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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 61, Iss. 6 — Jun. 1, 1971
  • pp: 789–796

Electromagnetic Image Formation with Holograms of Arbitrary Shape

ROBERT P. PORTER and WALTER C. SCHWAB  »View Author Affiliations


JOSA, Vol. 61, Issue 6, pp. 789-796 (1971)
http://dx.doi.org/10.1364/JOSA.61.000789


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Abstract

A diffraction-limited, electromagnetic theory of image formation is presented for a point-reference hologram whose recording arrangement consists of a surface of arbitrary shape, a point-reference source, and the object. The hologram is illuminated by a spherical electromagnetic wave during reconstruction. The electromagnetic hologram is assumed to have recorded two components of the field scattered from the object so that the vector field is completely reconstructed. The vector hologram is modeled by electric and magnetic surface currents determined from the irradiance of each of two orthogonal components of the object field on the film. The image field is described by a dyadic kernel, the system response to a point object, which is related to the scalar kernel by <b>Π</b> (<b>r</b>,<b>r</b>′) = <b>D</b><i>K</i> (<b>r</b>,<b>r</b>′), where <b>D</b> is the dyadic operator <b>D</b> =(<b>I</b>+<i>k</i><sup>-2</sup><b>∇∇</b>). It is shown that the conjugate-image field produced by a point-reference electromagnetic hologram approximates the field produced by the ideal system, which forms the image of a point object by launching a spherically converging wave.

Citation
ROBERT P. PORTER and WALTER C. SCHWAB, "Electromagnetic Image Formation with Holograms of Arbitrary Shape," J. Opt. Soc. Am. 61, 789-796 (1971)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-61-6-789


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References

  1. R. P. Porter, J. Opt. Soc. Am. 60, 1051 (1970).
  2. R. Barer, Nature 167, 642 (1951).
  3. G. L. Rogers, J. Opt. Soc. Am. 56, 831 (1966).
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  7. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), p. 143.
  8. H. M. Smith, Principles of Holography (Wiley, New York, 1969), pp. 20–21. The conjugate-image field arises from the transmittance term proportional to the complex conjugate of the object field; the primary-image field arises from the term proportional to the object field. Note the inversion of the words primary and conjugate on p. 21 of Smith.
  9. P. M. Morse and H. Feshbach, Methods of Theoretical Physics McGraw-Hill, New York, 1953), pp. 54–92.
  10. H. Levine and J. Schwinger, Commun. Pure Appl. Math 3, 355 (1950).
  11. R. P. Porter, Phys. Letters 29A, 193 (1969).
  12. A. Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1949), p. 89.
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  16. C. H. Wilcox, Commun. Pure Appl. Math 9, 115 (1956).
  17. The result is valid for an open surface Sh if Ie=Im=0 everywhere except on Sh.

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