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In the research of the color digital holography and digital holography measurement with multi-wavelength illumination, how to avoid the interpolation error in the wave-front reconstruction with variable magnification is an important subject to be studied. Since the Fresnel diffraction integral can be expressed as Fourier transformation as well as convolution form, there are two reconstruction approaches, one is the relay algorithm which divides the reconstruction distance into two parts, the other is the convolution algorithm which uses the spherical wave as reconstruction wave. In this paper, the two algorithms are theoretically analyzed and experimentally studied, and the condition satisfying the sampling theorem for the reconstruction calculation is discussed. The results show that the convolution approach satisfies the sampling theorem more readily, while higher quality reconstructed object wave field can be obtained with the convolution approach.
[1] ［1］Zhao J L, Jiang H H, Di J L 2008 Opt. Express 16 2514
[2] ［2］Wang X L， Zhang N， Zhao Y B， Li Z L， Zhai H C， Zhu X N2008 Acta Phys. Sin.57 354 (in Chinese) ［王晓雷、 张楠、 赵友博、 李智磊、 翟宏琛、 朱晓农 2008 57 354］
[3] ［3］Goodman J W 2006 An Introduction to Fourier Optics (3rd Ed.) (Roberts and Company Publishers. Inc,)
[4] ［4］David M, Javier G, Carlos F, Luis M B, Francisco M 1999 Opt. Commun. 164 233
[5] ［5］Xiong B H, Li J C 2009 Holography Interferometry —— Principles and Methods (Beijing: Science Press) P630 ［熊秉衡、 李俊昌 2009 全息干涉计量——原理和方法 （北京： 科学出版社） 第525, 630页］
[6] ［6］Zhang F， Yamaguchi I 2004 Opt.Lett.29 1668
[7] ［7］Li J C, Patrice T, Peng Z J, Pascal P 2009 Opt.Lett. 34 572
[8] ［8］Pascal P, Patrice T, Denis M, Peng J C， Li J C 2009 Opt. Express 17 9145
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[1] ［1］Zhao J L, Jiang H H, Di J L 2008 Opt. Express 16 2514
[2] ［2］Wang X L， Zhang N， Zhao Y B， Li Z L， Zhai H C， Zhu X N2008 Acta Phys. Sin.57 354 (in Chinese) ［王晓雷、 张楠、 赵友博、 李智磊、 翟宏琛、 朱晓农 2008 57 354］
[3] ［3］Goodman J W 2006 An Introduction to Fourier Optics (3rd Ed.) (Roberts and Company Publishers. Inc,)
[4] ［4］David M, Javier G, Carlos F, Luis M B, Francisco M 1999 Opt. Commun. 164 233
[5] ［5］Xiong B H, Li J C 2009 Holography Interferometry —— Principles and Methods (Beijing: Science Press) P630 ［熊秉衡、 李俊昌 2009 全息干涉计量——原理和方法 （北京： 科学出版社） 第525, 630页］
[6] ［6］Zhang F， Yamaguchi I 2004 Opt.Lett.29 1668
[7] ［7］Li J C, Patrice T, Peng Z J, Pascal P 2009 Opt.Lett. 34 572
[8] ［8］Pascal P, Patrice T, Denis M, Peng J C， Li J C 2009 Opt. Express 17 9145
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