1804	96	8	.	.	PUNCT
asir-1804	97	1	in	in	ADP
asir-1804	97	2	the	the	DET
asir-1804	97	3	case	case	NOUN
asir-1804	97	4	of	of	ADP
asir-1804	97	5	a	a	DET
asir-1804	97	6	lens	lens	NOUN
asir-1804	97	7	for	for	ADP
asir-1804	97	8	which	which	PRON
asir-1804	97	9	the	the	DET
asir-1804	97	10	left	left	ADJ
asir-1804	97	11	medium	medium	NOUN
asir-1804	97	12	has	have	VERB
asir-1804	97	13	index	index	NOUN
asir-1804	97	14	of	of	ADP
asir-1804	97	15	refraction	refraction	NOUN
asir-1804	97	16	n1=1	n1=1	PROPN
asir-1804	97	17	,	,	PUNCT
asir-1804	97	18	the	the	DET
asir-1804	97	19	lens	lens	NOUN
asir-1804	97	20	has	have	VERB
asir-1804	97	21	index	index	NOUN
asir-1804	97	22	of	of	ADP
asir-1804	97	23	refraction	refraction	NOUN
asir-1804	97	24	n2	n2	NOUN
asir-1804	97	25	,	,	PUNCT
asir-1804	97	26	and	and	CCONJ
asir-1804	97	27	the	the	DET
asir-1804	97	28	right	right	ADJ
asir-1804	97	29	side	side	NOUN
asir-1804	97	30	has	have	VERB
asir-1804	97	31	an	an	DET
asir-1804	97	32	index	index	NOUN
asir-1804	97	33	of	of	ADP
asir-1804	97	34	refraction	refraction	NOUN
asir-1804	97	35	n3	n3	NOUN
asir-1804	97	36	then	then	ADV
asir-1804	97	37	we	we	PRON
asir-1804	97	38	do	do	AUX
asir-1804	97	39	not	not	PART
asir-1804	97	40	have	have	VERB
asir-1804	97	41	one	one	NUM
asir-1804	97	42	value	value	NOUN
asir-1804	97	43	of	of	ADP
asir-1804	97	44	focal	focal	ADJ
asir-1804	97	45	length	length	NOUN
asir-1804	97	46	,	,	PUNCT
asir-1804	97	47	and	and	CCONJ
asir-1804	97	48	we	we	PRON
asir-1804	97	49	find	find	VERB
asir-1804	97	50	two	two	NUM
asir-1804	97	51	focal	focal	ADJ
asir-1804	97	52	lengths	length	NOUN
asir-1804	97	53	:	:	PUNCT
asir-1804	97	54	the	the	DET
asir-1804	97	55	focal	focal	ADJ
asir-1804	97	56	point	point	NOUN
asir-1804	97	57	f1	f1	NOUN
asir-1804	97	58	is	be	AUX
asir-1804	97	59	on	on	ADP
asir-1804	97	60	the	the	DET
asir-1804	97	61	left	left	NOUN
asir-1804	97	62	,	,	PUNCT
asir-1804	97	63	and	and	CCONJ
asir-1804	97	64	f2	f2	PROPN
asir-1804	97	65	is	be	AUX
asir-1804	97	66	on	on	ADP
asir-1804	97	67	the	the	DET
asir-1804	97	68	right	right	NOUN
asir-1804	97	69	.	.	PUNCT
asir-1804	98	1	if	if	SCONJ
asir-1804	98	2	t	t	PROPN
asir-1804	98	3	is	be	AUX
asir-1804	98	4	the	the	DET
asir-1804	98	5	width	width	NOUN
asir-1804	98	6	of	of	ADP
asir-1804	98	7	the	the	DET
asir-1804	98	8	lens	lens	NOUN
asir-1804	98	9	and	and	CCONJ
asir-1804	98	10	the	the	DET
asir-1804	98	11	radii	radius	NOUN
asir-1804	98	12	of	of	ADP
asir-1804	98	13	the	the	DET
asir-1804	98	14	surfaces	surface	NOUN
asir-1804	98	15	are	be	AUX
asir-1804	98	16	rb	rb	NOUN
asir-1804	98	17	(	(	PUNCT
asir-1804	98	18	for	for	ADP
asir-1804	98	19	the	the	DET
asir-1804	98	20	left	left	ADJ
asir-1804	98	21	surface	surface	NOUN
asir-1804	98	22	)	)	PUNCT
asir-1804	98	23	and	and	CCONJ
asir-1804	98	24	ra	ra	PROPN
asir-1804	98	25	(	(	PUNCT
asir-1804	98	26	for	for	ADP
asir-1804	98	27	the	the	DET
asir-1804	98	28	right	right	ADJ
asir-1804	98	29	surface	surface	NOUN
asir-1804	98	30	)	)	PUNCT
asir-1804	98	31	then	then	ADV
asir-1804	98	32	:	:	PUNCT
asir-1804	98	33	1	1	NUM
asir-1804	98	34	𝑓1	𝑓1	ADJ
asir-1804	98	35	=	=	SYM
asir-1804	98	36	𝑛2	𝑛2	NOUN
asir-1804	98	37	−	−	PROPN
asir-1804	98	38	𝑛3	𝑛3	NOUN
asir-1804	98	39	−𝑛1𝑅𝑎	−𝑛1𝑅𝑎	NOUN
asir-1804	98	40	−	−	NOUN
asir-1804	98	41	𝑛2	𝑛2	NOUN
asir-1804	98	42	−	−	PROPN
asir-1804	98	43	𝑛1	𝑛1	NOUN
asir-1804	98	44	−𝑛1𝑅𝑏	−𝑛1𝑅𝑏	NOUN
asir-1804	98	45	−	−	PROPN
asir-1804	98	46	(	(	PUNCT
asir-1804	98	47	𝑛2	𝑛2	NOUN
asir-1804	98	48	−	−	PROPN
asir-1804	98	49	𝑛1)(𝑛2	𝑛1)(𝑛2	X
asir-1804	98	50	−	−	PROPN
asir-1804	98	51	𝑛3	𝑛3	NOUN
asir-1804	98	52	)	)	PUNCT
asir-1804	98	53	𝑛1𝑛2	𝑛1𝑛2	PRON
asir-1804	98	54	𝑡	𝑡	PROPN
asir-1804	98	55	−𝑅𝑎𝑅𝑏	−𝑅𝑎𝑅𝑏	PROPN
asir-1804	98	56	𝑓2	𝑓2	PROPN
asir-1804	98	57	=	=	SYM
asir-1804	98	58	−	−	NOUN
asir-1804	98	59	𝑛3	𝑛3	NOUN
asir-1804	98	60	𝑛1	𝑛1	NOUN
asir-1804	98	61	𝑓1	𝑓1	PROPN
asir-1804	98	62	their	their	PRON
asir-1804	98	63	position	position	NOUN
asir-1804	98	64	are	be	AUX
asir-1804	98	65	:	:	PUNCT
asir-1804	98	66	f_left=	f_left=	PROPN
asir-1804	98	67	h1+f1	h1+f1	PROPN
asir-1804	98	68	,	,	PUNCT
asir-1804	98	69	f_right	f_right	NOUN
asir-1804	98	70	=	=	PUNCT
asir-1804	99	1	h2+f2	h2+f2	PROPN
asir-1804	99	2	2.1	2.1	NUM
asir-1804	99	3	finding	find	VERB
asir-1804	99	4	the	the	DET
asir-1804	99	5	image	image	NOUN
asir-1804	99	6	on	on	ADP
asir-1804	99	7	step	step	NOUN
asir-1804	99	8	10	10	NUM
asir-1804	99	9	are	be	AUX
asir-1804	99	10	depicted	depict	VERB
asir-1804	99	11	the	the	DET
asir-1804	99	12	object	object	NOUN
asir-1804	99	13	(	(	PUNCT
asir-1804	99	14	source	source	NOUN
asir-1804	99	15	)	)	PUNCT
asir-1804	99	16	,	,	PUNCT
asir-1804	99	17	the	the	DET
asir-1804	99	18	two	two	NUM
asir-1804	99	19	foci	focus	NOUN
asir-1804	99	20	and	and	CCONJ
asir-1804	99	21	the	the	DET
asir-1804	99	22	two	two	NUM
asir-1804	99	23	principal	principal	ADJ
asir-1804	99	24	planes	plane	NOUN
asir-1804	99	25	.	.	PUNCT
asir-1804	100	1	in	in	ADP
asir-1804	100	2	step	step	NOUN
asir-1804	100	3	11	11	NUM
asir-1804	100	4	a	a	DET
asir-1804	100	5	line	line	NOUN
asir-1804	100	6	is	be	AUX
asir-1804	100	7	drawn	draw	VERB
asir-1804	100	8	from	from	ADP
asir-1804	100	9	the	the	DET
asir-1804	100	10	upper	upper	ADJ
asir-1804	100	11	point	point	NOUN
asir-1804	100	12	to	to	ADP
asir-1804	100	13	the	the	DET
asir-1804	100	14	source	source	NOUN
asir-1804	100	15	,	,	PUNCT
asir-1804	100	16	so	so	SCONJ
asir-1804	100	17	that	that	SCONJ
asir-1804	100	18	its	its	PRON
asir-1804	100	19	back	back	ADJ
asir-1804	100	20	extrapolation	extrapolation	NOUN
asir-1804	100	21	meets	meet	VERB
asir-1804	100	22	the	the	DET
asir-1804	100	23	xaxis	xaxis	PROPN
asir-1804	100	24	in	in	ADP
asir-1804	100	25	the	the	DET
asir-1804	100	26	left	left	ADJ
asir-1804	100	27	focus	focus	NOUN
asir-1804	100	28	.	.	PUNCT
asir-1804	101	1	the	the	DET
asir-1804	101	2	line	line	NOUN
asir-1804	101	3	is	be	AUX
asir-1804	101	4	drawn	draw	VERB
asir-1804	101	5	up	up	ADP
asir-1804	101	6	to	to	ADP
asir-1804	101	7	the	the	DET
asir-1804	101	8	principal	principal	ADJ
asir-1804	101	9	plane	plane	NOUN
asir-1804	101	10	h1	h1	NOUN
asir-1804	101	11	.	.	PUNCT
asir-1804	102	1	from	from	ADP
asir-1804	102	2	h1	h1	PROPN
asir-1804	102	3	we	we	PRON
asir-1804	102	4	draw	draw	VERB
asir-1804	102	5	a	a	DET
asir-1804	102	6	line	line	NOUN
asir-1804	102	7	to	to	ADP
asir-1804	102	8	the	the	DET
asir-1804	102	9	right	right	ADJ
asir-1804	102	10	parallel	parallel	NOUN
asir-1804	102	11	to	to	ADP
asir-1804	102	12	the	the	DET
asir-1804	102	13	xaxis	xaxis	NOUN
asir-1804	102	14	.	.	PUNCT
asir-1804	103	1	in	in	ADP
asir-1804	103	2	the	the	DET
asir-1804	103	3	next	next	ADJ
asir-1804	103	4	step	step	NOUN
asir-1804	103	5	(	(	PUNCT
asir-1804	103	6	12	12	NUM
asir-1804	103	7	)	)	PUNCT
asir-1804	103	8	a	a	DET
asir-1804	103	9	line	line	NOUN
asir-1804	103	10	is	be	AUX
asir-1804	103	11	drawn	draw	VERB
asir-1804	103	12	from	from	ADP
asir-1804	103	13	the	the	DET
asir-1804	103	14	highest	high	ADJ
asir-1804	103	15	point	point	NOUN
asir-1804	103	16	of	of	ADP
asir-1804	103	17	the	the	DET
asir-1804	103	18	source	source	NOUN
asir-1804	103	19	,	,	PUNCT
asir-1804	103	20	parallel	parallel	ADJ
asir-1804	103	21	to	to	ADP
asir-1804	103	22	the	the	DET
asir-1804	103	23	x	x	NOUN
asir-1804	103	24	-	-	NOUN
asir-1804	103	25	axis	axis	NOUN
asir-1804	103	26	up	up	ADP
asir-1804	103	27	to	to	ADP
asir-1804	103	28	principal	principal	ADJ
asir-1804	103	29	plane	plane	NOUN
asir-1804	103	30	h2	h2	NOUN
asir-1804	103	31	.	.	PUNCT
asir-1804	104	1	from	from	ADP
asir-1804	104	2	h2	h2	NOUN
asir-1804	104	3	we	we	PRON
asir-1804	104	4	draw	draw	VERB
asir-1804	104	5	a	a	DET
asir-1804	104	6	line	line	NOUN
asir-1804	104	7	that	that	PRON
asir-1804	104	8	passes	pass	VERB
asir-1804	104	9	through	through	ADP
asir-1804	104	10	the	the	DET
asir-1804	104	11	right	right	ADJ
asir-1804	104	12	focus	focus	NOUN
asir-1804	104	13	.	.	PUNCT
asir-1804	105	1	in	in	ADP
asir-1804	105	2	the	the	DET
asir-1804	105	3	spreadsheet	spreadsheet	NOUN
asir-1804	105	4	the	the	DET
asir-1804	105	5	location	location	NOUN
asir-1804	105	6	of	of	ADP
asir-1804	105	7	the	the	DET
asir-1804	105	8	image	image	NOUN
asir-1804	105	9	is	be	AUX
asir-1804	105	10	found	find	VERB
asir-1804	105	11	as	as	SCONJ
asir-1804	105	12	follows	follow	VERB
asir-1804	105	13	:	:	PUNCT
asir-1804	105	14	if	if	SCONJ
asir-1804	105	15	the	the	DET
asir-1804	105	16	source	source	NOUN
asir-1804	105	17	has	have	VERB
asir-1804	105	18	a	a	DET
asir-1804	105	19	location	location	NOUN
asir-1804	105	20	(	(	PUNCT
asir-1804	105	21	xsource	xsource	PROPN
asir-1804	105	22	,	,	PUNCT
asir-1804	105	23	ysource	ysource	PROPN
asir-1804	105	24	)	)	PUNCT
asir-1804	105	25	then	then	ADV
asir-1804	105	26	so	so	ADV
asir-1804	105	27	=	=	PUNCT
asir-1804	105	28	object	object	NOUN
asir-1804	105	29	(	(	PUNCT
asir-1804	105	30	source	source	NOUN
asir-1804	105	31	)	)	PUNCT
asir-1804	105	32	distance	distance	NOUN
asir-1804	105	33	from	from	ADP
asir-1804	105	34	the	the	DET
asir-1804	105	35	principal	principal	ADJ
asir-1804	105	36	plane	plane	NOUN
asir-1804	105	37	h1	h1	PROPN
asir-1804	105	38	.	.	PUNCT
asir-1804	106	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-1804	106	2	applied	apply	VERB
asir-1804	106	3	science	science	NOUN
asir-1804	106	4	and	and	CCONJ
asir-1804	106	5	innovative	innovative	ADJ
asir-1804	106	6	research	research	NOUN
asir-1804	106	7	vol	vol	NOUN
asir-1804	106	8	.	.	PUNCT
asir-1804	107	1	3	3	NUM
asir-1804	107	2	,	,	PUNCT
asir-1804	107	3	no	no	INTJ
asir-1804	107	4	.	.	NOUN
asir-1804	107	5	1	1	NUM
asir-1804	107	6	,	,	PUNCT
asir-1804	107	7	2019	2019	NUM
asir-1804	107	8	20	20	NUM
asir-1804	107	9	published	publish	VERB
asir-1804	107	10	by	by	ADP
asir-1804	107	11	scholink	scholink	PROPN
asir-1804	107	12	inc	inc	PROPN
asir-1804	107	13	.	.	PROPN
asir-1804	108	1	so=	so=	PROPN
asir-1804	108	2	h1xsource	h1xsource	NOUN
asir-1804	108	3	and	and	CCONJ
asir-1804	108	4	si	si	NOUN
asir-1804	108	5	=	=	NOUN
asir-1804	108	6	image	image	NOUN
asir-1804	108	7	distance	distance	NOUN
asir-1804	108	8	from	from	ADP
asir-1804	108	9	the	the	DET
asir-1804	108	10	principal	principal	ADJ
asir-1804	108	11	plane	plane	NOUN
asir-1804	108	12	h2	h2	PROPN
asir-1804	108	13	then	then	ADV
asir-1804	108	14	according	accord	VERB
asir-1804	108	15	to	to	ADP
asir-1804	108	16	pedrotti	pedrotti	PROPN
asir-1804	108	17	(	(	PUNCT
asir-1804	108	18	2014	2014	NUM
asir-1804	108	19	)	)	PUNCT
asir-1804	108	20	chapter	chapter	NOUN
asir-1804	108	21	18	18	NUM
asir-1804	108	22	:	:	PUNCT
asir-1804	108	23	−	−	PROPN
asir-1804	108	24	𝑓1	𝑓1	PROPN
asir-1804	108	25	𝑆𝑂	𝑆𝑂	PROPN
asir-1804	108	26	+	+	CCONJ
asir-1804	108	27	𝑓2	𝑓2	PROPN
asir-1804	109	1	𝑆𝐼	𝑆𝐼	NOUN
asir-1804	109	2	=	=	SYM
asir-1804	109	3	1	1	NUM
asir-1804	109	4	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
asir-1804	109	5	𝑆𝐼	𝑆𝐼	PROPN
asir-1804	109	6	=	=	SYM
asir-1804	109	7	𝑓2	𝑓2	ADJ
asir-1804	109	8	1	1	NUM
asir-1804	109	9	+	+	CCONJ
asir-1804	109	10	𝑓1	𝑓1	ADJ
asir-1804	109	11	𝑆𝑂	𝑆𝑂	PROPN
asir-1804	109	12	and	and	CCONJ
asir-1804	109	13	the	the	DET
asir-1804	109	14	x	x	ADJ
asir-1804	109	15	position	position	NOUN
asir-1804	109	16	of	of	ADP
asir-1804	109	17	the	the	DET
asir-1804	109	18	image	image	NOUN
asir-1804	109	19	ximage	ximage	NOUN
asir-1804	109	20	=	=	SYM
asir-1804	109	21	h2+si	h2+si	PROPN
asir-1804	109	22	,	,	PUNCT
asir-1804	109	23	and	and	CCONJ
asir-1804	109	24	𝑦𝑖𝑚𝑎𝑔𝑒	𝑦𝑖𝑚𝑎𝑔𝑒	NOUN
asir-1804	109	25	=	=	SYM
asir-1804	109	26	(	(	PUNCT
asir-1804	109	27	h1	h1	PROPN
asir-1804	109	28	−	−	PROPN
asir-1804	109	29	𝑓𝑙𝑒𝑓𝑡	𝑓𝑙𝑒𝑓𝑡	ADJ
asir-1804	109	30	)	)	PUNCT
asir-1804	110	1	∙	∙	PROPN
asir-1804	110	2	𝑦𝑠𝑜𝑢𝑟𝑐𝑒/(𝑥𝑠𝑜𝑢𝑟𝑐𝑒	𝑦𝑠𝑜𝑢𝑟𝑐𝑒/(𝑥𝑠𝑜𝑢𝑟𝑐𝑒	PROPN
asir-1804	110	3	−	−	PROPN
asir-1804	110	4	𝑓𝑙𝑒𝑓𝑡	𝑓𝑙𝑒𝑓𝑡	X
asir-1804	110	5	)	)	PUNCT
asir-1804	110	6	2.2	2.2	NUM
asir-1804	110	7	experiments	experiment	NOUN
asir-1804	110	8	for	for	ADP
asir-1804	110	9	finding	find	VERB
asir-1804	110	10	the	the	DET
asir-1804	110	11	focal	focal	ADJ
asir-1804	110	12	length	length	NOUN
asir-1804	110	13	by	by	ADP
asir-1804	110	14	clicking	click	VERB
asir-1804	110	15	on	on	ADP
asir-1804	110	16	the	the	DET
asir-1804	110	17	button	button	NOUN
asir-1804	110	18	“	"	PUNCT
asir-1804	110	19	finding	find	VERB
asir-1804	110	20	f	f	X
asir-1804	110	21	by	by	ADP
asir-1804	110	22	plotting	plot	VERB
asir-1804	110	23	”	"	PUNCT
asir-1804	110	24	we	we	PRON
asir-1804	110	25	go	go	VERB
asir-1804	110	26	the	the	DET
asir-1804	110	27	worksheet	worksheet	NOUN
asir-1804	110	28	“	"	PUNCT
asir-1804	110	29	finding	find	VERB
asir-1804	110	30	f	f	X
asir-1804	110	31	”	"	PUNCT
asir-1804	110	32	and	and	CCONJ
asir-1804	110	33	appears	appear	VERB
asir-1804	110	34	a	a	DET
asir-1804	110	35	form	form	NOUN
asir-1804	110	36	with	with	ADP
asir-1804	110	37	several	several	ADJ
asir-1804	110	38	buttons	button	NOUN
asir-1804	110	39	:	:	PUNCT
asir-1804	110	40	2	2	NUM
asir-1804	110	41	buttons	button	NOUN
asir-1804	110	42	for	for	ADP
asir-1804	110	43	inserting	insert	VERB
asir-1804	110	44	data	datum	NOUN
asir-1804	110	45	and	and	CCONJ
asir-1804	110	46	other	other	ADJ
asir-1804	110	47	buttons	button	NOUN
asir-1804	110	48	for	for	ADP
asir-1804	110	49	working	work	VERB
asir-1804	110	50	on	on	ADP
asir-1804	110	51	the	the	DET
asir-1804	110	52	data	datum	NOUN
asir-1804	110	53	(	(	PUNCT
asir-1804	110	54	figure	figure	NOUN
asir-1804	110	55	5	5	NUM
asir-1804	110	56	)	)	PUNCT
asir-1804	110	57	.	.	PUNCT
asir-1804	111	1	by	by	ADP
asir-1804	111	2	clicking	click	VERB
asir-1804	111	3	“	"	PUNCT
asir-1804	111	4	insert	insert	ADJ
asir-1804	111	5	data	datum	NOUN
asir-1804	111	6	(	(	PUNCT
asir-1804	111	7	preferably	preferably	ADV
asir-1804	111	8	through	through	ADP
asir-1804	111	9	macro	macro	NOUN
asir-1804	111	10	)	)	PUNCT
asir-1804	111	11	”	"	PUNCT
asir-1804	111	12	the	the	DET
asir-1804	111	13	program	program	NOUN
asir-1804	111	14	asks	ask	VERB
asir-1804	111	15	for	for	ADP
asir-1804	111	16	how	how	SCONJ
asir-1804	111	17	many	many	ADJ
asir-1804	111	18	data	datum	NOUN
asir-1804	111	19	(	(	PUNCT
asir-1804	111	20	default	default	NOUN
asir-1804	111	21	8)	8)	NUM
asir-1804	111	22	and	and	CCONJ
asir-1804	111	23	then	then	ADV
asir-1804	111	24	the	the	DET
asir-1804	111	25	program	program	NOUN
asir-1804	111	26	inserts	insert	VERB
asir-1804	111	27	the	the	DET
asir-1804	111	28	object	object	NOUN
asir-1804	111	29	’s	’s	PART
asir-1804	111	30	distance	distance	NOUN
asir-1804	111	31	“	"	PUNCT
asir-1804	111	32	a	a	PRON
asir-1804	111	33	”	"	PUNCT
asir-1804	111	34	and	and	CCONJ
asir-1804	111	35	the	the	DET
