Abstract

Strongly aberrated wavefronts lead to inaccuracies and nonlinearities in holography-based modal wavefront sensing (HMWS). In this contribution, a low-resolution Shack–Hartmann sensor (LRSHS) is incorporated into HMWS via a compact holographic design to extend the dynamic range of HMWS. A static binary-phase computer-generated hologram is employed to generate the desired patterns for Shack–Hartmann sensing and HMWS. The low-order aberration modes dominating the wavefront error are first sensed with the LRSHS and corrected by the wavefront modulator. The system then switches to HMWS to obtain better sensor sensitivity and accuracy. Simulated as well as experimental results are shown for validating the proposed method.

© 2012 Optical Society of America

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References

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2012

2011

2010

2009

2008

2006

L. Seifert, T. Ruppel, T. Haist, and W. Osten, “Wavefront sensing by an aperiodic diffractive microlens array,” Proc. SPIE 6293, 629302 (2006).
[CrossRef]

2005

2001

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refr. Surg. 17, S573–S577 (2001).

2000

1998

1991

C. Koliopolis, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1991).
[CrossRef]

1988

F. Roddier, C. Roddier, and N. Roddier, “Curvature sensing: a new wavefront sensing method,” Proc. SPIE 976, 203–209 (1988).

1983

Andersen, G. P.

Bhatt, R.

Booth, M. J.

Boruah, B. R.

Browne, S. L.

Costa, J. B.

Dayton, D. C.

Dong, S.

Ghebremichael, F.

Gonglewski, J. D.

Gupta, A. K.

Gurley, K. S.

Haist, T.

S. Dong, T. Haist, W. Osten, T. Ruppel, and O. Sawodny, “Response analysis of holography-based modal wavefront sensor,” Appl. Opt. 51, 1318–1327 (2012).
[CrossRef]

L. Seifert, T. Ruppel, T. Haist, and W. Osten, “Wavefront sensing by an aperiodic diffractive microlens array,” Proc. SPIE 6293, 629302 (2006).
[CrossRef]

Huang, S.

Jiang, Z.

Koliopolis, C.

C. Koliopolis, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1991).
[CrossRef]

Kudryashov, A. V.

Liu, C.

Mahajan, V. N.

Mishra, S. K.

Mohan, D.

Neil, M. A. A.

Osten, W.

S. Dong, T. Haist, W. Osten, T. Ruppel, and O. Sawodny, “Response analysis of holography-based modal wavefront sensor,” Appl. Opt. 51, 1318–1327 (2012).
[CrossRef]

L. Seifert, T. Ruppel, T. Haist, and W. Osten, “Wavefront sensing by an aperiodic diffractive microlens array,” Proc. SPIE 6293, 629302 (2006).
[CrossRef]

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refr. Surg. 17, S573–S577 (2001).

Roddier, C.

F. Roddier, C. Roddier, and N. Roddier, “Curvature sensing: a new wavefront sensing method,” Proc. SPIE 976, 203–209 (1988).

Roddier, F.

F. Roddier, C. Roddier, and N. Roddier, “Curvature sensing: a new wavefront sensing method,” Proc. SPIE 976, 203–209 (1988).

Roddier, N.

F. Roddier, C. Roddier, and N. Roddier, “Curvature sensing: a new wavefront sensing method,” Proc. SPIE 976, 203–209 (1988).

Ruppel, T.

S. Dong, T. Haist, W. Osten, T. Ruppel, and O. Sawodny, “Response analysis of holography-based modal wavefront sensor,” Appl. Opt. 51, 1318–1327 (2012).
[CrossRef]

L. Seifert, T. Ruppel, T. Haist, and W. Osten, “Wavefront sensing by an aperiodic diffractive microlens array,” Proc. SPIE 6293, 629302 (2006).
[CrossRef]

Sandven, S. P.

Sawodny, O.

Seifert, L.

