id	sid	tid	token	lemma	pos
ispiv-185	1	1	microsoft	microsoft	PROPN
ispiv-185	1	2	word	word	NOUN
ispiv-185	1	3	ispiv-2021-abstract-v7.docx	ispiv-2021-abstract-v7.docx	VERB
ispiv-185	1	4	14th	14th	ADJ
ispiv-185	1	5	international	international	ADJ
ispiv-185	1	6	symposium	symposium	NOUN
ispiv-185	1	7	on	on	ADP
ispiv-185	1	8	particle	particle	NOUN
ispiv-185	1	9	image	image	NOUN
ispiv-185	1	10	velocimetry	velocimetry	NOUN
ispiv-185	1	11	–	–	PUNCT
ispiv-185	1	12	ispiv	ispiv	NOUN
ispiv-185	1	13	2021	2021	NUM
ispiv-185	1	14	august	august	PROPN
ispiv-185	1	15	1	1	NUM
ispiv-185	1	16	-	-	SYM
ispiv-185	1	17	5	5	NUM
ispiv-185	1	18	,	,	PUNCT
ispiv-185	1	19	2021	2021	NUM
ispiv-185	1	20	|	|	ADV
ispiv-185	1	21	chicago	chicago	PROPN
ispiv-185	1	22	,	,	PUNCT
ispiv-185	1	23	il	il	PROPN
ispiv-185	1	24	usa	usa	PROPN
ispiv-185	1	25	numerical	numerical	ADJ
ispiv-185	1	26	uncertainty	uncertainty	NOUN
ispiv-185	1	27	in	in	ADP
ispiv-185	1	28	density	density	NOUN
ispiv-185	1	29	estimation	estimation	NOUN
ispiv-185	1	30	for	for	ADP
ispiv-185	1	31	background	background	NOUN
ispiv-185	1	32	oriented	orient	VERB
ispiv-185	1	33	schlieren	schlieren	PROPN
ispiv-185	1	34	jiacheng	jiacheng	PROPN
ispiv-185	1	35	zhang1§	zhang1§	PROPN
ispiv-185	1	36	,	,	PUNCT
ispiv-185	1	37	lalit	lalit	PROPN
ispiv-185	1	38	k.	k.	PROPN
ispiv-185	1	39	rajendran2§	rajendran2§	PROPN
ispiv-185	1	40	,	,	PUNCT
ispiv-185	1	41	sally	sally	PROPN
ispiv-185	1	42	p.	p.	PROPN
ispiv-185	1	43	m.	m.	PROPN
ispiv-185	1	44	bane2	bane2	PROPN
ispiv-185	1	45	,	,	PUNCT
ispiv-185	1	46	pavlos	pavlos	PROPN
ispiv-185	2	1	p.	p.	PROPN
ispiv-185	2	2	vlachos1	vlachos1	PROPN
ispiv-185	3	1	*	*	PROPN
ispiv-185	3	2	1	1	NUM
ispiv-185	3	3	purdue	purdue	PROPN
ispiv-185	3	4	university	university	NOUN
ispiv-185	3	5	,	,	PUNCT
ispiv-185	3	6	school	school	NOUN
ispiv-185	3	7	of	of	ADP
ispiv-185	3	8	mechanical	mechanical	ADJ
ispiv-185	3	9	engineering	engineering	NOUN
ispiv-185	3	10	,	,	PUNCT
ispiv-185	3	11	west	west	PROPN
ispiv-185	3	12	lafayette	lafayette	PROPN
ispiv-185	3	13	,	,	PUNCT
ispiv-185	3	14	usa	usa	PROPN
ispiv-185	3	15	.	.	PROPN
ispiv-185	3	16	2	2	NUM
ispiv-185	3	17	purdue	purdue	PROPN
ispiv-185	3	18	university	university	NOUN
ispiv-185	3	19	,	,	PUNCT
ispiv-185	3	20	school	school	NOUN
ispiv-185	3	21	of	of	ADP
ispiv-185	3	22	aeronautics	aeronautic	NOUN
ispiv-185	3	23	and	and	CCONJ
ispiv-185	3	24	astronautics	astronautic	NOUN
ispiv-185	3	25	,	,	PUNCT
ispiv-185	3	26	west	west	PROPN
ispiv-185	3	27	lafayette	lafayette	PROPN
ispiv-185	3	28	,	,	PUNCT
ispiv-185	3	29	usa	usa	PROPN
ispiv-185	3	30	.	.	PROPN
ispiv-185	4	1	*	*	PUNCT
ispiv-185	4	2	pvlachos@purdue.edu	pvlachos@purdue.edu	PROPN
ispiv-185	4	3	abstract	abstract	ADJ
ispiv-185	4	4	background	background	NOUN
ispiv-185	4	5	oriented	orient	VERB
ispiv-185	4	6	schlieren	schlieren	PROPN
ispiv-185	4	7	(	(	PUNCT
ispiv-185	4	8	bos	bos	PROPN
ispiv-185	4	9	)	)	PUNCT
ispiv-185	4	10	is	be	AUX
ispiv-185	4	11	an	an	DET
ispiv-185	4	12	image	image	NOUN
ispiv-185	4	13	-	-	PUNCT
ispiv-185	4	14	based	base	VERB
ispiv-185	4	15	density	density	NOUN
ispiv-185	4	16	measurement	measurement	NOUN
ispiv-185	4	17	technique	technique	NOUN
ispiv-185	4	18	.	.	PUNCT
ispiv-185	5	1	bos	bos	PROPN
ispiv-185	5	2	estimates	estimate	VERB
ispiv-185	5	3	the	the	DET
ispiv-185	5	4	density	density	NOUN
ispiv-185	5	5	gradient	gradient	NOUN
ispiv-185	5	6	from	from	ADP
ispiv-185	5	7	the	the	DET
ispiv-185	5	8	apparent	apparent	ADJ
ispiv-185	5	9	distortion	distortion	NOUN
ispiv-185	5	10	of	of	ADP
ispiv-185	5	11	a	a	DET
ispiv-185	5	12	target	target	NOUN
ispiv-185	5	13	pattern	pattern	NOUN
ispiv-185	5	14	viewed	view	VERB
ispiv-185	5	15	through	through	ADP
ispiv-185	5	16	a	a	DET
ispiv-185	5	17	medium	medium	NOUN
ispiv-185	5	18	with	with	ADP
ispiv-185	5	19	varying	vary	VERB
ispiv-185	5	20	density	density	NOUN
ispiv-185	5	21	using	use	VERB
ispiv-185	5	22	cross	cross	NOUN
ispiv-185	5	23	-	-	NOUN
ispiv-185	5	24	correlation	correlation	NOUN
ispiv-185	5	25	,	,	PUNCT
ispiv-185	5	26	tracking	tracking	NOUN
ispiv-185	5	27	,	,	PUNCT
ispiv-185	5	28	or	or	CCONJ
ispiv-185	5	29	optical	optical	ADJ
ispiv-185	5	30	flow	flow	NOUN
ispiv-185	5	31	algorithms	algorithm	NOUN
ispiv-185	5	32	.	.	PUNCT
ispiv-185	6	1	the	the	DET
ispiv-185	6	2	density	density	NOUN
ispiv-185	6	3	gradient	gradient	NOUN
ispiv-185	6	4	can	can	AUX
ispiv-185	6	5	then	then	ADV
ispiv-185	6	6	be	be	AUX
ispiv-185	6	7	numerically	numerically	ADV
ispiv-185	6	8	integrated	integrate	VERB
ispiv-185	6	9	to	to	PART
ispiv-185	6	10	yield	yield	VERB
ispiv-185	6	11	a	a	DET
ispiv-185	6	12	spatially	spatially	ADV
ispiv-185	6	13	resolved	resolve	VERB
ispiv-185	6	14	estimate	estimate	NOUN
ispiv-185	6	15	of	of	ADP
ispiv-185	6	16	the	the	DET
ispiv-185	6	17	density	density	NOUN
ispiv-185	7	1	[	[	X
ispiv-185	7	2	1	1	NUM
ispiv-185	7	3	]	]	PUNCT
ispiv-185	7	4	.	.	PUNCT
ispiv-185	8	1	a	a	DET
ispiv-185	8	2	method	method	NOUN
ispiv-185	8	3	was	be	AUX
ispiv-185	8	4	recently	recently	ADV
ispiv-185	8	5	proposed	propose	VERB
ispiv-185	8	6	to	to	PART
ispiv-185	8	7	estimate	estimate	VERB
ispiv-185	8	8	the	the	DET
ispiv-185	8	9	a	a	DET
