Abstract

We present results for a digital holography experiment with anisoplanatic image correction through two discrete planes of phase errors. Using a nonlinear optimization technique, we maximize a modified sharpness metric to solve for estimates of the phase errors in the system in the multiple planes where they physically exist. We show that correcting for phase errors in multiple planes gives a superior image to correction in one plane.

© 2010 Optical Society of America

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References

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2009 (2)

2008 (2)

1994 (1)

1974 (1)

Buffington, A.

Fienup, J. R.

Grenander, U.

U. Grenander, Abstract Inference (Wiley, 1981).

Grow, T. D.

Hoft, T. A.

Johnston, D. C.

Kendrick, R. L.

Marron, J. C.

Muller, R. A.

Seldomridge, N.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Thurman, S. T.

Tippie, A. E.

Welsh, B. M.

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Figures (3)

Fig. 1
Fig. 1

Layout of the digital holography experimental setup including phase screens: B/S, beamsplitter; M, mirror; Det, detector array, and PS, phase screen.

Fig. 2
Fig. 2

Image with (a), (b) Screen A, (c), (d) Screen B, and (e), (f) both screens present in the imaging path. Images shown here are scaled, saturated, and cropped to show 530 × 650 pixels (left column, with ball bearings) and 535 × 575 pixels (right column, without ball bearings) of the entire 1024 × 1024 array.

Fig. 3
Fig. 3

Comparison of (a), (b) isoplanatic correction across the entire array, (c), (d) isoplanatic correction over a smaller region of the image, indicated by dashed line and (e), (f) anisoplanatic correction of phases in both the planes of Screens A and B. Figures cropped to show 530 × 650 pixels (left column) and 535 × 575 pixels (right column) of the entire 1024 × 1024 array. Images scaled and saturated to bring out details of the dim portions of the objects in addition to bright glints.

Equations (2)

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A [ z ; g ( x , y ) ] = FT 1 { FT [ g ( x , y ) ] exp [ i π λ z ( f x 2 + f y 2 ) ] } ,
S = ξ , η W ( ξ , η ) I β ( ξ , η ) α k = 1 K f ξ f η M k ( f ξ , f η ) | F k ( f ξ , f η ) | 2 ,

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