Paper:

# Dual-Wavelength Digital Holography Based on Phase-Division Multiplexing Using Four Wavelength-Multiplexed Phase-Shifted Holograms and Zeroth-Order Diffraction-Image Suppression

## Tatsuki Tahara^{*1,*2,†}, Reo Otani^{*3}, Yasuhiko Arai^{*1}, and Yasuhiro Takaki^{*4}

^{*1}Faculty of Engineering Science, Kansai University

3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan

^{*2}PRESTO, Japan Science and Technology Agency, Saitama, Japan

^{†}Corresponding author

^{*3}SIGMAKOKI Co., Ltd., Saitama, Japan

^{*4}Institute of Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan

We propose a dual-wavelength phase-shifting digital holography technique with four wavelength-multiplexed holograms based on phase-division multiplexing utilizing the 2π ambiguity and zeroth-order diffraction-image suppression. Zeroth-order wave suppression is implemented by introducing the averaging method. Its effectiveness is experimentally shown and numerically and quantitatively investigated. The numerical investigation demonstrates the tolerance of the proposed technique against incoherent light noise and changes in the reference wave intensity. The image quality in the proposed technique depends on the intensity ratio between the object and reference waves but does not degrade with constant changes in intensity. In contrast, a previously reported four-step dual-wavelength phase-shifting technique was affected by the factors described above.