ispiv-185	8	10	-	-	PUNCT
ispiv-185	8	11	posteriori	posteriori	NOUN
ispiv-185	8	12	instantaneous	instantaneous	ADJ
ispiv-185	8	13	and	and	CCONJ
ispiv-185	8	14	spatially	spatially	ADV
ispiv-185	8	15	resolved	resolve	VERB
ispiv-185	8	16	density	density	NOUN
ispiv-185	8	17	uncertainty	uncertainty	NOUN
ispiv-185	8	18	for	for	ADP
ispiv-185	8	19	bos	bos	NOUN
ispiv-185	9	1	[	[	X
ispiv-185	9	2	2	2	NUM
ispiv-185	9	3	]	]	PUNCT
ispiv-185	9	4	and	and	CCONJ
ispiv-185	9	5	showed	show	VERB
ispiv-185	9	6	good	good	ADJ
ispiv-185	9	7	agreement	agreement	NOUN
ispiv-185	9	8	between	between	ADP
ispiv-185	9	9	the	the	DET
ispiv-185	9	10	propagated	propagate	VERB
ispiv-185	9	11	uncertainties	uncertainty	NOUN
ispiv-185	9	12	and	and	CCONJ
ispiv-185	9	13	the	the	DET
ispiv-185	9	14	random	random	ADJ
ispiv-185	9	15	error	error	NOUN
ispiv-185	9	16	.	.	PUNCT
ispiv-185	10	1	however	however	ADV
ispiv-185	10	2	,	,	PUNCT
ispiv-185	10	3	the	the	DET
ispiv-185	10	4	density	density	NOUN
ispiv-185	10	5	uncertainty	uncertainty	NOUN
ispiv-185	10	6	quantification	quantification	NOUN
ispiv-185	10	7	method	method	NOUN
ispiv-185	10	8	could	could	AUX
ispiv-185	10	9	not	not	PART
ispiv-185	10	10	account	account	VERB
ispiv-185	10	11	for	for	ADP
ispiv-185	10	12	the	the	DET
ispiv-185	10	13	systematic	systematic	ADJ
ispiv-185	10	14	uncertainty	uncertainty	NOUN
ispiv-185	10	15	in	in	ADP
ispiv-185	10	16	the	the	DET
ispiv-185	10	17	density	density	NOUN
ispiv-185	10	18	field	field	NOUN
ispiv-185	10	19	due	due	ADP
ispiv-185	10	20	to	to	ADP
ispiv-185	10	21	the	the	DET
ispiv-185	10	22	discretization	discretization	NOUN
ispiv-185	10	23	errors	error	NOUN
ispiv-185	10	24	introduced	introduce	VERB
ispiv-185	10	25	during	during	ADP
ispiv-185	10	26	the	the	DET
ispiv-185	10	27	numerical	numerical	ADJ
ispiv-185	10	28	integration	integration	NOUN
ispiv-185	10	29	,	,	PUNCT
ispiv-185	10	30	which	which	PRON
ispiv-185	10	31	could	could	AUX
ispiv-185	10	32	be	be	AUX
ispiv-185	10	33	much	much	ADV
ispiv-185	10	34	larger	large	ADJ
ispiv-185	10	35	than	than	ADP
ispiv-185	10	36	the	the	DET
ispiv-185	10	37	displacement	displacement	ADJ
ispiv-185	10	38	random	random	ADJ
ispiv-185	10	39	errors	error	NOUN
ispiv-185	10	40	[	[	X
ispiv-185	10	41	2	2	NUM
ispiv-185	10	42	]	]	PUNCT
ispiv-185	10	43	.	.	PUNCT
ispiv-185	11	1	in	in	ADP
ispiv-185	11	2	this	this	DET
ispiv-185	11	3	work	work	NOUN
ispiv-185	11	4	,	,	PUNCT
ispiv-185	11	5	we	we	PRON
ispiv-185	11	6	propose	propose	VERB
ispiv-185	11	7	a	a	DET
ispiv-185	11	8	method	method	NOUN
ispiv-185	11	9	to	to	PART
ispiv-185	11	10	estimate	estimate	VERB
ispiv-185	11	11	the	the	DET
ispiv-185	11	12	numerical	numerical	ADJ
ispiv-185	11	13	uncertainty	uncertainty	NOUN
ispiv-185	11	14	introduced	introduce	VERB
ispiv-185	11	15	by	by	ADP
ispiv-185	11	16	the	the	DET
ispiv-185	11	17	density	density	NOUN
ispiv-185	11	18	integration	integration	NOUN
ispiv-185	11	19	in	in	ADP
ispiv-185	11	20	bos	bo	NOUN
ispiv-185	11	21	measurements	measurement	NOUN
ispiv-185	11	22	,	,	PUNCT
ispiv-185	11	23	using	use	VERB
ispiv-185	11	24	a	a	DET
ispiv-185	11	25	richardson	richardson	PROPN
ispiv-185	11	26	extrapolation	extrapolation	NOUN
ispiv-185	11	27	framework	framework	NOUN
ispiv-185	11	28	.	.	PUNCT
ispiv-185	12	1	a	a	DET
ispiv-185	12	2	procedure	procedure	NOUN
ispiv-185	12	3	is	be	AUX
ispiv-185	12	4	also	also	ADV
ispiv-185	12	5	introduced	introduce	VERB
ispiv-185	12	6	to	to	PART
ispiv-185	12	7	combine	combine	VERB
ispiv-185	12	8	this	this	DET
ispiv-185	12	9	systematic	systematic	ADJ
ispiv-185	12	10	uncertainty	uncertainty	NOUN
ispiv-185	12	11	with	with	ADP
ispiv-185	12	12	the	the	DET
ispiv-185	12	13	random	random	ADJ
ispiv-185	12	14	uncertainty	uncertainty	NOUN
ispiv-185	12	15	from	from	ADP
ispiv-185	12	16	the	the	DET
ispiv-185	12	17	previous	previous	ADJ
ispiv-185	12	18	work	work	NOUN
ispiv-185	12	19	to	to	PART
ispiv-185	12	20	provide	provide	VERB
ispiv-185	12	21	an	an	DET
ispiv-185	12	22	instantaneous	instantaneous	ADJ
ispiv-185	12	23	,	,	PUNCT
ispiv-185	12	24	spatially	spatially	ADV
ispiv-185	12	25	-	-	PUNCT
ispiv-185	12	26	resolved	resolve	VERB
ispiv-185	12	27	total	total	ADJ
ispiv-185	12	28	uncertainty	uncertainty	NOUN
ispiv-185	12	29	on	on	ADP
ispiv-185	12	30	the	the	DET
ispiv-185	12	31	density	density	NOUN
ispiv-185	12	32	estimates	estimate	NOUN
ispiv-185	12	33	.	.	PUNCT
ispiv-185	13	1	the	the	DET
ispiv-185	13	2	method	method	NOUN
ispiv-185	13	3	will	will	AUX
ispiv-185	13	4	be	be	AUX
ispiv-185	13	5	tested	test	VERB
ispiv-185	13	6	with	with	ADP
ispiv-185	13	7	synthetic	synthetic	ADJ
ispiv-185	13	8	fields	field	NOUN
ispiv-185	13	9	and	and	CCONJ
ispiv-185	13	10	synthetic	synthetic	ADJ
ispiv-185	13	11	bos	bo	NOUN
ispiv-185	13	12	images	image	NOUN
ispiv-185	13	13	.	.	PUNCT
ispiv-185	14	1	with	with	ADP
ispiv-185	14	2	the	the	DET
ispiv-185	14	3	richardson	richardson	PROPN
ispiv-185	14	4	extrapolation	extrapolation	NOUN
ispiv-185	15	1	[	[	X
ispiv-185	15	2	3	3	NUM
ispiv-185	15	3	]	]	PUNCT
ispiv-185	15	4	,	,	PUNCT
ispiv-185	15	5	the	the	DET
ispiv-185	15	6	discretization	discretization	NOUN
ispiv-185	15	7	error	error	NOUN
