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It is a simple and commonly-used approach to use an inclined plane reference wave to remove zero-order diffraction and conjugated image in digital off-axis holography. However, this method is encountering a difficulty, since an additional carrier frequency is incorporated into the inclined reference wave and it is difficult to accurately obtain this additional carrier frequency via experimental measurement, a certain tilt distortion of the phase image will occur in the hologram reconstruction. In this paper, a numerical reference plane algorithm is proposed to solve this problem. This method innovatively constructs a numerical reference plane which is able to exactly characterize the tilt of the phase image by choosing three different points from a local flat of the reconstructed image, and establishes a mathematical relation between the plane parameters and the carrier frequency of the reference wave, which is used as a criterion of correcting the tilt distortion of the phase image in the subsequent iterative computation. The procedures of the algorithm are as follows. 1) Input the nominal carrier frequencies, (fx', fy') of the plane reference wave and reconstruct the hologram. 2) Unwrap the phase with PUMA algorithm and suppress the noise using bilateral filtering and short time Fourier transform with wavelet shrinkage. 3) Construct the numerical reference plane reflecting the image inclination and establish the mathematical relation between the plane parameters and the carrier frequencies of the reference wave. 4) Perform the iterative computation to correct the nominal carrier frequencies, (fx', fy') by using the differential coefficients, (a, b) of the reference plane equation as the criterion. 5) Output the computation result and the corrected phase image. The algorithm is simple and effective. It is able not only to achieve accurate correction to the tilt phase distortion, but also to exactly obtain the additional carrier frequency of the inclined plane reference wave. Since in the phase unwrapping reconstruction, the proposed approach combines with bi-lateral filtering processing, wavelet shrinking and short time Fourier transform to remove the noise influence while the image details are preserved, the method would still be valid under the influences of environmental and system noise. The experimental result supports the theoretical prediction very well.
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Keywords:
- tilt phase distortion /
- digital off-axis holography
[1] Wang H Y, Liu F F, Song X F, Liao W, Zhao B Q, Yu M J, Liu Z Q 2013 Acta Phys. Sin. 62 024207 (in Chinese) [王华英, 刘飞飞, 宋修法, 廖薇, 赵宝群, 于梦杰, 刘佐强 2013 62 024207]
[2] Gu T T, Huang S J, Yan C, Miao Z, Chang Z, Wang T Y 2015 Acta Phys. Sin. 64 064204 (in Chinese) [谷婷婷, 黄素娟, 闫成, 缪庄, 常征, 王廷云 2015 64 064204]
[3] Wu Y C, Wu X C, Yao L C, Xue Z L, Wu C Y, Zhou H, Cen K 2017 Fuel 195 12
[4] Yuan C J, Zhong L Y, Wang Y P, Xu L X, Qian X F 2004 Laser Technol. 28 482
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[16] Liu Y, Wang Z, Li J, Gao J, Huang J 2016 Opt. Laser Eng. 86 115
[17] Nguyen T, Bui V, Lam V, Raub C B, Chang L C, Nehmetallah G 2017 Opt. Express 25 15043
[18] Kim D C, Cho H J, Shin S, Jung W, Yu Y H 2009 J. Opt. Soc. Korea 13 451
