Advertisement

Zoom Algorithms for Digital Holography

  • Bryan M. Hennelly
  • Damien P. Kelly
  • David S. Monaghan
  • Nitesh Pandey
Chapter

Abstract

Digital Holography is an imaging modality made up of two parts: (1) using a digital camera to record the interference pattern between a field scattered from an object and a known reference field so that the complex object wavefield can be obtained and (2) replaying or reconstructing the hologram on a computer by simulating the propagation of the object wavefield back to the object plane. Thus an image is obtained. The most commonly used algorithms for the reconstruction algorithm are the so-called direct method and the spectral method of calculating the Fresnel Transform, which describes free space propagation in the paraxial approximation. These algorithms differ in the output range that they display. For the direct method, the output image size is proportional to the distance making it more appropriate for large objects at large distances. The spectral method has an output image size equal to the size of the CCD. We show how to adapt this latter algorithm in a simple way to allow it to generate any output range and in any location making it far more versatile for zooming in on specific regions of our reconstructed image.

Keywords

Fast Fourier Transform Discrete Fourier Transform Spectral Method Object Size Polarize Beam Splitter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgement

This research is funded from the European Community’s Seventh Framework Programme FP7/2007–2013 under grant agreement 216105 “Real 3D.”

References

  1. 1.
    D. Gabor (1948), A new microscope principle, Nature, 161:777–778ADSCrossRefGoogle Scholar
  2. 2.
    E. N. Leith, J. Upatnieks (1962), Reconstructed wavefronts and communication theory, J. Opt. Soc. Am., 52:1123ADSCrossRefGoogle Scholar
  3. 3.
    E. N. Leith, J. Upatnieks (1963), Wavefront reconstruction with continuous-tone objects, J. Opt. Soc. Am., 53:1377ADSCrossRefGoogle Scholar
  4. 4.
    J. W. Goodman, R. Lawrence (1967), Digital image formation from electronically detected holograms, Appl. Phys. Lett., 11:77–79ADSCrossRefGoogle Scholar
  5. 5.
    L. P. Yaroslavskii, N. S. Merzlyakov (1980), Methods of Digital Holography, Consultants Bureau, New YorkGoogle Scholar
  6. 6.
    T. M. Kreis, M. Adams, W. P. O. Juptner (1997), Methods of digital holography: a comparison, Proc. SPIE, 3098:224–233ADSCrossRefGoogle Scholar
  7. 7.
    U. Schnars, W. P. O. Juptner (2002), Digital recording and numerical reconstruction of holograms, Meas. Sci. Technol., 13:85–101ADSCrossRefGoogle Scholar
  8. 8.
    D. P. Kelly, B. M. Hennelly, W. T. Rhodes, J. T. Sheridan (2006), Analytical and numerical analysis of linear optical systems, Opt. Eng., 45:008201CrossRefGoogle Scholar
  9. 9.
    B. M. Hennelly, J. T. Sheridan (2005), Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms, J. Opt. Soc. Am. A, 22:917–927MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    B. M. Hennelly, J. T. Sheridan (2005), Fast algorithm for the linear canonical transform, J. Opt. Soc. Am. A, 22:928–937MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    D. Mendlovic, Z. Zalevsky, N. Konforti, (1997) Computation considerations and fast algorithms for calculating the diffraction integral, J. Mod. Opt., 44:407–414MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    D. Mas, J. Garca, C. Ferreira, L. M. Bernardo, F. Marinho (1999), Fast algorithms for free-space diffraction patters calculation, Opt. Commun., 164:233–245ADSCrossRefGoogle Scholar
  13. 13.
    D. Mas, J. Prez, C. Hernndez, C. Vzquez, J. J Miret, C. Illueca (2003), Fast numerical calculation of Fresnel patterns in convergent systems, Opt. Commun., 227:245–258ADSCrossRefGoogle Scholar
  14. 14.
    E. Cuche, P. Marquet, C. Depeursinge (1999), Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms, Appl. Opt., 38:6994–7001ADSCrossRefGoogle Scholar
  15. 15.
    P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, C. Depeursinge (2005), Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy, Opt. Lett., 30: 468–470ADSCrossRefGoogle Scholar
  16. 16.
    J. W. Cooley, J. W. Tukey (1965), An algorithm for the machine calculation of complex Fourier series, Math. Comput., 19:297–301MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    X. Deng, B. Bihari, J. Gan, F. Zhao, R. T. Chen (2000), Fast algorithm for chirp transforms with zooming-in ability and its applications, J. Opt. Soc. Am. A, 17:762–771MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    F. Zhang, I. Yamaguchi, L. P. Yaroslavsky (2004), Algorithm for reconstruction of digital holograms with adjustable magnification, Opt. Lett., 29:1668–1670ADSCrossRefGoogle Scholar
  19. 19.
    I. Yamaguchi, T. Zhang (1997), Phase-shifting digital holography, Opt. Lett., 22:1268–1270ADSCrossRefGoogle Scholar
  20. 20.
    D. P. Kelly, B. M. Hennelly, J. T. Sheridan, W. T. Rhodes (2006), Finite-aperture effects for Fourier transform systems with convergent illumination, Part II, Opt. Commun. 263:180–188ADSGoogle Scholar
  21. 21.
    W. T. Rhodes (2002), Light tubes, Wigner diagrams and optical signal propagation simulation, in Optical Information Processing: A Tribute to Adolf Lohmann, H. J. Caulfield, ed., SPIE Press, Bellingham, WA, pp. 343–356Google Scholar
  22. 22.
    W. T. Rhodes (2001), Numerical simulation of Fresnel-regime wave propagation: the light tube model, in Wave-Optical Systems Engineering, F. Wyrowski, ed., Proc. SPIE 4436:21–26ADSCrossRefGoogle Scholar
  23. 23.
    M. Testorf, B. Hennelly, J. Ojeda-Castaneda (2009), Phase-Space Optics, McGrawHill, New YorkGoogle Scholar
  24. 24.
    P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, G. Pierattini (2004), Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms, Opt. Lett., 29:854–856ADSCrossRefGoogle Scholar
  25. 25.
    L. Yu, M. K. Kim (2006), Pixel resolution control in numerical reconstruction of digital holography, Opt. Lett., 31:897–899ADSCrossRefGoogle Scholar
  26. 26.
    J. Li, P. Tankam, Z. Peng, P. Picart (2009), Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification, Opt. Lett., 34:572–574ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Bryan M. Hennelly
    • 1
  • Damien P. Kelly
  • David S. Monaghan
  • Nitesh Pandey
  1. 1.National University of IrelandMaynoothIreland

Personalised recommendations