Three-dimensional Information and Refractive Index Measurement Using a Dual-wavelength Digital Holographic Microscope

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1 Journa of the Optica Society of Korea Vo. 13, No., June 009, pp DO: /JOSK Three-dimensiona nformation and Refractive ndex Measurement Using a Dua-waveength Digita oographic Microscope Sanghoon Shin AP & Tec, Suseo Dong, Kangnam Gu, Seou , Korea Younghun Yu* Department of Physics, Cheju Nationa University, Jeju , Korea (Received March 3, 009 : revised May 7, 009 : accepted June 9, 009) Digita hoographic microscopy aows optica path difference measurement. Optica path difference depends on the both refractive index and morphoogy of sampe. We deveoped a dua-waveength in-ine digita hoographic microscope that can measure simutaneousy the refractive index and morphoogy of a sampe, providing highy precise three-dimensiona information. ere we propose theoretica and experimenta methods for dua-waveength in-ine digita hoographic microscopy. The measured data were reasonabe, athough there was data error. By improving the experimenta method, we coud measure the refractive index more precisey and obtain more accurate threedimensiona information on sampes. Keywords : oography, mage reconstruction, Diffractive optics OCS codes : ( ) oography; ( ) mage reconstruction; ( ) Diffractive optics. NTRODUCTON oography is a method of recording phase moduation by using the ight refected or transmitted from a projected object onto a photopate in the form of interference patterns. Object and reference beams are required for the recording, and an interference pattern is generated from the combination of the two beams. n the past, the interference patterns were recorded on fim pates, but now charge-couped devices (CCDs) or compementary meta-oxide semiconductor cameras are normay used, and a computer is used to reconstruct the hoogram. Yarosavskii and his coeague proposed a method of numerica hoogram reconstruction in the 1970s, and Ounra and Scott used numerica reconstruction to measure the size of a partice after improving on the reconstruction agorithm [1-6]. This method of digitay recording and reconstructing a numerica hoogram is known as digita hoography [7-10]. Digita hoography has many advantages. For exampe, it does not require any chemica *Corresponding author: yyhyoung@cheju.ac.kr processing because the reconstructed image can be easiy observed on a computer monitor, and experts can obtain numerica data for three-dimensiona (3-D) objects [11,1]. n the reconstruction process, the refractive index of the sampe is either known or assumed to be homogeneous. Practicay, the phase shift, or optica path difference induced from the difference in refractive index between the sampe and the surrounding medium and is proportiona to the thickness of the sampe. f the refractive index of the sampe is unknown or not homogeneous, the reconstructed 3-D image wi not be identica to the origina sampe [8]. This is a imitation of digita hoography. f one measures the refractive index using digita hoography, one can determine the 3-D shape of the sampe [13,14]. n this study, we constructed a dua-waveength in-ine digita hoographic microscope system for measuring the refractive index of a sampe. After measuring some hoograms, we cacuated the refractive index of the sampes using the phase difference between the hoograms. The measured indexes represented the refractive vaues and refractive index distributions of the sampe

