Abstract

The centroid-based Shack–Hartmann wavefront sensor (SHWFS) treats the sampled wavefronts in the sub-apertures as planes, and the slopes of the sub-wavefronts are used to reconstruct the whole pupil wavefront. The problem is that the centroid method may fail to sense the high-order modes for strong turbulences, decreasing the precision of the whole pupil wavefront reconstruction. To solve this problem, we propose a sub-wavefront estimation method for SHWFS based on the focal plane sensing technique, by which more Zernike modes than the two slopes can be sensed in each sub-aperture. In this paper, the effects on the sub-wavefront estimation method of the related parameters, such as the spot size, the phase offset with its set amplitude and the pixels number in each sub-aperture, are analyzed and these parameters are optimized to achieve high efficiency. After the optimization, open-loop measurement is realized. For the sub-wavefront sensing, we achieve a large linearity range of 3.0 rad RMS for Zernike modes Z2 and Z3, and 2.0 rad RMS for Zernike modes Z4 to Z6 when the pixel number does not exceed 8 × 8 in each sub-aperture. The whole pupil wavefront reconstruction with the modified SHWFS is realized to analyze the improvements brought by the optimized sub-wavefront estimation method. Sixty-five Zernike modes can be reconstructed with a modified SHWFS containing only 7 × 7 sub-apertures, which could reconstruct only 35 modes by the centroid method, and the mean RMS errors of the residual phases are less than 0.2 rad2, which is lower than the 0.35 rad2 by the centroid method.

© 2016 Optical Society of America

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References

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2014 (3)

2013 (1)

2010 (1)

2009 (1)

2006 (2)

Q. Mu, Z. Cao, L. Hu, D. Li, and L. Xuan, “An adaptive optics imaging system based on a high-resolution liquid crystal on silicon device,” Opt. Express 14(18), 8013–8018 (2006).
[Crossref] [PubMed]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

2003 (1)

J. Primot, “Theoretical description of Shack–Hartmann wave-front sensor,” Opt. Commun. 222(1-6), 81–92 (2003).
[Crossref]

2001 (2)

R. A. Gonsalves, “Small-phase solution to the phase-retrieval problem,” Opt. Lett. 26(10), 684–685 (2001).
[Crossref] [PubMed]

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

1996 (3)

1994 (1)

G. Cao and X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33(7), 2331–2335 (1994).
[Crossref]

1982 (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21(5), 829–832 (1982).
[Crossref]

1976 (1)

Booth, M. J.

M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014).
[Crossref]

Cao, G.

G. Cao and X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33(7), 2331–2335 (1994).
[Crossref]

Cao, Z.

Conan, J.-M.

Dai, G.

Fusco, T.

Gonsalves, R. A.

R. A. Gonsalves, “Small-phase solution to the phase-retrieval problem,” Opt. Lett. 26(10), 684–685 (2001).
[Crossref] [PubMed]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21(5), 829–832 (1982).
[Crossref]

Hu, L.

Jenkins, C. R.

R. W. Wilson and C. R. Jenkins, “Adaptive optics for astronomy theoretical performance and limitations,” Mon. Not. R. Astron. Soc. 278(1), 39–61 (1996).
[Crossref]

Jiang, B.

Li, B.

Li, C.

Li, D.

Meimon, S.

Michau, V.

S. Meimon, T. Fusco, V. Michau, and C. Plantet, “Sensing more modes with fewer sub-apertures: the LIFTed Shack-Hartmann wavefront sensor,” Opt. Lett. 39(10), 2835–2837 (2014).
[Crossref] [PubMed]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Mu, Q.

Mugnier, L. M.

Nicolle, M.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Noll, R. J.

Plantet, C.

Platt, B. C.

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Primot, J.

J. Primot, “Theoretical description of Shack–Hartmann wave-front sensor,” Opt. Commun. 222(1-6), 81–92 (2003).
[Crossref]

Rousset, G.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Shack, R.

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Thomas, S.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Tokovinin, A.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Tyson, R. K.

Wilson, R. W.

R. W. Wilson and C. R. Jenkins, “Adaptive optics for astronomy theoretical performance and limitations,” Mon. Not. R. Astron. Soc. 278(1), 39–61 (1996).
[Crossref]

Xia, M.

Xuan, L.

Yu, X.