- [1] Y. Mizutani and T. Iwata, “Thin film thickness measurement by surface plasmon resonance using a modified Otto’s configuration combined with ellipsometry,” Int. J. of Automation Technology, Vol.5, No.2, pp. 236-240, 2011.
- [2] S. Jang, T. Asai, Y. Shimizu, and W. Gao, “Optical analysis of an optical probe for three-dimensional position detection of micro-objects,” Int. J. of Automation Technology, Vol.5, No.6, pp. 862-865, 2011.
- [3] T. Watanabe and Y. Saito, “Camera modeling for 3D sensing using fuzzy modeling concept based on stereo vision,” J. Adv. Comput. Intell. and Intell. Inform., Vol.19, No.1, pp. 158-164, 2015.
- [4] S. Usuki, M. Uno, and K. T. Miura, “Digital shape reconstruction of a micro-sized machining tool using light-field microscopy,” Int. J. of Automation Technology, Vol.10, No.2, pp. 172-178, 2016.
- [5] K. Maruno, M. Michihata, Y. Mizutani, and Y. Takaya, “Fundamental study on novel on-machine measurement method of a cutting tool edge profile wiwth a fluorescent confocal microscopy,” Int. J. of Automation Technology, Vol.10, No.1, pp. 106-113, 2016.
- [6] D. Gabor, “A new microscopic principle,” Nature, Vol.161, pp. 777-778, 1948.
- [7] E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am., Vol.52, pp. 1123-1128, 1962.
- [8] J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett., Vol.11, pp. 77-79, 1967.
- [9] T. C. Poon and J. P. Liu, Eds., “Introduction to Modern Digital Holography with MATLAB,” Cambridge University Press, 2014.
- [10] M. K. Kim (Ed.), “Digital Holographic Microscopy: Principles, Techniques, and Applications,” Springer, 2011.
- [11] M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am., Vol.72, pp. 156-160, 1982.
- [12] R. Onodera and Y. Ishii, “Two-wavelength interferometry that uses a Fourier-transform method,” Appl. Opt., Vol.37, pp. 7988-7994, 1998.
- [13] P. Ferraro, D. Alferi, S. De Nicola, L. De Petrocellis, A. Finizio, and G. Pierattini, “Quantitative phase-contrast microscopy by a lateral shear approach to digital holographic image reconstruction,” Opt. Lett., Vol.31, pp. 1405-1407, 2006.
- [14] T. C. Poon, M. H. Wu, K. K. Shinoda, Y. Suzuki, K. B. Doh, and B. W. Schilling, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng., Vol.34, pp. 1338-1344, 1995.
- [15] Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt., Vol.38, pp. 4990-4996, 1999.
- [16] Y. Takaki and H. Ohzu, “Hybrid Holographic Microscopy: Visualization of Three-Dimensional Object Information by use of Viewing Angles,” Appl. Opt., Vol.39, pp. 5302-5308, 2000.
- [17] G. Nehmetallah and P. P. Banerjee, “Applications of digital and analog holography in three-dimensional imaging,” Adv. Opt. Photon., Vol.4, pp. 472-553, 2012.
- [18] A. Wada, M. Kato, and Y. Ishii, “Large step-height measurements using multiple-wavelength holographic interferometry with tunable laser diodes,” J. Opt. Soc. Am. A, Vol.25, pp. 3013-3020, 2008.
- [19] M. Yokota and T. Adachi, “Digital holographic profilometry of the inner surface of a pipe using a current-induced wavelength change of a laser diode,” Appl. Opt., Vol.50, pp. 3937-3946, 2011.
- [20] A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE, Vol.7141, 714123, 2008.
- [21] A. Siemion, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng., Vol.49, 055802, 2010.
- [22] N. Chen, Z. Ren, H. Qu, and E. Y. Lam, “Resolution enhancement of optical scanning holography with a spiral modulated point spread function,” Photon. Res., Vol.4, pp. 1-6, 2016.
- [23] S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol., Vol.32, pp. 567-574, 2000.
- [24] C. Zhang and I. Sato, “Image-based separation of reflective and fluorescent components using illumination variant and invariant color,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol.35, pp. 2866-2877, 2013.
- [25] T. Kubota and T. Ose, “Lippmann color holograms recorded in methylene-blue-sensitized dichromated gelatin,” Opt. Lett., Vol.4, pp. 289-291, 1979.
- [26] T. Kubota, E. Takabayashi, T. Kashiawagi, M. Watanabe, and K. Ueda, “Color reflection holography using four recording wavelengths,” Proc. SPIE, Vol.4296, pp. 126-133, 2001.
- [27] K. Itoh, T. Inoue, T. Yoshida, and Y. Ichioka, “Interferometric supermultispectral imaging,” Appl. Opt., Vol.29, pp. 1625-1630, 1990.
- [28] M. Obara and K. Yoshimori, “3D spatial resolution and spectral resolution of interferometric 3D imaging spectrometry,” Appl. Opt., Vol.55, pp. 2489-2497, 2016.
- [29] Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Tech., Vol.8, pp. 570-576, 2012.
