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The method of calculating and correcting object wave reconstruction errors caused by phase shift errors in two-step phase-shifting interferometry is studied systematically. Based on the principle of random distribution and the amplitude-phase independence of diffractive object wave, the expression of objective wave reconstruction error is introduced and the formula for that in the two-step standard algorithm is deduced. The automatic error correction method is suggested by further analyzing the structures, the characters of those errors caused by phase shift errors, and the objective expression. By the proposed method, the reconstructive amplitude and phase errors can be corrected at the same time through simple operation on the objective complex amplitude reconstructed by the standard two-step method without the additional measurement or the acknowledge of phase shift. The computer simulations are carried out to verify the effectiveness of this method, and the results show that the method is robust and reduces the effect of phase shift error on object wave-front reconstruction by about 2 orders of magnitude. Optical experiments also indicate that this method is effective and efficient.
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Keywords:
- phase-shifting interferometry /
- digital holography /
- objective wave reconstruction /
- error correction
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[2] Li J C, Zhang Y P, Xu W 2009 Acta Phys. Sin. 58 5385(in Chinese)[李俊昌、张亚萍、许 蔚 2009 58 5385]
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[42] Meng X F, Cai L Z, Wang Y R, Peng X 2009 Acta Phys. Sin. 58 1668 (in Chinese) [孟祥锋、蔡履中、王玉荣、鹏 翔 2009 58 1668]
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[48] Xu X F, Cai L Z, Wang Y R, Li D L 2010 Chin. Phys. Lett. 27 024215
[49] [50] [51] Xu X F, Cai L Z, Wang Y R, Yan R S 2010 J. Opt. A 12 015301
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[1] Goodman J W, Lawrence R W 1967 Appl. Phys. Lett.11 77
[2] Li J C, Zhang Y P, Xu W 2009 Acta Phys. Sin. 58 5385(in Chinese)[李俊昌、张亚萍、许 蔚 2009 58 5385]
[3] [4] Zhong L Y, Zhang Y M, L X X, Qian X F, Xong B H 2004 Acta Opt. Sin. 24 465 (in Chinese)[钟丽云、张以谟、吕晓旭、钱晓凡、熊秉衡 2004 光学学报 24 465]
[5] [6] [7] Hu H F, Wang X L, Li Z L, Zhang N, Zhai H C 2009 Acta Phys. Sin. 58 7662 (in Chinese)[胡浩丰、王晓雷、李智磊、张 楠、翟宏琛 2009 58 7662]
[8] Leith E N, Upatnieks J 1962 J. Opt. Soc. A 52 1123
[9] [10] Yamaguchi I, Zhang T 1997 Opt. Lett. 22 1268
[11] [12] [13] Patil A, Raphael B, Rastogi P 2004 Opt. Lett. 29 1381
[14] [15] Langoju R, Patil A, Rastogi P 2007 Appl. Opt. 46 8007
[16] [17] Greivenkamp J E 1984 Opt. Eng. 23 350
[18] [19] Cai L Z, Liu Q, Yang X L 2003 Opt. Lett. 28 1808
[20] Cai L Z, Liu Q, Yang X L 2004 Opt. Lett. 29 183
[21] [22] Guo H W, Yu Y J, Chen M Y 2007 J. Opt. Soc. Am. A 24 25
[23] [24] Xu X F, Cai L Z, Meng X F, Dong G Y, Shen X X 2006 Opt. Lett. 31 1966
[25] [26] Brophy C P 1990 J. Opt. Soc. Am. A 7 537
[27] [28] [29] Han C, Han B 2006 Appl. Opt. 45 1124
[30] Xu X F, Cai L Z, Wang Y R, Meng X F, Cheng X C, Zhang H, Dong G Y, Shen X X 2008 J. Opt. A 10 085008
[31] [32] Cai L Z, Liu Q, Yang X L 2004 Opt. Commun. 233 21
[33] [34] Guo C S, Zhang L, Wang H T, Liao J, Zhu Y Y 2002 Opt. Lett. 27 1687
[35] [36] Zhang S 2006 Opt. Commun. 268 231
[37] [38] Xu X F, Cai L Z, Wang Y R, Yang X L, Meng X F, Dong G Y, Shen X X, Zhang H 2007 Appl. Phys. Lett. 90 121124
[39] [40] [41] Xu X F, Cai L Z, Wang Y R, Meng X F, Sun W J, Zhang H, Cheng X C, Dong G Y, Shen X X 2008 Opt. Lett. 33 776
[42] Meng X F, Cai L Z, Wang Y R, Peng X 2009 Acta Phys. Sin. 58 1668 (in Chinese) [孟祥锋、蔡履中、王玉荣、鹏 翔 2009 58 1668]
[43] [44] Cai L Z, Liu Q, Yang X L 2005 J. Mod. Opt. 52 45
[45] [46] [47] Gao P, Yao B L, Lindlein N, Mantel K, Harder I, Geist E 2009 Opt. Lett. 34 3553
[48] Xu X F, Cai L Z, Wang Y R, Li D L 2010 Chin. Phys. Lett. 27 024215
[49] [50] [51] Xu X F, Cai L Z, Wang Y R, Yan R S 2010 J. Opt. A 12 015301
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