ispiv-185	15	8	of	of	ADP
ispiv-185	15	9	a	a	DET
ispiv-185	15	10	numerical	numerical	ADJ
ispiv-185	15	11	estimation	estimation	NOUN
ispiv-185	15	12	can	can	AUX
ispiv-185	15	13	be	be	AUX
ispiv-185	15	14	estimated	estimate	VERB
ispiv-185	15	15	based	base	VERB
ispiv-185	15	16	on	on	ADP
ispiv-185	15	17	the	the	DET
ispiv-185	15	18	residual	residual	NOUN
ispiv-185	15	19	between	between	ADP
ispiv-185	15	20	two	two	NUM
ispiv-185	15	21	sets	set	NOUN
ispiv-185	15	22	of	of	ADP
ispiv-185	15	23	results	result	NOUN
ispiv-185	15	24	with	with	ADP
ispiv-185	15	25	different	different	ADJ
ispiv-185	15	26	grid	grid	NOUN
ispiv-185	15	27	levels	level	NOUN
ispiv-185	15	28	as	as	ADP
ispiv-185	15	29	:	:	PUNCT
ispiv-185	15	30	𝜖!̅	𝜖!̅	NOUN
ispiv-185	16	1	=	=	SYM
ispiv-185	16	2	−	−	PROPN
ispiv-185	16	3	"	"	PUNCT
ispiv-185	16	4	!	!	PUNCT
ispiv-185	16	5	#	#	ADP
ispiv-185	16	6	"	"	PUNCT
ispiv-185	16	7	"	"	PUNCT
ispiv-185	16	8	!	!	PUNCT
ispiv-185	16	9	$	$	SYM
ispiv-185	16	10	#	#	SYM
ispiv-185	16	11	#	#	NUM
ispiv-185	16	12	%	%	NOUN
ispiv-185	16	13	,	,	PUNCT
ispiv-185	16	14	(	(	PUNCT
ispiv-185	16	15	1	1	X
ispiv-185	16	16	)	)	PUNCT
ispiv-185	16	17	where	where	SCONJ
ispiv-185	16	18	𝜖!̅	𝜖!̅	NOUN
ispiv-185	16	19	is	be	AUX
ispiv-185	16	20	the	the	DET
ispiv-185	16	21	estimated	estimate	VERB
ispiv-185	16	22	numerical	numerical	ADJ
ispiv-185	16	23	error	error	NOUN
ispiv-185	16	24	of	of	ADP
ispiv-185	16	25	the	the	DET
ispiv-185	16	26	result	result	NOUN
ispiv-185	16	27	obtained	obtain	VERB
ispiv-185	16	28	on	on	ADP
ispiv-185	16	29	a	a	DET
ispiv-185	16	30	grid	grid	NOUN
ispiv-185	16	31	with	with	ADP
ispiv-185	16	32	spacing	space	VERB
ispiv-185	16	33	ℎ	ℎ	PROPN
ispiv-185	16	34	,	,	PUNCT
ispiv-185	16	35	𝑓	𝑓	PROPN
ispiv-185	16	36	!	!	PUNCT
ispiv-185	16	37	and	and	CCONJ
ispiv-185	16	38	𝑓$	𝑓$	NOUN
ispiv-185	16	39	!	!	PROPN
ispiv-185	16	40	are	be	AUX
ispiv-185	16	41	the	the	DET
ispiv-185	16	42	results	result	NOUN
ispiv-185	16	43	obtained	obtain	VERB
ispiv-185	16	44	on	on	ADP
ispiv-185	16	45	the	the	DET
ispiv-185	16	46	grids	grid	NOUN
ispiv-185	16	47	with	with	ADP
ispiv-185	16	48	spacing	space	VERB
ispiv-185	16	49	ℎ	ℎ	PROPN
ispiv-185	16	50	and	and	CCONJ
ispiv-185	16	51	𝑟ℎ	𝑟ℎ	NOUN
ispiv-185	16	52	,	,	PUNCT
ispiv-185	16	53	respectively	respectively	ADV
ispiv-185	16	54	,	,	PUNCT
ispiv-185	16	55	with	with	ADP
ispiv-185	16	56	𝑟	𝑟	NOUN
ispiv-185	16	57	being	be	AUX
ispiv-185	16	58	the	the	DET
ispiv-185	16	59	downsampling	downsample	VERB
ispiv-185	16	60	factor	factor	NOUN
ispiv-185	16	61	(	(	PUNCT
ispiv-185	16	62	usually	usually	ADV
ispiv-185	16	63	𝑟	𝑟	X
ispiv-185	16	64	=	=	SYM
ispiv-185	16	65	2	2	NUM
ispiv-185	16	66	)	)	PUNCT
ispiv-185	16	67	,	,	PUNCT
ispiv-185	16	68	and	and	CCONJ
ispiv-185	16	69	𝑝	𝑝	NOUN
ispiv-185	16	70	is	be	AUX
ispiv-185	16	71	the	the	DET
ispiv-185	16	72	order	order	NOUN
ispiv-185	16	73	of	of	ADP
ispiv-185	16	74	accuracy	accuracy	NOUN
ispiv-185	16	75	of	of	ADP
ispiv-185	16	76	the	the	DET
ispiv-185	16	77	discretization	discretization	NOUN
ispiv-185	16	78	scheme	scheme	NOUN
ispiv-185	16	79	.	.	PUNCT
ispiv-185	17	1	in	in	ADP
ispiv-185	17	2	this	this	DET
ispiv-185	17	3	study	study	NOUN
ispiv-185	17	4	,	,	PUNCT
ispiv-185	17	5	𝑝	𝑝	PROPN
ispiv-185	17	6	is	be	AUX
ispiv-185	17	7	2	2	NUM
ispiv-185	17	8	since	since	SCONJ
ispiv-185	17	9	the	the	DET
ispiv-185	17	10	second	second	ADJ
ispiv-185	17	11	-	-	PUNCT
ispiv-185	17	12	order	order	NOUN
ispiv-185	17	13	central	central	ADJ
ispiv-185	17	14	differencing	differencing	NOUN
ispiv-185	17	15	scheme	scheme	NOUN
ispiv-185	17	16	was	be	AUX
ispiv-185	17	17	used	use	VERB
ispiv-185	17	18	for	for	ADP
ispiv-185	17	19	carrying	carry	VERB
ispiv-185	17	20	the	the	DET
ispiv-185	17	21	numerical	numerical	ADJ
ispiv-185	17	22	integration	integration	NOUN
ispiv-185	17	23	.	.	PUNCT
ispiv-185	18	1	the	the	DET
ispiv-185	18	2	estimated	estimate	VERB
ispiv-185	18	3	error	error	NOUN
ispiv-185	18	4	is	be	AUX
ispiv-185	18	5	then	then	ADV
ispiv-185	18	6	employed	employ	VERB
ispiv-185	18	7	as	as	ADP
ispiv-185	18	8	the	the	DET
ispiv-185	18	9	numerical	numerical	ADJ
ispiv-185	18	10	uncertainty	uncertainty	NOUN
ispiv-185	18	11	(	(	PUNCT
ispiv-185	18	12	𝑈	𝑈	PROPN
ispiv-185	18	13	=	=	PUNCT
ispiv-185	18	14	|𝜖!|	|𝜖!|	NOUN
ispiv-185	18	15	)	)	PUNCT
ispiv-185	18	16	.	.	PUNCT
ispiv-185	19	1	with	with	ADP
ispiv-185	19	2	the	the	DET
ispiv-185	19	3	random	random	ADJ
ispiv-185	19	4	uncertainty	uncertainty	NOUN
ispiv-185	19	5	obtained	obtain	VERB
ispiv-185	19	6	using	use	VERB
ispiv-185	19	7	the	the	DET
ispiv-185	19	8	previous	previous	ADJ
ispiv-185	19	9	method	method	NOUN
ispiv-185	19	10	[	[	X
ispiv-185	19	11	2	2	NUM
ispiv-185	19	12	]	]	PUNCT
ispiv-185	19	13	as	as	ADP
ispiv-185	19	14	the	the	DET
ispiv-185	19	15	standard	standard	ADJ
ispiv-185	19	16	deviation	deviation	NOUN
ispiv-185	19	17	of	of	ADP
ispiv-185	19	18	the	the	DET
ispiv-185	19	19	random	random	ADJ
ispiv-185	19	20	error	error	NOUN
ispiv-185	19	21	distribution	distribution	NOUN
ispiv-185	19	22	,	,	PUNCT
ispiv-185	19	23	and	and	CCONJ
ispiv-185	19	24	the	the	DET
ispiv-185	19	25	numerical	numerical	ADJ
