Abstract

The crosstalk problem of holography-based modal wavefront sensing (HMWS) becomes more severe with increasing aberration. In this paper, crosstalk effects on the sensor response are analyzed statistically for typical aberrations due to atmospheric turbulence. For specific turbulence strength, we optimized the sensor by adjusting the detector radius and the encoded phase bias for each Zernike mode. Calibrated response curves of low-order Zernike modes were further utilized to improve the sensor accuracy. The simulation results validated our strategy. The number of iterations for obtaining a residual RMS wavefront error of 0.1λ is reduced from 18 to 3.

© 2012 Optical Society of America

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References

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2007

2006

T. Y. Chew, R. M. Clare, and R. G. Lane, “A comparison of the Shack–Hartmann and pyramid wavefront sensors,” Opt. Commun. 268, 189–195 (2006).
[CrossRef]

2003

M. J. Booth, “Direct measurement of Zernike aberration modes with a modal wavefront sensor,” Proc. SPIE 5162, 79– 90 (2003).
[CrossRef]

2000

1998

1997

1987

1976

Allebach, J. P.

Andersen, G. P.

Bhatt, R.

Booth, M. J.

Browne, S. L.

Chew, T. Y.

T. Y. Chew, R. M. Clare, and R. G. Lane, “A comparison of the Shack–Hartmann and pyramid wavefront sensors,” Opt. Commun. 268, 189–195 (2006).
[CrossRef]

Clare, R. M.

T. Y. Chew, R. M. Clare, and R. G. Lane, “A comparison of the Shack–Hartmann and pyramid wavefront sensors,” Opt. Commun. 268, 189–195 (2006).
[CrossRef]

Corbett, A. D.

Dayton, D. C.

Diaz-Santana, L.

Ellerbroek, B. L.

Geary, J. M.

J. M. Geary, Introduction to Wavefront Sensors, Vol. TT18 of SPIE Tutorial Texts in Optical Engineering (SPIE, 1995).

Ghebremichael, F.

Gonglewski, J. D.

Gupta, A. K.

Gurley, K. S.

Huang, S.

Jiang, Z.

Kudryashov, A. V.

Lane, R. G.

T. Y. Chew, R. M. Clare, and R. G. Lane, “A comparison of the Shack–Hartmann and pyramid wavefront sensors,” Opt. Commun. 268, 189–195 (2006).
[CrossRef]

Liu, C.

Mishra, S. K.

Mohan, D.

Neil, M. A. A.

Noll, R. J.

Northcot, M. J.

Rigaut, F.

Sandven, S. P.

Seldowitz, M. A.

Sharma, A.

Sweeney, D. W.

Wilkinson, T. D.

Wilson, T.

Xi, F.

Zhong, J. J.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

T. Y. Chew, R. M. Clare, and R. G. Lane, “A comparison of the Shack–Hartmann and pyramid wavefront sensors,” Opt. Commun. 268, 189–195 (2006).
[CrossRef]

Opt. Lett.

Proc. SPIE

M. J. Booth, “Direct measurement of Zernike aberration modes with a modal wavefront sensor,” Proc. SPIE 5162, 79– 90 (2003).
[CrossRef]

Other

J. M. Geary, Introduction to Wavefront Sensors, Vol. TT18 of SPIE Tutorial Texts in Optical Engineering (SPIE, 1995).

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Figures (12)

Fig. 1.
Fig. 1.

Basic principle of modal wavefront sensing. An incoming beam with positive phase bias u=exp(ibkZk) leads to a strong intensity at detector 1. The phase conjugate wavefront u=exp(ibkZk) leads to a strong intensity at detector 2.

Fig. 2.
Fig. 2.

Coding aberration into hologram as hologram record.

Fig. 3.
Fig. 3.

Layout of detector positions for each Zernike mode.

Fig. 4.
Fig. 4.

Response difference in detecting a single Zernike mode (Z4) using a single hologram or a multiplexed hologram.

Fig. 5.
Fig. 5.

Intermodal crosstalk effect when multiple modes are in the test beam. (a) Amplitudes of Zernike modes other than Z4 are set to 1 radians, (b) amplitudes of modes are generated using the HVB turbulence model.

Fig. 6.
Fig. 6.

Influence of intermodal crosstalk and hologram multiplexing on sensor response (a) Z4, (b) Z5, (c) Z6, (d) Z8, (e) Z11 and (f) Z22.

Fig. 7.
Fig. 7.

Sensor response with 3 random aberrations (a) Z4-Z5 as input, (b) Z4-Z11 as input and (c) Z4-Z23 as input.

Fig. 8.
Fig. 8.

Statistic results of iterations needed for correcting aberrations in closed-loop system (a) histogram for 200 random aberrations, (b) cumulative histogram of (a).

Fig. 9.
Fig. 9.

Response curves of Z4 after corrections (one random aberration with Z4 to Z23 modes is taken as input, Eq. (5) is used as direct output).

Fig. 10.
Fig. 10.

System performance using modified gain of the CRC. For each case, the number of iterations needed for 70% of the random aberrations to converge to 0.1λ RMS residual error was counted.

Fig. 11.
Fig. 11.

System performance with different phase bias bk and detector radius (a) bk=0.4, (b) bk=0.7 (c) bk=1.044 and (d) bk=1.5. For each case, the number of iterations needed for 70% of the random aberrations to converge to 0.1λ RMS residual error was counted.

Fig. 12.
Fig. 12.

Sensor performance with same optimized parameters, but different layout of detector positions. (a) Detectors arranged on a circle, (b) system performance with detectors in a line and (c) on a circle.

Tables (1)

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Table 1. System Parameters for Simulating the Atmospheric Turbulence

Equations (8)

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Hk(x,y)=|Ok(x,y)+Rk(x,y)|2=|Ok(x,y)|2+|Rk(x,y)|2+Ok(x,y)Rk*(x,y)+Ok*(x,y)Rk(x,y),
Hk(x,y)=Ok(x,y)Rk*(x,y)+Ok*(x,y)Rk(x,y)=exp[i(2πfkxx+2πfkyy)]exp[ibkZk(x,y)]+exp[i(2πfkxx+2πfkyy)]exp[ibkZk(x,y)].
Ik=|FT{Hk(x,y)R(x,y)}|2=|FT{exp[i(2πfkxx+2πfkyy)]exp[i(akbk)Zk(x,y)]+exp[i(2πfkxx+2πfkyy)]exp[i(ak+bk)Zk(x,y)]}|2=|[δ(xxk)δ(yyk)]FT{exp[i(akbk)Zk(x,y)]}+[δ(x+xk)δ(y+yk)]FT{exp[i(ak+bk)Zk(x,y)]}|2.
Ik1=A1|[δ(xxk)δ(yyk)]*FT{exp[i(akbk)Zk(x,y)]}|2dA1,Ik2=A2|[δ(x+xk)δ(y+yk)]*FT{exp[i(ak+bk)Zk(x,y)]}|2dA2,
ak=bkIk1Ik2Ik1+Ik2.
Ik1=A1|[δ(xxk)δ(yyk)]*FT{exp[ij=4NajZj(x,y)]exp[ibkZk(x,y)]}|2dA1=A1|[δ(xxk)δ(yyk)]*FT{exp[i(akbk)Zk(x,y)]exp[ijkNajZj(x,y)]}|2dA1.
H(x,y)=k=4NHk(x,y).
d=λfp,

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