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.

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  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).
  4. M. De and L. Sévigny, J. Opt. Soc. Am. 57, 110 (1967).
  5. A. W. Lohmann, Appl. Opt. 4, 1667 (1965).
  6. O. Bryngdahl, J. Opt. Soc. Am. 57, 545 (1967).
  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.
  13. H. Hönl, A. W. Maue, and K. Westpfahl, in Handbuch Der Physik, Vol. XXV/1, edited by S. Flügge (Springer, Berlin, 1961), p. 241
  14. C. Müller, Arch. Math 1, 296 (1948–1949).
  15. S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1949).
  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.

Barer, R.

R. Barer, Nature 167, 642 (1951).

Born, M.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), p. 143.

Bryngdahl, O.

O. Bryngdahl, J. Opt. Soc. Am. 57, 545 (1967).

De, M.

M. De and L. Sévigny, J. Opt. Soc. Am. 57, 110 (1967).

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics McGraw-Hill, New York, 1953), pp. 54–92.

Hönl, H.

H. Hönl, A. W. Maue, and K. Westpfahl, in Handbuch Der Physik, Vol. XXV/1, edited by S. Flügge (Springer, Berlin, 1961), p. 241

Levine, H.

H. Levine and J. Schwinger, Commun. Pure Appl. Math 3, 355 (1950).

Lohmann, A. W.

A. W. Lohmann, Appl. Opt. 4, 1667 (1965).

Maue, A. W.

H. Hönl, A. W. Maue, and K. Westpfahl, in Handbuch Der Physik, Vol. XXV/1, edited by S. Flügge (Springer, Berlin, 1961), p. 241

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics McGraw-Hill, New York, 1953), pp. 54–92.

Müller, C.

C. Müller, Arch. Math 1, 296 (1948–1949).

Porter, R. P.

R. P. Porter, J. Opt. Soc. Am. 60, 1051 (1970).

R. P. Porter, Phys. Letters 29A, 193 (1969).

Rogers, G. L.

G. L. Rogers, J. Opt. Soc. Am. 56, 831 (1966).

Schwinger, J.

H. Levine and J. Schwinger, Commun. Pure Appl. Math 3, 355 (1950).

Sévigny, L.

M. De and L. Sévigny, J. Opt. Soc. Am. 57, 110 (1967).

Silver, S.

S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1949).

Smith, H. M.

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.

Sommerfeld, A.

A. Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1949), p. 89.

Westpfahl, K.

H. Hönl, A. W. Maue, and K. Westpfahl, in Handbuch Der Physik, Vol. XXV/1, edited by S. Flügge (Springer, Berlin, 1961), p. 241

Wilcox, C. H.

C. H. Wilcox, Commun. Pure Appl. Math 9, 115 (1956).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), p. 143.

Other (17)

R. P. Porter, J. Opt. Soc. Am. 60, 1051 (1970).

R. Barer, Nature 167, 642 (1951).

G. L. Rogers, J. Opt. Soc. Am. 56, 831 (1966).

M. De and L. Sévigny, J. Opt. Soc. Am. 57, 110 (1967).

A. W. Lohmann, Appl. Opt. 4, 1667 (1965).

O. Bryngdahl, J. Opt. Soc. Am. 57, 545 (1967).

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), p. 143.

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.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics McGraw-Hill, New York, 1953), pp. 54–92.

H. Levine and J. Schwinger, Commun. Pure Appl. Math 3, 355 (1950).

R. P. Porter, Phys. Letters 29A, 193 (1969).

A. Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1949), p. 89.

H. Hönl, A. W. Maue, and K. Westpfahl, in Handbuch Der Physik, Vol. XXV/1, edited by S. Flügge (Springer, Berlin, 1961), p. 241

C. Müller, Arch. Math 1, 296 (1948–1949).

S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1949).

C. H. Wilcox, Commun. Pure Appl. Math 9, 115 (1956).

The result is valid for an open surface Sh if Ie=Im=0 everywhere except on Sh.

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