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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 5, Iss. 8 — Aug. 1, 1988
  • pp: 1297–1308

Holograms in motion. II. Diffracting capabilities of strained holograms

Juan C. Agüí and L. Hesselink  »View Author Affiliations


JOSA A, Vol. 5, Issue 8, pp. 1297-1308 (1988)
http://dx.doi.org/10.1364/JOSAA.5.001297


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Abstract

A general procedure for the analysis of the diffraction capabilities of a three-dimensional low-efficiency hologram is presented. Tightly coupled to a description of the hologram in terms of its three-dimensional spatial Fourier modes, the procedure uses the angular spectrum theory for decomposing the reading light into plane waves. The convolution in the Fourier domain between the two Fourier distributions produces the angular spectrum of the diffracted light. Of special interest are the angular moments of the diffracted light, as a means of detecting the average orientation and distortion of the fringes in the hologram. These vary, in the case studied here, as a consequence of the uneven motion of the supporting media, which subjects the hologram to convection, rotation, and deformation. Diffusion takes place simultaneously, reducing the hologram modulation. Computed time evolutions of diffracted spots from holograms deformed by simple case flows are presented. In this paper we deal only with the readout process of deformed holograms; the effect of the fluid motion on the hologram is studied in detail in the first part of this series [ J. Opt. Soc. Am. A 5, 1287 ( 1988)].

© 1988 Optical Society of America

History
Original Manuscript: October 6, 1987
Manuscript Accepted: April 7, 1988
Published: August 1, 1988

Citation
Juan C. Agüí and L. Hesselink, "Holograms in motion. II. Diffracting capabilities of strained holograms," J. Opt. Soc. Am. A 5, 1297-1308 (1988)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-5-8-1297


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References

  1. J. C. Agüí, J. Hesselink, “Holograms in motion. I. Effect of fluid motion on volume holograms,” J. Opt. Soc. Am. A 5, 1287–1296 (1988). [CrossRef]
  2. M. Cloitre, E. Guyon, “Forced Rayleigh scattering in turbulent plane poiseuille flows. I. Study of the transverse velocity-gradient component,”J. Fluid Mech. 164, 217–236 (1986). [CrossRef]
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  5. M. G. Moharam, T. K. Gaylord, R. Magnusson, “Diffraction characteristics of three-dimensional crossed-beam gratings,”J. Opt. Soc. Am. 70, 437–442 (1980). [CrossRef]
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  7. A. E. Siegman, “Bragg diffraction of a Gaussian beam by a crossed-Gaussian volume grating,”J. Opt. Soc. Am. 67, 545–550 (1977). [CrossRef]
  8. J. C. Agüí, J. Hesselink, “Holographic measurements of velocity gradients in fluids,” Bull. Am. Phys. Soc. 32, 2106 (1987).
  9. H. M. Smith, Principles of Holography (Wiley-Interscience, New York, 1969).
  10. L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic, New York, 1981).
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  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  14. Here a slight deviation from the standard definition of the angular spectrum14 is taken, since no clear axis of propagation is present in this case. The modification consists of not projecting the sphere in which the Ki vector lies upon a plane normal to the propagation direction. In this way, the arbitrary choice of an artificial propagation direction is avoided, as is the computational difficulty arising from rays that may be nearly parallel to the projection plane. In this new twist, the angular spectrum becomes almost undistinguishable from the three-dimensional Fourier transform.
  15. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  16. R. N. Bracewell, Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).
  17. G. B. Whitham, Linear and Nonlinear Waves (Wiley-Interscience, New York, 1974).

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