Abstract

The possibility of compensating for the aberrations of an imaging lens in digital holography is outlined theoretically. The principle is demonstrated with a Mach–Zehnder arrangement and transilluminated objects. Diffraction-limited resolution can be obtained with a plano–convex lens. Amplitude and phase objects were imaged.

© 2000 Optical Society of America

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References

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  1. W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, and C. K. Rhodes, Appl. Opt. 31, 4973 (1992).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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1999 (1)

1998 (1)

1992 (1)

1990 (1)

1982 (1)

1979 (1)

1966 (1)

Boyer, K.

Cullen, D.

Froehly, C.

Goodman, J. W.

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

Haddad, W. S.

Kawai, H.

Leith, E.

Leith, E. N.

Longworth, J. W.

Madjidi-Zolbanine, H.

McPherson, A.

Ohzu, H.

Rhodes, C. K.

Roddier, C.

Roddier, F.

Solem, J. C.

Swanson, G. J.

Takaki, Y.

Upatnieks, J.

Vander Lugt, A.

Yamaguchi, I.

Zhang, T.

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Figures (5)

Fig. 1
Fig. 1

Illustration of the basic apparatus.

Fig. 2
Fig. 2

Illustration of the experimental arrangement.

Fig. 3
Fig. 3

Reconstructed object without compensation for aberrations.

Fig. 4
Fig. 4

Reconstructed object with compensation for aberrations.

Fig. 5
Fig. 5

Reconstructed phase from a phase grating.

Equations (8)

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upx,yux,yPx,y×expjk/2fx2+y2-2xx-2yydxdy,
u˜x,y=ux,yexpjk/2fx2+y2
upx,yPx,yU˜x/λf,y/λf.
ix,yPx,y2U˜x/λf,y/λf2+A2+CPx,yU˜x/λf,y/λfexp-jkxx+kyy+C*P*x,yU˜x/λf,y/λfexpjkxx+kyy,
Px,y=Px,yexpjWx,y.
CPx,yU˜x/λf,y/λfexp-jkxx+kyy.
Wsax,y=Φmaxx2+y22rp4,
Wfx,y=ax2+y2rp2.

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