G. Cao and X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33(7), 2331–2335 (1994).
[Crossref]

Zhang, S.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Refract. Surg. (1)

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Light Sci. Appl. (1)

M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014).
[Crossref]

Mon. Not. R. Astron. Soc. (2)

R. W. Wilson and C. R. Jenkins, “Adaptive optics for astronomy theoretical performance and limitations,” Mon. Not. R. Astron. Soc. 278(1), 39–61 (1996).
[Crossref]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Opt. Commun. (1)

J. Primot, “Theoretical description of Shack–Hartmann wave-front sensor,” Opt. Commun. 222(1-6), 81–92 (2003).
[Crossref]

Opt. Eng. (2)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21(5), 829–832 (1982).
[Crossref]

G. Cao and X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33(7), 2331–2335 (1994).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Other (3)

F. Roddier, “Imaging through the atmosphere,” in Adaptive Optics in Astronomy, F. Roddier (Cambridge University, 1999) 9–22.

R. A. Gonsalves and R. Childlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III,A. G. Tescher, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 207, 32–39 (1979).

G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, F. Roddier (Cambridge University, 1999) 91–130.

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Figures (10)

Fig. 1
Fig. 1 Linearity range changes with the pixel number in a sub-aperture, analyzed with Z2.
Fig. 2
Fig. 2 Calculated coefficients change with the amplitude of the Z4 offset with kd = 13.0 and 4 × 4 pixels in each sub-aperture, (a), (b), (c), (d) and (e) are for Z2, Z3, Z4, Z5 and Z6 respectively.
Fig. 3
Fig. 3 Linear relations of the set and calculated coefficients in case of kd = 13.0, ϕ off = 5.5 rad RMS and 4 × 4 pixels in each sub-aperture, (a), (b), (c), (d) and (e) are for Z2, Z3, Z4, Z5 and Z6 respectively.
Fig. 4
Fig. 4 Sensing errors of the local five modes by the new method, (a), (b) and (c) are the comparisons for 4 × 4, 6 × 6 and 8 × 8 pixels in a sub-aperture for d/r0 = 1.0, respectively.
Fig. 5
Fig. 5 Optical setup for a single lenslet test.
Fig. 6
Fig. 6 Linearity range for Z2 with the experimental parameters ranging from –3.0 to 3.0 rad RMS when the Z4 offset is 5.0 rad RMS
Fig. 7
Fig. 7 Linearity range for Z5 with the experimental parameters ranging from −2.0 to 2.0 rad RMS when the Z4 offset is 5.0 rad RMS
Fig. 8
Fig. 8 Random phase analyzed (a) and the residual phases, (b) for 35 modes and five modes sensed, (c) for 35 modes and only slopes sensed (d) for 65 modes and five modes sensed, (e) for 65 modes and only slopes sensed, and a SHWFS of 10 × 10 sub-apertures is used in this case
Fig. 9
Fig. 9 Residual errors of the phase reconstruction with the 7 × 7 sub-apertures SHWFS
Fig. 10
Fig. 10 The residual error of the reconstruction with the new method compared with the reconstruction with the phase IM, (a) (b) (c) are the situations in which d/r0 = 1.0, 1.5 and 2.0 respectively

Tables (4)

Tables Icon

Table 1 Maximum permitted amplitude of the Z4 offset for the listed kd

Tables Icon

Table 2 The kd and the amplitude of the Z4 offset pairs with the minimum sensing error

Tables Icon

Table 3 Sensing errors in the five modes sensing test with the optimum parameters

Tables Icon

Table 4 Residual error of the reconstruction using the phase IM compared with that of the reconstruction using the new method IM built with 4 × 4, 6 × 6 or 8 × 8 pixels per sub-aperture

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

I(x,y)= I 0 | {p(ξ,η)exp[j(W(ξ,η)+ ϕ off )]} | 2
I(x,y)/ I 0 = I off + k a k I ( Z k + ϕ off ) ,
I ( Z k + ϕ off )= I(Δ a k Z k + ϕ off )I(Δ a k Z k + ϕ off ) 2Δ a k ,
ΔI=H( A off )A,
A= H ( A off )ΔI,
Y A5 n = [ a 2,1 , a 3,1 , a 4,1 , a 5,1 , a 6,1 ,, a 2,np , a 3,np , a 4,np , a 5,np , a 6,np ] T .
A= M Y,

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