asir-1804	111	36	image	image	NOUN
asir-1804	111	37	distance	distance	NOUN
asir-1804	111	38	“	"	PUNCT
asir-1804	111	39	b	b	NOUN
asir-1804	111	40	”	"	PUNCT
asir-1804	111	41	(	(	PUNCT
asir-1804	111	42	the	the	DET
asir-1804	111	43	program	program	NOUN
asir-1804	111	44	finds	find	VERB
asir-1804	111	45	the	the	DET
asir-1804	111	46	suitable	suitable	ADJ
asir-1804	111	47	b	b	NOUN
asir-1804	111	48	by	by	ADP
asir-1804	111	49	the	the	DET
asir-1804	111	50	method	method	NOUN
asir-1804	111	51	described	describe	VERB
asir-1804	111	52	on	on	ADP
asir-1804	111	53	biconvex	biconvex	NOUN
asir-1804	111	54	lenses	lense	VERB
asir-1804	111	55	the	the	DET
asir-1804	111	56	sharpest	sharp	ADJ
asir-1804	111	57	image	image	NOUN
asir-1804	111	58	)	)	PUNCT
asir-1804	111	59	,	,	PUNCT
asir-1804	111	60	and	and	CCONJ
asir-1804	111	61	also	also	ADV
asir-1804	111	62	it	it	PRON
asir-1804	111	63	determines	determine	VERB
asir-1804	111	64	the	the	DET
asir-1804	111	65	image	image	NOUN
asir-1804	111	66	’s	’s	PART
asir-1804	111	67	size	size	NOUN
asir-1804	111	68	y.	y.	PROPN
asir-1804	111	69	the	the	DET
asir-1804	111	70	worksheet	worksheet	NOUN
asir-1804	111	71	contains	contain	VERB
asir-1804	111	72	3	3	NUM
asir-1804	111	73	graphs	graph	NOUN
asir-1804	111	74	:	:	PUNCT
asir-1804	111	75	graph	graph	NOUN
asir-1804	111	76	of	of	ADP
asir-1804	111	77	lines	line	NOUN
asir-1804	111	78	(	(	PUNCT
asir-1804	111	79	ai,0)-(bi,0	ai,0)-(bi,0	NOUN
asir-1804	111	80	)	)	PUNCT
asir-1804	111	81	where	where	SCONJ
asir-1804	111	82	ai	ai	NOUN
asir-1804	111	83	is	be	AUX
asir-1804	111	84	the	the	DET
asir-1804	111	85	source	source	NOUN
asir-1804	111	86	distance	distance	NOUN
asir-1804	111	87	from	from	ADP
asir-1804	111	88	the	the	DET
asir-1804	111	89	center	center	NOUN
asir-1804	111	90	of	of	ADP
asir-1804	111	91	the	the	DET
asir-1804	111	92	lens	len	NOUN
asir-1804	111	93	,	,	PUNCT
asir-1804	111	94	bi	bi	NOUN
asir-1804	111	95	is	be	AUX
asir-1804	111	96	the	the	DET
asir-1804	111	97	distance	distance	NOUN
asir-1804	111	98	of	of	ADP
asir-1804	111	99	the	the	DET
asir-1804	111	100	image	image	NOUN
asir-1804	111	101	from	from	ADP
asir-1804	111	102	the	the	DET
asir-1804	111	103	center	center	NOUN
asir-1804	111	104	of	of	ADP
asir-1804	111	105	the	the	DET
asir-1804	111	106	lens	len	NOUN
asir-1804	111	107	,	,	PUNCT
asir-1804	111	108	a	a	DET
asir-1804	111	109	graph	graph	NOUN
asir-1804	111	110	of	of	ADP
asir-1804	111	111	1	1	NUM
asir-1804	111	112	/	/	SYM
asir-1804	111	113	a	a	PRON
asir-1804	111	114	vs	vs	ADP
asir-1804	111	115	1	1	NUM
asir-1804	111	116	/	/	SYM
asir-1804	111	117	b	b	NOUN
asir-1804	111	118	with	with	ADP
asir-1804	111	119	appropriate	appropriate	ADJ
asir-1804	111	120	fit	fit	ADJ
asir-1804	111	121	and	and	CCONJ
asir-1804	111	122	a	a	DET
asir-1804	111	123	graph	graph	NOUN
asir-1804	111	124	of	of	ADP
asir-1804	111	125	a+b	a+b	NUM
asir-1804	111	126	vs	vs	ADP
asir-1804	111	127	a.	a.	NOUN
asir-1804	111	128	figure	figure	NOUN
asir-1804	111	129	5	5	NUM
asir-1804	111	130	.	.	SYM
asir-1804	111	131	3	3	NUM
asir-1804	111	132	graphs	graph	NOUN
asir-1804	111	133	for	for	ADP
asir-1804	111	134	the	the	DET
asir-1804	111	135	data	datum	NOUN
asir-1804	111	136	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1804	111	137	applied	apply	VERB
asir-1804	111	138	science	science	NOUN
asir-1804	111	139	and	and	CCONJ
asir-1804	111	140	innovative	innovative	ADJ
asir-1804	111	141	research	research	NOUN
asir-1804	111	142	vol	vol	NOUN
asir-1804	111	143	.	.	PUNCT
asir-1804	112	1	3	3	NUM
asir-1804	112	2	,	,	PUNCT
asir-1804	112	3	no	no	INTJ
asir-1804	112	4	.	.	NOUN
asir-1804	112	5	1	1	NUM
asir-1804	112	6	,	,	PUNCT
asir-1804	112	7	2019	2019	NUM
asir-1804	112	8	21	21	NUM
asir-1804	112	9	published	publish	VERB
asir-1804	112	10	by	by	ADP
asir-1804	112	11	scholink	scholink	PROPN
asir-1804	112	12	inc	inc	PROPN
asir-1804	112	13	.	.	PROPN
asir-1804	112	14	figure	figure	NOUN
asir-1804	112	15	6	6	NUM
asir-1804	112	16	.	.	PUNCT
asir-1804	113	1	graph	graph	NOUN
asir-1804	113	2	of	of	ADP
asir-1804	113	3	image	image	NOUN
asir-1804	113	4	y	y	PROPN
asir-1804	113	5	vs	vs	ADP
asir-1804	113	6	b	b	PROPN
asir-1804	113	7	and	and	CCONJ
asir-1804	113	8	vs	vs	ADP
asir-1804	113	9	a	a	PRON
asir-1804	113	10	after	after	ADP
asir-1804	113	11	the	the	DET
asir-1804	113	12	preparation	preparation	NOUN
asir-1804	113	13	of	of	ADP
asir-1804	113	14	the	the	DET
asir-1804	113	15	data	datum	NOUN
asir-1804	113	16	appears	appear	VERB
asir-1804	113	17	the	the	DET
asir-1804	113	18	chart	chart	NOUN
asir-1804	113	19	“	"	PUNCT
asir-1804	113	20	image	image	NOUN
asir-1804	113	21	vs	vs	ADP
asir-1804	113	22	b	b	NOUN
asir-1804	113	23	”	"	PUNCT
asir-1804	113	24	(	(	PUNCT
asir-1804	113	25	figure	figure	NOUN
asir-1804	113	26	6	6	NUM
asir-1804	113	27	)	)	PUNCT
asir-1804	113	28	where	where	SCONJ
asir-1804	113	29	are	be	AUX
asir-1804	113	30	depicted	depict	VERB
asir-1804	113	31	with	with	ADP
asir-1804	113	32	dots	dot	NOUN
asir-1804	113	33	the	the	DET
asir-1804	113	34	images	image	NOUN
asir-1804	113	35	of	of	ADP
asir-1804	113	36	the	the	DET
asir-1804	113	37	object	object	NOUN
asir-1804	113	38	with	with	ADP
asir-1804	113	39	circles	circle	NOUN
asir-1804	113	40	as	as	ADP
asir-1804	113	41	a	a	DET
asir-1804	113	42	function	function	NOUN
asir-1804	113	43	of	of	ADP
asir-1804	113	44	the	the	DET
asir-1804	113	45	distance	distance	NOUN
asir-1804	113	46	b	b	NOUN
asir-1804	113	47	and	and	CCONJ
asir-1804	113	48	also	also	ADV
asir-1804	113	49	as	as	ADP
asir-1804	113	50	“	"	PUNCT
asir-1804	113	51	diamonds	diamond	NOUN
asir-1804	113	52	”	"	PUNCT
asir-1804	113	53	as	as	ADP
asir-1804	113	54	a	a	DET
asir-1804	113	55	function	function	NOUN
asir-1804	113	56	of	of	ADP
asir-1804	113	57	the	the	DET
asir-1804	113	58	distance	distance	NOUN
asir-1804	113	59	of	of	ADP
asir-1804	113	60	the	the	DET
asir-1804	113	61	object	object	NOUN
asir-1804	113	62	from	from	ADP
asir-1804	113	63	the	the	DET
asir-1804	113	64	lens	len	NOUN
asir-1804	113	65	.	.	PUNCT
asir-1804	114	1	the	the	DET
asir-1804	114	2	first	first	ADJ
asir-1804	114	3	set	set	NOUN
asir-1804	114	4	of	of	ADP
asir-1804	114	5	data	datum	NOUN
asir-1804	114	6	has	have	VERB
asir-1804	114	7	a	a	DET
asir-1804	114	8	linear	linear	ADJ
asir-1804	114	9	fit	fit	NOUN
asir-1804	114	10	through	through	ADP
asir-1804	114	11	the	the	DET
asir-1804	114	12	method	method	NOUN
asir-1804	114	13	of	of	ADP
asir-1804	114	14	“	"	PUNCT
asir-1804	114	15	least	least	ADJ
asir-1804	114	16	squares	square	NOUN
asir-1804	114	17	”	"	PUNCT
asir-1804	114	18	and	and	CCONJ
asir-1804	114	19	the	the	DET
asir-1804	114	20	second	second	ADJ
asir-1804	114	21	set	set	NOUN
asir-1804	114	22	has	have	VERB
asir-1804	114	23	a	a	DET
asir-1804	114	24	fit	fit	NOUN
asir-1804	114	25	of	of	ADP
asir-1804	114	26	a	a	DET
asir-1804	114	27	hyperbola	hyperbola	PROPN
asir-1804	114	28	.	.	PUNCT
asir-1804	115	1	the	the	DET
asir-1804	115	2	linear	linear	ADJ
asir-1804	115	3	fit	fit	NOUN
asir-1804	115	4	gives	give	VERB
asir-1804	115	5	the	the	DET
asir-1804	115	6	following	follow	VERB
asir-1804	115	7	information	information	NOUN
asir-1804	115	8	:	:	PUNCT
asir-1804	115	9	the	the	DET
asir-1804	115	10	linear	linear	ADJ
asir-1804	115	11	fit	fit	NOUN
asir-1804	115	12	has	have	VERB
asir-1804	115	13	the	the	DET
asir-1804	115	14	form	form	NOUN
asir-1804	115	15	:	:	PUNCT
asir-1804	115	16	yi	yi	PROPN
asir-1804	115	17	=	=	PROPN
asir-1804	115	18	ysource+ti·(bi	ysource+ti·(bi	PROPN
asir-1804	115	19	-	-	PUNCT
asir-1804	115	20	k	k	NOUN
asir-1804	115	21	)	)	PUNCT
asir-1804	115	22	where	where	SCONJ
asir-1804	115	23	ysource	ysource	NOUN
asir-1804	115	24	is	be	AUX
asir-1804	115	25	the	the	DET
asir-1804	115	26	object	object	NOUN
asir-1804	115	27	’s	’s	PART
asir-1804	115	28	y	y	NOUN
asir-1804	115	29	,	,	PUNCT
asir-1804	115	30	bi	bi	NOUN
asir-1804	115	31	is	be	AUX
asir-1804	115	32	the	the	DET
asir-1804	115	33	distance	distance	NOUN
asir-1804	115	34	of	of	ADP
asir-1804	115	35	the	the	DET
asir-1804	115	36	image	image	NOUN
asir-1804	115	37	from	from	ADP
asir-1804	115	38	the	the	DET
asir-1804	115	39	center	center	NOUN
asir-1804	115	40	of	of	ADP
asir-1804	115	41	the	the	DET
asir-1804	115	42	lens	len	NOUN
asir-1804	115	43	,	,	PUNCT
asir-1804	115	44	k	k	PROPN
asir-1804	115	45	is	be	AUX
asir-1804	115	46	the	the	DET
asir-1804	115	47	position	position	NOUN
asir-1804	115	48	of	of	ADP
asir-1804	115	49	the	the	DET
asir-1804	115	50	right	right	ADJ
asir-1804	115	51	principal	principal	ADJ
asir-1804	115	52	plane	plane	NOUN
asir-1804	115	53	and	and	CCONJ
asir-1804	115	54	ti	ti	X
asir-1804	115	55	the	the	DET
asir-1804	115	56	tangent	tangent	NOUN
asir-1804	115	57	of	of	ADP
asir-1804	115	58	the	the	DET
asir-1804	115	59	inclination	inclination	NOUN
asir-1804	115	60	angle	angle	NOUN
asir-1804	115	61	and	and	CCONJ
asir-1804	115	62	is	be	AUX
asir-1804	115	63	given	give	VERB
asir-1804	115	64	by	by	ADP
asir-1804	115	65	ti	ti	PROPN
asir-1804	115	66	=	=	PROPN
asir-1804	115	67	ysource	ysource	NOUN
asir-1804	115	68	/	/	SYM
asir-1804	115	69	f_right	f_right	NOUN
asir-1804	115	70	,	,	PUNCT
asir-1804	115	71	so	so	SCONJ
asir-1804	115	72	from	from	ADP
asir-1804	115	73	these	these	DET
asir-1804	115	74	two	two	NUM
asir-1804	115	75	parameters	parameter	NOUN
asir-1804	115	76	we	we	PRON
asir-1804	115	77	find	find	VERB
asir-1804	115	78	the	the	DET
asir-1804	115	79	principal	principal	ADJ
asir-1804	115	80	plane	plane	NOUN
asir-1804	115	81	h_2	h_2	PROPN
asir-1804	115	82	and	and	CCONJ
asir-1804	115	83	the	the	DET
asir-1804	115	84	focal	focal	ADJ
asir-1804	115	85	length	length	NOUN
asir-1804	115	86	on	on	ADP
asir-1804	115	87	the	the	DET
asir-1804	115	88	right	right	NOUN
asir-1804	115	89	.	.	PUNCT
asir-1804	116	1	the	the	DET
asir-1804	116	2	hyperbolic	hyperbolic	ADJ
asir-1804	116	3	fit	fit	NOUN
asir-1804	116	4	has	have	VERB
asir-1804	116	5	a	a	DET
asir-1804	116	6	form	form	NOUN
asir-1804	116	7	of	of	ADP
asir-1804	116	8	:	:	PUNCT
asir-1804	116	9	yi=-ysource·gama/(di	yi=-ysource·gama/(di	PROPN
asir-1804	116	10	-	-	PUNCT
asir-1804	116	11	beta	beta	NOUN
asir-1804	116	12	)	)	PUNCT
asir-1804	116	13	di=|ai|	di=|ai|	PROPN
asir-1804	116	14	y.	y.	PROPN
asir-1804	116	15	beta	beta	PROPN
asir-1804	117	1	=	=	PUNCT
asir-1804	117	2	the	the	DET
asir-1804	117	3	left	left	ADJ
asir-1804	117	4	focal	focal	ADJ
asir-1804	117	5	length+	length+	X
asir-1804	117	6	|h_1|	|h_1|	PUNCT
asir-1804	117	7	while	while	SCONJ
asir-1804	117	8	gama	gama	NOUN
asir-1804	117	9	=	=	SYM
asir-1804	117	10	distance	distance	NOUN
asir-1804	117	11	of	of	ADP
asir-1804	117	12	left	left	ADJ
asir-1804	117	13	focus	focus	NOUN
asir-1804	117	14	from	from	ADP
asir-1804	117	15	left	left	ADJ
asir-1804	117	16	principal	principal	ADJ
asir-1804	117	17	plane	plane	NOUN
asir-1804	117	18	.	.	PUNCT
asir-1804	118	1	a	a	DET
asir-1804	118	2	classic	classic	ADJ
asir-1804	118	3	experiment	experiment	NOUN
asir-1804	118	4	for	for	ADP
asir-1804	118	5	finding	find	VERB
asir-1804	118	6	the	the	DET
asir-1804	118	7	focal	focal	ADJ
asir-1804	118	8	length	length	NOUN
asir-1804	118	9	of	of	ADP
asir-1804	118	10	lenses	lense	NOUN
asir-1804	118	11	and	and	CCONJ
asir-1804	118	12	concave	concave	NOUN
asir-1804	118	13	mirrors	mirror	NOUN
asir-1804	118	14	is	be	AUX
asir-1804	118	15	described	describe	VERB
asir-1804	118	16	by	by	ADP
asir-1804	118	17	tyler	tyler	PROPN
asir-1804	118	18	(	(	PUNCT
asir-1804	118	19	1977	1977	NUM
asir-1804	118	20	,	,	PUNCT
asir-1804	118	21	pp	pp	ADJ
asir-1804	118	22	.	.	PUNCT
asir-1804	119	1	46	46	NUM
asir-1804	119	2	-	-	SYM
asir-1804	119	3	47	47	NUM
asir-1804	119	4	,	,	PUNCT
asir-1804	119	5	pp	pp	ADJ
asir-1804	119	6	.	.	PUNCT
asir-1804	120	1	52	52	NUM
asir-1804	120	2	-	-	SYM
asir-1804	120	3	53	53	NUM
asir-1804	120	4	)	)	PUNCT
asir-1804	120	5	.	.	PUNCT
asir-1804	121	1	the	the	DET
asir-1804	121	2	first	first	ADJ
asir-1804	121	3	one	one	NOUN
asir-1804	121	4	is	be	AUX
asir-1804	121	5	presented	present	VERB
asir-1804	121	6	as	as	SCONJ
asir-1804	121	7	used	use	VERB
asir-1804	121	8	to	to	PART
asir-1804	121	9	find	find	VERB
asir-1804	121	10	the	the	DET
asir-1804	121	11	focal	focal	ADJ
asir-1804	121	12	length	length	NOUN
asir-1804	121	13	of	of	ADP
asir-1804	121	14	a	a	DET
asir-1804	121	15	concave	concave	NOUN
asir-1804	121	16	mirror	mirror	NOUN
asir-1804	121	17	,	,	PUNCT
asir-1804	121	18	but	but	CCONJ
asir-1804	121	19	it	it	PRON
asir-1804	121	20	can	can	AUX
asir-1804	121	21	be	be	AUX
asir-1804	121	22	used	use	VERB
asir-1804	121	23	for	for	ADP
asir-1804	121	24	the	the	DET
asir-1804	121	25	focal	focal	ADJ
asir-1804	121	26	length	length	NOUN
asir-1804	121	27	of	of	ADP
asir-1804	121	28	a	a	DET
asir-1804	121	29	lens	len	NOUN
asir-1804	121	30	.	.	PUNCT
asir-1804	122	1	the	the	DET
asir-1804	122	2	second	second	ADJ
asir-1804	122	3	one	one	NOUN
asir-1804	122	4	is	be	AUX
asir-1804	122	5	especially	especially	ADV
asir-1804	122	6	valid	valid	ADJ
asir-1804	122	7	for	for	ADP
asir-1804	122	8	thin	thin	ADJ
asir-1804	122	9	lenses	lense	NOUN
asir-1804	122	10	.	.	PUNCT
asir-1804	123	1	in	in	ADP
asir-1804	123	2	the	the	DET
asir-1804	123	3	worksheet	worksheet	NOUN
asir-1804	123	4	there	there	PRON
asir-1804	123	5	are	be	VERB
asir-1804	123	6	two	two	NUM
asir-1804	123	7	sheets	sheet	NOUN
asir-1804	123	8	devoted	devote	VERB
asir-1804	123	9	at	at	ADP
asir-1804	123	10	the	the	DET
asir-1804	123	11	experiment	experiment	NOUN
asir-1804	123	12	of	of	ADP
asir-1804	123	13	finding	find	VERB
asir-1804	123	14	the	the	DET
asir-1804	123	15	focal	focal	ADJ
asir-1804	123	16	length	length	NOUN
asir-1804	123	17	by	by	ADP
asir-1804	123	18	finding	find	VERB
asir-1804	123	19	a	a	DET
asir-1804	123	20	number	number	NOUN
asir-1804	123	21	of	of	ADP
asir-1804	123	22	couples	couple	NOUN
asir-1804	123	23	of	of	ADP
asir-1804	123	24	a	a	DET
asir-1804	123	25	(	(	PUNCT
asir-1804	123	26	the	the	DET
asir-1804	123	27	distance	distance	NOUN
asir-1804	123	28	of	of	ADP
asir-1804	123	29	the	the	DET
asir-1804	123	30	source	source	NOUN
asir-1804	123	31	from	from	ADP
asir-1804	123	32	the	the	DET
asir-1804	123	33	y	y	NOUN
asir-1804	123	34	-	-	PUNCT
asir-1804	123	35	axis	axis	NOUN
asir-1804	123	36	)	)	PUNCT
asir-1804	123	37	and	and	CCONJ
asir-1804	123	38	b	b	X
asir-1804	123	39	(	(	PUNCT
asir-1804	123	40	the	the	DET
asir-1804	123	41	distance	distance	NOUN
asir-1804	123	42	of	of	ADP
asir-1804	123	43	the	the	DET
asir-1804	123	44	image	image	NOUN
asir-1804	123	45	from	from	ADP
asir-1804	123	46	the	the	DET
asir-1804	123	47	y	y	NOUN
