Abstract

The process of producing a hologram of an object that is transmitting or reflecting diffuse, partially coherent, quasimonochromatic light is described mathematically. The discussion shows how the degree of coherence between the reference beam and the beam illuminating the object affects the reconstruction. The types of image degradation resulting from the use of partially coherent light are outlined. The application of holography to the measurement of second-order spatial coherence is suggested and a possible experiment is described.

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  1. D. Gabor, Nature 161, 777 (1948).
  2. E. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
  3. E. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1295 (1964).
  4. For a discussion of the degree of coherence see M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), in particular 2nd ed., Sec. 10.3.
  5. Strictly speaking, this requires a positive plate with γ = 2 since, for a positive exposed to an irradiance I (P) for a time t0, [equation]. However, holograms can be made with other γ's and are, in fact, usually made with negative plates developed to γ's of 6 or more.
  6. U (P,t)_ reconstructs the conjugate real image. See Ref. 3, p. 1300.
  7. This discussion has been restricted to plane waves for simplicity. It is easy to show that for an undistorted reconstruction, it is essential that the reference beam have the same form as the reconstructing beam, but this form can be as complicated as desired. For an intelesting example of this, see H. Kogelnik, Bell System Tech. J. 44, 2451 (1965).
  8. See, for example, Ref. 4, p. 508 ff.

Born, M.

For a discussion of the degree of coherence see M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), in particular 2nd ed., Sec. 10.3.

Gabor, D.

D. Gabor, Nature 161, 777 (1948).

Kogelnik, H.

This discussion has been restricted to plane waves for simplicity. It is easy to show that for an undistorted reconstruction, it is essential that the reference beam have the same form as the reconstructing beam, but this form can be as complicated as desired. For an intelesting example of this, see H. Kogelnik, Bell System Tech. J. 44, 2451 (1965).

Leith, E.

E. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

E. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1295 (1964).

Upatnieks, J.

E. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1295 (1964).

E. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

Wolf, E.

For a discussion of the degree of coherence see M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), in particular 2nd ed., Sec. 10.3.

Other (8)

D. Gabor, Nature 161, 777 (1948).

E. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

E. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1295 (1964).

For a discussion of the degree of coherence see M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), in particular 2nd ed., Sec. 10.3.

Strictly speaking, this requires a positive plate with γ = 2 since, for a positive exposed to an irradiance I (P) for a time t0, [equation]. However, holograms can be made with other γ's and are, in fact, usually made with negative plates developed to γ's of 6 or more.

U (P,t)_ reconstructs the conjugate real image. See Ref. 3, p. 1300.

This discussion has been restricted to plane waves for simplicity. It is easy to show that for an undistorted reconstruction, it is essential that the reference beam have the same form as the reconstructing beam, but this form can be as complicated as desired. For an intelesting example of this, see H. Kogelnik, Bell System Tech. J. 44, 2451 (1965).

See, for example, Ref. 4, p. 508 ff.

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