ispiv-185	19	26	uncertainty	uncertainty	NOUN
ispiv-185	19	27	interpreted	interpret	VERB
ispiv-185	19	28	as	as	ADP
ispiv-185	19	29	the	the	DET
ispiv-185	19	30	standard	standard	ADJ
ispiv-185	19	31	deviation	deviation	NOUN
ispiv-185	19	32	of	of	ADP
ispiv-185	19	33	the	the	DET
ispiv-185	19	34	bias	bias	NOUN
ispiv-185	19	35	error	error	NOUN
ispiv-185	19	36	distribution	distribution	NOUN
ispiv-185	19	37	,	,	PUNCT
ispiv-185	19	38	the	the	DET
ispiv-185	19	39	standard	standard	ADJ
ispiv-185	19	40	total	total	ADJ
ispiv-185	19	41	uncertainty	uncertainty	NOUN
ispiv-185	19	42	can	can	AUX
ispiv-185	19	43	be	be	AUX
ispiv-185	19	44	expressed	express	VERB
ispiv-185	19	45	as	as	ADP
ispiv-185	19	46	𝑈	𝑈	PROPN
ispiv-185	19	47	&	&	CCONJ
ispiv-185	19	48	'	'	PUNCT
ispiv-185	19	49	&	&	CCONJ
ispiv-185	19	50	(	(	PUNCT
ispiv-185	19	51	)	)	PUNCT
ispiv-185	19	52	*	*	PUNCT
ispiv-185	20	1	=	=	PUNCT
ispiv-185	20	2	𝑈+,(-	𝑈+,(-	X
ispiv-185	20	3	*	*	NOUN
ispiv-185	20	4	+	+	NUM
ispiv-185	20	5	𝑈$(./'0	𝑈$(./'0	PROPN
ispiv-185	20	6	*	*	X
ispiv-185	20	7	,	,	PUNCT
ispiv-185	20	8	(	(	PUNCT
ispiv-185	20	9	2	2	X
ispiv-185	20	10	)	)	PUNCT
ispiv-185	20	11	thereby	thereby	ADV
ispiv-185	20	12	providing	provide	VERB
ispiv-185	20	13	a	a	DET
ispiv-185	20	14	framework	framework	NOUN
ispiv-185	20	15	for	for	ADP
ispiv-185	20	16	combining	combine	VERB
ispiv-185	20	17	the	the	DET
ispiv-185	20	18	random	random	ADJ
ispiv-185	20	19	uncertainty	uncertainty	NOUN
ispiv-185	20	20	estimates	estimate	VERB
ispiv-185	20	21	to	to	PART
ispiv-185	20	22	estimate	estimate	VERB
ispiv-185	20	23	the	the	DET
ispiv-185	20	24	overall	overall	ADJ
ispiv-185	20	25	uncertainty	uncertainty	NOUN
ispiv-185	20	26	in	in	ADP
ispiv-185	20	27	the	the	DET
ispiv-185	20	28	density	density	NOUN
ispiv-185	20	29	integration	integration	NOUN
ispiv-185	20	30	.	.	PUNCT
ispiv-185	21	1	the	the	DET
ispiv-185	21	2	proposed	propose	VERB
ispiv-185	21	3	uncertainty	uncertainty	NOUN
ispiv-185	21	4	estimation	estimation	NOUN
ispiv-185	21	5	method	method	NOUN
ispiv-185	21	6	was	be	AUX
ispiv-185	21	7	tested	test	VERB
ispiv-185	21	8	using	use	VERB
ispiv-185	21	9	a	a	DET
ispiv-185	21	10	synthetic	synthetic	ADJ
ispiv-185	21	11	sinusoidal	sinusoidal	NOUN
ispiv-185	21	12	scalar	scalar	ADJ
ispiv-185	21	13	field	field	NOUN
ispiv-185	21	14	as	as	ADP
ispiv-185	21	15	:	:	PUNCT
ispiv-185	21	16	𝑓(𝑋	𝑓(𝑋	NUM
ispiv-185	21	17	,	,	PUNCT
ispiv-185	21	18	𝑌	𝑌	PROPN
ispiv-185	21	19	)	)	PUNCT
ispiv-185	21	20	=	=	NOUN
ispiv-185	21	21	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
ispiv-185	21	22	6	6	NUM
ispiv-185	21	23	*	*	SYM
ispiv-185	21	24	1	1	NUM
ispiv-185	21	25	2	2	NUM
ispiv-185	21	26	𝑋7	𝑋7	NOUN
ispiv-185	21	27	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
ispiv-185	21	28	*	*	SYM
ispiv-185	21	29	1	1	NUM
ispiv-185	21	30	2	2	NUM
ispiv-185	21	31	𝑌	𝑌	PROPN
ispiv-185	21	32	,	,	PUNCT
ispiv-185	21	33	(	(	PUNCT
ispiv-185	21	34	3	3	X
ispiv-185	21	35	)	)	PUNCT
ispiv-185	21	36	where	where	SCONJ
ispiv-185	21	37	𝑓	𝑓	PROPN
ispiv-185	21	38	represents	represent	VERB
ispiv-185	21	39	the	the	DET
ispiv-185	21	40	scalar	scalar	ADJ
ispiv-185	21	41	field	field	NOUN
ispiv-185	21	42	,	,	PUNCT
ispiv-185	21	43	and	and	CCONJ
ispiv-185	21	44	𝜆	𝜆	X
ispiv-185	21	45	represents	represent	VERB
ispiv-185	21	46	the	the	DET
ispiv-185	21	47	wavelength	wavelength	NOUN
ispiv-185	21	48	.	.	PUNCT
ispiv-185	22	1	a	a	DET
ispiv-185	22	2	zero	zero	NUM
ispiv-185	22	3	-	-	PUNCT
ispiv-185	22	4	mean	mean	NOUN
ispiv-185	22	5	gaussian	gaussian	NOUN
ispiv-185	22	6	distributed	distribute	VERB
ispiv-185	22	7	noise	noise	NOUN
ispiv-185	22	8	was	be	AUX
ispiv-185	22	9	added	add	VERB
ispiv-185	22	10	to	to	ADP
ispiv-185	22	11	the	the	DET
ispiv-185	22	12	scalar	scalar	ADJ
ispiv-185	22	13	field	field	NOUN
ispiv-185	22	14	with	with	ADP
ispiv-185	22	15	prescribed	prescribed	ADJ
ispiv-185	22	16	noise	noise	NOUN
ispiv-185	22	17	levels	level	NOUN
ispiv-185	22	18	.	.	PUNCT
ispiv-185	23	1	one	one	NUM
ispiv-185	23	2	thousand	thousand	NUM
ispiv-185	23	3	(	(	PUNCT
ispiv-185	23	4	1000	1000	NUM
ispiv-185	23	5	)	)	PUNCT
ispiv-185	23	6	realizations	realization	NOUN
ispiv-185	23	7	of	of	ADP
ispiv-185	23	8	the	the	DET
ispiv-185	23	9	corrupted	corrupted	ADJ
ispiv-185	23	10	field	field	NOUN
ispiv-185	23	11	were	be	AUX
ispiv-185	23	12	generated	generate	VERB
ispiv-185	23	13	,	,	PUNCT
ispiv-185	23	14	and	and	CCONJ
ispiv-185	23	15	for	for	ADP
ispiv-185	23	16	each	each	DET
ispiv-185	23	17	realization	realization	NOUN
ispiv-185	23	18	,	,	PUNCT
ispiv-185	23	19	the	the	DET
ispiv-185	23	20	integration	integration	NOUN
ispiv-185	23	21	was	be	AUX
ispiv-185	23	22	performed	perform	VERB
ispiv-185	23	23	with	with	ADP
ispiv-185	23	24	the	the	DET
ispiv-185	23	25	noisy	noisy	ADJ
ispiv-185	23	26	gradient	gradient	NOUN
ispiv-185	23	27	fields	field	NOUN
ispiv-185	23	28	to	to	PART
ispiv-185	23	29	estimate	estimate	VERB
ispiv-185	23	30	the	the	DET
ispiv-185	23	31	error	error	NOUN
ispiv-185	23	32	.	.	PUNCT
ispiv-185	24	1	the	the	DET
ispiv-185	24	2	results	result	NOUN
ispiv-185	24	3	are	be	AUX
ispiv-185	24	4	shown	show	VERB
ispiv-185	24	5	in	in	ADP
ispiv-185	24	6	figure	figure	NOUN