- [30] I. Yamaguchi, T. Matsumura, and J. Kato, “Phase-shifting color digital holography,” Opt. Lett., Vol.27, pp. 1108-1110, 2002.
- [31] J. Kato, I. Yamaguchi, and T. Matsumura, “Multicolor digital holography with an achromatic phase shifter,” Opt. Lett., Vol.27, pp. 1403-1405, 2002.
- [32] B. E. Bayer, “Color imaging array,” US Patent 3971065, issued on July 20, 1976.
- [33] T. Hansel, G. Steinmeyer, R. Grunwald, C. Falldorf, J. Bonitz, C. Kaufmann, V. Kebbel, and U. Griebner, “Synthesized femtosecond laser pulse source for two-wavelength contouring with simultaneously recorded digital holograms,” Opt. Express, Vol.17, pp. 2686-2695, 2009.
- [34] P. Tankam, Q. Song, M. Karray, J. Li, J. M. Desse, and P. Picart, “Real-time three-sensitivity measurements based on three-color digital Fresnel holographic interferometry,” Opt. Lett., Vol.35, pp. 2055-2057, 2010.
- [35] R. Dändliker, R. Thalmann, and D. Prongué, “Two-wavelength laser interferometry using superheterodyne detection,” Opt. Lett., Vol.13, pp. 339-341, 1988.
- [36] D. Barada, T. Kiire, J. Sugisaka, S. Kawata, and T. Yatagai, “Simultaneous two-wavelength Doppler phase-shifting digital holography,” Appl. Opt., Vol.50, pp. H237-H244, 2011.
- [37] A. W. Lohmann, “Reconstruction of vectorial wavefronts,” Appl. Opt., Vol.4, pp. 1667-1668, 1965.
- [38] T. Tahara, S. Kikunaga, Y. Arai, and Y. Takaki, “Phase-shifting interferometry capable of selectively extracting multiple wavelength information and color three-dimensional imaging using a monochromatic image sensor,” Optics and Photonics Japan 2013 (OPJ), 13aE9, 2013 (in Japanese).
- [39] T. Tahara, S. Kikunaga, Y. Arai, and Y. Takaki, “Phase-shifting interferometry capable of selectively extracting multiple wavelength information and its applications to sequential and parallel phase-shifting digital holography,” Digital Holography and Three-Dimensional Imaging 2014 (DH), OSA Technical Digest, Optical Society of America, DM3B.4, 2014.
- [40] T. Tahara, R. Mori, S. Kikunaga, Y. Arai, and Y. Takaki, “Dual-wavelength phase-shifting digital holography selectively extracting wavelength information from wavelength-multiplexed holograms,” Opt. Lett., Vol.40, pp. 2810-2813, 2015.
- [41] T. Tahara, R. Otani, Y. Arai, and Y. Takaki, “Multiwavelength digital holography and phase-shifting interferometry selectively extracting wavelength information: phase-division multiplexing (PDM) of wavelengths,” Holographic Materials and Optical Systems, 2017.
- [42] T. Tahara, R. Otani, K. Omae, T. Gotohda, Y. Arai, and Y. Takaki, “Multiwavelength digital holography with wavelength-multiplexed holograms and arbitrary symmetric phase shifts,” Opt. Express, Vol.25, pp. 11157-11172, 2017.
- [43] 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., Vol.13, pp. 2693-2703, 1974.
- [44] I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett., Vol.22, pp. 1268-1270, 1997.
- [45] L. Granero, V. Micó, Z. Zalevsky, and J. García, “Superresolution imaging method using phase-shifting digital lensless Fourier holography,” Opt. Express, Vol.17, pp. 15008-15022, 2009.
- [46] A. H. Phan, J. H. Park, and N. Kim, “Super-resolution digital holographic microscopy for three dimensional sample using multipoint light source illumination,” Jpn. J. Appl. Phys., Vol.50, pp. 092503, 2011.
- [47] Y. C. Lin, C. J. Cheng, and T. C. Poon, “Optical sectioning with a low-coherence phase-shifting digital holographic microscope,” Appl. Opt., Vol.50, pp. B25-B30, 2011.
- [48] P. Clemente, V. Durán, E. Tajahuerce, V. T. Company, and J. Lancis, “Single-pixel digital ghost holography,” Phys. Rev. A, Vol.86, pp. 041803, 2012.
- [49] T. Tahara, R. Mori, Y. Arai, and Y. Takaki, “Four-step phase-shifting digital holography simultaneously sensing dual-wavelength information using a monochromatic image sensor,” J. Opt., Vol.17, pp. 125707, 2015.
- [50] X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett., Vol.31, pp. 1414-1416, 2006.
- [51] S. Almazán-Cuellar and D. Maracala-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng., Vol.42, pp. 3524-3531, 2003.
- [52] J. P. Liu and T. C. Poon, “Two-step-only quadrature phase-shifting digital holography,” Opt. Lett., Vol.34, pp. 250-252, 2009.
- [53] J. Vargas, J. Antonio Quiroga, T. Belenguer, M. Servín, and J. C. Estrada, “Two-step self-tuning phase-shifting interferometry,” Opt. Express, Vol.19, pp. 638-648, 2011.
- [54] T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng., Vol.36, pp. 2357-2360, 1997.