L. Seifert, T. Ruppel, T. Haist, and W. Osten, “Wavefront sensing by an aperiodic diffractive microlens array,” Proc. SPIE 6293, 629302 (2006).
[CrossRef]

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refr. Surg. 17, S573–S577 (2001).

Sharma, Anurag

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, 1991).

Wilson, T.

Xi, F.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Refr. Surg.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refr. Surg. 17, S573–S577 (2001).

Opt. Lett.

Proc. SPIE

C. Koliopolis, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1991).
[CrossRef]

F. Roddier, C. Roddier, and N. Roddier, “Curvature sensing: a new wavefront sensing method,” Proc. SPIE 976, 203–209 (1988).

L. Seifert, T. Ruppel, T. Haist, and W. Osten, “Wavefront sensing by an aperiodic diffractive microlens array,” Proc. SPIE 6293, 629302 (2006).
[CrossRef]

Other

R. K. Tyson, Principles of Adaptive Optics (Academic, 1991).

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Figures (12)

Fig. 1.
Fig. 1.

Basic principle of holography-based modal wavefront sensing.

Fig. 2.
Fig. 2.

Circular layout of detector positions.

Fig. 3.
Fig. 3.

Sensor response for detecting a single Zernike mode (Z4) using a multiplexed hologram.

Fig. 4.
Fig. 4.

Schematic configuration of holographic Shack–Hartmann sensor.

Fig. 5.
Fig. 5.

Exemplary hologram design for LRSHS and its diffraction pattern: (a) phase hologram with 256 phase level, (b) diffraction spots at predetermined positions.

Fig. 6.
Fig. 6.

Binary-phase hologram of the hybrid sensor and its diffraction pattern: (a) binary hologram, (b) characteristic patterns for LRSHS and HMWS. Note the conjugated spots pattern resulting from the hologram binarization.

Fig. 7.
Fig. 7.

Statistic study of iterations needed in the closed loop to obtain 0.1λ rms residual error using the cumulative histogram method.

Fig. 8.
Fig. 8.

Performance comparison of two sensors: (a) Only HMWS, (b) HMWS combined with LRSHS.

Fig. 9.
Fig. 9.

Schematic diagram of (a) the adaptive optics system for testing the hybrid sensor and (b) the CCD image for a plane wave illuminating the hologram.

Fig. 10.
Fig. 10.

Standard deviation of the amplitudes of (a) Zernike modes in the model and (b) one sample aberration.

Fig. 11.
Fig. 11.

The PSF of the system (a) before correction, (b) after one iteration with LRSHS, (c) after further one iteration with HMWS, (d) after two iterations with HMWS, and (e) comparison of their cross-section data.

Fig. 12.
Fig. 12.

Improvement of Strehl ratio (relative to the condition when zero aberration is present in the system) as a function of iterations.

Tables (1)

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Table 1. System Parameters for Simulating the Atmospheric Turbulence

Equations (8)

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Hk(x,y)=exp[i(2πfkxx+2πfkyy)]exp[ibkZk(x,y)]+exp[i(2πfkxx+2πfkyy)]exp[ibkZk(x,y)],
Ik+=A1|[δ(xxk)δ(yyk)]*h(x,y)*FT{exp[i(akbk)Zk(x,y)]}|2dA1,Ik=A2|[δ(x+xk)δ(y+yk)]*h(x,y)*FT{exp[i(ak+bk)Zk(x,y)]}|2dA2,
ak=bkIk+IkIk++Ik.
HHMWS(x,y)=k=4NHk(x,y).
Hm(x,y)=exp[i(2πx/pxm+2πy/pym)]rect[(xxm)/Dxm]rect[(yym)/Dym],
H(x,y)=HHMWS(x,y)+αHSHS(x,y)=k=4NHk(x,y)+αm=1MHm(x,y),
ϕ(x,y)=k=4NakZk(x,y).
σk=Ckk(D/r0)5/3,

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