articlebarseghyan.DVI


Mathematical Problems of Computer Science 32, 48{55, 2009.

P ointwise Reconstr uction of I nter fer ometr ic P hase

Y u r i A . B a r s e g h ya n

Yerevan State University

yuri.barseghyan@gmail.com

Abstract

In this work the problem of interferometric phase reconstruction is considered.
The pointwise approximation approach is proposed, which provides stable results even
for bad quality of interferogramms. Experimental results show that the developed
algorithm demonstrates better performance in comparison with some of the state-of-
the-art techniques.

Refer ences

[1 ] L . C. Gr a h a m , " S yn t h e t ic in t e r fe r o m e t e r r a d a r fo r t o p o g r a p h ic m a p p in g " , P roceedings
of the IE E E , vo l. 6 2 , p . 7 6 3 , 1 9 7 4 .

[2 ] R .M. Go ld s t e in , H .A . Ze b ke r , C.L . W e r n e r , " S a t e llit e r a d a r in t e r fe r o m e t r y: Two -
d im e n s io n a l p h a s e u n wr a p p in g " , R adio Science, vo l. 2 3 , p . 7 1 3 , 1 9 9 7 ,

[3 ] D .C. Gh ig lia , P .H . E ic h e l, " H ig h -r e s o lu t io n s yn t h e t ic a p e r t u r e r a d a r in t e r fe r o m e t r y:
Te c h n o lo g y fo r p r e c is e t e r r a in e le va t io n m a p p in g " . D S P a n d Mu lt im e d ia Te c h n o lo g y,
v.3 , 1 9 9 4 .

[4 ] D . L . Fr ie d , " L e a s t -s qu a r e s ¯ t t in g a wa ve -fr o n t d is t o r t io n e s t im a t e t o a n a r r a y o f
p h a s e -d i®e r e n c e m e a s u r e m e n t s " , J ournal of the Optical Society of America, vo l.6 7 ,
N o . 3 , p .3 7 0 -3 7 5 , 1 9 7 7 .

[5 ] W . W . A r r a s m it h , M. C. R o g g e m a n n , B . M W e ls h , " Op t im a l wa ve -fr o n t r e c o n s t r u c t io n
fo r a c o h e r e n t d i®r a c t e d ¯ e ld " , Applied Optics, vo l.3 7 , N o . 2 0 , p .4 4 5 7 -4 4 6 7 , 1 9 9 8 .

[6 ] R . J. N o ll, " P h a s e e s t im a t e s fr o m s lo p e -t yp e wa ve -fr o n t s e n s o r s " , J ournal of the Optical
Society of America, vo l.6 8 , N o . 1 , p .1 3 9 -1 4 0 , 1 9 7 8 .

[7 ] A . H e r m e n t , E . Mo u s s e a u x, O. Jo live t , A . D e Ce s a r e , F. Fr o u in , A . To d d -P o kr o p e k, J.
B it t o u n . " Im p r o ve d e s t im a t io n o f ve lo c it y a n d ° o w r a t e u s in g r e g u la r iz e d t h r e e -p o in t
p h a s e -c o n t r a s t ve lo c im e t r y" , M agnetic R esonance in medicine, vo l.4 4 , p .1 2 2 -1 2 8 , 2 0 0 0 .

[8 ] M. H e d le y, D . R o s e n fe ld . " A n e w t wo -d im e n s io n a l p h a s e u n wr a p p in g a lg o r it h m fo r
MR I im a g e s " , M agnetic R esonance in M edicine, vo l. 2 4 , p .1 7 7 -1 8 1 , 1 9 9 2 .

[9 ] G. H . Glo ve r , E . S c h n e id e r . \ Th r e e -p o in t d ixo n t e c h n iqu e fo r t r u e wa t e r / fa t d e c o m -
p o s it io n wit h B0 in h o m o g e n e it y c o r r e c t io n " , M agnetic R esonance in M edicine, vo l.1 2 ,
p .3 7 1 -3 8 3 , 1 9 9 1 .

[1 0 ] W . W . A r r a s m it h , M. C. R o g g e m a n n , B . M. W e ls h , " Op t im a l wa ve -fr o n t r e c o n s t r u c -
t io n fo r a c o h e r e n t d i®r a c t e d ¯ e ld " , Applied Optics, vo l.3 7 , N o .2 0 , p .4 4 -5 7 , 1 9 9 8 .