asir-1804	123	48	-	-	PUNCT
asir-1804	123	49	axis	axis	NOUN
asir-1804	123	50	)	)	PUNCT
asir-1804	123	51	.	.	PUNCT
asir-1804	124	1	graph	graph	NOUN
asir-1804	124	2	of	of	ADP
asir-1804	124	3	1	1	NUM
asir-1804	124	4	/	/	SYM
asir-1804	124	5	b	b	NOUN
asir-1804	124	6	vs	vs	ADP
asir-1804	124	7	1	1	NUM
asir-1804	124	8	/	/	SYM
asir-1804	124	9	a	a	NOUN
asir-1804	124	10	in	in	ADP
asir-1804	124	11	this	this	DET
asir-1804	124	12	elementary	elementary	ADJ
asir-1804	124	13	experiment	experiment	NOUN
asir-1804	124	14	it	it	PRON
asir-1804	124	15	is	be	AUX
asir-1804	124	16	well	well	ADV
asir-1804	124	17	known	know	VERB
asir-1804	124	18	that	that	SCONJ
asir-1804	124	19	by	by	ADP
asir-1804	124	20	plotting	plot	VERB
asir-1804	124	21	1	1	NUM
asir-1804	124	22	/	/	SYM
asir-1804	124	23	b	b	NOUN
asir-1804	124	24	vs	vs	ADP
asir-1804	124	25	1	1	NUM
asir-1804	124	26	/	/	SYM
asir-1804	124	27	a	a	DET
asir-1804	124	28	the	the	DET
asir-1804	124	29	intersection	intersection	NOUN
asir-1804	124	30	with	with	ADP
asir-1804	124	31	the	the	DET
asir-1804	124	32	axes	axis	NOUN
asir-1804	124	33	are	be	AUX
asir-1804	124	34	equal	equal	ADJ
asir-1804	124	35	to	to	ADP
asir-1804	124	36	the	the	DET
asir-1804	124	37	focal	focal	ADJ
asir-1804	124	38	length	length	NOUN
asir-1804	124	39	.	.	PUNCT
asir-1804	125	1	this	this	PRON
asir-1804	125	2	is	be	AUX
asir-1804	125	3	valid	valid	ADJ
asir-1804	125	4	only	only	ADV
asir-1804	125	5	for	for	ADP
asir-1804	125	6	thin	thin	ADJ
asir-1804	125	7	lenses	lense	NOUN
asir-1804	125	8	.	.	PUNCT
asir-1804	126	1	there	there	PRON
asir-1804	126	2	exist	exist	VERB
asir-1804	126	3	excel	excel	NOUN
asir-1804	126	4	files	file	NOUN
asir-1804	126	5	for	for	ADP
asir-1804	126	6	finding	find	VERB
asir-1804	126	7	the	the	DET
asir-1804	126	8	focal	focal	ADJ
asir-1804	126	9	lengths	length	NOUN
asir-1804	126	10	of	of	ADP
asir-1804	126	11	thin	thin	ADJ
asir-1804	126	12	lenses	lense	NOUN
asir-1804	126	13	.	.	PUNCT
asir-1804	127	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-1804	127	2	applied	apply	VERB
asir-1804	127	3	science	science	NOUN
asir-1804	127	4	and	and	CCONJ
asir-1804	127	5	innovative	innovative	ADJ
asir-1804	127	6	research	research	NOUN
asir-1804	127	7	vol	vol	NOUN
asir-1804	127	8	.	.	PUNCT
asir-1804	128	1	3	3	NUM
asir-1804	128	2	,	,	PUNCT
asir-1804	128	3	no	no	INTJ
asir-1804	128	4	.	.	NOUN
asir-1804	128	5	1	1	NUM
asir-1804	128	6	,	,	PUNCT
asir-1804	128	7	2019	2019	NUM
asir-1804	128	8	22	22	NUM
asir-1804	128	9	published	publish	VERB
asir-1804	128	10	by	by	ADP
asir-1804	128	11	scholink	scholink	PROPN
asir-1804	128	12	inc	inc	PROPN
asir-1804	128	13	.	.	PROPN
asir-1804	128	14	figure	figure	PROPN
asir-1804	128	15	7	7	NUM
asir-1804	128	16	.	.	X
asir-1804	129	1	for	for	ADP
asir-1804	129	2	narrow	narrow	ADJ
asir-1804	129	3	bundle	bundle	NOUN
asir-1804	129	4	and	and	CCONJ
asir-1804	129	5	the	the	DET
asir-1804	129	6	source	source	NOUN
asir-1804	129	7	very	very	ADV
asir-1804	129	8	near	near	ADP
asir-1804	129	9	the	the	DET
asir-1804	129	10	x	x	NOUN
asir-1804	129	11	-	-	NOUN
asir-1804	129	12	axis	axis	ADJ
asir-1804	129	13	all	all	DET
asir-1804	129	14	the	the	DET
asir-1804	129	15	curves	curve	NOUN
asir-1804	129	16	almost	almost	ADV
asir-1804	129	17	coincide	coincide	VERB
asir-1804	129	18	in	in	ADP
asir-1804	129	19	the	the	DET
asir-1804	129	20	case	case	NOUN
asir-1804	129	21	of	of	ADP
asir-1804	129	22	thick	thick	ADJ
asir-1804	129	23	lenses	lense	NOUN
asir-1804	129	24	we	we	PRON
asir-1804	129	25	proceed	proceed	VERB
asir-1804	129	26	in	in	ADP
asir-1804	129	27	a	a	DET
asir-1804	129	28	similar	similar	ADJ
asir-1804	129	29	way	way	NOUN
asir-1804	129	30	.	.	PUNCT
asir-1804	130	1	in	in	ADP
asir-1804	130	2	the	the	DET
asir-1804	130	3	worksheet	worksheet	NOUN
asir-1804	130	4	“	"	PUNCT
asir-1804	130	5	find	find	VERB
asir-1804	130	6	f	f	NOUN
asir-1804	130	7	”	"	PUNCT
asir-1804	130	8	there	there	ADV
asir-1804	130	9	we	we	PRON
asir-1804	130	10	can	can	AUX
asir-1804	130	11	input	input	VERB
asir-1804	130	12	the	the	DET
asir-1804	130	13	data	datum	NOUN
asir-1804	130	14	manually	manually	ADV
asir-1804	130	15	or	or	CCONJ
asir-1804	130	16	we	we	PRON
asir-1804	130	17	can	can	AUX
asir-1804	130	18	input	input	VERB
asir-1804	130	19	the	the	DET
asir-1804	130	20	data	datum	NOUN
asir-1804	130	21	by	by	ADP
asir-1804	130	22	using	use	VERB
asir-1804	130	23	a	a	DET
asir-1804	130	24	macro	macro	NOUN
asir-1804	130	25	.	.	PUNCT
asir-1804	131	1	if	if	SCONJ
asir-1804	131	2	we	we	PRON
asir-1804	131	3	press	press	VERB
asir-1804	131	4	the	the	DET
asir-1804	131	5	button	button	NOUN
asir-1804	131	6	“	"	PUNCT
asir-1804	131	7	graph	graph	NOUN
asir-1804	131	8	of	of	ADP
asir-1804	131	9	lines	line	NOUN
asir-1804	131	10	”	"	PUNCT
asir-1804	131	11	the	the	DET
asir-1804	131	12	spreadsheet	spreadsheet	NOUN
asir-1804	131	13	plots	plot	VERB
asir-1804	131	14	the	the	DET
asir-1804	131	15	lines	line	NOUN
asir-1804	131	16	that	that	PRON
asir-1804	131	17	join	join	VERB
asir-1804	131	18	the	the	DET
asir-1804	131	19	points	point	NOUN
asir-1804	131	20	(	(	PUNCT
asir-1804	131	21	a,0	a,0	NOUN
asir-1804	131	22	)	)	PUNCT
asir-1804	131	23	and	and	CCONJ
asir-1804	131	24	(	(	PUNCT
asir-1804	131	25	0,b	0,b	PROPN
asir-1804	131	26	)	)	PUNCT
asir-1804	131	27	.	.	PUNCT
asir-1804	132	1	these	these	DET
asir-1804	132	2	lines	line	NOUN
asir-1804	132	3	cut	cut	VERB
asir-1804	132	4	each	each	DET
asir-1804	132	5	other	other	ADJ
asir-1804	132	6	for	for	ADP
asir-1804	132	7	thin	thin	ADJ
asir-1804	132	8	lenses	lense	NOUN
asir-1804	132	9	on	on	ADP
asir-1804	132	10	the	the	DET
asir-1804	132	11	point	point	NOUN
asir-1804	132	12	(	(	PUNCT
asir-1804	132	13	f	f	X
asir-1804	132	14	,	,	PUNCT
asir-1804	132	15	f	f	PROPN
asir-1804	132	16	)	)	PUNCT
asir-1804	132	17	.	.	PUNCT
asir-1804	133	1	the	the	DET
asir-1804	133	2	other	other	ADJ
asir-1804	133	3	way	way	NOUN
asir-1804	133	4	as	as	SCONJ
asir-1804	133	5	mentioned	mention	VERB
asir-1804	133	6	is	be	AUX
asir-1804	133	7	to	to	PART
asir-1804	133	8	plot	plot	VERB
asir-1804	133	9	the	the	DET
asir-1804	133	10	1	1	NUM
asir-1804	133	11	/	/	SYM
asir-1804	133	12	b	b	NOUN
asir-1804	133	13	vs	vs	ADP
asir-1804	133	14	1	1	NUM
asir-1804	133	15	/	/	SYM
asir-1804	133	16	a	a	DET
asir-1804	133	17	(	(	PUNCT
asir-1804	133	18	figure	figure	NOUN
asir-1804	133	19	7	7	NUM
asir-1804	133	20	)	)	PUNCT
asir-1804	133	21	.	.	PUNCT
asir-1804	134	1	figure	figure	VERB
asir-1804	134	2	8	8	NUM
asir-1804	134	3	.	.	PUNCT
asir-1804	135	1	diagram	diagram	NOUN
asir-1804	135	2	of	of	ADP
asir-1804	135	3	the	the	DET
asir-1804	135	4	cuts	cut	NOUN
asir-1804	135	5	of	of	ADP
asir-1804	135	6	the	the	DET
asir-1804	135	7	lins	lin	NOUN
asir-1804	135	8	(	(	PUNCT
asir-1804	135	9	ai,0)-(0,bi	ai,0)-(0,bi	NOUN
asir-1804	135	10	)	)	PUNCT
asir-1804	135	11	this	this	DET
asir-1804	135	12	graph	graph	NOUN
asir-1804	135	13	is	be	AUX
asir-1804	135	14	also	also	ADV
asir-1804	135	15	a	a	DET
asir-1804	135	16	result	result	NOUN
asir-1804	135	17	we	we	PRON
asir-1804	135	18	get	get	VERB
asir-1804	135	19	by	by	ADP
asir-1804	135	20	pressing	press	VERB
asir-1804	135	21	this	this	DET
asir-1804	135	22	button	button	NOUN
asir-1804	135	23	.	.	PUNCT
asir-1804	136	1	in	in	ADP
asir-1804	136	2	the	the	DET
asir-1804	136	3	graph	graph	NOUN
asir-1804	136	4	we	we	PRON
asir-1804	136	5	get	get	VERB
asir-1804	136	6	the	the	DET
asir-1804	136	7	data	datum	NOUN
asir-1804	136	8	,	,	PUNCT
asir-1804	136	9	the	the	DET
asir-1804	136	10	line	line	NOUN
asir-1804	136	11	we	we	PRON
asir-1804	136	12	get	get	VERB
asir-1804	136	13	from	from	ADP
asir-1804	136	14	paraxial	paraxial	ADJ
asir-1804	136	15	theory	theory	NOUN
asir-1804	136	16	of	of	ADP
asir-1804	136	17	1	1	NUM
asir-1804	136	18	/	/	SYM
asir-1804	136	19	b	b	NOUN
asir-1804	136	20	vs	vs	ADP
asir-1804	136	21	1	1	NUM
asir-1804	136	22	/	/	SYM
asir-1804	136	23	a	a	NOUN
asir-1804	136	24	,	,	PUNCT
asir-1804	136	25	a	a	DET
asir-1804	136	26	linear	linear	ADJ
asir-1804	136	27	fit	fit	NOUN
asir-1804	136	28	of	of	ADP
asir-1804	136	29	the	the	DET
asir-1804	136	30	data	datum	NOUN
asir-1804	136	31	and	and	CCONJ
asir-1804	136	32	a	a	DET
asir-1804	136	33	parabolic	parabolic	ADJ
asir-1804	136	34	fit	fit	NOUN
asir-1804	136	35	of	of	ADP
asir-1804	136	36	the	the	DET
asir-1804	136	37	data	datum	NOUN
asir-1804	136	38	.	.	PUNCT
asir-1804	137	1	for	for	ADP
asir-1804	137	2	the	the	DET
asir-1804	137	3	thick	thick	ADJ
asir-1804	137	4	lenses	lense	NOUN
asir-1804	137	5	the	the	DET
asir-1804	137	6	parabolic	parabolic	ADJ
asir-1804	137	7	fit	fit	NOUN
asir-1804	137	8	gives	give	VERB
asir-1804	137	9	in	in	ADP
asir-1804	137	10	many	many	ADJ
asir-1804	137	11	cases	case	NOUN
asir-1804	137	12	better	well	ADJ
asir-1804	137	13	results	result	NOUN
asir-1804	137	14	than	than	ADP
asir-1804	137	15	the	the	DET
asir-1804	137	16	linear	linear	PROPN
asir-1804	137	17	fit	fit	NOUN
asir-1804	137	18	.	.	PUNCT
asir-1804	138	1	the	the	DET
asir-1804	138	2	points	point	NOUN
asir-1804	138	3	where	where	SCONJ
asir-1804	138	4	the	the	DET
asir-1804	138	5	fit	fit	NOUN
asir-1804	138	6	meets	meet	VERB
asir-1804	138	7	the	the	DET
asir-1804	138	8	axes	axis	NOUN
asir-1804	138	9	are	be	AUX
asir-1804	138	10	the	the	DET
asir-1804	138	11	left	left	ADJ
asir-1804	138	12	focus	focus	NOUN
asir-1804	138	13	and	and	CCONJ
asir-1804	138	14	the	the	DET
asir-1804	138	15	right	right	ADJ
asir-1804	138	16	focus	focus	NOUN
asir-1804	138	17	which	which	PRON
asir-1804	138	18	usually	usually	ADV
asir-1804	138	19	have	have	VERB
asir-1804	138	20	different	different	ADJ
asir-1804	138	21	values	value	NOUN
asir-1804	138	22	for	for	ADP
asir-1804	138	23	thick	thick	ADJ
asir-1804	138	24	lenses	lense	NOUN
asir-1804	138	25	.	.	PUNCT
asir-1804	139	1	in	in	ADP
asir-1804	139	2	paraxial	paraxial	ADJ
asir-1804	139	3	theory	theory	NOUN
asir-1804	139	4	we	we	PRON
asir-1804	139	5	get	get	VERB
asir-1804	139	6	:	:	PUNCT
asir-1804	139	7	1	1	NUM
asir-1804	139	8	𝑏	𝑏	NOUN
asir-1804	139	9	=	=	SYM
asir-1804	139	10	ℎ1+𝑓1	ℎ1+𝑓1	PROPN
asir-1804	139	11	𝑎	𝑎	PROPN
asir-1804	139	12	+1	+1	PROPN
asir-1804	139	13	ℎ2ℎ1+𝑓1ℎ2+𝑓2ℎ_2	ℎ2ℎ1+𝑓1ℎ2+𝑓2ℎ_2	PROPN
asir-1804	139	14	)	)	PUNCT
asir-1804	140	1	𝑎	𝑎	X
asir-1804	140	2	+	+	PROPN
asir-1804	140	3	(	(	PUNCT
asir-1804	140	4	ℎ2+𝑓2	ℎ2+𝑓2	NOUN
asir-1804	140	5	)	)	PUNCT
asir-1804	140	6	from	from	ADP
asir-1804	140	7	this	this	DET
asir-1804	140	8	formula	formula	NOUN
asir-1804	140	9	we	we	PRON
asir-1804	140	10	get	get	VERB
asir-1804	140	11	that	that	PRON
asir-1804	140	12	for	for	ADP
asir-1804	140	13	1	1	NUM
asir-1804	140	14	/	/	SYM
asir-1804	140	15	a=0	a=0	ADJ
asir-1804	140	16	,	,	PUNCT
asir-1804	140	17	1	1	NUM
asir-1804	140	18	/	/	SYM
asir-1804	140	19	b=1/(h2+f2	b=1/(h2+f2	NUM
asir-1804	140	20	)	)	PUNCT
asir-1804	141	1	so	so	SCONJ
asir-1804	141	2	the	the	DET
asir-1804	141	3	intersection	intersection	NOUN
asir-1804	141	4	of	of	ADP
asir-1804	141	5	this	this	DET
asir-1804	141	6	line	line	NOUN
asir-1804	141	7	give	give	VERB
asir-1804	141	8	the	the	DET
asir-1804	141	9	right	right	ADJ
asir-1804	141	10	focus	focus	NOUN
asir-1804	141	11	.	.	PUNCT
asir-1804	142	1	for	for	ADP
asir-1804	142	2	1	1	NUM
asir-1804	142	3	/	/	SYM
asir-1804	142	4	b=0	b=0	PROPN
asir-1804	142	5	then	then	ADV
asir-1804	142	6	1	1	NUM
asir-1804	142	7	/	/	SYM
asir-1804	142	8	a=-1/(f1+h1	a=-1/(f1+h1	NOUN
asir-1804	142	9	)	)	PUNCT
asir-1804	142	10	which	which	PRON
asir-1804	142	11	corresponds	correspond	VERB
asir-1804	142	12	to	to	ADP
asir-1804	142	13	the	the	DET
asir-1804	142	14	left	left	ADJ
asir-1804	142	15	focus	focus	NOUN
asir-1804	142	16	.	.	PUNCT
asir-1804	143	1	we	we	PRON
asir-1804	143	2	compare	compare	VERB
asir-1804	143	3	on	on	ADP
asir-1804	143	4	this	this	DET
asir-1804	143	5	graph	graph	NOUN
asir-1804	143	6	the	the	DET
asir-1804	143	7	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1804	143	8	applied	apply	VERB
asir-1804	143	9	science	science	NOUN
asir-1804	143	10	and	and	CCONJ
asir-1804	143	11	innovative	innovative	ADJ
asir-1804	143	12	research	research	NOUN
asir-1804	143	13	vol	vol	NOUN
asir-1804	143	14	.	.	PUNCT
asir-1804	144	1	3	3	NUM
asir-1804	144	2	,	,	PUNCT
asir-1804	144	3	no	no	INTJ
asir-1804	144	4	.	.	NOUN
asir-1804	144	5	1	1	NUM
asir-1804	144	6	,	,	PUNCT
asir-1804	144	7	2019	2019	NUM
asir-1804	144	8	23	23	NUM
asir-1804	144	9	published	publish	VERB
asir-1804	144	10	by	by	ADP
asir-1804	144	11	scholink	scholink	PROPN
asir-1804	144	12	inc	inc	PROPN
asir-1804	144	13	.	.	PROPN
asir-1804	144	14	values	value	NOUN
asir-1804	144	15	given	give	VERB
asir-1804	144	16	by	by	ADP
asir-1804	144	17	the	the	DET
asir-1804	144	18	theoretical	theoretical	ADJ
asir-1804	144	19	curve	curve	NOUN
asir-1804	144	20	(	(	PUNCT
asir-1804	144	21	dashed	dash	VERB
asir-1804	144	22	line	line	NOUN
asir-1804	144	23	)	)	PUNCT
asir-1804	144	24	with	with	ADP
asir-1804	144	25	the	the	DET
asir-1804	144	26	ones	one	NOUN
asir-1804	144	27	we	we	PRON
asir-1804	144	28	get	get	VERB
asir-1804	144	29	from	from	ADP
asir-1804	144	30	the	the	DET
asir-1804	144	31	couples	couple	NOUN
asir-1804	144	32	of	of	ADP
asir-1804	144	33	source	source	NOUN
asir-1804	144	34	and	and	CCONJ
asir-1804	144	35	image	image	NOUN
asir-1804	144	36	.	.	PUNCT
asir-1804	145	1	also	also	ADV
asir-1804	145	2	are	be	AUX
asir-1804	145	3	presented	present	VERB
asir-1804	145	4	the	the	DET
asir-1804	145	5	parabolic	parabolic	ADJ
asir-1804	145	6	fit	fit	NOUN
asir-1804	145	7	and	and	CCONJ
asir-1804	145	8	the	the	DET
asir-1804	145	9	linear	linear	ADJ
asir-1804	145	10	fit	fit	ADJ
asir-1804	145	11	(	(	PUNCT
asir-1804	145	12	dotted	dotted	ADJ
asir-1804	145	13	line	line	NOUN
asir-1804	145	14	)	)	PUNCT
asir-1804	145	15	.	.	PUNCT
asir-1804	146	1	another	another	DET
asir-1804	146	2	way	way	NOUN
asir-1804	146	3	of	of	ADP
asir-1804	146	4	finding	find	VERB
asir-1804	146	5	the	the	DET
asir-1804	146	6	focal	focal	ADJ
asir-1804	146	7	lengths	length	NOUN
asir-1804	146	8	is	be	AUX
asir-1804	146	9	by	by	ADP
asir-1804	146	10	plotting	plot	VERB
asir-1804	146	11	the	the	DET
asir-1804	146	12	cuts	cut	NOUN
asir-1804	146	13	of	of	ADP
asir-1804	146	14	the	the	DET
asir-1804	146	15	lines	line	NOUN
asir-1804	146	16	(	(	PUNCT
asir-1804	146	17	a,0	a,0	NOUN
asir-1804	146	18	)	)	PUNCT
asir-1804	146	19	–	–	PUNCT
asir-1804	146	20	(	(	PUNCT
asir-1804	146	21	0,b	0,b	PROPN
asir-1804	146	22	)	)	PUNCT
asir-1804	146	23	.	.	PUNCT
asir-1804	147	1	this	this	DET
asir-1804	147	2	method	method	NOUN
asir-1804	147	3	gives	give	VERB
asir-1804	147	4	the	the	DET