[19] Wang H Y, Liu F F, Song X F, Liao W, Yu M J, Liu Z Q 2013 Chin. J. Lasers 40 196 (in Chinese) [王华英, 刘飞飞, 宋修法, 廖微, 于梦杰, 刘佐强 2013 中国激光 40 196]
[20] Liu S, Xiao W, Pan F 2014 Opt. Laser Technol. 57 169
[21] Zhang D, Fan J, Zhao H, Lu X, Liu S, Zhong L 2014 Optik 125 5148
[22] Wang D Y, Wang Y X, Guo S, Rong L, Zhang Y Z 2014 Acta Phys. Sin. 63 154205 (in Chinese) [王大勇, 王云新, 郭莎, 戎路, 张亦卓 2014 63 154205]
[23] Schnars U, Falldorf C, Watson J, Jptner W 2015 Digital Holography and Wavefront Sensing (Berlin: Heidelberg) pp39-68
[24] Bioucas-Dias J M, Valadao G 2007 IEEE Trans. Image Process. 16 698
[25] Durand F, Dorsey J 2002 Acm. T. Graphic 21 257
[26] Allen J B 1977 IEEE. T. Acoust. Speech. 25 235
[27] Donoho D L, Johnstone J M 1994 Biometrika 81 425
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[1] Wang H Y, Liu F F, Song X F, Liao W, Zhao B Q, Yu M J, Liu Z Q 2013 Acta Phys. Sin. 62 024207 (in Chinese) [王华英, 刘飞飞, 宋修法, 廖薇, 赵宝群, 于梦杰, 刘佐强 2013 62 024207]
[2] Gu T T, Huang S J, Yan C, Miao Z, Chang Z, Wang T Y 2015 Acta Phys. Sin. 64 064204 (in Chinese) [谷婷婷, 黄素娟, 闫成, 缪庄, 常征, 王廷云 2015 64 064204]
[3] Wu Y C, Wu X C, Yao L C, Xue Z L, Wu C Y, Zhou H, Cen K 2017 Fuel 195 12
[4] Yuan C J, Zhong L Y, Wang Y P, Xu L X, Qian X F 2004 Laser Technol. 28 482
[5] Rong L, Xiao W, Pan F, Liu S, Li R 2010 Chin. Opt. Lett. 8 653
[6] Cuche E, Marquet P, Dahlgren P, Depeursinge C 2000 Interferometry in Speckle Light (Berlin: Springer-Verlag) pp213-218
[7] Ferraro P, de Nicola S, Finizio A, Coppola G, Grilli S, Magro C, Pierattini G 2003 Appl. Opt. 42 1938
[8] Liebling M, Blu T, Unser M 2004 J. Opt. Soc. Am. A 21 367
[9] Colomb T, Cuche E, Charrire F, Khn J, Aspert N, Frdric M, Pierre M, Christian D 2006 Appl. Opt. 45 851
[10] Miccio L, Alfieri D, Grilli S, Ferraro P 2007 Appl. Phys. Lett. 90 041104
[11] Cui H K, Wang D Y, Wang Y X, Liu C G, Zhao J, Li Y 2011 Acta Phys. Sin. 60 044201 (in Chinese) [崔华坤, 王大勇, 王云新, 刘长庚, 赵洁, 李艳 2011 60 044201]
[12] Belashov A V, Petrov N V, Semenova I V, Vasyutinskii O S 2014 J. Phys. C 536 012003
[13] Pang T 2015 J. Mod. Opt. 62 816
[14] Cuche E, Marquet P, Depeursinge C 2000 Appl. Opt. 39 4070
[15] Cui H, Wang D, Wang Y, Zhao J, Zhang Y 2011 Opt. Commun. 284 4152
[16] Liu Y, Wang Z, Li J, Gao J, Huang J 2016 Opt. Laser Eng. 86 115
[17] Nguyen T, Bui V, Lam V, Raub C B, Chang L C, Nehmetallah G 2017 Opt. Express 25 15043
[18] Kim D C, Cho H J, Shin S, Jung W, Yu Y H 2009 J. Opt. Soc. Korea 13 451
[19] Wang H Y, Liu F F, Song X F, Liao W, Yu M J, Liu Z Q 2013 Chin. J. Lasers 40 196 (in Chinese) [王华英, 刘飞飞, 宋修法, 廖微, 于梦杰, 刘佐强 2013 中国激光 40 196]
[20] Liu S, Xiao W, Pan F 2014 Opt. Laser Technol. 57 169
[21] Zhang D, Fan J, Zhao H, Lu X, Liu S, Zhong L 2014 Optik 125 5148
[22] Wang D Y, Wang Y X, Guo S, Rong L, Zhang Y Z 2014 Acta Phys. Sin. 63 154205 (in Chinese) [王大勇, 王云新, 郭莎, 戎路, 张亦卓 2014 63 154205]
[23] Schnars U, Falldorf C, Watson J, Jptner W 2015 Digital Holography and Wavefront Sensing (Berlin: Heidelberg) pp39-68
[24] Bioucas-Dias J M, Valadao G 2007 IEEE Trans. Image Process. 16 698
[25] Durand F, Dorsey J 2002 Acm. T. Graphic 21 257
[26] Allen J B 1977 IEEE. T. Acoust. Speech. 25 235
[27] Donoho D L, Johnstone J M 1994 Biometrika 81 425
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