Abstract

A novel holographic technique is described for unambiguous image reconstruction by using nonuniform illumination across an object. In contrast to conventional lensless Fourier holography, reconstruction is possible when one or more references are on the object.

© 1988 Optical Society of America

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References

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  1. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
    [CrossRef]
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  3. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  4. R. K. Erf, ed., Speckle Metrology (Academic, New York, 1978).

1962

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Leith, E. N.

Upatnieks, J.

J. Opt. Soc. Am.

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

R. K. Erf, ed., Speckle Metrology (Academic, New York, 1978).

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Figures (3)

Fig. 1
Fig. 1

Schematics of self-reference holographic imaging. An object with NR glints is illuminated by 2NR different nonuniform laser beams labeled by index p. The hologram formed for each beam is digitally Fourier transformed. F[·] denotes the Fourier transform. A set of 2NR independent linear equations for a(r) (for objects with constant complex reflectivity) or for 〈|a(r)|2〉 (for diffuse objects) is solved to obtain an unambiguous image of this object.

Fig. 2
Fig. 2

Image reconstruction for one glint on a diffuse object by using two identical Gaussian beams with half-width σ equal to object length. A, Object with a glint indicated by a black dot; beam centers indicated by crosses. B, Conventional reconstruction (for the beam at the far left) results in two overlapping images. C, New method results in a single image (averaged over eight realizations of complex reflectivity).

Fig. 3
Fig. 3

Image reconstruction for two glints on a diffuse object by using four identical Gaussian beams with σ equal to object length. A, Object with two glints indicated by black dots; beam centers indicated by crosses. B, Conventional reconstruction (for the bottom right beam) results in four overlapping images. C, New method results in a single image (averaged over eight realizations of complex reflectivity).

Equations (6)

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U ( r ) = U R ( r ) + U 0 ( r ) ,
U R ( r ) n = 1 N R A ( r n ) B 1 ( r n ) exp [ i π ( r r n ) 2 / λ z ] , U 0 ( r ) d r 0 a ( r 0 ) B 1 ( r 0 ) exp [ i π ( r r 0 ) 2 / λ z ] ,
| U | 2 = | U R | 2 + U R U 0 * + U R * U 0 + | U 0 | 2 .
Δ U ( r ) = U R U 0 * + U R * U 0 .
F 1 ( r ) = d r Δ U ( r ) exp [ i ( 2 π / λ z ) r · r ] n = 1 N R [ A ˜ * ( r n ) B 1 * ( r n ) B 1 ( r n + r ) a ˜ ( r n + r ) + A ˜ ( r n ) B 1 ( r n ) B 1 * ( r n r ) a ˜ * ( r n r ) ] ,
| F p ( r ) | 2 n = 1 N R | A ( r n ) | 2 | B p ( r n ) | 2 × [ | B p ( r n + r ) | 2 | a ( r n + r ) | 2 + | B p ( r n r ) | 2 | a ( r n r ) | 2 ] .

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