asir-1804	147	5	average	average	ADJ
asir-1804	147	6	value	value	NOUN
asir-1804	147	7	of	of	ADP
asir-1804	147	8	the	the	DET
asir-1804	147	9	cuts	cut	NOUN
asir-1804	147	10	and	and	CCONJ
asir-1804	147	11	the	the	DET
asir-1804	147	12	standard	standard	ADJ
asir-1804	147	13	deviation	deviation	NOUN
asir-1804	147	14	of	of	ADP
asir-1804	147	15	the	the	DET
asir-1804	147	16	cuts	cut	NOUN
asir-1804	147	17	.	.	PUNCT
asir-1804	148	1	in	in	ADP
asir-1804	148	2	this	this	DET
asir-1804	148	3	graph	graph	NOUN
asir-1804	148	4	we	we	PRON
asir-1804	148	5	get	get	VERB
asir-1804	148	6	a	a	DET
asir-1804	148	7	plot	plot	NOUN
asir-1804	148	8	of	of	ADP
asir-1804	148	9	all	all	DET
asir-1804	148	10	the	the	DET
asir-1804	148	11	cuts	cut	NOUN
asir-1804	148	12	and	and	CCONJ
asir-1804	148	13	the	the	DET
asir-1804	148	14	position	position	NOUN
asir-1804	148	15	of	of	ADP
asir-1804	148	16	the	the	DET
asir-1804	148	17	average	average	NOUN
asir-1804	148	18	of	of	ADP
asir-1804	148	19	the	the	DET
asir-1804	148	20	cuts	cut	NOUN
asir-1804	148	21	and	and	CCONJ
asir-1804	148	22	lines	line	NOUN
asir-1804	148	23	showing	show	VERB
asir-1804	148	24	the	the	DET
asir-1804	148	25	standard	standard	ADJ
asir-1804	148	26	deviation	deviation	NOUN
asir-1804	148	27	of	of	ADP
asir-1804	148	28	the	the	DET
asir-1804	148	29	cuts	cut	NOUN
asir-1804	148	30	in	in	ADP
asir-1804	148	31	the	the	DET
asir-1804	148	32	two	two	NUM
asir-1804	148	33	dimensions	dimension	NOUN
asir-1804	148	34	.	.	PUNCT
asir-1804	149	1	for	for	ADP
asir-1804	149	2	thin	thin	ADJ
asir-1804	149	3	lenses	lense	NOUN
asir-1804	149	4	this	this	DET
asir-1804	149	5	graph	graph	NOUN
asir-1804	149	6	gives	give	VERB
asir-1804	149	7	the	the	DET
asir-1804	149	8	average	average	ADJ
asir-1804	149	9	point	point	NOUN
asir-1804	149	10	(	(	PUNCT
asir-1804	149	11	f	f	X
asir-1804	149	12	,	,	PUNCT
asir-1804	149	13	f	f	PROPN
asir-1804	149	14	)	)	PUNCT
asir-1804	149	15	.	.	PUNCT
asir-1804	150	1	this	this	DET
asir-1804	150	2	option	option	NOUN
asir-1804	150	3	permits	permit	VERB
asir-1804	150	4	a	a	DET
asir-1804	150	5	pictorial	pictorial	ADJ
asir-1804	150	6	depiction	depiction	NOUN
asir-1804	150	7	of	of	ADP
asir-1804	150	8	the	the	DET
asir-1804	150	9	notion	notion	NOUN
asir-1804	150	10	of	of	ADP
asir-1804	150	11	standard	standard	ADJ
asir-1804	150	12	deviation	deviation	NOUN
asir-1804	150	13	(	(	PUNCT
asir-1804	150	14	figure	figure	NOUN
asir-1804	150	15	8)	8)	NUM
asir-1804	150	16	.	.	PUNCT
asir-1804	151	1	these	these	DET
asir-1804	151	2	methods	method	NOUN
asir-1804	151	3	were	be	AUX
asir-1804	151	4	used	use	VERB
asir-1804	151	5	in	in	ADP
asir-1804	151	6	the	the	DET
asir-1804	151	7	past	past	NOUN
asir-1804	151	8	for	for	ADP
asir-1804	151	9	thin	thin	ADJ
asir-1804	151	10	lenses	lense	NOUN
asir-1804	151	11	(	(	PUNCT
asir-1804	151	12	mihas	miha	NOUN
asir-1804	151	13	,	,	PUNCT
asir-1804	151	14	1998	1998	NUM
asir-1804	151	15	)	)	PUNCT
asir-1804	151	16	.	.	PUNCT
asir-1804	152	1	graph	graph	NOUN
asir-1804	152	2	a+b	a+b	PROPN
asir-1804	152	3	vs	vs	ADP
asir-1804	152	4	a	a	DET
asir-1804	152	5	figure	figure	NOUN
asir-1804	152	6	9	9	NUM
asir-1804	152	7	.	.	PUNCT
asir-1804	152	8	plot	plot	NOUN
asir-1804	152	9	of	of	ADP
asir-1804	152	10	the	the	DET
asir-1804	152	11	sum	sum	NOUN
asir-1804	152	12	of	of	ADP
asir-1804	152	13	the	the	DET
asir-1804	152	14	position	position	NOUN
asir-1804	152	15	of	of	ADP
asir-1804	152	16	the	the	DET
asir-1804	152	17	source	source	NOUN
asir-1804	152	18	and	and	CCONJ
asir-1804	152	19	image	image	NOUN
asir-1804	152	20	vs	vs	ADP
asir-1804	152	21	the	the	DET
asir-1804	152	22	position	position	NOUN
asir-1804	152	23	of	of	ADP
asir-1804	152	24	the	the	DET
asir-1804	152	25	source	source	NOUN
asir-1804	152	26	the	the	DET
asir-1804	152	27	2nd	2nd	ADJ
asir-1804	152	28	experiment	experiment	NOUN
asir-1804	152	29	uses	use	VERB
asir-1804	152	30	a	a	DET
asir-1804	152	31	plot	plot	NOUN
asir-1804	152	32	of	of	ADP
asir-1804	152	33	a+b	a+b	NUM
asir-1804	152	34	vs	vs	ADP
asir-1804	152	35	a.	a.	NOUN
asir-1804	152	36	we	we	PRON
asir-1804	152	37	use	use	VERB
asir-1804	152	38	the	the	DET
asir-1804	152	39	same	same	ADJ
asir-1804	152	40	buttons	button	NOUN
asir-1804	152	41	to	to	PART
asir-1804	152	42	insert	insert	VERB
asir-1804	152	43	the	the	DET
asir-1804	152	44	data	datum	NOUN
asir-1804	152	45	and	and	CCONJ
asir-1804	152	46	the	the	DET
asir-1804	152	47	button	button	NOUN
asir-1804	152	48	“	"	PUNCT
asir-1804	152	49	a+b	a+b	PROPN
asir-1804	152	50	vs	vs	ADP
asir-1804	152	51	a	a	PRON
asir-1804	152	52	”	"	PUNCT
asir-1804	152	53	to	to	PART
asir-1804	152	54	produce	produce	VERB
asir-1804	152	55	the	the	DET
asir-1804	152	56	graph	graph	NOUN
asir-1804	152	57	.	.	PUNCT
asir-1804	153	1	we	we	PRON
asir-1804	153	2	get	get	VERB
asir-1804	153	3	a	a	DET
asir-1804	153	4	hyperbola	hyperbola	NOUN
asir-1804	153	5	by	by	ADP
asir-1804	153	6	fitting	fit	VERB
asir-1804	153	7	the	the	DET
asir-1804	153	8	data	datum	NOUN
asir-1804	153	9	with	with	ADP
asir-1804	153	10	the	the	DET
asir-1804	153	11	curve	curve	NOUN
asir-1804	153	12	y	y	PROPN
asir-1804	153	13	=	=	PUNCT
asir-1804	153	14	a²/(a	a²/(a	PROPN
asir-1804	153	15	-	-	SYM
asir-1804	153	16	f	f	NOUN
asir-1804	153	17	)	)	PUNCT
asir-1804	153	18	where	where	SCONJ
asir-1804	153	19	y	y	PROPN
asir-1804	153	20	=	=	AUX
asir-1804	153	21	a+b	a+b	X
asir-1804	153	22	(	(	PUNCT
asir-1804	153	23	figure	figure	NOUN
asir-1804	153	24	9	9	NUM
asir-1804	153	25	)	)	PUNCT
asir-1804	153	26	.	.	PUNCT
asir-1804	154	1	the	the	DET
asir-1804	154	2	2	2	NUM
asir-1804	154	3	asymptotes	asymptote	NOUN
asir-1804	154	4	give	give	VERB
asir-1804	154	5	the	the	DET
asir-1804	154	6	value	value	NOUN
asir-1804	154	7	of	of	ADP
asir-1804	154	8	focal	focal	ADJ
asir-1804	154	9	length	length	NOUN
asir-1804	154	10	while	while	SCONJ
asir-1804	154	11	the	the	DET
asir-1804	154	12	minimum	minimum	NOUN
asir-1804	154	13	has	have	VERB
asir-1804	154	14	coordinates	coordinate	NOUN
asir-1804	154	15	(	(	PUNCT
asir-1804	154	16	2f	2f	NUM
asir-1804	154	17	,	,	PUNCT
asir-1804	154	18	4f	4f	NUM
asir-1804	154	19	)	)	PUNCT
asir-1804	154	20	,	,	PUNCT
asir-1804	154	21	where	where	SCONJ
asir-1804	154	22	f	f	X
asir-1804	154	23	=	=	ADJ
asir-1804	154	24	focal	focal	ADJ
asir-1804	154	25	length	length	NOUN
asir-1804	154	26	.	.	PUNCT
asir-1804	155	1	for	for	ADP
asir-1804	155	2	thick	thick	ADJ
asir-1804	155	3	lenses	lense	NOUN
asir-1804	155	4	we	we	PRON
asir-1804	155	5	use	use	VERB
asir-1804	155	6	the	the	DET
asir-1804	155	7	notation	notation	NOUN
asir-1804	155	8	so	so	SCONJ
asir-1804	155	9	=	=	PUNCT
asir-1804	155	10	object	object	NOUN
asir-1804	155	11	distance	distance	NOUN
asir-1804	155	12	from	from	ADP
asir-1804	155	13	the	the	DET
asir-1804	155	14	principal	principal	ADJ
asir-1804	155	15	plane	plane	NOUN
asir-1804	155	16	h1	h1	PROPN
asir-1804	155	17	so=	so=	PROPN
asir-1804	155	18	h1xsource=	h1xsource=	PROPN
asir-1804	155	19	h1	h1	VERB
asir-1804	155	20	+	+	PROPN
asir-1804	155	21	a	a	PRON
asir-1804	155	22	and	and	CCONJ
asir-1804	155	23	si	si	NOUN
asir-1804	155	24	=	=	NOUN
asir-1804	155	25	image	image	NOUN
asir-1804	155	26	distance	distance	NOUN
asir-1804	155	27	from	from	ADP
asir-1804	155	28	the	the	DET
asir-1804	155	29	principal	principal	ADJ
asir-1804	155	30	plane	plane	NOUN
asir-1804	155	31	h2	h2	NOUN
asir-1804	155	32	(	(	PUNCT
asir-1804	155	33	b	b	NOUN
asir-1804	155	34	=	=	SYM
asir-1804	155	35	h2+si	h2+si	NOUN
asir-1804	155	36	)	)	PUNCT
asir-1804	155	37	then	then	ADV
asir-1804	155	38	:	:	PUNCT
asir-1804	155	39	−	−	PROPN
asir-1804	155	40	𝑓1	𝑓1	PROPN
asir-1804	155	41	𝑆𝑂	𝑆𝑂	PROPN
asir-1804	155	42	+	+	CCONJ
asir-1804	155	43	𝑓2	𝑓2	PROPN
asir-1804	155	44	𝑆𝐼	𝑆𝐼	NOUN
asir-1804	155	45	=	=	SYM
asir-1804	155	46	1	1	NUM
asir-1804	155	47	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
asir-1804	155	48	𝑆𝐼	𝑆𝐼	PROPN
asir-1804	155	49	=	=	PUNCT
asir-1804	155	50	𝑓2	𝑓2	PROPN
asir-1804	155	51	1	1	NUM
asir-1804	155	52	+	+	NUM
asir-1804	155	53	𝑓1	𝑓1	ADJ
asir-1804	155	54	𝑆𝑂	𝑆𝑂	PROPN
asir-1804	155	55	𝑢	𝑢	PROPN
asir-1804	155	56	=	=	SYM
asir-1804	155	57	𝑆𝑂	𝑆𝑂	PROPN
asir-1804	155	58	+	+	CCONJ
asir-1804	155	59	𝑆𝐼	𝑆𝐼	PROPN
asir-1804	155	60	=	=	PUNCT
asir-1804	155	61	𝑆𝑂2+𝑆𝑂∙(𝑓1+𝑓2	𝑆𝑂2+𝑆𝑂∙(𝑓1+𝑓2	NOUN
asir-1804	155	62	)	)	PUNCT
asir-1804	155	63	𝑆𝑂+𝑓1	𝑆𝑂+𝑓1	NOUN
asir-1804	155	64	we	we	PRON
asir-1804	155	65	find	find	VERB
asir-1804	155	66	for	for	ADP
asir-1804	155	67	the	the	DET
asir-1804	155	68	derivative	derivative	ADJ
asir-1804	155	69	𝑑𝑢	𝑑𝑢	INTJ
asir-1804	155	70	𝑑𝑆𝑂	𝑑𝑆𝑂	NOUN
asir-1804	155	71	=	=	NOUN
asir-1804	155	72	0	0	PUNCT
asir-1804	155	73	when	when	SCONJ
asir-1804	155	74	𝑆𝑂2	𝑆𝑂2	PRON
asir-1804	155	75	+	+	CCONJ
asir-1804	155	76	2𝑆𝑂𝑓1	2𝑆𝑂𝑓1	NUM
asir-1804	155	77	+	+	CCONJ
asir-1804	155	78	𝑓1(𝑓1	𝑓1(𝑓1	NUM
asir-1804	155	79	+	+	CCONJ
asir-1804	155	80	𝑓2	𝑓2	NOUN
asir-1804	155	81	)	)	PUNCT
asir-1804	155	82	=	=	SYM
asir-1804	155	83	0	0	NUM
asir-1804	155	84	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
asir-1804	155	85	𝑠𝑖𝑛𝑐𝑒	𝑠𝑖𝑛𝑐𝑒	PROPN
asir-1804	155	86	𝑓2	𝑓2	PROPN
asir-1804	155	87	=	=	PUNCT
asir-1804	155	88	−𝑓1𝑛3/𝑛1	−𝑓1𝑛3/𝑛1	X
asir-1804	155	89	we	we	PRON
asir-1804	155	90	get	get	VERB
asir-1804	155	91	so=-f1	so=-f1	NOUN
asir-1804	155	92	-	-	ADJ
asir-1804	155	93	f1√𝑛3/𝑛1	f1√𝑛3/𝑛1	PRON
asir-1804	155	94	for	for	ADP
asir-1804	155	95	the	the	DET
asir-1804	155	96	case	case	NOUN
asir-1804	155	97	of	of	ADP
asir-1804	155	98	a	a	DET
asir-1804	155	99	lens	lens	NOUN
asir-1804	155	100	in	in	ADP
asir-1804	155	101	the	the	DET
asir-1804	155	102	air	air	NOUN
asir-1804	155	103	n3	n3	PROPN
asir-1804	155	104	=	=	NOUN
asir-1804	155	105	n1	n1	PROPN
asir-1804	155	106	and	and	CCONJ
asir-1804	155	107	so=-2f1	so=-2f1	VERB
asir-1804	155	108	=	=	CCONJ
asir-1804	155	109	a+h1	a+h1	NOUN
asir-1804	155	110	and	and	CCONJ
asir-1804	155	111	a=-2f1	a=-2f1	PROPN
asir-1804	155	112	-	-	PUNCT
asir-1804	155	113	h1	h1	NOUN
asir-1804	155	114	𝜐	𝜐	NOUN
asir-1804	155	115	=	=	SYM
asir-1804	156	1	𝑎	𝑎	PROPN
asir-1804	156	2	+	+	X
asir-1804	156	3	𝑏	𝑏	NOUN
asir-1804	156	4	=	=	SYM
asir-1804	156	5	𝑆𝑂	𝑆𝑂	PROPN
asir-1804	156	6	+	+	CCONJ
asir-1804	156	7	𝑆𝐼	𝑆𝐼	PROPN
asir-1804	156	8	+	+	CCONJ
asir-1804	156	9	(	(	PUNCT
asir-1804	156	10	−ℎ1	−ℎ1	PROPN
asir-1804	156	11	+	+	CCONJ
asir-1804	156	12	ℎ2	ℎ2	NOUN
asir-1804	156	13	)	)	PUNCT
asir-1804	156	14	=	=	SYM
asir-1804	157	1	𝑎2+𝑎∙(𝑓1+𝑓2+ℎ1+ℎ2)+ℎ1ℎ2−ℎ1	𝑎2+𝑎∙(𝑓1+𝑓2+ℎ1+ℎ2)+ℎ1ℎ2−ℎ1	PROPN
asir-1804	157	2	2+ℎ1𝑓2+ℎ2𝑓1	2+ℎ1𝑓2+ℎ2𝑓1	NUM
asir-1804	157	3	𝑎+ℎ1+𝑓1	𝑎+ℎ1+𝑓1	NOUN
asir-1804	157	4	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
asir-1804	157	5	𝑑𝜐	𝑑𝜐	VERB
asir-1804	157	6	𝑑𝑎	𝑑𝑎	PROPN
asir-1804	157	7	=	=	SYM
asir-1804	157	8	0	0	NUM
asir-1804	157	9	𝑤ℎ𝑒𝑛	𝑤ℎ𝑒𝑛	NOUN
asir-1804	157	10	:	:	PUNCT
asir-1804	157	11	𝑎	𝑎	X
asir-1804	157	12	=	=	SYM
asir-1804	157	13	−(𝑓1	−(𝑓1	NUM
asir-1804	157	14	+	+	ADJ
asir-1804	157	15	ℎ1	ℎ1	PROPN
asir-1804	157	16	)	)	PUNCT
asir-1804	157	17	+	+	CCONJ
asir-1804	158	1	√−(𝑓1	√−(𝑓1	PROPN
asir-1804	158	2	+	+	CCONJ
asir-1804	158	3	ℎ1)(𝑓2	ℎ1)(𝑓2	NOUN
asir-1804	159	1	+	+	CCONJ
asir-1804	159	2	ℎ2	ℎ2	NOUN
asir-1804	159	3	)	)	PUNCT
asir-1804	159	4	+	+	CCONJ
asir-1804	159	5	ℎ1ℎ2	ℎ1ℎ2	PRON
asir-1804	159	6	−	−	NOUN
asir-1804	159	7	ℎ1	ℎ1	PROPN
asir-1804	159	8	2	2	NUM
asir-1804	159	9	+	+	NOUN
asir-1804	159	10	ℎ1𝑓2	ℎ1𝑓2	NOUN
asir-1804	160	1	+	+	CCONJ
asir-1804	160	2	ℎ2𝑓1	ℎ2𝑓1	VERB
asir-1804	160	3	the	the	DET
asir-1804	160	4	corresponding	corresponding	ADJ
asir-1804	160	5	minimum	minimum	NOUN
asir-1804	160	6	for	for	ADP
asir-1804	160	7	paraxial	paraxial	ADJ
asir-1804	160	8	theory	theory	NOUN
asir-1804	160	9	is	be	AUX
asir-1804	160	10	(	(	PUNCT
asir-1804	160	11	with	with	ADP
asir-1804	160	12	d=	d=	NUM
asir-1804	160	13	−(𝑓1	−(𝑓1	NUM
asir-1804	160	14	+	+	NUM
asir-1804	160	15	ℎ1)(𝑓2	ℎ1)(𝑓2	NOUN
asir-1804	160	16	+	+	CCONJ
asir-1804	160	17	ℎ2	ℎ2	NOUN
asir-1804	160	18	)	)	PUNCT
asir-1804	160	19	+	+	CCONJ
asir-1804	161	1	ℎ1ℎ2	ℎ1ℎ2	PRON
asir-1804	161	2	−	−	NOUN
asir-1804	161	3	ℎ1	ℎ1	PROPN
asir-1804	161	4	2	2	NUM
asir-1804	161	5	+	+	NOUN
asir-1804	161	6	ℎ1𝑓2	ℎ1𝑓2	NOUN
asir-1804	161	7	+	+	CCONJ
asir-1804	161	8	ℎ2𝑓1	ℎ2𝑓1	NOUN
asir-1804	161	9	):	):	PUNCT
asir-1804	161	10	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1804	161	11	applied	apply	VERB
asir-1804	161	12	science	science	NOUN
asir-1804	161	13	and	and	CCONJ
asir-1804	161	14	innovative	innovative	ADJ
asir-1804	161	15	research	research	NOUN
asir-1804	161	16	vol	vol	NOUN
asir-1804	161	17	.	.	PUNCT
asir-1804	162	1	3	3	NUM
asir-1804	162	2	,	,	PUNCT
asir-1804	162	3	no	no	INTJ
asir-1804	162	4	.	.	NOUN
asir-1804	162	5	1	1	NUM
asir-1804	162	6	,	,	PUNCT
asir-1804	162	7	2019	2019	NUM
asir-1804	162	8	24	24	NUM
asir-1804	162	9	published	publish	VERB
asir-1804	162	10	by	by	ADP
asir-1804	162	11	scholink	scholink	PROPN
asir-1804	162	12	inc	inc	PROPN
asir-1804	162	13	.	.	PUNCT
asir-1804	163	1	(	(	PUNCT
asir-1804	163	2	𝑎	𝑎	X
asir-1804	163	3	+	+	NUM
asir-1804	163	4	𝑏)𝑚𝑖𝑛	𝑏)𝑚𝑖𝑛	NOUN
asir-1804	163	5	=	=	SYM
asir-1804	163	6	2√𝐷	2√𝐷	PROPN
asir-1804	163	7	+	+	CCONJ
asir-1804	163	8	𝑓2	𝑓2	NOUN
asir-1804	163	9	+	+	CCONJ
asir-1804	163	10	ℎ2	ℎ2	ADJ
asir-1804	163	11	−	−	PROPN
asir-1804	163	12	𝑓1	𝑓1	ADJ
asir-1804	163	13	−	−	PROPN
asir-1804	163	14	ℎ1	ℎ1	PROPN
asir-1804	163	15	,	,	PUNCT
asir-1804	163	16	which	which	PRON
asir-1804	163	17	is	be	AUX
asir-1804	163	18	depicted	depict	VERB
asir-1804	163	19	on	on	ADP
asir-1804	163	20	figure	figure	NOUN
asir-1804	163	21	and	and	CCONJ
asir-1804	163	22	also	also	ADV
asir-1804	163	23	the	the	DET
asir-1804	163	24	corresponding	corresponding	ADJ
asir-1804	163	25	value	value	NOUN
asir-1804	163	26	for	for	ADP
asir-1804	163	27	the	the	DET
asir-1804	163	28	case	case	NOUN
asir-1804	163	29	of	of	ADP
asir-1804	163	30	non	non	ADJ
asir-1804	163	31	-	-	ADJ
asir-1804	163	32	paraxial	paraxial	ADJ
asir-1804	163	33	theory	theory	NOUN
asir-1804	163	34	.	.	PUNCT
asir-1804	164	1	from	from	ADP
asir-1804	164	2	the	the	DET
asir-1804	164	3	hyperbola	hyperbola	PROPN
asir-1804	164	4	we	we	PRON
asir-1804	164	5	beta	beta	VERB
asir-1804	164	6	two	two	NUM
asir-1804	164	7	asymptotes	asymptote	NOUN
asir-1804	164	8	:	:	PUNCT
asir-1804	164	9	one	one	NUM
asir-1804	164	10	perpendicular	perpendicular	NOUN
asir-1804	164	11	to	to	ADP
asir-1804	164	12	the	the	DET
asir-1804	164	13	a	a	DET
asir-1804	164	14	-	-	PUNCT
asir-1804	164	15	axis	axis	NOUN
asir-1804	164	16	which	which	PRON
asir-1804	164	17	passes	pass	VERB
asir-1804	164	18	through	through	ADP
asir-1804	164	19	–	–	PUNCT
asir-1804	164	20	f1	f1	NOUN
asir-1804	164	21	–	–	PUNCT
