Journal of the European Optical Society - Rapid publications, Vol 6 (2011)

Digital in-line holography with a spatially partially coherent beam

S. Coëtmellec, C. Remacha, M. Brunel, D. Lebrun, A. J. E. M. Janssen


We propose in this paper an analytical solution to the problem of scalar diffraction of a partially coherent beam by an opaque disk. This analytical solution is applied in digital in-line holography of particles. We demonstrate that the reconstruction by means of fractional Fourier transformation is still possible when a spatially partially coherent beam is used. Numerical simulations and experiments have been carried out.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2011.11060]

Full Text: PDF

Citation Details

Cite this article


J.-M. Desse, P. Picart, and P. Tankam, "Digital three-color holographic interferometry for flow analysis" Opt. Express 16, 5471-5480 (2008).

O. Kafri, and I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1989).

F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, "Near-field Lorenz-Mie theory and its application to microholography" Appl. Opt. 23, 4140-4148 (1984).

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH Verlag GmbH & Co. KGaA, 2004).

F. Nicolas, S. Coëtmellec, M. Brunel, and D. Lebrun, "Digital in-line holography with a sub-picosecond laser beam" Opt. Commun. 268, 27-33 (2006).

L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).

H. T. Eyyubo_glu, Y. Baykal, and Y. Cai, "Complex degree of coherence for partially coherent general beams in atmospheric turbulence" J. Opt. Soc. Am. A 24, 2891-2901 (2007).

D. Gabor, "A new microscopic principle" Nature 161, 777-778 (1948).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, Greenwood village, USA, 2005).

U. Schnars, and W. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction" Appl. Opt. 33, 179-181 (1994).

D. J. Stigliani, JR., R. Mittra, and R. G. Semonin, "Particle-Size Measurement Using Forward-Scatter Holography" J. Opt. Soc. Am. 60, 1059-1067 (1970)

F. Nicolas, S. Coëtmellec, M. Brunel, D. Allano, D. Lebrun, and A. J. E. M. Janssen, "Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam" J. Opt. Soc. Am. A 22, 2569-2577 (2005).

J. J. Wen, and M. Breazeale, "Gaussian beam functions as a base function set for acoustical field calculations" in Proceedings to IEEE Ultrasonics Symposium 1137-1140 (IEEE, Denver, 1987).

J. J. Wen, and M. Breazeale, "A diffraction beam expressed as the superposition of Gaussian beams," J. Acoust. Soc. Am. 83, 1752-1756 (1988).

S. Coëtmellec, N. Verrier, M. Brunel, D. Lebrun, "General formulation of digital in-line holography from correlation with a chirplet function", J. Eur. Opt. Soc.-Rapid 5, 10027 (2010).

F. Dubois, M. L. N. Requena, C. Minetti, O. Monnom, and E. Istasse, "Partial spatial coherence effects in digital holographic microscopy with a laser source," Appl. Opt. 43, 1131-1139 (2004).

J. W. Goodman, Statistical Optics (Wiley Classics Library, New York, 2000).

A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986).

X. Du, and D. Zhao, "Propagation of elliptical Gaussian beams in apertured and misaligned optical systems," J. Opt. Soc. Am. A 23, 1946-1950 (2006).

N. Verrier, S. Coëtmellec, M. Brunel, D. Lebrun, and A. J. E. M Janssen, "Digital in-line holography with an elliptical, astigmatic Gaussian beam: wide-angle reconstruction," J. Opt. Soc. Am. A 25, 1459-1466 (2008).

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, "Focus plane detection criteria in digital holography microscopy by amplitude analysis," Opt. Express 14, 5895-5908 (2006).

B. Ge, Q. Lu, and Y. Zhang, "Particle digital in-line holography with spherical wave recording", Chin. Opt. Lett. 01, 517 (2003).

R. B. Owen, and A. A. Zozulya, "In-line digital holographic sensor for monitoring and characterizing marine particulates", Opt. Eng. 39, 2187 (2000).

A. C. McBride, and F. H. Kerr, "On Namias's fractional Fourier transforms", IMA J. Appl. Math. 39, 159-175 (1987).

V. Namias, "The fractional order Fourier transform and its application to quantum mechanics", J. Inst. Maths Its Applics, 25, 241-265 (1980).

A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform", J. Opt. Soc. Am. A 10, 2181-2186 (1993).

M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, Inc., New York, 1970).

J. J. M. Braat, P. Dirksen, and A. J. E. M. Janssen, "Assessment of an extended Nijboer-Zernike approach for the computation of optical point-spread functions", J. Opt. Soc. Am. A 19, 858-870 (2002).

A. J. E. M. Janssen, "Extended Nijboer-Zernike approach for the computation of optical point-spread functions", J. Opt. Soc. Am. A 19, 849-857 (2002).

A. J. E. M. Janssen, "New analytic results for the Zernike circle polynomials from a basic result in the Nijboer-Zernike diffraction theory", J. Europ. Opt. Soc. Rap. Public. 6, 11028 (2011).

A. J. E. M. Janssen, J. J. M. Braat, and P. Dirksen, "On the computation of the Nijboer-Zernike aberration integrals at arbitrary defocus," J. Mod. Opt. 51, 687-703 (2004).

W. J. Tango, "The circle polynomials of Zernike and their application in optics", Appl. Phys. 13, 327-332 (1977).