Ronald Driggers, Editor-in-Chief
Daisuke Barada, Tomohiro Kiire, Jun-ichiro Sugisaka, Shigeo Kawata, and Toyohiko Yatagai
Daisuke Barada,1,2,* Tomohiro Kiire,2 Jun-ichiro Sugisaka,2 Shigeo Kawata,1,2 and Toyohiko Yatagai1,2
1Graduate School of Engineering, Utsunomiya University, 7-1-2 Yoto, Utsunomiya, Tochigi 321-8585, Japan
2Center for Optical Research and Education, Utsunomiya University, 7-1-2 Yoto, Utsunomiya, Tochigi 321-8585, Japan
*Corresponding author: firstname.lastname@example.org‐u.ac.jp
This paper presents a method based on the use of an image sensor for obtaining the complex amplitudes of beams diffracted from an object at two different wavelengths. The complex amplitude for each wavelength is extracted by the Doppler phase-shifting method. The principle underlying the proposed method is experimentally verified by using the method with two lasers having different wavelengths to measure the surface shape of a concave mirror.
© 2011 Optical Society of America
R. Jang, C. S. Kang, J. A. Kim, J. W. Kim, J. E. Kim, and H. Y. Park, “High-speed measurement of three-dimensional surface profiles up to 10 μm using two-wavelength phase-shifting interferometry utilizing an injection locking technique,” Appl. Opt. 50, 1541–1547 (2011).
Y. Kikuchi, D. Barada, T. Kiire, and T. Yatagai, “Doppler phase-shifting digital holography and its application to surface shape measurement,” Opt. Lett. 35, 1548–1550 (2010).
P. K. Upputuri, N. K. Mohan, and M. P. Kothiyal, “Measurement of discontinuous surface using multiple-wavelength interferometry,” Opt. Eng. 48073603 (2009).
S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48, 09LB01 (2009).
C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16, 9753–9764 (2008).
T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787–4792 (2008).
J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phaseshifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. 28, 1141–1143 (2003).
C. E. Towers, D. P. Towers, and J. D. C. Jones, “Optimum frequency selection in multifrequency interferometry,” Opt. Lett. 28, 887–889 (2003).
A. Hettwer, J. Kranz, and J. Schwider, “Three channel phaseshifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960–966 (2000).
I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
R. Onodera and Y. Ishii, “Two-wavelength phase-shifting interferometry insensitive to the intensity modulation of dual laser diodes,” Appl. Opt. 33, 5052–5061 (1994).
P. Groot and S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. 30, 4026–4033 (1991).
K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816(1987).
L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
Y. Y. Cheng and J. C. Wyant, “Multiple-wavelength phase-shifting interferometry,” Appl. Opt. 24, 804–807(1985).
Y. Y. Cheng and J. C. Wyant, “Two-wavelength phase-shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with computer,” Soviet Physics Technical Physics 17, 333–334 (1972).
J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Company, 2005), pp. 57–61.
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Schematic of simultaneous two-wavelength phase-shifting digital holography. BS, OL, and SF denote beam splitter, objective lens, and spatial filter, respectively.
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Experimental setup for simultaneous two-wavelength phase-shifting digital holography. LD, BS, OL, and SF denote diode laser, beam splitter, objective lens, and spatial filter, respectively. The optical system is installed on a breadboard.
Temporal variation of digital hologram. (a) and (b) are images captured on the CMOS image sensor in different timing. (c) and (d) are the temporal variation of the pixel values at two pixels A and B as shown in (a) and (b).
Beat frequency spectrum and beat signals. (a) is the beat frequency spectrum obtained by temporal Fourier transform of the temporally varied pixel values as shown in Fig. 3(c) and (d). (b) and (c) are extracted beat signals for the wavelength of 635 nm and 650 nm, respectively. Solid and dashed lines are beat frequency spectrum and extracted beat signal at the pixels A and B, respectively.
Phase distributions for the wavelengths of (a) 635 nm and (b) 650 nm.
Surface shape of the concave mirror reconstructed from the phase difference between two phase distributions as shown in Figs. 5(a) and (b). (a) is the three-dimensional shape. Wire frame shows an ideal concave shape. (b) is a profile along the x-direction through the center pixels in y-direction. Solid and dashed lines are the experimental result and the ideal concave shape, respectively.
Surface shape of the concave mirror reconstructed from the phase distribution in Fig. 5(a). The phase is unwrapped by determining the number of the uncertainty. (a) is the three-dimensional shape. Wire frame shows an ideal concave shape. (b) is a profile along the x-direction through the center pixels in y-direction. Solid and dashed lines are the experimental result and the ideal concave shape, respectively.
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