asir-1804	164	22	h1	h1	NOUN
asir-1804	164	23	and	and	CCONJ
asir-1804	164	24	u	u	NOUN
asir-1804	164	25	=	=	PROPN
asir-1804	164	26	a+(f2+h2	a+(f2+h2	PROPN
asir-1804	164	27	)	)	PUNCT
asir-1804	164	28	.	.	PUNCT
asir-1804	165	1	so	so	ADV
asir-1804	165	2	we	we	PRON
asir-1804	165	3	can	can	AUX
asir-1804	165	4	determine	determine	VERB
asir-1804	165	5	a	a	DET
asir-1804	165	6	(	(	PUNCT
asir-1804	165	7	a=	a=	PROPN
asir-1804	165	8	-f1	-f1	PROPN
asir-1804	165	9	-	-	PUNCT
asir-1804	165	10	h1	h1	PROPN
asir-1804	165	11	)	)	PUNCT
asir-1804	165	12	and	and	CCONJ
asir-1804	165	13	b=-n3f1+h2	b=-n3f1+h2	ADV
asir-1804	165	14	from	from	ADP
asir-1804	165	15	the	the	DET
asir-1804	165	16	asymptotes	asymptote	NOUN
asir-1804	165	17	and	and	CCONJ
asir-1804	165	18	from	from	ADP
asir-1804	165	19	the	the	DET
asir-1804	165	20	minimum	minimum	NOUN
asir-1804	165	21	we	we	PRON
asir-1804	165	22	can	can	AUX
asir-1804	165	23	find	find	VERB
asir-1804	165	24	f1	f1	NOUN
asir-1804	165	25	and	and	CCONJ
asir-1804	165	26	then	then	ADV
asir-1804	165	27	h1	h1	PROPN
asir-1804	165	28	,	,	PUNCT
asir-1804	165	29	h2	h2	PROPN
asir-1804	165	30	.	.	PUNCT
asir-1804	166	1	the	the	DET
asir-1804	166	2	nodal	nodal	NOUN
asir-1804	166	3	points	point	NOUN
asir-1804	166	4	coincide	coincide	VERB
asir-1804	166	5	with	with	ADP
asir-1804	166	6	the	the	DET
asir-1804	166	7	principal	principal	ADJ
asir-1804	166	8	points	point	NOUN
asir-1804	166	9	when	when	SCONJ
asir-1804	166	10	the	the	DET
asir-1804	166	11	index	index	NOUN
asir-1804	166	12	of	of	ADP
asir-1804	166	13	refraction	refraction	NOUN
asir-1804	166	14	on	on	ADP
asir-1804	166	15	the	the	DET
asir-1804	166	16	left	left	NOUN
asir-1804	166	17	of	of	ADP
asir-1804	166	18	the	the	DET
asir-1804	166	19	lens	lens	NOUN
asir-1804	166	20	has	have	VERB
asir-1804	166	21	the	the	DET
asir-1804	166	22	same	same	ADJ
asir-1804	166	23	index	index	NOUN
asir-1804	166	24	of	of	ADP
asir-1804	166	25	refraction	refraction	NOUN
asir-1804	166	26	as	as	ADP
asir-1804	166	27	the	the	DET
asir-1804	166	28	medium	medium	NOUN
asir-1804	166	29	on	on	ADP
asir-1804	166	30	the	the	DET
asir-1804	166	31	right	right	NOUN
asir-1804	166	32	of	of	ADP
asir-1804	166	33	the	the	DET
asir-1804	166	34	lens	len	NOUN
asir-1804	166	35	.	.	PUNCT
asir-1804	167	1	2.4	2.4	NUM
asir-1804	167	2	lenses	lense	NOUN
asir-1804	167	3	with	with	ADP
asir-1804	167	4	variable	variable	ADJ
asir-1804	167	5	shape	shape	NOUN
asir-1804	167	6	(	(	PUNCT
asir-1804	167	7	huygens	huygen	NOUN
asir-1804	167	8	’	'	PUNCT
asir-1804	167	9	lens	len	NOUN
asir-1804	167	10	)	)	PUNCT
asir-1804	167	11	these	these	DET
asir-1804	167	12	lenses	lense	NOUN
asir-1804	167	13	are	be	AUX
asir-1804	167	14	of	of	ADP
asir-1804	167	15	great	great	ADJ
asir-1804	167	16	significance	significance	NOUN
asir-1804	167	17	in	in	ADP
asir-1804	167	18	modern	modern	ADJ
asir-1804	167	19	technology	technology	NOUN
asir-1804	167	20	,	,	PUNCT
asir-1804	167	21	but	but	CCONJ
asir-1804	167	22	also	also	ADV
asir-1804	167	23	give	give	VERB
asir-1804	167	24	a	a	DET
asir-1804	167	25	model	model	NOUN
asir-1804	167	26	for	for	ADP
asir-1804	167	27	the	the	DET
asir-1804	167	28	lens	lens	NOUN
asir-1804	167	29	of	of	ADP
asir-1804	167	30	the	the	DET
asir-1804	167	31	eye	eye	NOUN
asir-1804	167	32	which	which	PRON
asir-1804	167	33	accommodates	accommodate	VERB
asir-1804	167	34	its	its	PRON
asir-1804	167	35	back	back	NOUN
asir-1804	167	36	.	.	PUNCT
asir-1804	168	1	also	also	ADV
asir-1804	168	2	liquid	liquid	ADJ
asir-1804	168	3	lenses	lense	NOUN
asir-1804	168	4	can	can	AUX
asir-1804	168	5	change	change	VERB
asir-1804	168	6	their	their	PRON
asir-1804	168	7	shape	shape	NOUN
asir-1804	168	8	by	by	ADP
asir-1804	168	9	using	use	VERB
asir-1804	168	10	small	small	ADJ
asir-1804	168	11	electric	electric	ADJ
asir-1804	168	12	fields	field	NOUN
asir-1804	168	13	(	(	PUNCT
asir-1804	168	14	hendriks	hendriks	PROPN
asir-1804	168	15	&	&	CCONJ
asir-1804	168	16	kuiper	kuiper	PROPN
asir-1804	168	17	,	,	PUNCT
asir-1804	168	18	2004	2004	NUM
asir-1804	168	19	)	)	PUNCT
asir-1804	168	20	.	.	PUNCT
asir-1804	169	1	actually	actually	ADV
asir-1804	169	2	the	the	DET
asir-1804	169	3	first	first	ADJ
asir-1804	169	4	lens	lens	NOUN
asir-1804	169	5	that	that	PRON
asir-1804	169	6	was	be	AUX
asir-1804	169	7	studied	study	VERB
asir-1804	169	8	mathematically	mathematically	ADV
asir-1804	169	9	was	be	AUX
asir-1804	169	10	a	a	DET
asir-1804	169	11	hyperbolic	hyperbolic	ADJ
asir-1804	169	12	lens	lens	NOUN
asir-1804	169	13	which	which	PRON
asir-1804	169	14	changes	change	VERB
asir-1804	169	15	shape	shape	NOUN
asir-1804	169	16	depending	depend	VERB
asir-1804	169	17	on	on	ADP
asir-1804	169	18	the	the	DET
asir-1804	169	19	position	position	NOUN
asir-1804	169	20	of	of	ADP
asir-1804	169	21	the	the	DET
asir-1804	169	22	source	source	NOUN
asir-1804	169	23	and	and	CCONJ
asir-1804	169	24	the	the	DET
asir-1804	169	25	refractive	refractive	ADJ
asir-1804	169	26	index	index	NOUN
asir-1804	169	27	(	(	PUNCT
asir-1804	169	28	rashed	rashe	VERB
asir-1804	169	29	,	,	PUNCT
asir-1804	169	30	1992	1992	NUM
asir-1804	169	31	;	;	PUNCT
asir-1804	169	32	mihas	miha	NOUN
asir-1804	169	33	,	,	PUNCT
asir-1804	169	34	2008	2008	NUM
asir-1804	169	35	)	)	PUNCT
asir-1804	169	36	.	.	PUNCT
asir-1804	170	1	huygens	huygen	NOUN
asir-1804	170	2	lens	lens	PROPN
asir-1804	170	3	is	be	AUX
asir-1804	170	4	the	the	DET
asir-1804	170	5	lens	lens	NOUN
asir-1804	170	6	that	that	PRON
asir-1804	170	7	was	be	AUX
asir-1804	170	8	proposed	propose	VERB
asir-1804	170	9	by	by	ADP
asir-1804	170	10	christian	christian	PROPN
asir-1804	170	11	huygens	huygens	PROPN
asir-1804	170	12	(	(	PUNCT
asir-1804	170	13	huygens	huygen	NOUN
asir-1804	170	14	,	,	PUNCT
asir-1804	170	15	1690	1690	NUM
asir-1804	170	16	)	)	PUNCT
asir-1804	170	17	as	as	SCONJ
asir-1804	170	18	is	be	AUX
asir-1804	170	19	a	a	DET
asir-1804	170	20	direct	direct	ADJ
asir-1804	170	21	application	application	NOUN
asir-1804	170	22	of	of	ADP
asir-1804	170	23	fermat	fermat	PROPN
asir-1804	170	24	’s	’s	PART
asir-1804	170	25	principle	principle	NOUN
asir-1804	170	26	.	.	PUNCT
asir-1804	171	1	the	the	DET
asir-1804	171	2	lens	lens	NOUN
asir-1804	171	3	is	be	AUX
asir-1804	171	4	constructed	construct	VERB
asir-1804	171	5	so	so	SCONJ
asir-1804	171	6	that	that	SCONJ
asir-1804	171	7	all	all	DET
asir-1804	171	8	the	the	DET
asir-1804	171	9	rays	ray	NOUN
asir-1804	171	10	that	that	PRON
asir-1804	171	11	are	be	AUX
asir-1804	171	12	originating	originate	VERB
asir-1804	171	13	from	from	ADP
asir-1804	171	14	the	the	DET
asir-1804	171	15	source	source	NOUN
asir-1804	171	16	and	and	CCONJ
asir-1804	171	17	passing	pass	VERB
asir-1804	171	18	through	through	ADP
asir-1804	171	19	the	the	DET
asir-1804	171	20	lens	lens	NOUN
asir-1804	171	21	will	will	AUX
asir-1804	171	22	pass	pass	VERB
asir-1804	171	23	through	through	ADP
asir-1804	171	24	the	the	DET
asir-1804	171	25	focus	focus	NOUN
asir-1804	171	26	and	and	CCONJ
asir-1804	171	27	the	the	DET
asir-1804	171	28	time	time	NOUN
asir-1804	171	29	for	for	SCONJ
asir-1804	171	30	the	the	DET
asir-1804	171	31	light	light	NOUN
asir-1804	171	32	to	to	PART
asir-1804	171	33	move	move	VERB
asir-1804	171	34	on	on	ADP
asir-1804	171	35	all	all	DET
asir-1804	171	36	ray	ray	NOUN
asir-1804	171	37	-paths	-path	NOUN
asir-1804	171	38	is	be	AUX
asir-1804	171	39	the	the	DET
asir-1804	171	40	same	same	ADJ
asir-1804	171	41	.	.	PUNCT
asir-1804	172	1	this	this	DET
asir-1804	172	2	method	method	NOUN
asir-1804	172	3	was	be	AUX
asir-1804	172	4	incorporated	incorporate	VERB
asir-1804	172	5	in	in	ADP
asir-1804	172	6	teaching	teaching	NOUN
asir-1804	172	7	of	of	ADP
asir-1804	172	8	optics	optic	NOUN
asir-1804	172	9	(	(	PUNCT
asir-1804	172	10	mihas	miha	NOUN
asir-1804	172	11	,	,	PUNCT
asir-1804	172	12	2012	2012	NUM
asir-1804	172	13	)	)	PUNCT
asir-1804	172	14	.	.	PUNCT
asir-1804	173	1	let	let	VERB
asir-1804	173	2	us	we	PRON
asir-1804	173	3	assume	assume	VERB
asir-1804	173	4	that	that	SCONJ
asir-1804	173	5	the	the	DET
asir-1804	173	6	source	source	NOUN
asir-1804	173	7	of	of	ADP
asir-1804	173	8	light	light	NOUN
asir-1804	173	9	is	be	AUX
asir-1804	173	10	located	locate	VERB
asir-1804	173	11	on	on	ADP
asir-1804	173	12	the	the	DET
asir-1804	173	13	left	left	NOUN
asir-1804	173	14	of	of	ADP
asir-1804	173	15	the	the	DET
asir-1804	173	16	lens	lens	NOUN
asir-1804	173	17	and	and	CCONJ
asir-1804	173	18	the	the	DET
asir-1804	173	19	focus	focus	NOUN
asir-1804	173	20	on	on	ADP
asir-1804	173	21	the	the	DET
asir-1804	173	22	right	right	NOUN
asir-1804	173	23	(	(	PUNCT
asir-1804	173	24	figure	figure	NOUN
asir-1804	173	25	10	10	NUM
asir-1804	173	26	)	)	PUNCT
asir-1804	173	27	.	.	PUNCT
asir-1804	174	1	to	to	PART
asir-1804	174	2	construct	construct	VERB
asir-1804	174	3	the	the	DET
asir-1804	174	4	lens	len	NOUN
asir-1804	174	5	we	we	PRON
asir-1804	174	6	employ	employ	VERB
asir-1804	174	7	the	the	DET
asir-1804	174	8	fermat	fermat	PROPN
asir-1804	174	9	’s	’s	PART
asir-1804	174	10	principle	principle	NOUN
asir-1804	174	11	in	in	ADP
asir-1804	174	12	the	the	DET
asir-1804	174	13	form	form	NOUN
asir-1804	174	14	of	of	ADP
asir-1804	174	15	the	the	DET
asir-1804	174	16	time	time	NOUN
asir-1804	174	17	needed	need	VERB
asir-1804	174	18	for	for	SCONJ
asir-1804	174	19	a	a	DET
asir-1804	174	20	ray	ray	NOUN
asir-1804	174	21	to	to	PART
asir-1804	174	22	move	move	VERB
asir-1804	174	23	from	from	ADP
asir-1804	174	24	the	the	DET
asir-1804	174	25	source	source	NOUN
asir-1804	174	26	through	through	ADP
asir-1804	174	27	the	the	DET
asir-1804	174	28	lens	lens	NOUN
asir-1804	174	29	and	and	CCONJ
asir-1804	174	30	then	then	ADV
asir-1804	174	31	to	to	ADP
asir-1804	174	32	the	the	DET
asir-1804	174	33	focus	focus	NOUN
asir-1804	174	34	is	be	AUX
asir-1804	174	35	constant	constant	ADJ
asir-1804	174	36	figure	figure	NOUN
asir-1804	174	37	10	10	NUM
asir-1804	174	38	.	.	PUNCT
asir-1804	174	39	geometry	geometry	NOUN
asir-1804	174	40	for	for	ADP
asir-1804	174	41	finding	find	VERB
asir-1804	174	42	the	the	DET
asir-1804	174	43	back	back	NOUN
asir-1804	174	44	of	of	ADP
asir-1804	174	45	the	the	DET
asir-1804	174	46	lens	lens	NOUN
asir-1804	174	47	if	if	SCONJ
asir-1804	174	48	x0	x0	PROPN
asir-1804	174	49	is	be	AUX
asir-1804	174	50	the	the	DET
asir-1804	174	51	source	source	NOUN
asir-1804	174	52	point	point	NOUN
asir-1804	174	53	,	,	PUNCT
asir-1804	174	54	x1	x1	PROPN
asir-1804	174	55	the	the	DET
asir-1804	174	56	point	point	NOUN
asir-1804	174	57	on	on	ADP
asir-1804	174	58	a	a	DET
asir-1804	174	59	spherical	spherical	ADJ
asir-1804	174	60	or	or	CCONJ
asir-1804	174	61	hyperbolic	hyperbolic	ADJ
asir-1804	174	62	surface	surface	NOUN
asir-1804	174	63	,	,	PUNCT
asir-1804	174	64	x	x	PROPN
asir-1804	174	65	the	the	DET
asir-1804	174	66	point	point	NOUN
asir-1804	174	67	on	on	ADP
asir-1804	174	68	the	the	DET
asir-1804	174	69	back	back	NOUN
asir-1804	174	70	of	of	ADP
asir-1804	174	71	the	the	DET
asir-1804	174	72	lens	lens	NOUN
asir-1804	174	73	and	and	CCONJ
asir-1804	174	74	xf	xf	PROPN
asir-1804	174	75	is	be	AUX
asir-1804	174	76	the	the	DET
asir-1804	174	77	focal	focal	ADJ
asir-1804	174	78	point	point	NOUN
asir-1804	174	79	,	,	PUNCT
asir-1804	174	80	then	then	ADV
asir-1804	174	81	the	the	DET
asir-1804	174	82	total	total	ADJ
asir-1804	174	83	time	time	NOUN
asir-1804	174	84	from	from	ADP
asir-1804	174	85	x0	x0	PROPN
asir-1804	174	86	to	to	ADP
asir-1804	174	87	xf	xf	PROPN
asir-1804	174	88	is	be	AUX
asir-1804	174	89	constant	constant	ADJ
asir-1804	174	90	.	.	PUNCT
asir-1804	175	1	so	so	ADV
asir-1804	175	2	tx0_x1+tx1_x+tx_xf	tx0_x1+tx1_x+tx_xf	PROPN
asir-1804	175	3	=	=	PUNCT
asir-1804	176	1	k	k	PROPN
asir-1804	177	1	or	or	CCONJ
asir-1804	177	2	if	if	SCONJ
asir-1804	177	3	c	c	PROPN
asir-1804	177	4	is	be	AUX
asir-1804	177	5	the	the	DET
asir-1804	177	6	speed	speed	NOUN
asir-1804	177	7	of	of	ADP
asir-1804	177	8	light	light	NOUN
asir-1804	177	9	outside	outside	ADP
asir-1804	177	10	the	the	DET
asir-1804	177	11	lens	lens	NOUN
asir-1804	177	12	and	and	CCONJ
asir-1804	177	13	c	c	X
asir-1804	177	14	/	/	SYM
asir-1804	177	15	n	n	PROPN
asir-1804	177	16	is	be	AUX
asir-1804	177	17	the	the	DET
asir-1804	177	18	speed	speed	NOUN
asir-1804	177	19	of	of	ADP
asir-1804	177	20	light	light	NOUN
asir-1804	177	21	inside	inside	ADP
asir-1804	177	22	the	the	DET
asir-1804	177	23	lens	lens	NOUN
asir-1804	177	24	(	(	PUNCT
asir-1804	177	25	where	where	SCONJ
asir-1804	177	26	n	n	X
asir-1804	177	27	is	be	AUX
asir-1804	177	28	the	the	DET
asir-1804	177	29	index	index	NOUN
asir-1804	177	30	of	of	ADP
asir-1804	177	31	refraction	refraction	NOUN
asir-1804	177	32	of	of	ADP
asir-1804	177	33	the	the	DET
asir-1804	177	34	lens	len	NOUN
asir-1804	177	35	)	)	PUNCT
asir-1804	178	1	then	then	ADV
asir-1804	178	2	if	if	SCONJ
asir-1804	178	3	dx0_x1	dx0_x1	VERB
asir-1804	178	4	the	the	DET
asir-1804	178	5	distance	distance	NOUN
asir-1804	178	6	of	of	ADP
asir-1804	178	7	the	the	DET
asir-1804	178	8	source	source	NOUN
asir-1804	178	9	to	to	ADP
asir-1804	178	10	the	the	DET
asir-1804	178	11	point	point	NOUN
asir-1804	178	12	on	on	ADP
asir-1804	178	13	the	the	DET
asir-1804	178	14	circle	circle	NOUN
asir-1804	178	15	,	,	PUNCT
asir-1804	178	16	d2	d2	PROPN
asir-1804	178	17	is	be	AUX
asir-1804	178	18	the	the	DET
asir-1804	178	19	distance	distance	NOUN
asir-1804	178	20	from	from	ADP
asir-1804	178	21	the	the	DET
asir-1804	178	22	point	point	NOUN
asir-1804	178	23	on	on	ADP
asir-1804	178	24	the	the	DET
asir-1804	178	25	circle	circle	NOUN
asir-1804	178	26	to	to	ADP
asir-1804	178	27	the	the	DET
asir-1804	178	28	back	back	NOUN
asir-1804	178	29	of	of	ADP
asir-1804	178	30	the	the	DET
asir-1804	178	31	lens	lens	NOUN
asir-1804	178	32	and	and	CCONJ
asir-1804	178	33	d3	d3	PROPN
asir-1804	178	34	is	be	AUX
asir-1804	178	35	the	the	DET
asir-1804	178	36	distance	distance	NOUN
asir-1804	178	37	from	from	ADP
asir-1804	178	38	the	the	DET
asir-1804	178	39	point	point	NOUN
asir-1804	178	40	on	on	ADP
asir-1804	178	41	the	the	DET
asir-1804	178	42	back	back	NOUN
asir-1804	178	43	of	of	ADP
asir-1804	178	44	the	the	DET
asir-1804	178	45	lens	lens	NOUN
asir-1804	178	46	to	to	ADP
asir-1804	178	47	the	the	DET
asir-1804	178	48	focus	focus	NOUN
asir-1804	178	49	then	then	ADV
asir-1804	178	50	(	(	PUNCT
asir-1804	178	51	with	with	ADP
asir-1804	178	52	n	n	PRON
asir-1804	178	53	the	the	DET
asir-1804	178	54	index	index	NOUN
asir-1804	178	55	of	of	ADP
asir-1804	178	56	refraction	refraction	NOUN
asir-1804	178	57	of	of	ADP