ispiv-185	24	7	1	1	NUM
ispiv-185	24	8	for	for	ADP
ispiv-185	24	9	two	two	NUM
ispiv-185	24	10	noise	noise	NOUN
ispiv-185	24	11	levels	level	NOUN
ispiv-185	24	12	:	:	PUNCT
ispiv-185	24	13	1	1	NUM
ispiv-185	24	14	%	%	NOUN
ispiv-185	24	15	and	and	CCONJ
ispiv-185	24	16	10	10	NUM
ispiv-185	24	17	%	%	NOUN
ispiv-185	24	18	of	of	ADP
ispiv-185	24	19	the	the	DET
ispiv-185	24	20	peak	peak	NOUN
ispiv-185	24	21	value	value	NOUN
ispiv-185	24	22	of	of	ADP
ispiv-185	24	23	the	the	DET
ispiv-185	24	24	scalar	scalar	ADJ
ispiv-185	24	25	field	field	NOUN
ispiv-185	24	26	.	.	PUNCT
ispiv-185	25	1	it	it	PRON
ispiv-185	25	2	is	be	AUX
ispiv-185	25	3	seen	see	VERB
ispiv-185	25	4	in	in	ADP
ispiv-185	25	5	both	both	DET
ispiv-185	25	6	levels	level	NOUN
ispiv-185	25	7	that	that	SCONJ
ispiv-185	25	8	the	the	DET
ispiv-185	25	9	spatial	spatial	ADJ
ispiv-185	25	10	variation	variation	NOUN
ispiv-185	25	11	of	of	ADP
ispiv-185	25	12	the	the	DET
ispiv-185	25	13	total	total	ADJ
ispiv-185	25	14	uncertainty	uncertainty	NOUN
ispiv-185	25	15	matches	match	VERB
ispiv-185	25	16	that	that	PRON
ispiv-185	25	17	of	of	ADP
ispiv-185	25	18	the	the	DET
ispiv-185	25	19	total	total	ADJ
ispiv-185	25	20	error	error	NOUN
ispiv-185	25	21	,	,	PUNCT
ispiv-185	25	22	and	and	CCONJ
ispiv-185	25	23	the	the	DET
ispiv-185	25	24	rms	rm	NOUN
ispiv-185	25	25	of	of	ADP
ispiv-185	25	26	the	the	DET
ispiv-185	25	27	total	total	ADJ
ispiv-185	25	28	uncertainty	uncertainty	NOUN
ispiv-185	25	29	coincides	coincide	VERB
ispiv-185	25	30	with	with	ADP
ispiv-185	25	31	the	the	DET
ispiv-185	25	32	rms	rm	NOUN
ispiv-185	25	33	of	of	ADP
ispiv-185	25	34	the	the	DET
ispiv-185	25	35	error	error	NOUN
ispiv-185	25	36	distribution	distribution	NOUN
ispiv-185	25	37	.	.	PUNCT
ispiv-185	26	1	this	this	PRON
ispiv-185	26	2	validates	validate	VERB
ispiv-185	26	3	the	the	DET
ispiv-185	26	4	framework	framework	NOUN
ispiv-185	26	5	used	use	VERB
ispiv-185	26	6	to	to	PART
ispiv-185	26	7	combine	combine	VERB
ispiv-185	26	8	the	the	DET
ispiv-185	26	9	bias	bias	NOUN
ispiv-185	26	10	and	and	CCONJ
ispiv-185	26	11	random	random	ADJ
ispiv-185	26	12	uncertainty	uncertainty	NOUN
ispiv-185	26	13	estimates	estimate	VERB
ispiv-185	26	14	.	.	PUNCT
ispiv-185	27	1	§	§	NOUN
ispiv-185	27	2	these	these	DET
ispiv-185	27	3	authors	author	NOUN
ispiv-185	27	4	contributed	contribute	VERB
ispiv-185	27	5	equally	equally	ADV
ispiv-185	27	6	to	to	ADP
ispiv-185	27	7	this	this	DET
ispiv-185	27	8	work	work	NOUN
ispiv-185	27	9	.	.	PUNCT
ispiv-185	28	1	the	the	DET
ispiv-185	28	2	numerical	numerical	ADJ
ispiv-185	28	3	uncertainty	uncertainty	NOUN
ispiv-185	28	4	estimation	estimation	NOUN
ispiv-185	28	5	was	be	AUX
ispiv-185	28	6	also	also	ADV
ispiv-185	28	7	applied	apply	VERB
ispiv-185	28	8	to	to	ADP
ispiv-185	28	9	the	the	DET
ispiv-185	28	10	synthetic	synthetic	ADJ
ispiv-185	28	11	bos	bos	NOUN
ispiv-185	28	12	images	image	NOUN
ispiv-185	28	13	rendered	render	VERB
ispiv-185	28	14	using	use	VERB
ispiv-185	28	15	a	a	DET
ispiv-185	28	16	raytracing	raytracing	NOUN
ispiv-185	28	17	based	base	VERB
ispiv-185	28	18	image	image	NOUN
ispiv-185	28	19	generation	generation	NOUN
ispiv-185	28	20	methodology	methodology	NOUN
ispiv-185	28	21	[	[	X
ispiv-185	28	22	4	4	NUM
ispiv-185	28	23	]	]	PUNCT
ispiv-185	28	24	.	.	PUNCT
ispiv-185	29	1	a	a	DET
ispiv-185	29	2	sinusoidal	sinusoidal	ADJ
ispiv-185	29	3	density	density	NOUN
ispiv-185	29	4	field	field	NOUN
ispiv-185	29	5	was	be	AUX
ispiv-185	29	6	chosen	choose	VERB
ispiv-185	29	7	for	for	ADP
ispiv-185	29	8	the	the	DET
ispiv-185	29	9	error	error	NOUN
ispiv-185	29	10	analysis	analysis	NOUN
ispiv-185	29	11	as	as	SCONJ
ispiv-185	29	12	described	describe	VERB
ispiv-185	29	13	by	by	ADP
ispiv-185	29	14	equation	equation	NOUN
ispiv-185	29	15	(	(	PUNCT
ispiv-185	29	16	4	4	NUM
ispiv-185	29	17	):	):	PUNCT
ispiv-185	29	18	𝜌(𝑋	𝜌(𝑋	NUM
ispiv-185	29	19	,	,	PUNCT
ispiv-185	29	20	𝑌	𝑌	PROPN
ispiv-185	29	21	)	)	PUNCT
ispiv-185	29	22	=	=	SYM
ispiv-185	29	23	𝜌3	𝜌3	NOUN
ispiv-185	29	24	+	+	NUM
ispiv-185	29	25	𝛥𝜌3	𝛥𝜌3	NOUN
ispiv-185	29	26	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
ispiv-185	29	27	6	6	NUM
ispiv-185	29	28	*	*	SYM
ispiv-185	29	29	1	1	NUM
ispiv-185	29	30	2	2	NUM
ispiv-185	29	31	𝑋7	𝑋7	NOUN
ispiv-185	29	32	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
ispiv-185	29	33	6	6	NUM
ispiv-185	29	34	*	*	SYM
ispiv-185	29	35	1	1	NUM
ispiv-185	29	36	2	2	NUM
ispiv-185	29	37	𝑌7	𝑌7	NOUN
ispiv-185	29	38	,	,	PUNCT
ispiv-185	29	39	(	(	PUNCT
ispiv-185	29	40	4	4	X
ispiv-185	29	41	)	)	PUNCT
ispiv-185	29	42	where	where	SCONJ
ispiv-185	29	43	𝜌3	𝜌3	NOUN
ispiv-185	29	44	is	be	AUX
ispiv-185	29	45	the	the	DET
ispiv-185	29	46	ambient	ambient	ADJ
ispiv-185	29	47	density	density	NOUN
ispiv-185	29	48	,	,	PUNCT
ispiv-185	29	49	δ𝜌3	δ𝜌3	PROPN
ispiv-185	29	50	is	be	AUX
ispiv-185	29	51	the	the	DET
ispiv-185	29	52	peak	peak	NOUN
ispiv-185	29	53	density	density	NOUN
ispiv-185	29	54	difference	difference	NOUN
ispiv-185	29	55	and	and	CCONJ
ispiv-185	29	56	𝜆	𝜆	NOUN
ispiv-185	29	57	is	be	AUX
ispiv-185	29	58	the	the	DET
ispiv-185	29	59	wavelength	wavelength	NOUN
ispiv-185	29	60	.	.	PUNCT
