Abstract

It is shown how both the amplitude and the phase of a scattered field may be determined by holography. It is estimated that information about details down to about nine wavelengths of light can be obtained by this technique. The result is of importance for unambiguous determination of the three-dimensional structure of semitransparent objects, such as are frequently encountered, for example, in biology.

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  1. E. Wolf, Optics Communications 1, No. 4, 153 (1969).
  2. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 53, 1377 (1963).
  3. If the field distribution U1 (x,y) does not satisfy this band-limitation condition, the unwanted spatial-frequency components could be eliminated by using standard optical spatial-filtering techniques. Such spatial-frequency components cannot, of course, be reconstructed at a later stage, i.e., only the filtered field can be reconstructed.
  4. Because of the finite size of the hologram, the intensity distribution IH(x,y) cannot be determined throughout the whole infinite plane z=z1, as formally needed in formula (15). However, because the sinc function in Eq. (15) effectively vanishes when |x-x′| and |y-y′| exceed a moderate multiple of π/ū and π/υ¯, respectively, the integration in Eq. (15) needs only be extended over such a finite x′,y′ domain. This result implies, incidently, that information about the scattered field U1 at the point (x,y) is stored in a region of the hologram, centered on the point (x,y), whose linear dimensions are moderate multiples of π/u¯ and π/υ¯ in the x and y directions, respectively.
  5. High-resolution photographic plates are available that would appear, at first sight, to make it profitable to employ reference beams with appreciably larger values of θr. It seems doubtful, however, that this would lead to a significant improvement of the resolution limit of this technique, because of the difficulty of measuring, to sufficient accuracy, the intensity distribution 1 H (x,y) of the transilluminated hologram.

Leith, E. N.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 53, 1377 (1963).

Upatnieks, J.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 53, 1377 (1963).

Wolf, E.

E. Wolf, Optics Communications 1, No. 4, 153 (1969).

Other

E. Wolf, Optics Communications 1, No. 4, 153 (1969).

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 53, 1377 (1963).

If the field distribution U1 (x,y) does not satisfy this band-limitation condition, the unwanted spatial-frequency components could be eliminated by using standard optical spatial-filtering techniques. Such spatial-frequency components cannot, of course, be reconstructed at a later stage, i.e., only the filtered field can be reconstructed.

Because of the finite size of the hologram, the intensity distribution IH(x,y) cannot be determined throughout the whole infinite plane z=z1, as formally needed in formula (15). However, because the sinc function in Eq. (15) effectively vanishes when |x-x′| and |y-y′| exceed a moderate multiple of π/ū and π/υ¯, respectively, the integration in Eq. (15) needs only be extended over such a finite x′,y′ domain. This result implies, incidently, that information about the scattered field U1 at the point (x,y) is stored in a region of the hologram, centered on the point (x,y), whose linear dimensions are moderate multiples of π/u¯ and π/υ¯ in the x and y directions, respectively.

High-resolution photographic plates are available that would appear, at first sight, to make it profitable to employ reference beams with appreciably larger values of θr. It seems doubtful, however, that this would lead to a significant improvement of the resolution limit of this technique, because of the difficulty of measuring, to sufficient accuracy, the intensity distribution 1 H (x,y) of the transilluminated hologram.

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