Using an aliasing operator and a single discrete Fourier transform to down-sample the Fresnel transform

doi:10.1364/OE.20.008815

Using an aliasing operator and a single discrete Fourier transform to down-sample the Fresnel transform

Modesto Medina-Melendrez, Albertina Castro, and Miguel Arias-Estrada »View Author Affiliations

Optics Express, Vol. 20, Issue 8, pp. 8815-8823 (2012)
http://dx.doi.org/10.1364/OE.20.008815

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Abstract
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Abstract

In Digital Holography there are applications where computing a few samples of a wavefield is sufficient to retrieve an image of the region of interest. In such cases, the sampling rate achieved by the direct and the spectral methods of the discrete Fresnel transform could be excessive. A few algorithmic methods have been proposed to numerically compute samples of propagated wavefields while allowing down-sampling control. Nevertheless, all of them require the computation of at least two 2D discrete Fourier transforms which increases the computational load. Here, we propose the use of an aliasing operator and a single discrete Fourier transform to achieve an efficient method to down-sample the wavefields obtained by the Fresnel transform.

OCIS Codes
(090.1760) Holography : Computer holography
(090.1995) Holography : Digital holography

ToC Category:
Holography

History
Original Manuscript: January 13, 2012
Revised Manuscript: March 2, 2012
Manuscript Accepted: March 6, 2012
Published: April 2, 2012

Citation
Modesto Medina-Melendrez, Albertina Castro, and Miguel Arias-Estrada, "Using an aliasing operator and a single discrete Fourier transform to down-sample the Fresnel transform," Opt. Express 20, 8815-8823 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-8815

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References

T. M. Kreis, M. Adams, and W. P. P. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE3098, 224–233 (1997). [CrossRef]
U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).
B. M. Hennelly, D. P. Kelly, D. S. Monaghan, and N. Pandey, “Zoom Algorithms for Digital Holography,” in Information Optics and Photonics: Algorithms, Systems, and Applications, T. Fournel and B. Javidi, eds. (Springer, 2010), pp. 187–204.
X. Deng, B. Bihari, J. Gan, F. Zhao, and R. T. Chen, “Fast algorithm for chirp transforms with zooming-in ability and its applications,” J. Opt. Soc. Am. A17(4), 762–771 (2000). [CrossRef] [PubMed]
F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett.29(14), 1668–1670 (2004). [CrossRef] [PubMed]
W. T. Rhodes, “Light tubes, Wigner diagrams and optical signal propagation simulation,” in Optical Information Processing: A Tribute to Adolf Lohmann, H. J. Caulfield, ed. (SPIE Press, 2002), pp. 343–356.
J. C. Li, P. Tankam, Z. J. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett.34(5), 572–574 (2009). [CrossRef] [PubMed]
L. Yu and M. K. Kim, “Pixel resolution control in numerical reconstruction of digital holography,” Opt. Lett.31(7), 897–899 (2006). [CrossRef] [PubMed]
P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett.29(8), 854–856 (2004). [CrossRef] [PubMed]
D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng.48(9), 095801 (2009). [CrossRef]
E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am.52(10), 1123–1130 (1962). [CrossRef]
S. Satake, T. Kunugi, K. Sato, and T. Ito, “Digital Holographic Particle Tracking Velocimetry for 3-D Transient Flow around an Obstacle in a Narrow Channel,” Opt. Rev.11, 162–164 (2004).
A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing (Prentice Hall, 1999).
M. Frigo and S. G. Johnson, “The FFTW web page,” (2007), http://www.fftw.org/ .

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[1] T. M. Kreis, M. Adams, and W. P. P. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE3098, 224–233 (1997). [CrossRef]

[2] U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

[3] B. M. Hennelly, D. P. Kelly, D. S. Monaghan, and N. Pandey, “Zoom Algorithms for Digital Holography,” in Information Optics and Photonics: Algorithms, Systems, and Applications, T. Fournel and B. Javidi, eds. (Springer, 2010), pp. 187–204.

[4] X. Deng, B. Bihari, J. Gan, F. Zhao, and R. T. Chen, “Fast algorithm for chirp transforms with zooming-in ability and its applications,” J. Opt. Soc. Am. A17(4), 762–771 (2000). [CrossRef] [PubMed]

[5] F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett.29(14), 1668–1670 (2004). [CrossRef] [PubMed]

[6] W. T. Rhodes, “Light tubes, Wigner diagrams and optical signal propagation simulation,” in Optical Information Processing: A Tribute to Adolf Lohmann, H. J. Caulfield, ed. (SPIE Press, 2002), pp. 343–356.

[7] J. C. Li, P. Tankam, Z. J. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett.34(5), 572–574 (2009). [CrossRef] [PubMed]

[8] L. Yu and M. K. Kim, “Pixel resolution control in numerical reconstruction of digital holography,” Opt. Lett.31(7), 897–899 (2006). [CrossRef] [PubMed]

[9] P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett.29(8), 854–856 (2004). [CrossRef] [PubMed]

[10] D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng.48(9), 095801 (2009). [CrossRef]

[11] E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am.52(10), 1123–1130 (1962). [CrossRef]

[12] S. Satake, T. Kunugi, K. Sato, and T. Ito, “Digital Holographic Particle Tracking Velocimetry for 3-D Transient Flow around an Obstacle in a Narrow Channel,” Opt. Rev.11, 162–164 (2004).

[13] A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing (Prentice Hall, 1999).

[14] M. Frigo and S. G. Johnson, “The FFTW web page,” (2007), http://www.fftw.org/ .

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Using an aliasing operator and a single discrete Fourier transform to down-sample the Fresnel transform