2 174 Journa of the Optica Society of Korea, Vo. 13, No., June 009. TEORETCAL MODEL 1. oogram recording and reconstruction n the hoogram recording process, a pane reference wave (R) and a diffusivey refected object wave (O) interfere at the CCD. The hoogram intensity is given by * * ( = R + O + R O + RO, (1) n s,h n m where R * and O * denote the compex conjugates of the reference and object waves, respectivey [1,]. The digita hoographic image can be recorded using a back-andwhite CCD camera. The digita hoogram (k.) is an N N array resuting from the two-dimensiona samping of ( by the CCD camera. t is given by ( k, ) = x y N / N / ( rect(, ) å å d ( x - kd y - D L L k=-n / =-N /, () where K and are integers, L L denotes the area of the CCD chip, and Δx and Δy indicate the pixe size of the CCD. n cassica optica hoography, the object wave can be reconstructed by iuminating the processed hoogram with a pane wave simiar to that used in the recording process. Looking through the hoogram, one observes a virtua image. f a screen is paced at a distance d behind the hoogram, a rea image is formed on it. Mathematicay, the ampitude and phase distributions in the pane of the rea image can be found using the Fresne- Kirchhoff integra [1,]. f a pane wave iuminates the hoogram with an ampitude transmittance (, the Fresne-Kirchhoff integra yieds a compex ampitude in the rea image pane exp( i p d / ) ip ip Y ( x, h) = exp[ ( x + h )] ò ò ( exp[ ( x + y )] id d d ip exp[ ( x + h ] dxdy,, d (3) where λ is the waveength and d is the reconstruction distance. From Eq. (3), the Fresne-Kirchhoff integra can be considered the Fourier transformation of the function ( exp[ ip ( x + y ) / d] at the spatia frequencies and. Because is an array of compex numbers, one can obtain an ampitude-contrast image using the intensity ( h) = Re[ Y( + m[ Y(. (4) The phase-contrast image is obtained by cacuating FG. 1. Optica path difference between sampes with different refractive indexes. the argument m[ Y( y ( h) = arctan{ } Re[ Y(. (5) The rea three-dimensiona information is acquired by phase unwrapping with phase contrast image.. Measurement of the refractive index using a duawaveength hoogram Consider the optica path difference of a beam traveing through the transparent sampe aong the arrow in Fig. 1: OPD( = ( n ( n ( ) h(. (6) s - m The phases with dua waveengths are given by p f1( y; = OPD( y, 1 p f ( y; = OPD( y, ). (7) f n m and n s remain amost the same between two waveengths and one refractive index n m or n s is known at two waveengths, one can cacuate simutaneousy the average of the other refractive index and the height. The refractive index of sampe is given by 1f1 nm ( 1 ) + nm ( ) f n s ( = (8) 1f1-1 f To cacuate the refractive index of the sampe, the dua waveength hoogram recording is performed sequentiay. The concept of recording two hoograms at different waveength has been demonstrated and is proposed to sove π ambiguities in digita hoography [15-18]. We can cacuate the distribution of refractive indices of the sampe simutaneousy using dua-waveength digita hoography. This is a merit of dua-waveength digita hoo-

$Three-dimensiona nformation and Refractive ndex - Sanghoon Shin et a. 175 e-ne Laser BS graphy.$ To cacuate the phase of the same point from a hoogram with a different waveength, one shoud resize the hoograms [19-0]. Laser Diode M. EXPERMENTAL SETUP AND RESULTS FG.

To cacuate the phase of the same point from a hoogram with a different waveength, one shoud resize the hoograms [19-0]. Laser Diode M. EXPERMENTAL SETUP AND RESULTS FG.

$(a) (c) (e) (b) (d) (f) FG. 3. Dua-waveength hoography and refractive index of a micro-ens array. (a), (d) oogram created using e- Ne aser (63 nm) and aser diode (53 nm).$ $(b), (e) Phase unwrapping grayscae image of hoograms (a) and (d), respectivey. (c) Three-dimensiona image and (f) grayscae of refractive index.$ A 10-mW e-ne aser and 53-nm aser diode were used as the ight source, and the objective ens of a microscope (ML) was used to expand the beam passing through the sampe.

A 10-mW e-ne aser and 53-nm aser diode were used as the ight source, and the objective ens of a microscope (ML) was used to expand the beam passing through the sampe.

We used a CCD camera (Sony PX4M15L) to record the hoograms. The pixe size and the number of pixes were 7.4 μm 7.4 μm and 048 048, respectivey.