asir-1804	178	58	the	the	DET
asir-1804	178	59	lens	len	NOUN
asir-1804	178	60	,	,	PUNCT
asir-1804	178	61	n2	n2	ADJ
asir-1804	178	62	the	the	DET
asir-1804	178	63	index	index	NOUN
asir-1804	178	64	of	of	ADP
asir-1804	178	65	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1804	178	66	applied	apply	VERB
asir-1804	178	67	science	science	NOUN
asir-1804	178	68	and	and	CCONJ
asir-1804	178	69	innovative	innovative	ADJ
asir-1804	178	70	research	research	NOUN
asir-1804	178	71	vol	vol	NOUN
asir-1804	178	72	.	.	PUNCT
asir-1804	179	1	3	3	NUM
asir-1804	179	2	,	,	PUNCT
asir-1804	179	3	no	no	INTJ
asir-1804	179	4	.	.	NOUN
asir-1804	179	5	1	1	NUM
asir-1804	179	6	,	,	PUNCT
asir-1804	179	7	2019	2019	NUM
asir-1804	179	8	25	25	NUM
asir-1804	179	9	published	publish	VERB
asir-1804	179	10	by	by	ADP
asir-1804	179	11	scholink	scholink	PROPN
asir-1804	179	12	inc	inc	PROPN
asir-1804	179	13	.	.	PROPN
asir-1804	179	14	refraction	refraction	NOUN
asir-1804	179	15	of	of	ADP
asir-1804	179	16	the	the	DET
asir-1804	179	17	medium	medium	NOUN
asir-1804	179	18	after	after	ADP
asir-1804	179	19	the	the	DET
asir-1804	179	20	lens	len	NOUN
asir-1804	179	21	):	):	PUNCT
asir-1804	179	22	d1	d1	PROPN
asir-1804	179	23	+	+	CCONJ
asir-1804	179	24	n·d2	n·d2	ADJ
asir-1804	179	25	+	+	CCONJ
asir-1804	179	26	n2d3	n2d3	ADJ
asir-1804	179	27	=	=	X
asir-1804	179	28	constant	constant	ADJ
asir-1804	179	29	(	(	PUNCT
asir-1804	179	30	1	1	NUM
asir-1804	179	31	)	)	PUNCT
asir-1804	179	32	for	for	ADP
asir-1804	179	33	a	a	DET
asir-1804	179	34	given	give	VERB
asir-1804	179	35	incident	incident	NOUN
asir-1804	179	36	ray	ray	NOUN
asir-1804	179	37	we	we	PRON
asir-1804	179	38	can	can	AUX
asir-1804	179	39	calculate	calculate	VERB
asir-1804	179	40	the	the	DET
asir-1804	179	41	x1	x1	PROPN
asir-1804	179	42	,	,	PUNCT
asir-1804	179	43	y1	y1	NOUN
asir-1804	179	44	,	,	PUNCT
asir-1804	179	45	d1	d1	PROPN
asir-1804	179	46	and	and	CCONJ
asir-1804	179	47	then	then	ADV
asir-1804	179	48	to	to	PART
asir-1804	179	49	find	find	VERB
asir-1804	179	50	the	the	DET
asir-1804	179	51	point	point	NOUN
asir-1804	179	52	of	of	ADP
asir-1804	179	53	the	the	DET
asir-1804	179	54	pack	pack	NOUN
asir-1804	179	55	of	of	ADP
asir-1804	179	56	the	the	DET
asir-1804	179	57	lens	lens	NOUN
asir-1804	179	58	(	(	PUNCT
asir-1804	179	59	x	x	X
asir-1804	179	60	,	,	PUNCT
asir-1804	179	61	y	y	NOUN
asir-1804	179	62	)	)	PUNCT
asir-1804	179	63	we	we	PRON
asir-1804	179	64	use	use	VERB
asir-1804	179	65	(	(	PUNCT
asir-1804	179	66	1	1	NUM
asir-1804	179	67	)	)	PUNCT
asir-1804	179	68	as	as	ADP
asir-1804	179	69	+	+	NUM
asir-1804	179	70	n·d2	n·d2	PROPN
asir-1804	179	71	+	+	NOUN
asir-1804	179	72	n2	n2	ADJ
asir-1804	179	73	·	·	PUNCT
asir-1804	179	74	d3	d3	PROPN
asir-1804	179	75	=	=	PUNCT
asir-1804	179	76	l	l	NOUN
asir-1804	179	77	where	where	SCONJ
asir-1804	179	78	l	l	NOUN
asir-1804	179	79	is	be	AUX
asir-1804	179	80	already	already	ADV
asir-1804	179	81	known	know	VERB
asir-1804	179	82	.	.	PUNCT
asir-1804	180	1	we	we	PRON
asir-1804	180	2	express	express	VERB
asir-1804	180	3	the	the	DET
asir-1804	180	4	above	above	ADJ
asir-1804	180	5	equation	equation	NOUN
asir-1804	180	6	as	as	ADP
asir-1804	180	7	𝑛	𝑛	DET
asir-1804	180	8	∙	∙	PROPN
asir-1804	180	9	√(𝑥1	√(𝑥1	PROPN
asir-1804	180	10	−	−	PROPN
asir-1804	180	11	𝑥)2	𝑥)2	PROPN
asir-1804	180	12	+	+	NUM
asir-1804	180	13	(	(	PUNCT
asir-1804	180	14	𝑦1	𝑦1	PROPN
asir-1804	180	15	−	−	PROPN
asir-1804	180	16	𝑦)2	𝑦)2	NOUN
asir-1804	180	17	+	+	CCONJ
asir-1804	180	18	𝑛2√(𝑥𝑓	𝑛2√(𝑥𝑓	X
asir-1804	180	19	−	−	NOUN
asir-1804	180	20	𝑥)2	𝑥)2	NOUN
asir-1804	180	21	+	+	NUM
asir-1804	180	22	𝑦2	𝑦2	NOUN
asir-1804	180	23	=	=	SYM
asir-1804	180	24	𝐿	𝐿	PROPN
asir-1804	180	25	we	we	PRON
asir-1804	180	26	put	put	VERB
asir-1804	180	27	a	a	PRON
asir-1804	180	28	=	=	PUNCT
asir-1804	180	29	(	(	PUNCT
asir-1804	180	30	x1	x1	PROPN
asir-1804	180	31	–	–	PUNCT
asir-1804	180	32	x)²+(y1	x)²+(y1	NOUN
asir-1804	180	33	-	-	ADJ
asir-1804	180	34	y)²	y)²	ADJ
asir-1804	180	35	and	and	CCONJ
asir-1804	180	36	b	b	NOUN
asir-1804	180	37	=(	=(	X
asir-1804	180	38	xf	xf	PROPN
asir-1804	180	39	–	–	PUNCT
asir-1804	180	40	x)²+y²	x)²+y²	PROPN
asir-1804	180	41	let	let	VERB
asir-1804	180	42	us	we	PRON
asir-1804	180	43	move	move	VERB
asir-1804	180	44	the	the	DET
asir-1804	180	45	origin	origin	NOUN
asir-1804	180	46	to	to	ADP
asir-1804	180	47	the	the	DET
asir-1804	180	48	focus	focus	NOUN
asir-1804	180	49	point	point	NOUN
asir-1804	180	50	then	then	ADV
asir-1804	180	51	:	:	PUNCT
asir-1804	180	52	xf	xf	PROPN
asir-1804	180	53	=	=	PROPN
asir-1804	180	54	0	0	PROPN
asir-1804	180	55	.	.	PUNCT
asir-1804	181	1	(	(	PUNCT
asir-1804	181	2	we	we	PRON
asir-1804	181	3	have	have	VERB
asir-1804	181	4	the	the	DET
asir-1804	181	5	transformation	transformation	NOUN
asir-1804	181	6	x	x	NOUN
asir-1804	181	7	’	'	PUNCT
asir-1804	181	8	=	=	ADJ
asir-1804	181	9	x	x	NOUN
asir-1804	181	10	-	-	PUNCT
asir-1804	181	11	xf	xf	VERB
asir-1804	182	1	so	so	ADV
asir-1804	182	2	the	the	DET
asir-1804	182	3	following	follow	VERB
asir-1804	182	4	relations	relation	NOUN
asir-1804	182	5	are	be	AUX
asir-1804	182	6	done	do	VERB
asir-1804	182	7	with	with	ADP
asir-1804	182	8	this	this	DET
asir-1804	182	9	transformation	transformation	NOUN
asir-1804	183	1	so	so	SCONJ
asir-1804	183	2	x1	x1	PROPN
asir-1804	183	3	’	'	PUNCT
asir-1804	183	4	is	be	AUX
asir-1804	183	5	x1	x1	PROPN
asir-1804	183	6	-	-	PUNCT
asir-1804	183	7	xf	xf	PROPN
asir-1804	183	8	x’=x	x’=x	PROPN
asir-1804	183	9	=	=	PROPN
asir-1804	183	10	xf	xf	NOUN
asir-1804	183	11	)	)	PUNCT
asir-1804	183	12	𝑛	𝑛	VERB
asir-1804	183	13	∙	∙	PROPN
asir-1804	183	14	√𝐴	√𝐴	NOUN
asir-1804	183	15	+	+	CCONJ
asir-1804	183	16	𝑛2√𝐵	𝑛2√𝐵	PROPN
asir-1804	183	17	=	=	SYM
asir-1804	183	18	𝐿	𝐿	PROPN
asir-1804	183	19	(	(	PUNCT
asir-1804	183	20	2	2	NUM
asir-1804	183	21	)	)	PUNCT
asir-1804	183	22	with	with	ADP
asir-1804	183	23	x’-x’1	x’-x’1	PROPN
asir-1804	183	24	=	=	SYM
asir-1804	183	25	ξ	ξ	PROPN
asir-1804	183	26	(	(	PUNCT
asir-1804	183	27	so	so	SCONJ
asir-1804	183	28	x	x	SYM
asir-1804	183	29	=	=	ADJ
asir-1804	183	30	x1+ξ	x1+ξ	PROPN
asir-1804	183	31	)	)	PUNCT
asir-1804	183	32	equation	equation	NOUN
asir-1804	183	33	2	2	NUM
asir-1804	183	34	is	be	AUX
asir-1804	183	35	written	write	VERB
asir-1804	183	36	𝑛	𝑛	ADP
asir-1804	183	37	∙	∙	PROPN
asir-1804	183	38	𝜉	𝜉	X
asir-1804	183	39	𝑐𝑜𝑠𝜔	𝑐𝑜𝑠𝜔	VERB
asir-1804	183	40	−	−	PROPN
asir-1804	183	41	𝐿	𝐿	PROPN
asir-1804	183	42	=	=	PROPN
asir-1804	183	43	𝑛2	𝑛2	NOUN
asir-1804	183	44	√𝑥′	√𝑥′	VERB
asir-1804	183	45	1	1	NUM
asir-1804	183	46	2	2	NUM
asir-1804	183	47	+	+	CCONJ
asir-1804	183	48	𝑦1	𝑦1	PROPN
asir-1804	183	49	2	2	NUM
asir-1804	183	50	+	+	CCONJ
asir-1804	183	51	2(𝑥′	2(𝑥′	NUM
asir-1804	183	52	1	1	NUM
asir-1804	183	53	+	+	NUM
asir-1804	183	54	𝑦1𝑡𝑎𝑛𝜔)𝜉	𝑦1𝑡𝑎𝑛𝜔)𝜉	NOUN
asir-1804	183	55	+	+	CCONJ
asir-1804	183	56	𝜉2	𝜉2	PROPN
asir-1804	183	57	𝑐𝑜𝑠2𝜔	𝑐𝑜𝑠2𝜔	PUNCT
asir-1804	184	1	=	=	SYM
asir-1804	184	2	𝑛2	𝑛2	NOUN
asir-1804	184	3	√𝛿	√𝛿	VERB
asir-1804	184	4	+	+	CCONJ
asir-1804	184	5	2휀𝜉	2휀𝜉	ADJ
asir-1804	184	6	+	+	CCONJ
asir-1804	184	7	𝜉2	𝜉2	ADJ
asir-1804	184	8	𝑐𝑜𝑠2𝜔	𝑐𝑜𝑠2𝜔	PUNCT
asir-1804	185	1	so	so	ADV
asir-1804	185	2	we	we	PRON
asir-1804	185	3	get	get	VERB
asir-1804	185	4	a	a	DET
asir-1804	185	5	quadratic	quadratic	ADJ
asir-1804	185	6	equation	equation	NOUN
asir-1804	185	7	.	.	PUNCT
asir-1804	186	1	we	we	PRON
asir-1804	186	2	put	put	VERB
asir-1804	186	3	:	:	PUNCT
asir-1804	186	4	휀	휀	NOUN
asir-1804	186	5	=	=	PUNCT
asir-1804	186	6	𝑥′1	𝑥′1	X
asir-1804	186	7	+	+	CCONJ
asir-1804	186	8	𝑦1𝑡𝑎𝑛𝜔	𝑦1𝑡𝑎𝑛𝜔	NOUN
asir-1804	186	9	,	,	PUNCT
asir-1804	187	1	𝛿	𝛿	ADJ
asir-1804	187	2	=	=	ADJ
asir-1804	187	3	𝑥′1	𝑥′1	ADJ
asir-1804	187	4	2	2	NUM
asir-1804	188	1	+	+	CCONJ
asir-1804	188	2	𝑦1	𝑦1	PROPN
asir-1804	188	3	2	2	NUM
asir-1804	188	4	(	(	PUNCT
asir-1804	188	5	𝑛2	𝑛2	NOUN
asir-1804	188	6	−	−	PROPN
asir-1804	188	7	𝑛2	𝑛2	NOUN
asir-1804	188	8	2	2	NUM
asir-1804	188	9	)	)	PUNCT
asir-1804	188	10	∙	∙	PROPN
asir-1804	188	11	𝜉2	𝜉2	PROPN
asir-1804	188	12	𝑐𝑜𝑠2𝜔	𝑐𝑜𝑠2𝜔	NOUN
asir-1804	189	1	−	−	NOUN
asir-1804	189	2	2(𝐿	2(𝐿	NOUN
asir-1804	189	3	∙	∙	PROPN
asir-1804	189	4	𝑛	𝑛	PRON
asir-1804	190	1	+	+	PUNCT
asir-1804	190	2	𝑛2	𝑛2	NOUN
asir-1804	190	3	2	2	NUM
asir-1804	190	4	∙	∙	PROPN
asir-1804	190	5	휀	휀	X
asir-1804	190	6	∙	∙	PROPN
asir-1804	190	7	𝑐𝑜𝑠𝜔	𝑐𝑜𝑠𝜔	X
asir-1804	190	8	)	)	PUNCT
asir-1804	190	9	𝜉	𝜉	VERB
asir-1804	190	10	𝑐𝑜𝑠𝜔	𝑐𝑜𝑠𝜔	X
asir-1804	190	11	+	+	CCONJ
asir-1804	190	12	𝐿2	𝐿2	NOUN
asir-1804	190	13	−	−	NOUN
asir-1804	190	14	𝑛2	𝑛2	NOUN
asir-1804	190	15	2𝛿	2𝛿	NOUN
asir-1804	190	16	=	=	SYM
asir-1804	190	17	0	0	NUM
asir-1804	191	1	(	(	PUNCT
asir-1804	192	1	3	3	NUM
asir-1804	192	2	)	)	PUNCT
asir-1804	192	3	for	for	ADP
asir-1804	192	4	finding	find	VERB
asir-1804	192	5	the	the	DET
asir-1804	192	6	perpendicular	perpendicular	NOUN
asir-1804	192	7	at	at	ADP
asir-1804	192	8	a	a	DET
asir-1804	192	9	point	point	NOUN
asir-1804	192	10	on	on	ADP
asir-1804	192	11	the	the	DET
asir-1804	192	12	back	back	NOUN
asir-1804	192	13	of	of	ADP
asir-1804	192	14	the	the	DET
asir-1804	192	15	lens	len	NOUN
asir-1804	192	16	,	,	PUNCT
asir-1804	192	17	we	we	PRON
asir-1804	192	18	need	need	VERB
asir-1804	192	19	the	the	DET
asir-1804	192	20	value	value	NOUN
asir-1804	192	21	of	of	ADP
asir-1804	192	22	dx	dx	PROPN
asir-1804	192	23	/	/	SYM
asir-1804	192	24	dy	dy	X
asir-1804	192	25	.	.	PUNCT
asir-1804	193	1	this	this	PRON
asir-1804	193	2	can	can	AUX
asir-1804	193	3	be	be	AUX
asir-1804	193	4	found	find	VERB
asir-1804	193	5	explicitly	explicitly	ADV
asir-1804	193	6	by	by	ADP
asir-1804	193	7	finding	find	VERB
asir-1804	193	8	the	the	DET
asir-1804	193	9	derivatives	derivative	NOUN
asir-1804	193	10	of	of	ADP
asir-1804	193	11	x1	x1	PROPN
asir-1804	193	12	y1	y1	PROPN
asir-1804	193	13	φ1	φ1	PROPN
asir-1804	193	14	,	,	PUNCT
asir-1804	193	15	angle	angle	NOUN
asir-1804	193	16	of	of	ADP
asir-1804	193	17	incidence	incidence	NOUN
asir-1804	193	18	,	,	PUNCT
asir-1804	193	19	angle	angle	NOUN
asir-1804	193	20	of	of	ADP
asir-1804	193	21	refraction	refraction	NOUN
asir-1804	193	22	,	,	PUNCT
asir-1804	193	23	angle	angle	NOUN
asir-1804	193	24	of	of	ADP
asir-1804	193	25	inclination	inclination	NOUN
asir-1804	193	26	ω	ω	PROPN
asir-1804	193	27	,	,	PUNCT
asir-1804	193	28	ξ	ξ	PROPN
asir-1804	193	29	.	.	PUNCT
asir-1804	194	1	in	in	ADP
asir-1804	194	2	the	the	DET
asir-1804	194	3	excel	excel	NOUN
asir-1804	194	4	file	file	NOUN
asir-1804	194	5	“	"	PUNCT
asir-1804	194	6	spherical	spherical	ADJ
asir-1804	194	7	and	and	CCONJ
asir-1804	194	8	huygens	huygen	NOUN
asir-1804	194	9	lens	len	NOUN
asir-1804	194	10	”	"	PUNCT
asir-1804	194	11	,	,	PUNCT
asir-1804	194	12	there	there	PRON
asir-1804	194	13	is	be	VERB
asir-1804	194	14	a	a	DET
asir-1804	194	15	user	user	NOUN
asir-1804	194	16	function	function	NOUN
asir-1804	194	17	which	which	PRON
asir-1804	194	18	determines	determine	VERB
asir-1804	194	19	the	the	DET
asir-1804	194	20	derivative	derivative	ADJ
asir-1804	194	21	dx	dx	PROPN
asir-1804	194	22	/	/	SYM
asir-1804	194	23	dy	dy	NOUN
asir-1804	194	24	at	at	ADP
asir-1804	194	25	a	a	DET
asir-1804	194	26	point	point	NOUN
asir-1804	194	27	(	(	PUNCT
asir-1804	194	28	x2	x2	NOUN
asir-1804	194	29	,	,	PUNCT
asir-1804	194	30	y2	y2	PROPN
asir-1804	194	31	)	)	PUNCT
asir-1804	194	32	of	of	ADP
asir-1804	194	33	the	the	DET
asir-1804	194	34	curve	curve	NOUN
asir-1804	194	35	that	that	PRON
asir-1804	194	36	is	be	AUX
asir-1804	194	37	determined	determine	VERB
asir-1804	194	38	by	by	ADP
asir-1804	194	39	the	the	DET
asir-1804	194	40	above	above	ADJ
asir-1804	194	41	method	method	NOUN
asir-1804	194	42	.	.	PUNCT
asir-1804	195	1	from	from	ADP
asir-1804	195	2	the	the	DET
asir-1804	195	3	vector	vector	NOUN
asir-1804	195	4	joining	join	VERB
asir-1804	195	5	the	the	DET
asir-1804	195	6	points	point	NOUN
asir-1804	195	7	(	(	PUNCT
asir-1804	195	8	x1	x1	PROPN
asir-1804	195	9	,	,	PUNCT
asir-1804	195	10	y1	y1	PROPN
asir-1804	195	11	)	)	PUNCT
asir-1804	195	12	and	and	CCONJ
asir-1804	195	13	(	(	PUNCT
asir-1804	195	14	x2	x2	PROPN
asir-1804	195	15	,	,	PUNCT
asir-1804	195	16	y2	y2	PROPN
asir-1804	195	17	)	)	PUNCT
asir-1804	195	18	and	and	CCONJ
asir-1804	195	19	the	the	DET
asir-1804	195	20	perpendicular	perpendicular	ADJ
asir-1804	195	21	–	–	PUNCT
asir-1804	195	22	dx	dx	PROPN
asir-1804	195	23	/	/	SYM
asir-1804	195	24	dy	dy	NOUN
asir-1804	195	25	we	we	PRON
asir-1804	195	26	find	find	VERB
asir-1804	195	27	the	the	DET
asir-1804	195	28	angle	angle	NOUN
asir-1804	195	29	of	of	ADP
asir-1804	195	30	incidence	incidence	NOUN
asir-1804	195	31	,	,	PUNCT
asir-1804	195	32	the	the	DET
asir-1804	195	33	angle	angle	NOUN
asir-1804	195	34	of	of	ADP
asir-1804	195	35	refraction	refraction	NOUN
asir-1804	195	36	,	,	PUNCT
asir-1804	195	37	and	and	CCONJ
asir-1804	195	38	the	the	DET
asir-1804	195	39	angle	angle	NOUN
asir-1804	195	40	of	of	ADP
asir-1804	195	41	inclination	inclination	NOUN
asir-1804	195	42	of	of	ADP
asir-1804	195	43	the	the	DET
asir-1804	195	44	emerging	emerge	VERB
asir-1804	195	45	ray	ray	NOUN
asir-1804	195	46	.	.	PUNCT
asir-1804	196	1	figure	figure	VERB
asir-1804	196	2	11	11	NUM
asir-1804	196	3	.	.	PUNCT
asir-1804	197	1	huygen	huygen	PROPN
asir-1804	197	2	’s	’s	PART
asir-1804	197	3	lens	lens	NOUN
asir-1804	197	4	for	for	ADP
asir-1804	197	5	the	the	DET
asir-1804	197	6	case	case	NOUN
asir-1804	197	7	of	of	ADP
asir-1804	197	8	a	a	DET
asir-1804	197	9	spherical	spherical	ADJ
asir-1804	197	10	and	and	CCONJ
asir-1804	197	11	a	a	DET
asir-1804	197	12	hyperbolic	hyperbolic	ADJ
asir-1804	197	13	case	case	NOUN
asir-1804	197	14	.	.	PUNCT
asir-1804	198	1	the	the	DET
asir-1804	198	2	upper	upper	ADJ
asir-1804	198	3	graphs	graph	NOUN
asir-1804	198	4	change	change	VERB
asir-1804	198	5	when	when	SCONJ
asir-1804	198	6	we	we	PRON
asir-1804	198	7	choose	choose	VERB
asir-1804	198	8	not	not	PART
asir-1804	198	9	to	to	PART
asir-1804	198	10	show	show	VERB
asir-1804	198	11	the	the	DET
asir-1804	198	12	rays	ray	NOUN
asir-1804	198	13	from	from	ADP
asir-1804	198	14	the	the	DET
asir-1804	198	15	source	source	NOUN
asir-1804	198	16	located	locate	VERB
asir-1804	198	17	at	at	ADP
asir-1804	198	18	y0	y0	PROPN
asir-1804	198	19	≠0	≠0	NOUN
asir-1804	198	20	while	while	SCONJ
asir-1804	198	21	the	the	DET
asir-1804	198	22	lower	low	ADJ
asir-1804	198	23	shows	show	VERB
asir-1804	198	24	the	the	DET
asir-1804	198	25	rays	ray	NOUN
asir-1804	198	26	from	from	ADP
asir-1804	198	27	the	the	DET
asir-1804	198	28	source	source	NOUN
asir-1804	198	29	in	in	ADP
asir-1804	198	30	all	all	DET
