Abstract

Wavefront sensorless adaptive optics (AO) systems have been widely studied in recent years. To reach optimum results, such systems require an efficient correction method. In this paper, a general model-based correction method for a wavefront sensorless AO system is presented. The general model-based approach is set up based on a relationship wherein the second moments (SM) of the wavefront gradients are approximately proportionate to the FWHM of the far-field intensity distribution. The general model-based method is capable of taking various common sets of functions as predetermined bias functions and correcting the aberrations by using fewer photodetector measurements. Numerical simulations of AO corrections of various random aberrations are performed. The results show that the Strehl ratio is improved from 0.07 to about 0.90, with only N + 1 photodetector measurement for the AO correction system using N aberration modes as the predetermined bias functions.

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References

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  1. B. Wang and M. J. Booth, “Optimum deformable mirror modes for sensorless adaptive optics,” Opt. Commun. 282(23), 4467–4474 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2009

B. Wang and M. J. Booth, “Optimum deformable mirror modes for sensorless adaptive optics,” Opt. Commun. 282(23), 4467–4474 (2009).
[CrossRef]

2007

2006

2000

1987

1976

Booth, M. J.

Braat, J.

Carhart, G. W.

Cauwenberghs, G.

Cohen, M.

Noll, R.

Piatrou, P.

Roggemann, M.

Vorontsov, M. A.

Wang, B.

B. Wang and M. J. Booth, “Optimum deformable mirror modes for sensorless adaptive optics,” Opt. Commun. 282(23), 4467–4474 (2009).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the adaptive system.

Fig. 2
Fig. 2

Signal response between SM of aberration gradient and MDS. 500 random aberrations are taken for study.

Fig. 3
Fig. 3

Signal response between aberration magnitude |V| and MDS. Each point in the figure stands for the mean MDS values of 100 random aberrations.

Fig. 4
Fig. 4

Set of aberration modes: (a) 18 Zernike modes (3–20); (b) 18 L–Z modes (3–20).

Fig. 5
Fig. 5

Corresponding inverse S−1 of sets of aberration modes in Fig. 4: The inverse S−1 of (a) 18 Zernike modes (3-20), (b) 18 L–Z modes (3-20).

Fig. 6
Fig. 6

Results of AO correction using (a) L–Z modes and (b) Zernike modes as the predetermined bias functions; the surfaces of the modes are drawn in Fig. 4. The icons “method 1” and “method 2” in the figure refer to the method proposed by M. J. Booth and the method proposed in this paper.

Fig. 7
Fig. 7

Results of AO correction using (a) L–Z and (b) Zernike modes when coefficientαvary from 0.02 to 0.4 λ. The icons “method 1” and “method 2” in the figure refer to the method proposed by M. J. Booth and the method proposed in this paper.

Tables (1)

Tables Icon

Table 1 SR Results of AO Correction Using L–Z Modes by Our Method and Previous Works

Equations (19)

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I ( x ' , y ' ) = I 0 | A ( x , y ) exp [ j R ( x , y ) ] e j k 2 z [ ( x x ' ) 2 + ( y y ' ) 2 ] d x d y | 2 ,
Φ ( x , y ) = i = 1 M ν i F i ( x , y ) , Ψ ( x , y ) = i = 1 N μ i F i ( x , y ) .
[ x Φ ( x , y ) ] 2 + [ y Φ ( x , y ) ] 2 ( x ' 2 + y ' 2 ) .
i = 0 T L { [ x Φ i ( x , y ) ] 2 + [ y Φ i ( x , y ) ] 2 } i = 0 T L F I i ( x ' , y ' ) ( x ' 2 + y ' 2 ) ,
x y { [ x Φ ( x , y ) ] 2 + [ y Φ ( x , y ) ] 2 } d x d y x ' y ' I ( x ' , y ' ) ( x ' 2 + y ' 2 ) d x ' d y ' ,
x ' y ' I ( x ' , y ' ) ( x ' 2 + y ' 2 ) d x ' d y ' = R 2 x ' y ' I ( x ' , y ' ) ( x ' 2 + y ' 2 ) R 2 d x ' d y ' = R 2 { x ' y ' I ( x ' , y ' ) d x ' d y ' x ' y ' I ( x ' , y ' ) [ 1 r 2 R 2 ] d x ' d y ' } .
MDS = x ' y ' I ( x ' , y ' ) [ 1 r 2 R 2 ] d x ' d y ' x ' y ' I ( x ' , y ' ) d x ' d y ' .
SM c 0 ( 1 M D S ) ,
Φ ( x , y ) = i = 1 M ν i F i ( x , y ) .
x Φ ( x , y ) = i = 1 M ν i x F i ( x , y ) , y Φ ( x , y ) = i = 1 M ν i y F i ( x , y ) ,
w i , 0 = S M i S M 0 = s { [ x Φ ( x , y ) + α x F i ( x , y ) ] 2 + [ y Φ ( x , y ) + α y F i ( x , y ) ] 2 } { [ x Φ ( x , y ) ] 2 + [ y Φ ( x , y ) ] 2 } d x d y s ,
w i , 0 = s [ α x F i ( x , y ) 2 x Φ ( x , y ) ] d x d y s + s [ α x F i ( x , y ) ] 2 d x d y s + s [ α y F i ( x , y ) 2 y Φ ( x , y ) ] d x d y s + s [ α y F i ( x , y ) ] 2 d x d y s = s 2 α [ x F i ( x , y ) x Φ ( x , y ) + y F i ( x , y ) y Φ ( x , y ) ] d x d y s + s α 2 { [ x F i ( x , y ) ] 2 + [ y F i ( x , y ) ] 2 } d x d y s .
w i , 0 = s 2 α [ x F i ( x , y ) x Φ ( x , y ) + y F i ( x , y ) y Φ ( x , y ) ] d x d y s + s α 2 { [ x F i ( x , y ) ] 2 + [ y F i ( x , y ) ] 2 } d x d y s , i = 1 ~ N .
W = 2 α * S * V + α 2 * S m ,
s n , m = s { [ x F n ( x , y ) * x F m ( x , y ) ] + [ y F n ( x , y ) * y F m ( x , y ) ] } d x d y s .
V = S 1 ( W α 2 * S m ) 2 * α .
w i , 0 = S M i S M 0 c 0 ( 1 M D S i )- c 0 ( 1 M D S 0 ) - c 0 ( M D S i - M D S 0 ) ,
V S 1 ( c 0 * M α 2 * S m ) 2 * α ,
S R = P [ I ( x , y ) ] P [ I 0 ( x , y ) ] ,

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