3 Three-dimensiona nformation and Refractive ndex - Sanghoon Shin et a. 175 e-ne Laser BS graphy. Usuay, scanning processes are necessary to measure the refractive indices distribution on the sampe in previous work. To cacuate the phase of the same point from a hoogram with a different waveength, one shoud resize the hoograms [19-0]. Laser Diode M. EXPERMENTAL SETUP AND RESULTS FG.. Transmission-type dua-waveength digita hoographic microscope. VN: variabe-density fiter; BS: beam spitter; M: mirror; O: object wave; R: reference wave; BE: beam expander with spatia fiter; ML: microscope objective ens; CCD: charge-couped device. (a) (c) (e) (b) (d) (f) FG. 3. Dua-waveength hoography and refractive index of a micro-ens array. (a), (d) oogram created using e- Ne aser (63 nm) and aser diode (53 nm). (b), (e) Phase unwrapping grayscae image of hoograms (a) and (d), respectivey. (c) Three-dimensiona image and (f) grayscae of refractive index. Figure shows a schematic of a dua-waveength transmission hoographic microscope. The basic experimenta setup is simiar to that of a Mach-Zehnder-type interferometer. A 10-mW e-ne aser and 53-nm aser diode were used as the ight source, and the objective ens of a microscope (ML) was used to expand the beam passing through the sampe. We used neutra-density fiters (VN) to obtain the interference patterns for maximum contrast. A beam expander (BE) was used for the reference beam in the TEM 00 mode. We used a CCD camera (Sony PX4M15L) to record the hoograms. The pixe size and the number of pixes were 7.4 μm 7.4 μm and , respectivey. The CCD was paced 0 cm from the ML, and the overapping ange between the reference and objective rays was maintained at 0, resuting in in-ine hoography. Figure 3 shows the experimenta resuts of a micro-ens array. The height and diameter of micro-ens are 50 μm and 30 μm, respectivey. The refractive index of this ens, which was made of poyethyene terephthaate, was at the 550-nm waveength. The index matching oi was used for reference (n m ). ts refractive index was 1.56 at the 63-nm waveength and at the 53-nm waveength. We used index matching oi to resove the π ambiguity, because the height of the sampe was greater than that of the waveength [17,18]. f the height of the sampe had been ess than the waveength, the matching oi woud not have been necessary. Figures 3(a) and (d) are hoograms created by the e-ne aser (63 nm) and aser diode (53 nm), respectivey. To cacuate the optica path difference by refractive index of the micro-ens array, we constructed a 3-D image using phase unwrapping. Figures 3(b) and (e) are the 3-D gray-eve images of hoograms (a) and (d). Resizing was necessary to cacuate the phase of the same point from a hoogram of different waveength. Remember that dua-waveength digita hoography measures the refractive index of a pane rather than a point in the sampe. We cacuated the refractive index of the micro-ens using Eqs. (7) and (8). Figure 3(f) shows the cacuated gray-eve refractive index image. As shown in Fig. 3(f), the gray eves were amost the same, which means that the whoe region had the same refractive index. This resut is reasonabe, because the micro-ens array was made from one materia. Athough the measured vaue of 1.56 was different from the manufacturer's specification of 1.575, dua-waveength digita hoography

$176 Journa of the Optica Society of Korea, Vo. 13, No., June 009 (a) (b) (c) (d) (e) FG. 4. Dua-waveength hoography and refractive index of a thin fim transistor on gass.$ $is appicabe to measurements of the refractive index. Figure 3(c) shows a 3-D image of the micro-ens. Figure 4 shows experimenta resuts for the thin fim transistor on gass.$ $Figure 4(d) is the 3-D image of the thin fim transistor on the gass. Figure 4(c) shows the cacuated refractive index using phase unwrapping resuts (a) and (b). As shown in Fig.$ $4(c), the gray eves were different for the gass and PR regions. This is a resut of the difference in the refractive indexes of PR and gass.$ $From these resuts, we confirmed that dua-waveength digita hoography is appicabe to refractive index and 3-D shape measurement. V.$

4 176 Journa of the Optica Society of Korea, Vo. 13, No., June 009 (a) (b) (c) (d) (e) FG. 4. Dua-waveength hoography and refractive index of a thin fim transistor on gass. (a), (b) Phase unwrapping image of hoogram created using a e-ne aser (63 nm) and aser diode (53 nm), respectivey. (c) gray eve of refractive index and (d) 3-D image, (e) design of TFT. is appicabe to measurements of the refractive index. Figure 3(c) shows a 3-D image of the micro-ens. Figure 4 shows experimenta resuts for the thin fim transistor on gass. The pattern was fabricated by a photo-resistor (PR). The refractive index of the PR and gass were 1.68 and 1.54, respectivey. Figures 4(a) and (b) show the phase unwrapping image of the hoogram created using dua-waveength digita hoography, where (a) is the resut of the e-ne aser (63 nm) and (c) the aser diode (53 nm). Figure 4(d) is the 3-D image of the thin fim transistor on the gass. Figure 4(c) shows the cacuated refractive index using phase unwrapping resuts (a) and (b). As shown in Fig. 4(c), the gray eves were different for the gass and PR regions. This is a resut of the difference in the refractive indexes of PR and gass. The cacuated average refractive indexes of PR and gass were 1.64 and 1.5, which were in reasonabe agreement with actua vaues. From these resuts, we confirmed that dua-waveength digita hoography is appicabe to refractive index and 3-D shape measurement. V. CONCLUSONS measure optica path differences with a high degree of accuracy. Optica path differences depend on the refractive index and morphoogy of the sampes. To acquire 3-D information on a sampe, one must know either the refractive index or the morphoogy. We have deveoped a dua-waveength digita hoographic microscope that can measure the refractive index and morphoogy separatey. And we can cacuate the distribution of refractive indices of the sampe simutaneousy using dua-waveength digita hoography. This is a merit of dua-waveength digita hoography. Usuay, scanning processes are necessary to measure the refractive indices distribution on the sampe in previous work. This system is appicabe to measure the refractive index vaue and distribution of sampe. ACKNOWLEDGMENT This study was supported by the Korean Ministry of Commerce, ndustry, and Energy. A number of the researchers participating in this study were supported by a grant from the Second-phase BK1 project. Digita hoographic microscopy can be used to

