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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1999

1998

1992

1990

1982

1979

1966

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)

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

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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