Abstract
The diffraction theory is at the basis of development of digital holography and allows calculation of holographic images from the recorded holographic interference patterns [1]. In this chapter, we highlight some of the theoretical tools developed to enhance the capabilities of digital holography and applications.
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References
E. Wolf, “Determination of Amplitude and Phase of Scattered Fields by Holography,” Journal of the Optical Society of America 60, 18–20 (1970).
C. Wagner, S. Seebacher, W. Osten, and W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Applied Optics 38, 4812–4820 (1999).
I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001).
L. Onural, “Sampling of the diffraction field,” Applied Optics 39, 5929–5935 (2000).
T. M. Kreis, “Frequency analysis of digital holography,” Optical Engineering 41, 771–778 (2002).
T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Optical Engineering 41, 1829–1839 (2002).
C. S. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the papers “Frequency analysis of digital holography” and “Frequency analysis of digital holography with reconstruction by convolution”,” Optical Engineering 42, 2768–2771 (2003).
T. M. Kreis, “Response to “Effect of the fill factor of CCD pixels on digital holograms: comment on the papers ‘Frequency analysis of digital holography’ and ‘Frequency analysis of digital holography with reconstruction by convolution’”, Optical Engineering 42, 2772–2772 (2003).
K. Khare, and N. George, “Direct coarse sampling of electronic holograms,” Optics Letters 28, 1004–1006 (2003).
A. Stern, and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Optical Engineering 43, 239–250 (2004).
H. Z. Jin, H. Wan, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” Journal of Modern Optics 55, 2989–3000 (2008).
P. Picart, and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” Journal of the Optical Society of America a-Optics Image Science and Vision 25, 1744–1761 (2008).
D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Optical Engineering 48, 095801 (2009).
E. Wolf, “Determination of the Amplitude and the Phase of Scattered Fields by Holography,” Journal of the Optical Society of America 60, 18–20 (1970).
L. Onural, “Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations,” Optical Engineering 43, 2557–2563 (2004).
E. Carcole, J. Campos, and S. Bosch, “Diffraction Theory of Fresnel Lenses Encoded in Low-Resolution Devices,” Applied Optics 33, 162–174 (1994).
L. Xu, X. Y. Peng, Z. X. Guo, J. M. Miao, and A. Asundi, “Imaging analysis of digital holography,” Optics Express 13, 2444–2452 (2005).
B. M. Hennelly, and J. T. Sheridan, “Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms,” Journal of the Optical Society of America a-Optics Image Science and Vision 22, 917–927 (2005).
A. Stern, and B. Javidi, “Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields,” Journal of the Optical Society of America a-Optics Image Science and Vision 23, 1227–1235 (2006).
G. Situ, and J. T. Sheridan, “Holography: an interpretation from the phase-space point of view,” Optics Letters 32, 3492–3494 (2007).
A. Stern, and B. Javidi, “Space-bandwith conditions for efficient phase-shifting digital holographic microscopy,” Journal of the Optical Society of America a-Optics Image Science and Vision 25, 736–741 (2008).
M. Testorf, and A. W. Lohmann, “Holography in phase space,” Applied Optics 47, A70-A77 (2008).
P. Pellat-Finet, “Fresnel diffraction and fractional-order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994).
Z.-T. Deng, H. J. Caulfield, and M. Schamschula, “Fractional discrete Fourier transforms,” Opt. Lett. 21, 1430–1432 (1996).
S. C. Pei, and M. H. Yeh, “Improved discrete fractional Fourier transform,” Opt. Lett. 22, 1047–1049 (1997).
Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Applications of fractional transforms to object reconstruction from in-line holograms,” Optics Letters 29, 1793–1795 (2004).
J. T. Sheridan, and R. Patten, “Holographic interferometry and the fractional Fourier transformation,” Opt. Lett. 25, 448–450 (2000).
F. Nicolas, S. Coetmellec, M. Brunel, D. Allano, D. Lebrun, and A. Janssen, “Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam,” Journal of the Optical Society of America a-Optics Image Science and Vision 22, 2569–2577 (2005).
N. Verrier, S. Coetmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Applied Optics 47, 4147–4157 (2008).
N. Verrier, S. Coetmellec, M. Brunel, D. Lebrun, and A. Janssen, “Digital in-line holography with an elliptical, astigmatic Gaussian beam: wide-angle reconstruction,” Journal of the Optical Society of America a-Optics Image Science and Vision 25, 1459–1466 (2008).
J. Hahn, H. Kim, and B. Lee, “Optical implementation of iterative fractional Fourier transform algorithm,” Optics Express 14, 11103–11112 (2006).
J. W. Weng, J. G. Zhong, and C. Y. Hu, “Phase reconstruction of digital holography with the peak of the two-dimensional Gabor wavelet transform,” Applied Optics 48, 3308–3316 (2009).
P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
R. Recknagel, and G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Comm. 148, 122–128 (1998).
C. Shakher, R. Kumar, S. K. Singh, and S. A. Kazmi, “Application of wavelet filtering for vibration analysis using digital speckle pattern interferometry,” Optical Engineering 41, 176–180 (2002).
J. Zhong, and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. 43, 4993–4998 (2004).
L. Onural, “Diffraction from a Wavelet Point-of-View,” Optics Letters 18, 846–848 (1993).
M. Liebling, T. Blu, and M. Unser, “Fresnelets: New multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
J. W. Weng, J. G. Zhong, and C. Y. Hu, “Digital reconstruction based on angular spectrum diffraction with the ridge of wavelet transform in holographic phase-contrast microscopy,” Optics Express 16, 21971–21981 (2008).
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Kim, M.K. (2011). Theoretical Studies of Digital Holography. In: Digital Holographic Microscopy. Springer Series in Optical Sciences, vol 162. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7793-9_6
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DOI: https://doi.org/10.1007/978-1-4419-7793-9_6
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