ispiv-185	30	1	a	a	DET
ispiv-185	30	2	2d	2d	NUM
ispiv-185	30	3	slice	slice	NOUN
ispiv-185	30	4	of	of	ADP
ispiv-185	30	5	the	the	DET
ispiv-185	30	6	density	density	NOUN
ispiv-185	30	7	field	field	NOUN
ispiv-185	30	8	is	be	AUX
ispiv-185	30	9	shown	show	VERB
ispiv-185	30	10	in	in	ADP
ispiv-185	30	11	figure	figure	NOUN
ispiv-185	30	12	2(a	2(a	NUM
ispiv-185	30	13	)	)	PUNCT
ispiv-185	30	14	.	.	PUNCT
ispiv-185	31	1	the	the	DET
ispiv-185	31	2	rendered	render	VERB
ispiv-185	31	3	images	image	NOUN
ispiv-185	31	4	were	be	AUX
ispiv-185	31	5	processed	process	VERB
ispiv-185	31	6	using	use	VERB
ispiv-185	31	7	prana	prana	NOUN
ispiv-185	31	8	with	with	ADP
ispiv-185	31	9	a	a	DET
ispiv-185	31	10	standard	standard	ADJ
ispiv-185	31	11	crosscorrelation	crosscorrelation	NOUN
ispiv-185	31	12	procedure	procedure	NOUN
ispiv-185	31	13	for	for	ADP
ispiv-185	31	14	two	two	NUM
ispiv-185	31	15	passes	pass	NOUN
ispiv-185	31	16	in	in	ADP
ispiv-185	31	17	an	an	DET
ispiv-185	31	18	iterative	iterative	ADJ
ispiv-185	31	19	window	window	NOUN
ispiv-185	31	20	deformation	deformation	NOUN
ispiv-185	31	21	framework	framework	NOUN
ispiv-185	31	22	.	.	PUNCT
ispiv-185	32	1	a	a	DET
ispiv-185	32	2	sample	sample	NOUN
ispiv-185	32	3	instantaneous	instantaneous	ADJ
ispiv-185	32	4	displacement	displacement	ADJ
ispiv-185	32	5	field	field	NOUN
ispiv-185	32	6	are	be	AUX
ispiv-185	32	7	shown	show	VERB
ispiv-185	32	8	in	in	ADP
ispiv-185	32	9	figure	figure	NOUN
ispiv-185	32	10	2(b	2(b	NUM
ispiv-185	32	11	)	)	PUNCT
ispiv-185	32	12	.	.	PUNCT
ispiv-185	33	1	the	the	DET
ispiv-185	33	2	displacement	displacement	ADJ
ispiv-185	33	3	fields	field	NOUN
ispiv-185	33	4	were	be	AUX
ispiv-185	33	5	used	use	VERB
ispiv-185	33	6	to	to	PART
ispiv-185	33	7	calculate	calculate	VERB
ispiv-185	33	8	the	the	DET
ispiv-185	33	9	depth	depth	NOUN
ispiv-185	33	10	averaged	average	VERB
ispiv-185	33	11	density	density	NOUN
ispiv-185	33	12	gradient	gradient	NOUN
ispiv-185	33	13	field	field	NOUN
ispiv-185	33	14	∇𝜌	∇𝜌	PROPN
ispiv-185	33	15	,	,	PUNCT
ispiv-185	33	16	which	which	PRON
ispiv-185	33	17	were	be	AUX
ispiv-185	33	18	then	then	ADV
ispiv-185	33	19	spatially	spatially	ADV
ispiv-185	33	20	integrated	integrate	VERB
ispiv-185	33	21	using	use	VERB
ispiv-185	33	22	the	the	DET
ispiv-185	33	23	poisson	poisson	NOUN
ispiv-185	33	24	solver	solver	VERB
ispiv-185	33	25	to	to	PART
ispiv-185	33	26	obtain	obtain	VERB
ispiv-185	33	27	the	the	DET
ispiv-185	33	28	projected	project	VERB
ispiv-185	33	29	density	density	NOUN
ispiv-185	33	30	field	field	NOUN
ispiv-185	33	31	.	.	PUNCT
ispiv-185	34	1	the	the	DET
ispiv-185	34	2	error	error	NOUN
ispiv-185	34	3	of	of	ADP
ispiv-185	34	4	the	the	DET
ispiv-185	34	5	density	density	NOUN
ispiv-185	34	6	field	field	NOUN
ispiv-185	34	7	was	be	AUX
ispiv-185	34	8	determined	determine	VERB
ispiv-185	34	9	as	as	ADP
ispiv-185	34	10	the	the	DET
ispiv-185	34	11	deviation	deviation	NOUN
ispiv-185	34	12	from	from	ADP
ispiv-185	34	13	the	the	DET
ispiv-185	34	14	original	original	ADJ
ispiv-185	34	15	density	density	NOUN
ispiv-185	34	16	field	field	NOUN
ispiv-185	34	17	used	use	VERB
ispiv-185	34	18	to	to	PART
ispiv-185	34	19	render	render	VERB
ispiv-185	34	20	the	the	DET
ispiv-185	34	21	synthetic	synthetic	ADJ
ispiv-185	34	22	images	image	NOUN
ispiv-185	34	23	,	,	PUNCT
ispiv-185	34	24	and	and	CCONJ
ispiv-185	34	25	the	the	DET
ispiv-185	34	26	numerical	numerical	ADJ
ispiv-185	34	27	uncertainty	uncertainty	NOUN
ispiv-185	34	28	was	be	AUX
ispiv-185	34	29	estimated	estimate	VERB
ispiv-185	34	30	using	use	VERB
ispiv-185	34	31	the	the	DET
ispiv-185	34	32	richardson	richardson	PROPN
ispiv-185	34	33	extrapolation	extrapolation	NOUN
ispiv-185	34	34	method	method	NOUN
ispiv-185	34	35	.	.	PUNCT
ispiv-185	35	1	the	the	DET
ispiv-185	35	2	results	result	NOUN
ispiv-185	35	3	of	of	ADP
ispiv-185	35	4	the	the	DET
ispiv-185	35	5	density	density	NOUN
ispiv-185	35	6	error	error	NOUN
ispiv-185	35	7	and	and	CCONJ
ispiv-185	35	8	uncertainty	uncertainty	NOUN
ispiv-185	35	9	are	be	AUX
ispiv-185	35	10	compared	compare	VERB
ispiv-185	35	11	in	in	ADP
ispiv-185	35	12	figure	figure	NOUN
ispiv-185	35	13	2(c	2(c	NUM
ispiv-185	35	14	)	)	PUNCT
ispiv-185	35	15	and	and	CCONJ
ispiv-185	35	16	(	(	PUNCT
ispiv-185	35	17	d	d	NOUN
ispiv-185	35	18	)	)	PUNCT
ispiv-185	35	19	.	.	PUNCT
ispiv-185	36	1	the	the	DET
ispiv-185	36	2	numerical	numerical	ADJ
ispiv-185	36	3	uncertainty	uncertainty	NOUN
ispiv-185	36	4	of	of	ADP
ispiv-185	36	5	the	the	DET
ispiv-185	36	6	density	density	NOUN
ispiv-185	36	7	integration	integration	NOUN
ispiv-185	36	8	was	be	AUX
ispiv-185	36	9	lower	low	ADJ
ispiv-185	36	10	than	than	ADP
ispiv-185	36	11	the	the	DET
ispiv-185	36	12	total	total	ADJ
ispiv-185	36	13	density	density	NOUN
ispiv-185	36	14	error	error	NOUN
ispiv-185	36	15	,	,	PUNCT
ispiv-185	36	16	because	because	SCONJ
ispiv-185	36	17	the	the	DET
ispiv-185	36	18	density	density	NOUN
ispiv-185	36	19	error	error	NOUN
ispiv-185	36	20	was	be	AUX
ispiv-185	36	21	also	also	ADV
ispiv-185	36	22	due	due	ADJ
ispiv-185	36	23	to	to	ADP
ispiv-185	36	24	the	the	DET
ispiv-185	36	25	discrepancy	discrepancy	NOUN
