Abstract

It is demonstrated for the first time to the authors’ knowledge that digital holographic image reconstruction can be applied to correction of image reconstruction in the presence of severe anamorphism and aberrations. It is shown that anamorphism and aberrations can be taken into account and compensated for separately to yield a correct-image reconstruction. Anamorphism and aberrations are introduced by a holographic recording system based on a reflective grating interferometer (RGI). The strong anamorphic behavior of the RGI prevents reconstruction of a correct image unless that behavior is compensated for in the process of numerical holographic reconstruction.

© 2001 Optical Society of America

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References

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  1. Y. Takaki, H. Kawai, and H. Ohzu, Appl. Opt. 38, 4990 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2000 (2)

1999 (3)

Cuche, E.

De Nicola, S.

DeNicola, S.

Depeursinge, C.

Ferraro, P.

Finizio, A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), Chap.  5.

Kawai, H.

Kreis, T.

T. Kreis, in Trends in Optical Non-Destructive Testing and Inspection, P. K. Rastogi and D. Inaudi, eds. (Elsevier, New York, 2000), p. 116.

Marquet, P.

Massig, J. H.

Ohzu, H.

Pierattini, G.

Stadelmaier, A.

Takaki, Y.

Appl. Opt. (4)

Opt. Lett. (1)

Other (2)

T. Kreis, in Trends in Optical Non-Destructive Testing and Inspection, P. K. Rastogi and D. Inaudi, eds. (Elsevier, New York, 2000), p. 116.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), Chap.  5.

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Figures (8)

Fig. 1
Fig. 1

RGI in a holographic setup: BE, beam expander; M, mirror; G, grating; o, object beam; r, reference beam.

Fig. 2
Fig. 2

Test object, a photo slide with transparent letters.

Fig. 3
Fig. 3

Test object imaged through the reflective grating, showing strong anamorphism.

Fig. 4
Fig. 4

Experimental setup for direct imaging through reflective grating G in white light.

Fig. 5
Fig. 5

Incorrect-image holographic reconstruction of the test object; magnified image at the right.

Fig. 6
Fig. 6

Reconstruction of the test object with anamorphic correction and d1=240 mm; magnified image at the right.

Fig. 7
Fig. 7

Reconstruction of the test object with anamorphic correction and d2=260 mm; magnified image at the right.

Fig. 8
Fig. 8

Reconstruction of the test object with anamorphic correction and compensation for astigmatism aberrations; magnified image at the right.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

oν,μhx,yrx,yexpiπdλx2+y2×exp-2iπxν+yμdxdy,
expiπdλx2+y2.
oν,μhx,yrx,yexpiπdλx2+y2cosα2×exp-2iπxν+yμdxdy,
expiπλx2dx+y2dy.

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