asir-1804	198	31	cases	case	NOUN
asir-1804	198	32	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	VERB
asir-1804	198	33	applied	apply	VERB
asir-1804	198	34	science	science	NOUN
asir-1804	198	35	and	and	CCONJ
asir-1804	198	36	innovative	innovative	ADJ
asir-1804	198	37	research	research	NOUN
asir-1804	198	38	vol	vol	NOUN
asir-1804	198	39	.	.	PUNCT
asir-1804	199	1	3	3	NUM
asir-1804	199	2	,	,	PUNCT
asir-1804	199	3	no	no	INTJ
asir-1804	199	4	.	.	NOUN
asir-1804	199	5	1	1	NUM
asir-1804	199	6	,	,	PUNCT
asir-1804	199	7	2019	2019	NUM
asir-1804	199	8	26	26	NUM
asir-1804	199	9	published	publish	VERB
asir-1804	199	10	by	by	ADP
asir-1804	199	11	scholink	scholink	PROPN
asir-1804	199	12	inc	inc	PROPN
asir-1804	199	13	.	.	PROPN
asir-1804	199	14	for	for	ADP
asir-1804	199	15	both	both	CCONJ
asir-1804	199	16	spherical	spherical	ADJ
asir-1804	199	17	and	and	CCONJ
asir-1804	199	18	hyperbolic	hyperbolic	ADJ
asir-1804	199	19	huygens	huygen	NOUN
asir-1804	199	20	’	'	PUNCT
asir-1804	199	21	lenses	lense	VERB
asir-1804	199	22	the	the	DET
asir-1804	199	23	user	user	NOUN
asir-1804	199	24	can	can	AUX
asir-1804	199	25	change	change	VERB
asir-1804	199	26	the	the	DET
asir-1804	199	27	location	location	NOUN
asir-1804	199	28	of	of	ADP
asir-1804	199	29	the	the	DET
asir-1804	199	30	source	source	NOUN
asir-1804	199	31	of	of	ADP
asir-1804	199	32	light	light	NOUN
asir-1804	199	33	on	on	ADP
asir-1804	199	34	the	the	DET
asir-1804	199	35	x	x	ADJ
asir-1804	199	36	–	–	PUNCT
asir-1804	199	37	axis	axis	ADJ
asir-1804	199	38	,	,	PUNCT
asir-1804	199	39	the	the	DET
asir-1804	199	40	point	point	NOUN
asir-1804	199	41	on	on	ADP
asir-1804	199	42	the	the	DET
asir-1804	199	43	back	back	NOUN
asir-1804	199	44	through	through	ADP
asir-1804	199	45	which	which	PRON
asir-1804	199	46	pass	pass	VERB
asir-1804	199	47	the	the	DET
asir-1804	199	48	rays	ray	NOUN
asir-1804	199	49	,	,	PUNCT
asir-1804	199	50	the	the	DET
asir-1804	199	51	index	index	NOUN
asir-1804	199	52	of	of	ADP
asir-1804	199	53	refraction	refraction	NOUN
asir-1804	199	54	for	for	ADP
asir-1804	199	55	the	the	DET
asir-1804	199	56	lens	lens	NOUN
asir-1804	199	57	and	and	CCONJ
asir-1804	199	58	the	the	DET
asir-1804	199	59	back	back	ADJ
asir-1804	199	60	medium	medium	NOUN
asir-1804	199	61	.	.	PUNCT
asir-1804	200	1	these	these	DET
asir-1804	200	2	changes	change	NOUN
asir-1804	200	3	can	can	AUX
asir-1804	200	4	be	be	AUX
asir-1804	200	5	done	do	VERB
asir-1804	200	6	when	when	SCONJ
asir-1804	200	7	the	the	DET
asir-1804	200	8	user	user	NOUN
asir-1804	200	9	presses	press	VERB
asir-1804	200	10	the	the	DET
asir-1804	200	11	button	button	NOUN
asir-1804	200	12	“	"	PUNCT
asir-1804	200	13	show	show	VERB
asir-1804	200	14	form	form	NOUN
asir-1804	200	15	for	for	ADP
asir-1804	200	16	parameters	parameter	NOUN
asir-1804	200	17	”	"	PUNCT
asir-1804	200	18	.	.	PUNCT
asir-1804	201	1	then	then	ADV
asir-1804	201	2	a	a	DET
asir-1804	201	3	form	form	NOUN
asir-1804	201	4	appears	appear	VERB
asir-1804	201	5	with	with	ADP
asir-1804	201	6	all	all	DET
asir-1804	201	7	the	the	DET
asir-1804	201	8	scroll	scroll	NOUN
asir-1804	201	9	bars	bar	NOUN
asir-1804	201	10	and	and	CCONJ
asir-1804	201	11	the	the	DET
asir-1804	201	12	buttons	button	NOUN
asir-1804	201	13	.	.	PUNCT
asir-1804	202	1	some	some	DET
asir-1804	202	2	buttons	button	NOUN
asir-1804	202	3	are	be	AUX
asir-1804	202	4	put	put	VERB
asir-1804	202	5	outside	outside	ADP
asir-1804	202	6	the	the	DET
asir-1804	202	7	form	form	NOUN
asir-1804	202	8	.	.	PUNCT
asir-1804	203	1	when	when	SCONJ
asir-1804	203	2	the	the	DET
asir-1804	203	3	form	form	NOUN
asir-1804	203	4	appears	appear	VERB
asir-1804	203	5	then	then	ADV
asir-1804	203	6	the	the	DET
asir-1804	203	7	upper	upper	ADJ
asir-1804	203	8	graphs	graph	NOUN
asir-1804	203	9	which	which	PRON
asir-1804	203	10	appear	appear	VERB
asir-1804	203	11	(	(	PUNCT
asir-1804	203	12	like	like	INTJ
asir-1804	203	13	in	in	ADP
asir-1804	203	14	figure	figure	NOUN
asir-1804	203	15	11	11	NUM
asir-1804	203	16	)	)	PUNCT
asir-1804	203	17	are	be	AUX
asir-1804	203	18	showing	show	VERB
asir-1804	203	19	the	the	DET
asir-1804	203	20	rays	ray	NOUN
asir-1804	203	21	and	and	CCONJ
asir-1804	203	22	wave	wave	VERB
asir-1804	203	23	fronts	front	NOUN
asir-1804	203	24	from	from	ADP
asir-1804	203	25	the	the	DET
asir-1804	203	26	point	point	NOUN
asir-1804	203	27	(	(	PUNCT
asir-1804	203	28	x0	x0	PROPN
asir-1804	203	29	,	,	PUNCT
asir-1804	203	30	0	0	NUM
asir-1804	203	31	)	)	PUNCT
asir-1804	203	32	to	to	ADP
asir-1804	203	33	the	the	DET
asir-1804	203	34	focal	focal	ADJ
asir-1804	203	35	back	back	NOUN
asir-1804	203	36	point	point	NOUN
asir-1804	203	37	(	(	PUNCT
asir-1804	203	38	f	f	X
asir-1804	203	39	,	,	PUNCT
asir-1804	203	40	0	0	NUM
asir-1804	203	41	)	)	PUNCT
asir-1804	203	42	while	while	SCONJ
asir-1804	203	43	the	the	DET
asir-1804	203	44	3rd	3rd	ADJ
asir-1804	203	45	graph	graph	NOUN
asir-1804	203	46	shows	show	VERB
asir-1804	203	47	the	the	DET
asir-1804	203	48	rays	ray	NOUN
asir-1804	203	49	and	and	CCONJ
asir-1804	203	50	wave	wave	VERB
asir-1804	203	51	fronts	front	NOUN
asir-1804	203	52	from	from	ADP
asir-1804	203	53	the	the	DET
asir-1804	203	54	source	source	NOUN
asir-1804	203	55	at	at	ADP
asir-1804	203	56	(	(	PUNCT
asir-1804	203	57	x0	x0	PROPN
asir-1804	203	58	,	,	PUNCT
asir-1804	203	59	y0≠0	y0≠0	PROPN
asir-1804	203	60	)	)	PUNCT
asir-1804	203	61	.	.	PUNCT
asir-1804	204	1	there	there	PRON
asir-1804	204	2	are	be	VERB
asir-1804	204	3	two	two	NUM
asir-1804	204	4	buttons	button	NOUN
asir-1804	204	5	that	that	PRON
asir-1804	204	6	are	be	AUX
asir-1804	204	7	shown	show	VERB
asir-1804	204	8	on	on	ADP
asir-1804	204	9	the	the	DET
asir-1804	204	10	right	right	ADJ
asir-1804	204	11	side	side	NOUN
asir-1804	204	12	of	of	ADP
asir-1804	204	13	the	the	DET
asir-1804	204	14	figure	figure	NOUN
asir-1804	204	15	10	10	NUM
asir-1804	204	16	(	(	PUNCT
asir-1804	204	17	not	not	PART
asir-1804	204	18	located	locate	VERB
asir-1804	204	19	on	on	ADP
asir-1804	204	20	the	the	DET
asir-1804	204	21	form	form	NOUN
asir-1804	204	22	)	)	PUNCT
asir-1804	204	23	.	.	PUNCT
asir-1804	205	1	which	which	PRON
asir-1804	205	2	permit	permit	VERB
asir-1804	205	3	the	the	DET
asir-1804	205	4	user	user	NOUN
asir-1804	205	5	to	to	PART
asir-1804	205	6	see	see	VERB
asir-1804	205	7	also	also	ADV
asir-1804	205	8	in	in	ADP
asir-1804	205	9	the	the	DET
asir-1804	205	10	upper	upper	ADJ
asir-1804	205	11	graphs	graph	NOUN
asir-1804	205	12	the	the	DET
asir-1804	205	13	rays	ray	NOUN
asir-1804	205	14	from	from	ADP
asir-1804	205	15	the	the	DET
asir-1804	205	16	source	source	NOUN
asir-1804	205	17	at	at	ADP
asir-1804	205	18	y0≠0	y0≠0	PROPN
asir-1804	205	19	.	.	PUNCT
asir-1804	206	1	also	also	ADV
asir-1804	206	2	outside	outside	ADP
asir-1804	206	3	the	the	DET
asir-1804	206	4	form	form	NOUN
asir-1804	206	5	are	be	AUX
asir-1804	206	6	3	3	NUM
asir-1804	206	7	buttons	button	NOUN
asir-1804	206	8	which	which	PRON
asir-1804	206	9	permit	permit	VERB
asir-1804	206	10	the	the	DET
asir-1804	206	11	user	user	NOUN
asir-1804	206	12	to	to	PART
asir-1804	206	13	start	start	VERB
asir-1804	206	14	the	the	DET
asir-1804	206	15	movement	movement	NOUN
asir-1804	206	16	of	of	ADP
asir-1804	206	17	the	the	DET
asir-1804	206	18	wave	wave	NOUN
asir-1804	206	19	fronts	front	NOUN
asir-1804	206	20	and	and	CCONJ
asir-1804	206	21	to	to	PART
asir-1804	206	22	stop	stop	VERB
asir-1804	206	23	them	they	PRON
asir-1804	206	24	.	.	PUNCT
asir-1804	207	1	a	a	DET
asir-1804	207	2	horizontal	horizontal	ADJ
asir-1804	207	3	scroll	scroll	NOUN
asir-1804	207	4	bar	bar	NOUN
asir-1804	207	5	permits	permit	VERB
asir-1804	207	6	the	the	DET
asir-1804	207	7	user	user	NOUN
asir-1804	207	8	to	to	PART
asir-1804	207	9	move	move	VERB
asir-1804	207	10	the	the	DET
asir-1804	207	11	wave	wave	NOUN
asir-1804	207	12	fronts	front	NOUN
asir-1804	207	13	back	back	ADV
asir-1804	207	14	and	and	CCONJ
asir-1804	207	15	forth	forth	ADV
asir-1804	207	16	.	.	PUNCT
asir-1804	208	1	when	when	SCONJ
asir-1804	208	2	we	we	PRON
asir-1804	208	3	impose	impose	VERB
asir-1804	208	4	the	the	DET
asir-1804	208	5	condition	condition	NOUN
asir-1804	208	6	that	that	SCONJ
asir-1804	208	7	the	the	DET
asir-1804	208	8	back	back	NOUN
asir-1804	208	9	and	and	CCONJ
asir-1804	208	10	the	the	DET
asir-1804	208	11	front	front	ADJ
asir-1804	208	12	surfaces	surface	NOUN
asir-1804	208	13	meet	meet	VERB
asir-1804	208	14	at	at	ADP
asir-1804	208	15	x=0	x=0	PROPN
asir-1804	208	16	then	then	ADV
asir-1804	208	17	we	we	PRON
asir-1804	208	18	have	have	VERB
asir-1804	208	19	a	a	DET
asir-1804	208	20	modified	modify	VERB
asir-1804	208	21	behavior	behavior	NOUN
asir-1804	208	22	of	of	ADP
asir-1804	208	23	the	the	DET
asir-1804	208	24	spherical	spherical	ADJ
asir-1804	208	25	surface	surface	NOUN
asir-1804	208	26	on	on	ADP
asir-1804	208	27	the	the	DET
asir-1804	208	28	front	front	NOUN
asir-1804	208	29	.	.	PUNCT
asir-1804	209	1	now	now	ADV
asir-1804	209	2	we	we	PRON
asir-1804	209	3	get	get	VERB
asir-1804	209	4	a	a	DET
asir-1804	209	5	more	more	ADV
asir-1804	209	6	classical	classical	ADJ
asir-1804	209	7	“	"	PUNCT
asir-1804	209	8	huygens	huygens	PROPN
asir-1804	209	9	lens	len	NOUN
asir-1804	209	10	”	"	PUNCT
asir-1804	209	11	(	(	PUNCT
asir-1804	209	12	figure	figure	NOUN
asir-1804	209	13	12	12	NUM
asir-1804	209	14	)	)	PUNCT
asir-1804	209	15	.	.	PUNCT
asir-1804	210	1	to	to	PART
asir-1804	210	2	draw	draw	VERB
asir-1804	210	3	the	the	DET
asir-1804	210	4	rays	ray	NOUN
asir-1804	210	5	in	in	ADP
asir-1804	210	6	the	the	DET
asir-1804	210	7	two	two	NUM
asir-1804	210	8	lenses	lense	NOUN
asir-1804	210	9	we	we	PRON
asir-1804	210	10	use	use	VERB
asir-1804	210	11	the	the	DET
asir-1804	210	12	parametric	parametric	ADJ
asir-1804	210	13	equations	equation	NOUN
asir-1804	210	14	of	of	ADP
asir-1804	210	15	the	the	DET
asir-1804	210	16	circle	circle	NOUN
asir-1804	210	17	and	and	CCONJ
asir-1804	210	18	the	the	DET
asir-1804	210	19	hyperbola	hyperbola	PROPN
asir-1804	210	20	.	.	PUNCT
asir-1804	211	1	so	so	ADV
asir-1804	211	2	instead	instead	ADV
asir-1804	211	3	of	of	ADP
asir-1804	211	4	the	the	DET
asir-1804	211	5	form	form	NOUN
asir-1804	211	6	x2+y2	x2+y2	NOUN
asir-1804	211	7	=	=	NOUN
asir-1804	211	8	r2	r2	NOUN
asir-1804	211	9	where	where	SCONJ
asir-1804	211	10	r	r	NOUN
asir-1804	211	11	is	be	AUX
asir-1804	211	12	the	the	DET
asir-1804	211	13	radius	radius	NOUN
asir-1804	211	14	of	of	ADP
asir-1804	211	15	the	the	DET
asir-1804	211	16	circle	circle	NOUN
asir-1804	211	17	we	we	PRON
asir-1804	211	18	use	use	VERB
asir-1804	211	19	x=-r·cos(φ	x=-r·cos(φ	PROPN
asir-1804	211	20	)	)	PUNCT
asir-1804	211	21	,	,	PUNCT
asir-1804	211	22	y	y	PROPN
asir-1804	211	23	=	=	NOUN
asir-1804	211	24	r·sin(φ	r·sin(φ	PROPN
asir-1804	211	25	)	)	PUNCT
asir-1804	211	26	.	.	PUNCT
asir-1804	212	1	for	for	ADP
asir-1804	212	2	the	the	DET
asir-1804	212	3	case	case	NOUN
asir-1804	212	4	of	of	ADP
asir-1804	212	5	a	a	DET
asir-1804	212	6	hyperbolic	hyperbolic	ADJ
asir-1804	212	7	lens	lens	NOUN
asir-1804	212	8	instead	instead	ADV
asir-1804	212	9	of	of	ADP
asir-1804	212	10	𝑦	𝑦	NOUN
asir-1804	212	11	=	=	PUNCT
asir-1804	212	12	𝑏	𝑏	ADP
asir-1804	212	13	∙	∙	PROPN
asir-1804	212	14	√	√	NUM
asir-1804	212	15	(	(	PUNCT
asir-1804	212	16	𝑥+2𝑎)2	𝑥+2𝑎)2	NOUN
asir-1804	212	17	𝑎2	𝑎2	NOUN
asir-1804	212	18	−	−	PROPN
asir-1804	212	19	1	1	NUM
asir-1804	212	20	we	we	PRON
asir-1804	212	21	use	use	VERB
asir-1804	212	22	x=-2·a+a	x=-2·a+a	PROPN
asir-1804	212	23	/	/	SYM
asir-1804	212	24	cos(φ	cos(φ	NOUN
asir-1804	212	25	)	)	PUNCT
asir-1804	212	26	,	,	PUNCT
asir-1804	212	27	y	y	PROPN
asir-1804	212	28	=	=	PROPN
asir-1804	212	29	b·tan(φ	b·tan(φ	PROPN
asir-1804	212	30	)	)	PUNCT
asir-1804	212	31	.	.	PUNCT
asir-1804	213	1	this	this	PRON
asir-1804	213	2	permits	permit	VERB
asir-1804	213	3	to	to	PART
asir-1804	213	4	use	use	VERB
asir-1804	213	5	a	a	DET
asir-1804	213	6	similar	similar	ADJ
asir-1804	213	7	method	method	NOUN
asir-1804	213	8	to	to	PART
asir-1804	213	9	calculate	calculate	VERB
asir-1804	213	10	the	the	DET
asir-1804	213	11	rays	ray	NOUN
asir-1804	213	12	.	.	PUNCT
asir-1804	214	1	the	the	DET
asir-1804	214	2	rays	ray	NOUN
asir-1804	214	3	from	from	ADP
asir-1804	214	4	an	an	DET
asir-1804	214	5	object	object	NOUN
asir-1804	214	6	that	that	PRON
asir-1804	214	7	is	be	AUX
asir-1804	214	8	located	locate	VERB
asir-1804	214	9	at	at	ADP
asir-1804	214	10	the	the	DET
asir-1804	214	11	point	point	NOUN
asir-1804	214	12	(	(	PUNCT
asir-1804	214	13	x0	x0	PROPN
asir-1804	214	14	,	,	PUNCT
asir-1804	214	15	y0	y0	PROPN
asir-1804	214	16	)	)	PUNCT
asir-1804	214	17	are	be	AUX
asir-1804	214	18	calculated	calculate	VERB
asir-1804	214	19	for	for	ADP
asir-1804	214	20	both	both	CCONJ
asir-1804	214	21	the	the	DET
asir-1804	214	22	lens	lens	NOUN
asir-1804	214	23	with	with	ADP
asir-1804	214	24	a	a	DET
asir-1804	214	25	spherical	spherical	ADJ
asir-1804	214	26	surface	surface	NOUN
asir-1804	214	27	in	in	ADP
asir-1804	214	28	front	front	NOUN
asir-1804	214	29	and	and	CCONJ
asir-1804	214	30	a	a	DET
asir-1804	214	31	hyperbolic	hyperbolic	ADJ
asir-1804	214	32	surface	surface	NOUN
asir-1804	214	33	in	in	ADP
asir-1804	214	34	front	front	NOUN
asir-1804	214	35	by	by	ADP
asir-1804	214	36	the	the	DET
asir-1804	214	37	same	same	ADJ
asir-1804	214	38	method	method	NOUN
asir-1804	214	39	.	.	PUNCT
asir-1804	215	1	we	we	PRON
asir-1804	215	2	choose	choose	VERB
asir-1804	215	3	a	a	DET
asir-1804	215	4	point	point	NOUN
asir-1804	215	5	(	(	PUNCT
asir-1804	215	6	x2	x2	NOUN
asir-1804	215	7	,	,	PUNCT
asir-1804	215	8	y2	y2	PROPN
asir-1804	215	9	)	)	PUNCT
asir-1804	215	10	on	on	ADP
asir-1804	215	11	the	the	DET
asir-1804	215	12	back	back	ADJ
asir-1804	215	13	surface	surface	NOUN
asir-1804	215	14	of	of	ADP
asir-1804	215	15	the	the	DET
asir-1804	215	16	lens	len	NOUN
asir-1804	215	17	and	and	CCONJ
asir-1804	215	18	we	we	PRON
asir-1804	215	19	try	try	VERB
asir-1804	215	20	to	to	PART
asir-1804	215	21	find	find	VERB
asir-1804	215	22	a	a	DET
asir-1804	215	23	point	point	NOUN
asir-1804	215	24	(	(	PUNCT
asir-1804	215	25	x1	x1	PROPN
asir-1804	215	26	,	,	PUNCT
asir-1804	215	27	y1	y1	PROPN
asir-1804	215	28	)	)	PUNCT
asir-1804	215	29	on	on	ADP
asir-1804	215	30	the	the	DET
asir-1804	215	31	front	front	ADJ
asir-1804	215	32	surface	surface	NOUN
asir-1804	215	33	for	for	ADP
asir-1804	215	34	which	which	PRON
asir-1804	215	35	the	the	DET
asir-1804	215	36	time	time	NOUN
asir-1804	215	37	from	from	ADP
asir-1804	215	38	the	the	DET
asir-1804	215	39	source	source	NOUN