4 8



Y. Barseghyan 4 9

[1 1 ] D . C. Gh ig lia , M. D . P r it t , Two-dimensional phase unwrapping: theory, algorithms,
and software. N e w Y o r k: W ille y, 1 9 9 8 .

[1 2 ] K . H o a n d J. K a h n , " E xa c t p r o b a b ilit y d e n s it y fu n c t io n fo r p h a s e m e a s u r e m e n t in t e r -
fe r o m e t r y" . J . Opt. Soc. Amer., vo l. 1 2 , p .1 9 8 4 -1 9 8 9 , 1 9 9 5 .

[1 3 ] J. L e e , K . H o p p e l, S . Ma n g o , a n d A . Mille r , " In t e n s it y a n d p h a s e s t a t is t ic s o f m u lt ilo o k
p o la r im e t r ic a n d in t e r fe r o m e t r ic S A R im a g e r y" , IE E E Trans. Geosci. R emote Sensing,
vo l.3 2 , p .1 0 1 7 -1 0 2 8 , 1 9 9 4 .

[1 4 ] S . Ma d s e n , " S p e c t r a l p r o p e r t ie s o f h o m o g e n e o u s a n d n o n h o m o g e n e o u s r a d a r im a g e s " ,
IE E E Trans. Aerosp. E lectron. Syst., vo l. A E S -2 3 , p . 5 8 3 -5 8 8 , 1 9 8 7 .

[1 5 ] C. R a t h je n , " S t a t is t ic a l p r o p e r t ie s o f p h a s e -s h ift a lg o r it h m s " , J . Opt. Soc. Amer., vo l.
1 2 , p . 1 9 9 7 -2 0 0 8 , 1 9 9 5 .

[1 6 ] V . K a t ko vn ik, K . E g ia z a r ia n , J. A s t o la , L ocal approximation techniques in signal and
image processing. S P IE P R E S S , B e llin g h a m , W a s h in g t o n , 2 0 0 6 .

[1 7 ] J. D ia s a n d J. L e it a o , \ Th e a lg o r it h m : A m e t h o d fo r in t e r fe r o m e t r ic im a g e r e c o n s t r u c -
t io n in S A R / S A S " , IE E E Trans. Image P rocess., vo l. 1 1 , N o . 4 , p . 4 0 8 -4 2 2 , 2 0 0 2 .

ÆÝï»ñý»ñ»ÝóÇáÝ ÷áõÉÇ Ï»ï ³é Ï»ï í»ñ³Ï³Ý·ÝáõÙ

Ú. ´³ñë»ÕÛ³Ý

²Ù÷á÷áõÙ

²ß˳ï³ÝùáõÙ ùÝݳñÏíáõÙ ¿ ÇÝï»ñí»ñáÙ»ïñÇÏ³Ï³Ý ÷áõÉÇ í»ñ³Ï³Ý·ÝÙ³Ý
ËݹÇñÁ: ²é³ç³ñÏíáõÙ ¿ Ï»ï ³é Ï»ï Ùáï³ñÏÙ³Ý Ù»Ãá¹, áñÁ ³å³ÑáíáõÙ ¿
ϳÛáõÝ ³ñ¹ÛáõÝùÝ»ñ ÝáõÛÝÇëÏ ÇÝï»ñý»ñ»ÝóÇáÝ å³ïÏ»ñÝ»ñÇ í³ï áñ³ÏÇ ¹»åùáõÙ:
öáñÓ»ñÇ ³ñ¹ÛáõÝùÝ»ñÁ óáõÛó »Ý ï³ÉÇë, áñ ³é³ç³ñÏí³Í ³É·áñÇÃÙÁª ѳٻٳï³Í ³ÛÉ
³é³ç³ï³ñ Ù»Ãá¹Ý»ñÇ Ñ»ï, ï³ÉÇë ¿÷áõÉÇ í»ñ³Ï³Ý·ÝÙ³Ý ×ßïáõÃÛ³Ý ½·³ÉÇ É³í³óáõÙ: