Abstract

The quality of coherent images computed from digital holography or heterodyne array data is sensitive to phase errors of the reference and/or object beams. A number of algorithms exist for correcting phase errors in or very near the hologram plane. In the case of phase errors introduced a nonnegligible distance away from hologram plane, the resulting imagery exhibits anisoplanatism. A feature of coherent imaging is that such phase errors may be corrected by simply propagating the aberrated fields (from the object) from the hologram plane to the plane where the phase errors were introduced and applying the phase-error correction algorithms to the fields in that plane. We present experimental results that demonstrate correction of such anisoplanatic phase errors.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2008 (1)

S. T. Thurman and J. R. Fienup, “Phase error correction in digital holography,” J. Opt. Soc. Am. A 25, xxx-xxx (2008).

2003 (1)

1994 (1)

J. R. Fienup, A. M. Kowalczyk, and J. E. Van Buhler, “Phasing sparse arrays of heterodyne receivers,” Proc. SPIE 2241, 127-131 (1994).

1991 (1)

J. N. Cederquist, J. R. Fienup, J. C. Marron, T. J. Schulz, and J. H. Seldin, “Digital shearing laser interferometry for heterodyne array phasing,” Proc. SPIE 1416, 266-277 (1991).

1988 (1)

R. G. Paxman and J. C. Marron, “Aberration correction of speckled imagery with an image-sharpness criterion,” Proc. SPIE 976, 37-47 (1988).

1974 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

1962 (1)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

S. T. Thurman and J. R. Fienup, “Phase error correction in digital holography,” J. Opt. Soc. Am. A 25, xxx-xxx (2008).

J. R. Fienup and J. J. Miller, “Aberration correction by maximizing generalized sharpness metrics,” J. Opt. Soc. Am. A 20, 609-620 (2003).
[CrossRef]

Proc. SPIE (3)

J. N. Cederquist, J. R. Fienup, J. C. Marron, T. J. Schulz, and J. H. Seldin, “Digital shearing laser interferometry for heterodyne array phasing,” Proc. SPIE 1416, 266-277 (1991).

R. G. Paxman and J. C. Marron, “Aberration correction of speckled imagery with an image-sharpness criterion,” Proc. SPIE 976, 37-47 (1988).

J. R. Fienup, A. M. Kowalczyk, and J. E. Van Buhler, “Phasing sparse arrays of heterodyne receivers,” Proc. SPIE 2241, 127-131 (1994).

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Figures (6)

Fig. 1
Fig. 1

Setup for recording digital holograms.

Fig. 2
Fig. 2

Diagram showing origin of anisoplanatism when the distance between the phase screen and the detector array is nonnegligible.

Fig. 3
Fig. 3

Experimental results obtained without the phase screen: (a) speckle-averaged image correcting for defocus only, (b) speckle-averaged image using a 12th-order polynomial to correct for nominal phase errors in the system, (c) phase-error estimate, moduluo 2 π (black = π , white = π ) used to compute (b).

Fig. 4
Fig. 4

(a) and (b) show magnified portions of Fig. 3a, the speckle-averaged image correcting for defocus only, and (c) and (d) show magnified portions of Fig. 3b, with a 12th-order polynomial phase-error correction.

Fig. 5
Fig. 5

Experimental results obtained with the phase screen and attempting to compensate in the plane of the detector array for a phase error that is actually in the plane of the phase screen: (a) speckle-averaged image correcting for defocus only, (b) speckle-averaged image using a 12th-order polynomial to correct for nominal phase errors in the system, (c) phase-error estimate, modulo 2 π , used to compute (b). Note the space variance of the residual blur in (b).

Fig. 6
Fig. 6

Experimental results obtained with the phase screen by propagating the aberrated fields to the phase screen and correcting for a phase error in that plane: (a) speckle-averaged image correcting for defocus only, (b) speckle-averaged image using a 12th-order polynomial to correct for the phase errors in the system, (c) phase-error estimate, modulo 2 π , used to compute (b).

Equations (6)

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G 0 ( x , y ) = F 0 ( x , y ) exp [ i ϕ ( x , y ) ] ,
G 1 ( u , v ) = F 1 ( u , v ) exp [ i θ ( u , v ) ] ,
F ̂ 0 , n ( x , y ) = G 0 , n ( x , y ) exp [ i ϕ ̂ ( x , y ) ] ,
I ̂ ( ξ , η ) = 1 N n f ̂ n ( ξ , η ) 2 ,
M = ( ξ , η ) I ̂ 2 ( ξ , η ) .
F ̂ 1 , n ( u , v ) = G 1 , n ( u , v ) exp [ i θ ̂ ( u , v ) ] ,

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