asir-1804	215	40	(	(	PUNCT
asir-1804	215	41	x0	x0	PROPN
asir-1804	215	42	,	,	PUNCT
asir-1804	215	43	y0	y0	PROPN
asir-1804	215	44	)	)	PUNCT
asir-1804	215	45	to	to	ADP
asir-1804	215	46	(	(	PUNCT
asir-1804	215	47	x1	x1	PROPN
asir-1804	215	48	,	,	PUNCT
asir-1804	215	49	y1	y1	PROPN
asir-1804	215	50	)	)	PUNCT
asir-1804	215	51	and	and	CCONJ
asir-1804	215	52	then	then	ADV
asir-1804	215	53	to	to	PART
asir-1804	215	54	(	(	PUNCT
asir-1804	215	55	x2	x2	PROPN
asir-1804	215	56	,	,	PUNCT
asir-1804	215	57	y2	y2	PROPN
asir-1804	215	58	)	)	PUNCT
asir-1804	215	59	is	be	AUX
asir-1804	215	60	the	the	DET
asir-1804	215	61	least	least	ADJ
asir-1804	215	62	.	.	PUNCT
asir-1804	216	1	this	this	PRON
asir-1804	216	2	is	be	AUX
asir-1804	216	3	accomplished	accomplish	VERB
asir-1804	216	4	by	by	ADP
asir-1804	216	5	a	a	DET
asir-1804	216	6	“	"	PUNCT
asir-1804	216	7	user	user	NOUN
asir-1804	216	8	’s	’s	PART
asir-1804	216	9	”	"	PUNCT
asir-1804	216	10	function	function	NOUN
asir-1804	216	11	.	.	PUNCT
asir-1804	217	1	the	the	DET
asir-1804	217	2	perpendicular	perpendicular	NOUN
asir-1804	217	3	to	to	ADP
asir-1804	217	4	this	this	DET
asir-1804	217	5	point	point	NOUN
asir-1804	217	6	(	(	PUNCT
asir-1804	217	7	x2	x2	NOUN
asir-1804	217	8	,	,	PUNCT
asir-1804	217	9	y2	y2	PROPN
asir-1804	217	10	)	)	PUNCT
asir-1804	217	11	is	be	AUX
asir-1804	217	12	determined	determine	VERB
asir-1804	217	13	by	by	ADP
asir-1804	217	14	another	another	DET
asir-1804	217	15	“	"	PUNCT
asir-1804	217	16	user	user	NOUN
asir-1804	217	17	’s	’s	PART
asir-1804	217	18	”	"	PUNCT
asir-1804	217	19	function	function	NOUN
asir-1804	217	20	and	and	CCONJ
asir-1804	217	21	then	then	ADV
asir-1804	217	22	the	the	DET
asir-1804	217	23	continuation	continuation	NOUN
asir-1804	217	24	of	of	ADP
asir-1804	217	25	the	the	DET
asir-1804	217	26	rays	ray	NOUN
asir-1804	217	27	to	to	ADP
asir-1804	217	28	a	a	DET
asir-1804	217	29	distant	distant	ADJ
asir-1804	217	30	point	point	NOUN
asir-1804	217	31	(	(	PUNCT
asir-1804	217	32	not	not	PART
asir-1804	217	33	the	the	DET
asir-1804	217	34	“	"	PUNCT
asir-1804	217	35	focus	focus	NOUN
asir-1804	217	36	”	"	PUNCT
asir-1804	217	37	)	)	PUNCT
asir-1804	217	38	.	.	PUNCT
asir-1804	218	1	on	on	ADP
asir-1804	218	2	the	the	DET
asir-1804	218	3	basis	basis	NOUN
asir-1804	218	4	of	of	ADP
asir-1804	218	5	the	the	DET
asir-1804	218	6	rays	ray	NOUN
asir-1804	218	7	we	we	PRON
asir-1804	218	8	determine	determine	VERB
asir-1804	218	9	the	the	DET
asir-1804	218	10	wave	wave	NOUN
asir-1804	218	11	fronts	front	NOUN
asir-1804	218	12	.	.	PUNCT
asir-1804	219	1	figure	figure	NOUN
asir-1804	219	2	12	12	NUM
asir-1804	219	3	.	.	PUNCT
asir-1804	220	1	huygens	huygen	NOUN
asir-1804	220	2	lens	lens	VERB
asir-1804	220	3	with	with	ADP
asir-1804	220	4	front	front	ADJ
asir-1804	220	5	surface	surface	NOUN
asir-1804	220	6	spherical	spherical	ADJ
asir-1804	220	7	and	and	CCONJ
asir-1804	220	8	back	back	ADV
asir-1804	220	9	meeting	meet	VERB
asir-1804	220	10	the	the	DET
asir-1804	220	11	front	front	NOUN
asir-1804	220	12	in	in	ADP
asir-1804	220	13	x=0	x=0	PROPN
asir-1804	220	14	.	.	PUNCT
asir-1804	221	1	in	in	ADP
asir-1804	221	2	this	this	DET
asir-1804	221	3	case	case	NOUN
asir-1804	221	4	the	the	DET
asir-1804	221	5	front	front	ADJ
asir-1804	221	6	circle	circle	NOUN
asir-1804	221	7	has	have	VERB
asir-1804	221	8	a	a	DET
asir-1804	221	9	movable	movable	ADJ
asir-1804	221	10	center	center	NOUN
asir-1804	221	11	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1804	221	12	applied	apply	VERB
asir-1804	221	13	science	science	NOUN
asir-1804	221	14	and	and	CCONJ
asir-1804	221	15	innovative	innovative	ADJ
asir-1804	221	16	research	research	NOUN
asir-1804	221	17	vol	vol	NOUN
asir-1804	221	18	.	.	PUNCT
asir-1804	222	1	3	3	NUM
asir-1804	222	2	,	,	PUNCT
asir-1804	222	3	no	no	INTJ
asir-1804	222	4	.	.	NOUN
asir-1804	222	5	1	1	NUM
asir-1804	222	6	,	,	PUNCT
asir-1804	222	7	2019	2019	NUM
asir-1804	222	8	27	27	NUM
asir-1804	222	9	published	publish	VERB
asir-1804	222	10	by	by	ADP
asir-1804	222	11	scholink	scholink	PROPN
asir-1804	222	12	inc	inc	PROPN
asir-1804	222	13	.	.	PROPN
asir-1804	222	14	as	as	SCONJ
asir-1804	222	15	it	it	PRON
asir-1804	222	16	can	can	AUX
asir-1804	222	17	be	be	AUX
asir-1804	222	18	seen	see	VERB
asir-1804	222	19	the	the	DET
asir-1804	222	20	hyperbolic	hyperbolic	ADJ
asir-1804	222	21	lens	lens	NOUN
asir-1804	222	22	has	have	VERB
asir-1804	222	23	a	a	DET
asir-1804	222	24	better	well	ADJ
asir-1804	222	25	behavior	behavior	NOUN
asir-1804	222	26	for	for	ADP
asir-1804	222	27	a	a	DET
asir-1804	222	28	source	source	NOUN
asir-1804	222	29	at	at	ADP
asir-1804	222	30	y0≠0	y0≠0	PROPN
asir-1804	222	31	.	.	PUNCT
asir-1804	223	1	the	the	DET
asir-1804	223	2	third	third	ADJ
asir-1804	223	3	graph	graph	NOUN
asir-1804	223	4	in	in	ADP
asir-1804	223	5	figure	figure	NOUN
asir-1804	223	6	11	11	NUM
asir-1804	223	7	is	be	AUX
asir-1804	223	8	used	use	VERB
asir-1804	223	9	to	to	PART
asir-1804	223	10	show	show	VERB
asir-1804	223	11	the	the	DET
asir-1804	223	12	case	case	NOUN
asir-1804	223	13	of	of	ADP
asir-1804	223	14	rays	ray	NOUN
asir-1804	223	15	and	and	CCONJ
asir-1804	223	16	wave	wave	VERB
asir-1804	223	17	fronts	front	NOUN
asir-1804	223	18	for	for	ADP
asir-1804	223	19	the	the	DET
asir-1804	223	20	ray	ray	NOUN
asir-1804	223	21	having	have	VERB
asir-1804	223	22	source	source	NOUN
asir-1804	223	23	at	at	ADP
asir-1804	223	24	(	(	PUNCT
asir-1804	223	25	x0	x0	PROPN
asir-1804	223	26	,	,	PUNCT
asir-1804	223	27	y0	y0	PROPN
asir-1804	223	28	)	)	PUNCT
asir-1804	223	29	we	we	PRON
asir-1804	223	30	need	need	VERB
asir-1804	223	31	more	more	ADJ
asir-1804	223	32	rays	ray	NOUN
asir-1804	223	33	in	in	ADP
asir-1804	223	34	the	the	DET
asir-1804	223	35	spherical	spherical	ADJ
asir-1804	223	36	case	case	NOUN
asir-1804	223	37	to	to	PART
asir-1804	223	38	determine	determine	VERB
asir-1804	223	39	the	the	DET
asir-1804	223	40	wave	wave	NOUN
asir-1804	223	41	fronts	front	NOUN
asir-1804	223	42	.	.	PUNCT
asir-1804	224	1	note	note	NOUN
asir-1804	224	2	:	:	PUNCT
asir-1804	224	3	the	the	DET
asir-1804	224	4	spreadsheet	spreadsheet	NOUN
asir-1804	224	5	spherical	spherical	ADJ
asir-1804	224	6	and	and	CCONJ
asir-1804	224	7	huygens	huygen	NOUN
asir-1804	224	8	lens	lens	NOUN
asir-1804	224	9	with	with	ADP
asir-1804	224	10	forms	form	NOUN
asir-1804	224	11	and	and	CCONJ
asir-1804	224	12	macros.xlsm	macros.xlsm	NOUN
asir-1804	224	13	can	can	AUX
asir-1804	224	14	be	be	AUX
asir-1804	224	15	downloaded	download	VERB
asir-1804	224	16	from	from	ADP
asir-1804	224	17	http://www.kyriakosxolio.gr	http://www.kyriakosxolio.gr	NOUN
asir-1804	224	18	and	and	CCONJ
asir-1804	224	19	click	click	VERB
asir-1804	224	20	on	on	ADP
asir-1804	224	21	lenses	lense	NOUN
asir-1804	224	22	spherical	spherical	ADJ
asir-1804	224	23	and	and	CCONJ
asir-1804	224	24	huygens	huygens	PROPN
asir-1804	224	25	references	reference	NOUN
asir-1804	224	26	hendricks	hendrick	NOUN
asir-1804	224	27	,	,	PUNCT
asir-1804	224	28	b.	b.	PROPN
asir-1804	224	29	,	,	PUNCT
asir-1804	224	30	&	&	CCONJ
asir-1804	224	31	kuiper	kuiper	PROPN
asir-1804	224	32	,	,	PUNCT
asir-1804	224	33	s.	s.	PROPN
asir-1804	224	34	(	(	PUNCT
asir-1804	224	35	2004	2004	NUM
asir-1804	224	36	)	)	PUNCT
asir-1804	224	37	.	.	PUNCT
asir-1804	225	1	through	through	ADP
asir-1804	225	2	lens	lens	NOUN
asir-1804	225	3	sharply	sharply	ADV
asir-1804	225	4	,	,	PUNCT
asir-1804	225	5	ieee	ieee	NOUN
asir-1804	225	6	spectrum	spectrum	NOUN
asir-1804	225	7	(	(	PUNCT
asir-1804	225	8	pp	pp	ADJ
asir-1804	225	9	.	.	PUNCT
asir-1804	225	10	32	32	NUM
asir-1804	225	11	-	-	SYM
asir-1804	225	12	36	36	NUM
asir-1804	225	13	)	)	PUNCT
asir-1804	225	14	.	.	PUNCT
asir-1804	226	1	rashed	rashe	VERB
asir-1804	226	2	r.:1992	r.:1992	PROPN
asir-1804	226	3	,	,	PUNCT
asir-1804	226	4	optique	optique	X
asir-1804	226	5	et	et	NOUN
asir-1804	226	6	mathematiques	mathematique	NOUN
asir-1804	226	7	:	:	PUNCT
asir-1804	226	8	recherches	recherche	VERB
asir-1804	226	9	sur	sur	PROPN
asir-1804	226	10	l’histoire	l’histoire	PROPN
asir-1804	226	11	de	de	X
asir-1804	226	12	la	la	PROPN
asir-1804	226	13	pensee	pensee	PROPN
asir-1804	226	14	scientifique	scientifique	PROPN
asir-1804	226	15	en	en	X
asir-1804	226	16	arabe	arabe	X
asir-1804	226	17	(	(	PUNCT
asir-1804	226	18	collected	collect	VERB
asir-1804	226	19	works	work	NOUN
asir-1804	226	20	)	)	PUNCT
asir-1804	226	21	,	,	PUNCT
asir-1804	226	22	variorum	variorum	PROPN
asir-1804	226	23	.	.	PUNCT
asir-1804	226	24	huygens	huygens	PROPN
asir-1804	226	25	,	,	PUNCT
asir-1804	226	26	c.	c.	PROPN
asir-1804	226	27	(	(	PUNCT
asir-1804	226	28	1966	1966	NUM
asir-1804	226	29	)	)	PUNCT
asir-1804	226	30	.	.	PUNCT
asir-1804	227	1	traite	traite	PROPN
asir-1804	227	2	de	de	X
asir-1804	227	3	la	la	X
asir-1804	227	4	lumière	lumière	PROPN
asir-1804	227	5	.	.	PUNCT
asir-1804	228	1	reprinting	reprint	VERB
asir-1804	228	2	of	of	ADP
asir-1804	228	3	the	the	DET
asir-1804	228	4	original	original	ADJ
asir-1804	228	5	1690	1690	NUM
asir-1804	228	6	edition	edition	NOUN
asir-1804	228	7	by	by	ADP
asir-1804	228	8	kripssthoek	kripssthoek	PROPN
asir-1804	228	9	,	,	PUNCT
asir-1804	228	10	netherlands	netherlands	PROPN
asir-1804	228	11	.	.	PUNCT
asir-1804	229	1	mihas	miha	NOUN
asir-1804	229	2	,	,	PUNCT
asir-1804	229	3	p.	p.	NOUN
asir-1804	229	4	(	(	PUNCT
asir-1804	229	5	1998	1998	NUM
asir-1804	229	6	)	)	PUNCT
asir-1804	229	7	.	.	PUNCT
asir-1804	230	1	using	use	VERB
asir-1804	230	2	spreadsheets	spreadsheet	NOUN
asir-1804	230	3	to	to	PART
asir-1804	230	4	find	find	VERB
asir-1804	230	5	focal	focal	ADJ
asir-1804	230	6	lengths	length	NOUN
asir-1804	230	7	,	,	PUNCT
asir-1804	230	8	computereducation	computereducation	NOUN
asir-1804	230	9	,	,	PUNCT
asir-1804	230	10	90	90	NUM
asir-1804	230	11	.	.	PUNCT
asir-1804	231	1	mihas	miha	NOUN
asir-1804	231	2	,	,	PUNCT
asir-1804	231	3	p.	p.	NOUN
asir-1804	231	4	(	(	PUNCT
asir-1804	231	5	2008	2008	NUM
asir-1804	231	6	)	)	PUNCT
asir-1804	231	7	.	.	PUNCT
asir-1804	232	1	the	the	DET
asir-1804	232	2	problem	problem	NOUN
asir-1804	232	3	of	of	ADP
asir-1804	232	4	focusing	focus	VERB
asir-1804	232	5	and	and	CCONJ
asir-1804	232	6	real	real	ADJ
asir-1804	232	7	images	image	NOUN
asir-1804	232	8	.	.	PUNCT
asir-1804	233	1	european	european	PROPN
asir-1804	233	2	journal	journal	PROPN
asir-1804	233	3	of	of	ADP
asir-1804	233	4	physics	physics	PROPN
asir-1804	233	5	,	,	PUNCT
asir-1804	233	6	29	29	NUM
asir-1804	233	7	,	,	PUNCT
asir-1804	233	8	539	539	NUM
asir-1804	233	9	-	-	SYM
asir-1804	233	10	555	555	NUM
asir-1804	233	11	.	.	PUNCT
asir-1804	234	1	https://doi.org/10.1088/0143-0807/29/3/014	https://doi.org/10.1088/0143-0807/29/3/014	PROPN
asir-1804	234	2	mihas	mihas	PROPN
asir-1804	234	3	,	,	PUNCT
asir-1804	234	4	p.	p.	NOUN
asir-1804	234	5	(	(	PUNCT
asir-1804	234	6	2012	2012	NUM
asir-1804	234	7	)	)	PUNCT
asir-1804	234	8	.	.	PUNCT
asir-1804	235	1	software	software	NOUN
asir-1804	235	2	for	for	ADP
asir-1804	235	3	fermat	fermat	PROPN
asir-1804	235	4	’s	’s	PART
asir-1804	235	5	principle	principle	NOUN
asir-1804	235	6	and	and	CCONJ
asir-1804	235	7	lenses	lense	NOUN
asir-1804	235	8	.	.	PUNCT
asir-1804	236	1	physics	physics	NOUN
asir-1804	236	2	education	education	PROPN
asir-1804	236	3	,	,	PUNCT
asir-1804	236	4	27	27	NUM
asir-1804	236	5	,	,	PUNCT
asir-1804	236	6	313	313	NUM
asir-1804	236	7	-	-	SYM
asir-1804	236	8	320	320	NUM
asir-1804	236	9	.	.	PUNCT
asir-1804	237	1	https://doi.org/10.1088/0031-9120/47/3/313	https://doi.org/10.1088/0031-9120/47/3/313	PROPN
asir-1804	237	2	pedrotti	pedrotti	PROPN
asir-1804	237	3	,	,	PUNCT
asir-1804	237	4	f.	f.	PROPN
asir-1804	237	5	l.	l.	PROPN
asir-1804	237	6	,	,	PUNCT
asir-1804	237	7	&	&	CCONJ
asir-1804	237	8	pedrotti	pedrotti	PROPN
asir-1804	237	9	,	,	PUNCT
asir-1804	237	10	l.	l.	PROPN
asir-1804	237	11	m.	m.	PROPN
asir-1804	237	12	(	(	PUNCT
asir-1804	237	13	2014	2014	NUM
asir-1804	237	14	)	)	PUNCT
asir-1804	237	15	.	.	PUNCT
asir-1804	238	1	introduction	introduction	NOUN
asir-1804	238	2	to	to	ADP
asir-1804	238	3	optics	optic	NOUN
asir-1804	238	4	.	.	PUNCT
asir-1804	239	1	pearson	pearson	PROPN
asir-1804	239	2	new	new	PROPN
asir-1804	239	3	international	international	PROPN
asir-1804	239	4	edition	edition	PROPN
asir-1804	239	5	.	.	PUNCT
asir-1804	240	1	reinhard	reinhard	PROPN
asir-1804	240	2	,	,	PUNCT
asir-1804	240	3	jenny	jenny	PROPN
asir-1804	240	4	.	.	PUNCT
asir-1804	241	1	(	(	PUNCT
asir-1804	241	2	2001	2001	NUM
asir-1804	241	3	)	)	PUNCT
asir-1804	241	4	.	.	PUNCT
asir-1804	242	1	fundamental	fundamental	ADJ
asir-1804	242	2	of	of	ADP
asir-1804	242	3	optics	optic	NOUN
asir-1804	242	4	an	an	DET
asir-1804	242	5	introduction	introduction	NOUN
asir-1804	242	6	to	to	ADP
asir-1804	242	7	beginners	beginner	NOUN
asir-1804	242	8	.	.	PUNCT
asir-1804	243	1	retrieved	retrieve	VERB
asir-1804	243	2	from	from	ADP
asir-1804	243	3	https//www.volpi	https//www.volpi	PROPN
asir-1804	243	4	/	/	SYM
asir-1804	243	5	ch	ch	PROPN
asir-1804	243	6	/	/	SYM
asir-1804	243	7	en	en	NOUN
asir-1804	243	8	/	/	SYM
asir-1804	243	9	contact	contact	NOUN
asir-1804	243	10	-	-	PUNCT
asir-1804	243	11	services	service	NOUN
asir-1804	243	12	/	/	SYM
asir-1804	243	13	download	download	PROPN
asir-1804	243	14	tyler	tyler	PROPN
asir-1804	243	15	,	,	PUNCT
asir-1804	243	16	f.	f.	PROPN
asir-1804	243	17	(	(	PUNCT
asir-1804	243	18	1977	1977	NUM
asir-1804	243	19	)	)	PUNCT
asir-1804	243	20	.	.	PUNCT
asir-1804	244	1	a	a	DET
asir-1804	244	2	laboratory	laboratory	NOUN
asir-1804	244	3	manual	manual	NOUN
asir-1804	244	4	of	of	ADP
asir-1804	244	5	physics	physics	PROPN
asir-1804	244	6	.	.	PUNCT
asir-1804	245	1	walther	walther	NOUN
asir-1804	245	2	,	,	PUNCT
asir-1804	245	3	a.	a.	NOUN
asir-1804	245	4	(	(	PUNCT
asir-1804	245	5	1996	1996	NUM
asir-1804	245	6	)	)	PUNCT
asir-1804	245	7	.	.	PUNCT
asir-1804	246	1	teaching	teach	VERB
asir-1804	246	2	the	the	DET
asir-1804	246	3	theory	theory	NOUN
asir-1804	246	4	of	of	ADP
asir-1804	246	5	real	real	ADJ
asir-1804	246	6	lenses	lense	NOUN
asir-1804	246	7	.	.	PUNCT
asir-1804	247	1	american	american	PROPN
asir-1804	247	2	journal	journal	PROPN
asir-1804	247	3	of	of	ADP
asir-1804	247	4	physics	physics	PROPN
asir-1804	247	5	,	,	PUNCT
asir-1804	247	6	64(9	64(9	NUM
asir-1804	247	7	)	)	PUNCT
asir-1804	247	8	,	,	PUNCT
asir-1804	247	9	1161	1161	NUM
asir-1804	247	10	-	-	SYM
asir-1804	247	11	1165	1165	NUM
asir-1804	247	12	.	.	PUNCT
asir-1804	248	1	https://doi.org/10.1119/1.18359	https://doi.org/10.1119/1.18359	PROPN