Abstract

Matching wavefront correctors and wavefront sensors by minimizing the condition number and mean wavefront variance is proposed. The particular cases of two continuous-sheet deformable mirrors and a Shack-Hartmann wavefront sensor with square packing geometry are studied in the presence of photon noise, background noise and electronics noise. Optimal number of lenslets across each actuator are obtained for both deformable mirrors, and a simple experimental procedure for optimal alignment is described. The results show that high-performance adaptive optics can be achieved even with low cost off-the-shelf Shack-Hartmann arrays with lenslet spacing that do not necessarily match those of the wavefront correcting elements.

© 2007 Optical Society of America

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References

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2005

2004

2000

1997

M. E. Furber, "Optimal design of wavefront sensors for adaptive optical systems: part 1, controlability and observability analysis," Opt. Eng. 36, 1843-1855, 1997.
[CrossRef]

1996

R. Ragazzoni and J. Farinato, "Sensitivity of a pyramidic wave front sensor in closed loop adaptive optics," J. Mod. Opt. 43, 289-293, 1996.
[CrossRef]

1980

Dainty, C.

Dainty, J. C.

Dalimier, E.

Dubra, A.

Farinato, J.

R. Ragazzoni and J. Farinato, "Sensitivity of a pyramidic wave front sensor in closed loop adaptive optics," J. Mod. Opt. 43, 289-293, 1996.
[CrossRef]

Furber, M. E.

M. E. Furber, "Optimal design of wavefront sensors for adaptive optical systems: part 1, controlability and observability analysis," Opt. Eng. 36, 1843-1855, 1997.
[CrossRef]

Munro, I.

Paterson, C.

Ragazzoni, R.

R. Ragazzoni and J. Farinato, "Sensitivity of a pyramidic wave front sensor in closed loop adaptive optics," J. Mod. Opt. 43, 289-293, 1996.
[CrossRef]

Southwell, W. H.

Appl. Opt.

J. Mod. Opt.

R. Ragazzoni and J. Farinato, "Sensitivity of a pyramidic wave front sensor in closed loop adaptive optics," J. Mod. Opt. 43, 289-293, 1996.
[CrossRef]

J. Opt. Soc. Am.

Opt. Eng.

M. E. Furber, "Optimal design of wavefront sensors for adaptive optical systems: part 1, controlability and observability analysis," Opt. Eng. 36, 1843-1855, 1997.
[CrossRef]

Opt. Express

Opt. Lett.

Other

W. Jiang, Y. Zhang, H. Xian, C. Guan, and N. Ling, "A wavefront correction system for inertial confinement fusion," Proc. of the Second International Workshop on Adaptive Optics for Industry and Medicine pages 8-15, 2000.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, "Numerical recipes in C: The art of scientific computing," Cambridge University Press, Cambridge, United Kingdom, 2nd edition, 1992.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen. LAPACK Users’ Guide. Society for Industrial and Applied Mathematics, Philadelphia, PA, third edition, 1999.

G. Rousset, "Wave-front sensors" in Adaptive optics in Astronomy, Franco¸ is Roddier, eds. (Cambridge University Press, Cambridge, U.K.), pp. 91-130.

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Figures (2)

Fig. 1.
Fig. 1.

Geometry used for the calculation of the mean wavefront over a lenslet, which does not need to be hexagonal. The mean wavefront over the lenslet area Ω is calculated as the integral of the difference of the wavefront values over the curves Cmax and Cmin.

Fig. 2.
Fig. 2.

Condition number and E 2 plots for AO systems using a square packing SH and a Mirao 52 or a Multi-DM. The areas between the blue solid lines comprise the range of values for all possible SH orientations and alignment with respect to the DMs. The dashed curve in the condition number plots correspond to the configurations that produce the lowest E 2 for all three sources of noise, and the dashed curve in the E 2 plots to the configurations with lowest condition number.

Equations (14)

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s = Ax ,
A = U Λ V T ,
x = g Bs ,
B pinv = V Λ 1 U T ,
E 2 = 1 A pupil i , j B ij 2 σ j 2 ,
E 2 = σ i λ i 2 ,
W x Ω = Ω W x d x d y Ω d x d y .
W x Ω = 𝓒 max W ( x max ( y ) , y ) dy 𝓒 min W ( x min ( y ) , y ) dy Ω d x d y
σ shot 2 N T 2 n ph N D 2 ,
σ bg 2 n bg N T 2 n ph 2 N D 2 ,
σ elec 2 σ e N S 4 n ph 2 N D 2 ,
σ shot 2 A lenslet 1 ,
σ bg 2 A lenslet 2 ,
σ elec 2 A lenslet 3 ,

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