Abstract

The traditional Shack–Hartmann wavefront sensing (SHWS) system measures the wavefront slope by calculating the centroid shift between the sample and a reference piece, and then the wavefront is reconstructed by a suitable iterative reconstruction method. Because of the necessity of a reference, many issues are brought up, which limit the system in most applications. This Letter proposes a reference-free wavefront sensing (RFWS) methodology, and an RFWS system is built up where wavefront slope changes are measured by introducing a lateral disturbance to the sampling aperture. By using Southwell reconstruction two times to process the measured data, the form of the wavefront at the sampling plane can be well reconstructed. A theoretical simulation platform of RFWS is established, and various surface forms are investigated. Practical measurements with two measurement systems—SHWS and our RFWS—are conducted, analyzed, and compared. All the simulation and measurement results prove and demonstrate the correctness and effectiveness of the method.

© 2011 Optical Society of America

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References

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  1. Z. Hartmann, Instrumentenk 20, 47 (1900).
  2. R. V. Shack and B.C.Platt, J. Opt. Soc. Am. 61, 656 (1971).
  3. B. C. Platt and R. Shack, J. Refract. Surg. 17, 573 (2001).
  4. Z. W. Zhong, L. P. Zhao, and A. A. Hein, Proc. SPIE 7155, 71552X-1 (2008).
  5. S. M. Jobling and P. G. Kwiat, Opt. Express 18, 8772 (2010).
    [CrossRef] [PubMed]
  6. L. Zhao, N. Bai, X. Li, L. S. Ong, Z. P. Fang, and A. K. Asundi, Appl. Opt. 45, 90 (2006).
    [CrossRef] [PubMed]
  7. W. H. Southwell, J. Opt. Soc. Am. 70, 998 (1980).
    [CrossRef]

2010

2006

2001

B. C. Platt and R. Shack, J. Refract. Surg. 17, 573 (2001).

1980

1971

R. V. Shack and B.C.Platt, J. Opt. Soc. Am. 61, 656 (1971).

1900

Z. Hartmann, Instrumentenk 20, 47 (1900).

Asundi, A. K.

Bai, N.

Fang, Z. P.

Hartmann, Z.

Z. Hartmann, Instrumentenk 20, 47 (1900).

Hein, A. A.

Z. W. Zhong, L. P. Zhao, and A. A. Hein, Proc. SPIE 7155, 71552X-1 (2008).

Jobling, S. M.

Kwiat, P. G.

Li, X.

Ong, L. S.

Platt, B. C.

B. C. Platt and R. Shack, J. Refract. Surg. 17, 573 (2001).

R. V. Shack and B.C.Platt, J. Opt. Soc. Am. 61, 656 (1971).

Shack, R.

B. C. Platt and R. Shack, J. Refract. Surg. 17, 573 (2001).

Shack, R. V.

R. V. Shack and B.C.Platt, J. Opt. Soc. Am. 61, 656 (1971).

Southwell, W. H.

Zhao, L.

Zhao, L. P.

Z. W. Zhong, L. P. Zhao, and A. A. Hein, Proc. SPIE 7155, 71552X-1 (2008).

Zhong, Z. W.

Z. W. Zhong, L. P. Zhao, and A. A. Hein, Proc. SPIE 7155, 71552X-1 (2008).

Appl. Opt.

Instrumentenk

Z. Hartmann, Instrumentenk 20, 47 (1900).

J. Opt. Soc. Am.

R. V. Shack and B.C.Platt, J. Opt. Soc. Am. 61, 656 (1971).

W. H. Southwell, J. Opt. Soc. Am. 70, 998 (1980).
[CrossRef]

J. Refract. Surg.

B. C. Platt and R. Shack, J. Refract. Surg. 17, 573 (2001).

Opt. Express

Proc. SPIE

Z. W. Zhong, L. P. Zhao, and A. A. Hein, Proc. SPIE 7155, 71552X-1 (2008).

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Figures (6)

Fig. 1
Fig. 1

RFWS with a lateral shift introduced to the sampling aperture. Black solid lines, beams corresponding to the sampling aperture before lateral shift. Red dashed lines, beams corresponding to the sampling aperture after lateral shift.

Fig. 2
Fig. 2

Wavefront slope change at grid points. A i , grid point before shifting; B i , grid point that is measured by the same subsampling aperture after shifting.

Fig. 3
Fig. 3

Comparison of the nominal wavefront slope (solid line) and the wavefront slope obtained in the simulation platform (dots).

Fig. 4
Fig. 4

Comparison of the nominal wavefront (solid line) and the wavefront obtained in the simulation platform (dots).

Fig. 5
Fig. 5

Experiment setup.

Fig. 6
Fig. 6

Experimental results obtained after two steps of wavefront reconstruction, as (a) measurement data from RFWS system; (b) measurement data from SHWS system; (c) difference of the results from the two measurement systems; (d) averaged reconstructed wavefront along the form, varying direction compared with stylus measurement results.

Equations (3)

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Δ S = Δ x f .
S i = 1 2 ( S i 1 + S i + 1 ) + P 4 Δ d ( Δ S i 1 Δ S i + 1 ) ,
φ = 0.016 4.5372 × 10 4 x 2 + 6.181 × 10 6 x 4 3.018 × 10 8 x 6 + 5.9494 × 10 11 x 8 4.0408 × 10 14 x 10 .

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