ispiv-185	36	26	between	between	ADP
ispiv-185	36	27	the	the	DET
ispiv-185	36	28	ray	ray	NOUN
ispiv-185	36	29	tracing	trace	VERB
ispiv-185	36	30	displacements	displacement	NOUN
ispiv-185	36	31	and	and	CCONJ
ispiv-185	36	32	the	the	DET
ispiv-185	36	33	theoretical	theoretical	ADJ
ispiv-185	36	34	displacements	displacement	NOUN
ispiv-185	36	35	because	because	SCONJ
ispiv-185	36	36	of	of	ADP
ispiv-185	36	37	the	the	DET
ispiv-185	36	38	linear	linear	ADJ
ispiv-185	36	39	approximation	approximation	NOUN
ispiv-185	36	40	of	of	ADP
ispiv-185	36	41	the	the	DET
ispiv-185	36	42	non	non	ADJ
ispiv-185	36	43	-	-	ADJ
ispiv-185	36	44	linear	linear	ADJ
ispiv-185	36	45	ray	ray	NOUN
ispiv-185	36	46	trajectory	trajectory	NOUN
ispiv-185	36	47	through	through	ADP
ispiv-185	36	48	density	density	NOUN
ispiv-185	36	49	gradients	gradient	NOUN
ispiv-185	36	50	[	[	X
ispiv-185	36	51	4	4	NUM
ispiv-185	36	52	]	]	PUNCT
ispiv-185	36	53	.	.	PUNCT
ispiv-185	37	1	efforts	effort	NOUN
ispiv-185	37	2	are	be	AUX
ispiv-185	37	3	ongoing	ongoing	ADJ
ispiv-185	37	4	to	to	PART
ispiv-185	37	5	apply	apply	VERB
ispiv-185	37	6	the	the	DET
ispiv-185	37	7	proposed	propose	VERB
ispiv-185	37	8	method	method	NOUN
ispiv-185	37	9	to	to	ADP
ispiv-185	37	10	experimental	experimental	ADJ
ispiv-185	37	11	bos	bo	NOUN
ispiv-185	37	12	data	datum	NOUN
ispiv-185	37	13	.	.	PUNCT
ispiv-185	38	1	references	reference	NOUN
ispiv-185	38	2	[	[	X
ispiv-185	38	3	1	1	NUM
ispiv-185	38	4	]	]	PUNCT
ispiv-185	38	5	m.	m.	NOUN
ispiv-185	38	6	raffel	raffel	NOUN
ispiv-185	38	7	,	,	PUNCT
ispiv-185	38	8	“	"	PUNCT
ispiv-185	38	9	background	background	NOUN
ispiv-185	38	10	-	-	PUNCT
ispiv-185	38	11	oriented	orient	VERB
ispiv-185	38	12	schlieren	schlieren	PROPN
ispiv-185	38	13	(	(	PUNCT
ispiv-185	38	14	bos	bos	PROPN
ispiv-185	38	15	)	)	PUNCT
ispiv-185	38	16	techniques	technique	NOUN
ispiv-185	38	17	,	,	PUNCT
ispiv-185	38	18	”	"	PUNCT
ispiv-185	38	19	exp	exp	NOUN
ispiv-185	38	20	.	.	PUNCT
ispiv-185	38	21	fluids	fluid	NOUN
ispiv-185	38	22	,	,	PUNCT
ispiv-185	38	23	vol	vol	NOUN
ispiv-185	38	24	.	.	PROPN
ispiv-185	39	1	56	56	NUM
ispiv-185	39	2	,	,	PUNCT
ispiv-185	39	3	no	no	INTJ
ispiv-185	39	4	.	.	NOUN
ispiv-185	39	5	3	3	NUM
ispiv-185	39	6	,	,	PUNCT
ispiv-185	39	7	pp	pp	ADJ
ispiv-185	39	8	.	.	PUNCT
ispiv-185	40	1	1–17	1–17	NOUN
ispiv-185	40	2	,	,	PUNCT
ispiv-185	40	3	2015	2015	NUM
ispiv-185	40	4	.	.	PUNCT
ispiv-185	41	1	[	[	X
ispiv-185	41	2	2	2	NUM
ispiv-185	41	3	]	]	PUNCT
ispiv-185	41	4	l.	l.	PROPN
ispiv-185	41	5	k.	k.	PROPN
ispiv-185	41	6	rajendran	rajendran	PROPN
ispiv-185	41	7	,	,	PUNCT
ispiv-185	41	8	j.	j.	PROPN
ispiv-185	41	9	zhang	zhang	PROPN
ispiv-185	41	10	,	,	PUNCT
ispiv-185	41	11	s.	s.	PROPN
ispiv-185	41	12	bhattacharya	bhattacharya	PROPN
ispiv-185	41	13	,	,	PUNCT
ispiv-185	41	14	s.	s.	PROPN
ispiv-185	41	15	p.	p.	PROPN
ispiv-185	41	16	m.	m.	PROPN
ispiv-185	41	17	bane	bane	NOUN
ispiv-185	41	18	,	,	PUNCT
ispiv-185	41	19	and	and	CCONJ
ispiv-185	41	20	p.	p.	PROPN
ispiv-185	41	21	p.	p.	NOUN
ispiv-185	42	1	vlachos	vlachos	ADV
ispiv-185	42	2	,	,	PUNCT
ispiv-185	42	3	“	"	PUNCT
ispiv-185	42	4	uncertainty	uncertainty	NOUN
ispiv-185	42	5	quantification	quantification	NOUN
ispiv-185	42	6	in	in	ADP
ispiv-185	42	7	density	density	NOUN
ispiv-185	42	8	estimation	estimation	NOUN
ispiv-185	42	9	from	from	ADP
ispiv-185	42	10	background	background	NOUN
ispiv-185	42	11	-	-	PUNCT
ispiv-185	42	12	oriented	orient	VERB
ispiv-185	42	13	schlieren	schlieren	PROPN
ispiv-185	42	14	measurements	measurement	NOUN
ispiv-185	42	15	,	,	PUNCT
ispiv-185	42	16	”	"	PUNCT
ispiv-185	42	17	meas	mea	NOUN
ispiv-185	42	18	.	.	PUNCT
ispiv-185	43	1	sci	sci	PROPN
ispiv-185	43	2	.	.	PROPN
ispiv-185	43	3	technol	technol	PROPN
ispiv-185	43	4	.	.	PROPN
ispiv-185	43	5	,	,	PUNCT
ispiv-185	43	6	vol	vol	NOUN
ispiv-185	43	7	.	.	PROPN
ispiv-185	44	1	31	31	NUM
ispiv-185	44	2	,	,	PUNCT
ispiv-185	44	3	no	no	INTJ
ispiv-185	44	4	.	.	NOUN
ispiv-185	44	5	5	5	NUM
ispiv-185	44	6	,	,	PUNCT
ispiv-185	44	7	2020	2020	NUM
ispiv-185	44	8	.	.	PUNCT
ispiv-185	45	1	[	[	X
ispiv-185	45	2	3	3	X
ispiv-185	45	3	]	]	PUNCT
ispiv-185	45	4	p.	p.	NOUN
ispiv-185	45	5	j.	j.	PROPN
ispiv-185	45	6	roache	roache	PROPN
ispiv-185	45	7	and	and	CCONJ
ispiv-185	45	8	p.	p.	PROPN
ispiv-185	45	9	m.	m.	NOUN
ispiv-185	45	10	knupp	knupp	PROPN
ispiv-185	45	11	,	,	PUNCT
ispiv-185	45	12	“	"	PUNCT
ispiv-185	45	13	completed	complete	VERB
ispiv-185	45	14	richardson	richardson	PROPN
ispiv-185	45	15	extrapolation	extrapolation	NOUN
ispiv-185	45	16	,	,	PUNCT
ispiv-185	45	17	”	"	PUNCT
ispiv-185	45	18	commun	commun	PROPN
ispiv-185	45	19	.	.	PUNCT
ispiv-185	46	1	numer	numer	PROPN
ispiv-185	46	2	.	.	PUNCT
ispiv-185	47	1	methods	methods	PROPN
ispiv-185	47	2	eng	eng	PROPN
ispiv-185	47	3	.	.	PROPN
ispiv-185	47	4	,	,	PUNCT
ispiv-185	47	5	vol	vol	NOUN
ispiv-185	47	6	.	.	PROPN
ispiv-185	48	1	9	9	NUM
ispiv-185	48	2	,	,	PUNCT
ispiv-185	48	3	no	no	INTJ
ispiv-185	48	4	.	.	NOUN
ispiv-185	48	5	5	5	NUM
ispiv-185	48	6	,	,	PUNCT
ispiv-185	48	7	pp	pp	ADJ
ispiv-185	48	8	.	.	PUNCT
ispiv-185	49	1	365–374	365–374	NUM
ispiv-185	49	2	,	,	PUNCT