5 Three-dimensiona nformation and Refractive ndex - Sanghoon Shin et a. 177 REFERENCES 1. E. Cuche, P. Marquet, and C. Depeursinge, Simutaneous ampitude-contrast and quantitative phase-contrast microscopy by numerica reconstruction of Fresne off-axis hoograms, App. Opt. 38, (1999).. L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, Studies of digita microscopic with appication to microstructure testing, App. Opt. 40, (001). 3. M. Jeong, N. Kim, and J.. Park, Eementa image synthesis for integra imaging using phase-shifting digita hoography, J. Opt. Soc. Korea 1, (008). 4. M. A. Kronrod, N. S. Merzyakov, and L. P. Yarosavski, Reconstruction of hoogram with a computer, Sov. Phys. Tech. 17, (197). 5. L. P. Yarosavskii and N. S. Merzyakov, Methods of Digita oography (Consutants Bureau, New York, USA, 1980). 6. L. Onura and P. D. Scott, Digita decoding of in-ine hoograms, Opt. Eng. 6, (1987). 7. J. W. Goodman, ntroduction to Fourier Optics, nd ed., edited by J. Goodman (McGraw i, New York, USA, 005), Chapter U. Schnars and W. Juepther, Digita oography, edited by U. Schnars and W. Juepther (Springer, eideberg, Germany, 005). 9. L. Xu, J. Miao, and A. Asundi, Properties of digita hoography based on in-ine configuration, Opt. Eng. 39, (1999). 10. C. Depeursinge, Digita oography and Three-dimensiona Dispay, edited by T. C. Poon (Springer, New York, USA, 006). 11. D. Kim, B. J. Baek, Y. D. Kim, and B. Javidi, 3D nano object recognition based on phase measurement technique, J. Opt. Soc. Korea 11, (007). 1. J. W. Kang and C. K. ong, Three dimensiona shape measurement of a micro Fresne ens with in-ine phaseshifting digita hoographic microscopy, J. Opt. Soc. Korea 10, (006) Cho, J. Lim, D. C. Kim, S. Shin, and Y. Yu, Threedimensiona information and two-dimensiona refractive index measurements using combined digita hoographic microscope, J. Korean Phys. Soc. 53, (008). 14. J. Kühn, F. Charrièrea, T. Coomba, E. Cuche, Y. Emery, and C. Depeursinge, Measurements of Corner cubes microstructures by high-magnification digita hoographic microscopy, Proc. SPE 6188, (006). 15. C. Pohemus, Two-waveength interferometry, App. Opt. 1, (1973). 16. J. Gass, A. Dako, and M. K. Kim, Phase imaging without pi ambiguity by mutiwaveength digita hoography," Opt. Lett. 8, (003). 17. Y. Fu, G. Pedrini, B. enney, R. Groves, and W. Osten, Dua-waveength image-pane digita hoography for dynamic measurement, Opt. Laser Techno. 47, (008) 18. K. Creath, Y. Cheng, and J. C. Wyant, Contouring aspheric surfaces using two-waveength phase-shifting interferometry, Optica Acta 3, (1985). 19. P. Ferraro, S. D. Nicoa, G. Coppoa, A. Finizio, D. Afieri, and G. Pierattini, Controing image size as a function of distance and waveength in Fresne-transform reconstruction of digita hoograms, Opt. Lett. 9, (004). 0. N. Demoi, D. Vukicevic, and M. Torzynski, Dynamic digita hoographic interferometry with three waveengths, Opt. Exp. 11, (003).

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