-optical Engineering 47(5), 054301 (May 2008)
Shearographic phase retrieval using one single specklegram: a clustering approach Yuan H. Huang Slu P. Ng, MEMBER SPJE Long Liu Yun S. Chen Michael Y. Y. Hung, MEMBER SPlE City University of Hong Kong Department of Manufacturing Engineering and Engineering Management 83 Tat Chee Avenue Hong Kong, Hong Kong 888888 E-mail:
[email protected]
Abstract. !n the field of optical measurement, phase always represents the physlcal quantity to be measured. Thus, phase retrieval from a fringe pattern is a key step for quantitative measurement and evaluation. Much research work has been conducted to develop phase evaluation math· ods such as fr\nge tracking and fringe skeletons in earlier, and the more precise methods of phase-shifting and Fourier transform more recently. For phase evaluation, the phase-shifting method requires three or more phase-shilled speckle patterns at each defonned stage; thus, it is not suitable for measurement of continuous deformation. The Fourier trans· form, on the other hand, requires a high-frequency carrier for phase separation in the spectra! domain, which places an additional requirement on experimental arrangement. Thus, it would be desirable to develop a convenient method that can retrieve the modulated phase from a single fringe pattern. We propose an approach that utilizes tho phaseclustering property to extract phase Information from a single interterence spccklegram. To explore the ability and limitation for the proposed technique, typical shoarographic fringe patterns are used for phase evaluation. Results obtained are similar to those from the standard fourstep phase-shifting method. Nonrepeatab!e continuous movement is a!so measured by the proposed method, and the results confirm the robustness and accuracy of the clustering method. © 2008 Social>' of PilotoOplfcallnslrumoolation Engineers. [001: 10.1117/1.2927462]
Subject terms: shearography; phase evaluation: clustering method; cont1nuous deformation measurement.
Paper 07102.1R received Dec. 26, 2007; revised manuscript received Feb. 18, 2008; accepted lor publicat!on Feb. 20, 2008; published online May 16, 2008.
Introduction Shearography is an interferometric technique developed to address sevemllimitations of holography. n~ significant advantages include (1) not requiring a reference light-beam, thuS leading to simple optical setups, reduced coherence length requirement of the laser, and lux vibration isolation; and (2) direct measurement of surface strains (first-order derivatives of sutface di:;placemcnts). These distinct advantages have rendered sheurography a practical measurement tool and it has already gained wide industtial acceptance for nonJe.~tructive testing. TI1e rubber iadustry routinely uses shearography for evaluating tires, anJ the aerospace indushy has adopted it for nondestructive testing of composite structures. [n particular, the teclUJiquc was endorsed by the Federal Aviation Administration (FAA) for impeding aircraft tires. Other appli;.;ations of sllearography indude meawremcnt of strain~, material properties, re~idual stresses, 3-D shapes, vibrations and leakage r.letedion. A detailed Jescriptioa of shearography and applications can be found in Ref. 1. A key step in applying shearography for slope ami displacement mea.~uremcnt is phase retrieval. The ~base· shifting tedmique2 and the Fourier transform method have been reported by many researchers to obtain shearographic phase. However, the phase-shifting technique requires three 009l.-3286!2ClO:;J$2S.OO Q)
Optical Engineering
200~
SPIE
or more speckle pa!lerus at each deformed stage. This makes it difficult to measure nonrepeatable dynamic deformation. The Fourier transform method, though involving only one specklegram, requires a high-frequency carrier flinges fur phase separation in the spectrum ([omain. Thus, there is a need for a simpk but accurate method to extract ph ami accuracy of the jn\ljltlseJ method.
2
(e)
1'1
,,,
lo)
Principles
2.1 Background In liolugraphy anJ :;heurogr;tphy, the speckle pattern resulted from random illti;rfercncc can be
e.\pn~s5ed a~
I(x,y) "'a(x,y) + b(x,y) cos [4•(x,y)],
(I)
where I(x,y}=intetlsily of the speckle u("1 ,y) "'buchground inteno.ily b(_,·,y)-=fringc 1\\oJulation tn
I~"' a+ b[cos (¢+A+ 71")],
I'(x,y) = a(x,y) + b(x,y) cos ['¢(x,y) + ll(x,y)],
wboon.l .:l(x ,y) is thll
pha~.o
(b)
{2)
dwuge related to ll1e ddunna"
tion. The uitimutc; aim of all th.:: phase rctrieval1ndhoJ~ is tn ac..:uratdy ll,\trad .l(x,y) fmm the sped.Je pattems ob(,;ined before anJ after tlw dcfunnalion. Tbe four-step phu..w ~hifting method, which is must commonly used for pha~e na[llcllion, employs four image~ before aud four af~ t 0.
(7)
By u~ing the: spccia!Iy Je~igned mcbn2 funaiuJl in~tead of the nonml an:tlim~tm," J. Opr. Soc. Am, A 22(12), 276fJ- 2773 (2005) 9. F. Chen, "'Digil~l sil~arography: >late f th~ ml anti ~om~ applications," J. Elccmm. fm~''' "F'i"ge-pu\t~UJ uu~ly ·'io u.,in~; a 2-D f'
6. M. Adachi, J. N. Petzing, and David Kerr, "Dduunution-pl~o•>~ mc~ oUt"c.mcnt Df J,ttuoc object& that haw, otallcd nunrepc~t~bie Jyn:unj,; Jd"onuuliun," tlpp!, Opr., 4(1(34), 6187-6192 (200!). 7 M. Ada~bi, Y. l!~y,\fWL, -.nJ lC lnabe, "Aut()LLL~lic: Jefuunati"" mluiy· W; in elcctroni~ opccLk patkw interfc
