Abstract

In some adaptive optics systems the aberration is determined not by using a wavefront sensor but by sequential optimization of the adaptive correction element. Efficient schemes for the control of such systems are essential if they are to be effective. A scheme is introduced that permits the efficient measurement of large amplitude wavefront aberrations that are represented by an appropriate series of modes. This scheme uses an optimization metric based on the root-mean-square spot radius (or focal spot second moment) and an aberration expansion using polynomials suited to the representation of lateral aberrations. Experimental correction of N aberration modes is demonstrated with a minimum of N+1 photodetector measurements. The geometrical optics basis means that the scheme can be extended to arbitrarily large aberrations.

© 2006 Optical Society of America

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References

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  1. M. J. Booth, Opt. Express 14, 1339 (2006).
    [CrossRef] [PubMed]
  2. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1983).
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    [CrossRef]
  4. W. Lukosz, Opt. Acta 10, 1 (1963).
    [CrossRef]
  5. J. Braat, J. Opt. Soc. Am. A 4, 643 (1987).
    [CrossRef]
  6. M. A. A. Neil, M. J. Booth, and T. Wilson, Opt. Lett. 23, 1849 (1998).
    [CrossRef]

2006

1998

1987

1976

1963

W. Lukosz, Opt. Acta 10, 1 (1963).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

W. Lukosz, Opt. Acta 10, 1 (1963).
[CrossRef]

Opt. Express

Opt. Lett.

Other

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1983).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the optical system. (b) Normalized signal response, using LZ modes and quadratic detector (upper, blue curve), experimentally determined figures (red squares), pointlike detector and Zernike modes (lower, green curve).

Fig. 2
Fig. 2

Focal spot images before and after the measurement and correction cycles for three different starting aberrations. First column, initial aberrated spot; second column, after the first correction cycle; third column, after two correction cycles. The multiplication factor indicates the relative brightness of each spot image.

Fig. 3
Fig. 3

Variation of W with aberration magnitude b for detector radius R, showing the mean, 10th, and 90th percentiles from 100 random aberrations.

Equations (9)

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S 1 a 2 ,
L n m ( r , θ ) = B n m ( r ) { cos ( m θ ) m 0 sin ( m θ ) m < 0 ,
B n m ( r ) = { 1 n [ R n 0 ( r ) R n 2 0 ( r ) ] m = 0 2 n [ R n m ( r ) R n 2 m ( r ) ] n m 0 2 n R n n ( r ) m = n 0 .
R n m ( r ) = k = 0 n m 2 ( 1 ) k ( n k ) ! r n 2 k k ! ( n + m 2 k ) ! ( n m 2 k ) ! .
ρ 2 = ( λ NA ) 2 n , m b n , m 2 = ( λ NA ) 2 b 2 ,
W = ν ξ I ( ν , ξ ) D ( ν , ξ ) ν d ν d ξ ,
b out = S 1 ( w w 0 ) ,
w = ( i = 1 N + 1 β i W i ) ( i = 1 N + 1 W i ) .
S i k = W i b k ,

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