ispiv-185	49	3	1993	1993	NUM
ispiv-185	49	4	.	.	PUNCT
ispiv-185	50	1	[	[	X
ispiv-185	50	2	4	4	X
ispiv-185	50	3	]	]	PUNCT
ispiv-185	50	4	l.	l.	PROPN
ispiv-185	50	5	k.	k.	PROPN
ispiv-185	50	6	rajendran	rajendran	PROPN
ispiv-185	50	7	,	,	PUNCT
ispiv-185	50	8	s.	s.	PROPN
ispiv-185	50	9	p.	p.	PROPN
ispiv-185	50	10	m.	m.	PROPN
ispiv-185	50	11	bane	bane	NOUN
ispiv-185	50	12	,	,	PUNCT
ispiv-185	50	13	and	and	CCONJ
ispiv-185	50	14	p.	p.	PROPN
ispiv-185	50	15	p.	p.	NOUN
ispiv-185	51	1	vlachos	vlachos	ADV
ispiv-185	51	2	,	,	PUNCT
ispiv-185	51	3	“	"	PUNCT
ispiv-185	51	4	piv	piv	NOUN
ispiv-185	51	5	/	/	SYM
ispiv-185	51	6	bos	bos	NOUN
ispiv-185	51	7	synthetic	synthetic	ADJ
ispiv-185	51	8	image	image	NOUN
ispiv-185	51	9	generation	generation	NOUN
ispiv-185	51	10	in	in	ADP
ispiv-185	51	11	variable	variable	ADJ
ispiv-185	51	12	density	density	NOUN
ispiv-185	51	13	environments	environment	NOUN
ispiv-185	51	14	for	for	ADP
ispiv-185	51	15	error	error	NOUN
ispiv-185	51	16	analysis	analysis	NOUN
ispiv-185	51	17	and	and	CCONJ
ispiv-185	51	18	experiment	experiment	NOUN
ispiv-185	51	19	design	design	NOUN
ispiv-185	51	20	,	,	PUNCT
ispiv-185	51	21	”	"	PUNCT
ispiv-185	51	22	meas	mea	NOUN
ispiv-185	51	23	.	.	PUNCT
ispiv-185	52	1	sci	sci	PROPN
ispiv-185	52	2	.	.	PROPN
ispiv-185	52	3	technol	technol	PROPN
ispiv-185	52	4	.	.	PROPN
ispiv-185	52	5	,	,	PUNCT
ispiv-185	52	6	vol	vol	NOUN
ispiv-185	52	7	.	.	PROPN
ispiv-185	52	8	30	30	NUM
ispiv-185	52	9	,	,	PUNCT
ispiv-185	52	10	no	no	INTJ
ispiv-185	52	11	.	.	NOUN
ispiv-185	52	12	8	8	NUM
ispiv-185	52	13	,	,	PUNCT
ispiv-185	52	14	2019	2019	NUM
ispiv-185	52	15	.	.	PUNCT
ispiv-185	53	1	figure	figure	VERB
ispiv-185	53	2	1	1	NUM
ispiv-185	53	3	error	error	NOUN
ispiv-185	53	4	and	and	CCONJ
ispiv-185	53	5	uncertainty	uncertainty	NOUN
ispiv-185	53	6	statistics	statistic	NOUN
ispiv-185	53	7	for	for	ADP
ispiv-185	53	8	the	the	DET
ispiv-185	53	9	sinusoidal	sinusoidal	ADJ
ispiv-185	53	10	field	field	NOUN
ispiv-185	53	11	for	for	ADP
ispiv-185	53	12	two	two	NUM
ispiv-185	53	13	noise	noise	NOUN
ispiv-185	53	14	levels	level	NOUN
ispiv-185	53	15	.	.	PUNCT
ispiv-185	54	1	(	(	PUNCT
ispiv-185	54	2	a	a	X
ispiv-185	54	3	)	)	PUNCT
ispiv-185	54	4	and	and	CCONJ
ispiv-185	54	5	(	(	PUNCT
ispiv-185	54	6	b	b	X
ispiv-185	54	7	)	)	PUNCT
ispiv-185	54	8	represent	represent	VERB
ispiv-185	54	9	the	the	DET
ispiv-185	54	10	spatial	spatial	ADJ
ispiv-185	54	11	variation	variation	NOUN
ispiv-185	54	12	of	of	ADP
ispiv-185	54	13	the	the	DET
ispiv-185	54	14	statistics	statistic	NOUN
ispiv-185	54	15	and	and	CCONJ
ispiv-185	54	16	probability	probability	NOUN
ispiv-185	54	17	density	density	NOUN
ispiv-185	54	18	functions	function	NOUN
ispiv-185	54	19	respectively	respectively	ADV
ispiv-185	54	20	for	for	ADP
ispiv-185	54	21	a	a	DET
ispiv-185	54	22	1	1	NUM
ispiv-185	54	23	%	%	NOUN
ispiv-185	54	24	noise	noise	NOUN
ispiv-185	54	25	level	level	NOUN
ispiv-185	54	26	,	,	PUNCT
ispiv-185	54	27	with	with	ADP
ispiv-185	54	28	(	(	PUNCT
ispiv-185	54	29	c	c	NOUN
ispiv-185	54	30	)	)	PUNCT
ispiv-185	54	31	and	and	CCONJ
ispiv-185	54	32	(	(	PUNCT
ispiv-185	54	33	d	d	X
ispiv-185	54	34	)	)	PUNCT
ispiv-185	54	35	representing	represent	VERB
ispiv-185	54	36	the	the	DET
ispiv-185	54	37	results	result	NOUN
ispiv-185	54	38	for	for	ADP
ispiv-185	54	39	the	the	DET
ispiv-185	54	40	10	10	NUM
ispiv-185	54	41	%	%	NOUN
ispiv-185	54	42	noise	noise	NOUN
ispiv-185	54	43	level	level	NOUN
ispiv-185	54	44	.	.	PUNCT
ispiv-185	55	1	figure	figure	NOUN
ispiv-185	55	2	2	2	NUM
ispiv-185	55	3	results	result	NOUN
ispiv-185	55	4	of	of	ADP
ispiv-185	55	5	the	the	DET
ispiv-185	55	6	analysis	analysis	NOUN
ispiv-185	55	7	with	with	ADP
ispiv-185	55	8	synthetic	synthetic	ADJ
ispiv-185	55	9	bos	bo	NOUN
ispiv-185	55	10	images	image	NOUN
ispiv-185	55	11	.	.	PUNCT
ispiv-185	56	1	(	(	PUNCT
ispiv-185	56	2	a	a	X
ispiv-185	56	3	)	)	PUNCT
ispiv-185	56	4	2d	2d	NUM
ispiv-185	56	5	slice	slice	NOUN
ispiv-185	56	6	of	of	ADP
ispiv-185	56	7	the	the	DET
ispiv-185	56	8	density	density	NOUN
ispiv-185	56	9	field	field	NOUN
ispiv-185	56	10	used	use	VERB
ispiv-185	56	11	to	to	PART
ispiv-185	56	12	render	render	VERB
ispiv-185	56	13	the	the	DET
ispiv-185	56	14	synthetic	synthetic	ADJ
ispiv-185	56	15	bos	bo	NOUN
ispiv-185	56	16	images	image	NOUN
ispiv-185	56	17	,	,	PUNCT
ispiv-185	56	18	(	(	PUNCT
ispiv-185	56	19	b	b	X
ispiv-185	56	20	)	)	PUNCT
ispiv-185	56	21	image	image	NOUN
ispiv-185	56	22	displacements	displacement	NOUN
ispiv-185	56	23	from	from	ADP
ispiv-185	56	24	cross	cross	ADJ
ispiv-185	56	25	-	-	ADJ
ispiv-185	56	26	correlation	correlation	ADJ
ispiv-185	56	27	analysis	analysis	NOUN
ispiv-185	56	28	,	,	PUNCT
ispiv-185	56	29	(	(	PUNCT
ispiv-185	56	30	c	c	NOUN
ispiv-185	56	31	)	)	PUNCT
ispiv-185	56	32	error	error	NOUN
ispiv-185	56	33	in	in	ADP
ispiv-185	56	34	the	the	DET
ispiv-185	56	35	density	density	NOUN
ispiv-185	56	36	field	field	NOUN
ispiv-185	56	37	,	,	PUNCT
ispiv-185	56	38	and	and	CCONJ
ispiv-185	56	39	(	(	PUNCT
ispiv-185	56	40	d	d	X
ispiv-185	56	41	)	)	PUNCT
ispiv-185	56	42	numerical	numerical	ADJ
ispiv-185	56	43	uncertainty	uncertainty	NOUN