Digital in-line holography with an elliptical, astigmatic Gaussian beam: wide-angle reconstruction.

We demonstrate that the effect of object shift in an elliptical, astigmatic Gaussian beam does not affect the optimal fractional orders used to reconstruct the holographic image of a particle or another opaque object in the field. Simulations and experimental results are presented.

[1]  Denis Lebrun,et al.  Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform. , 2002, Applied optics.

[2]  F. Nicolas,et al.  Digital in-line holography with a sub-picosecond laser beam , 2006 .

[3]  Mikael Sebesta,et al.  Object characterization with refractometric digital Fourier holography. , 2005, Optics letters.

[4]  Peter Dirksen,et al.  Assessment of an extended Nijboer-Zernike approach for the computation of optical point-spread functions. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  Z. Zalevsky,et al.  The Fractional Fourier Transform: with Applications in Optics and Signal Processing , 2001 .

[6]  A. Janssen,et al.  On the computation of the nijboer-zernike aberration integrals at arbitrary defocus , 2004 .

[7]  A. Janssen Extended Nijboer-Zernike approach for the computation of optical point-spread functions. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  V. Namias The Fractional Order Fourier Transform and its Application to Quantum Mechanics , 1980 .

[9]  David Mas,et al.  Fast numerical calculation of Fresnel patterns in convergent systems , 2003 .

[10]  U. Schnars Direct phase determination in hologram interferometry with use of digitally recorded holograms , 1994 .

[11]  Gongxin Shen,et al.  Digital holography particle image velocimetry for the measurement of 3Dt-3c flows , 2005 .

[12]  F. Dubois,et al.  Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence. , 1999, Applied optics.

[13]  Franz Hlawatsch,et al.  The Wigner distribution : theory and applications in signal processing , 1997 .

[14]  M H Jericho,et al.  Tracking particles in four dimensions with in-line holographic microscopy. , 2003, Optics letters.

[15]  A. Lohmann Image rotation, Wigner rotation, and the fractional Fourier transform , 1993 .

[16]  Leon M. Hall,et al.  Special Functions , 1998 .

[17]  J. Becker,et al.  Simultaneous 3D-PIV and temperature measurements using a new CCD-based holographic interferometer , 1996 .

[18]  Levent Onural,et al.  DIGITAL DECODING OF IN-LINE HOLOGRAMS , 1987 .

[19]  Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[20]  F. H. Kerr,et al.  On Namias's fractional Fourier transforms , 1987 .

[21]  L. Onural,et al.  Diffraction from a wavelet point of view. , 1993, Optics letters.

[22]  Pierre Pellat-Finet,et al.  Agreement of fractional Fourier optics with the Huygens–Fresnel principle , 2007 .