Abstract

A new wavefront sensing and reconstruction technique is presented. It is possible to measure Laplacian and gradient information of a wavefront with a Hartmann–Shack setup. By simultaneously using the Laplacian and gradient data we reconstruct the wavefront by sequentially solving two partial differential equations.

© 2006 Optical Society of America

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References

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  1. R. K. Tyson, Principles of Adaptive Optics (Academic, 1998).
  2. K. A. Nugent, D. Paganin, and T. E. Gureyev, Phys. Today 54, 27 (2001).
    [CrossRef]
  3. D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).
  4. A. Sommerfeld and J. I. Runge, Ann. Phys. 35, 277 (1911).
    [CrossRef]
  5. M. R. Teague, J. Opt. Soc. Am. 73, 1434 (1983).
    [CrossRef]
  6. S. Bara, J. Opt. Soc. Am. A 20, 2237 (2003).
    [CrossRef]
  7. S. Barbero and L. N. Thibos, ''Error analysis and correction in wavefront reconstruction from Transport-of-Intensity-Equation,'' Opt. Eng. (to be published).
  8. C. Paterson and J. C. Dainty, Opt. Lett. 25, 1687 (2000).
    [CrossRef]
  9. Y. Pinchover and J. Rubinstein, Introduction to Partial Differential Equations (Cambridge U. Press, 2005).
    [CrossRef]
  10. L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 16, S654 (2000).
    [PubMed]

2005 (1)

Y. Pinchover and J. Rubinstein, Introduction to Partial Differential Equations (Cambridge U. Press, 2005).
[CrossRef]

2003 (1)

2001 (1)

K. A. Nugent, D. Paganin, and T. E. Gureyev, Phys. Today 54, 27 (2001).
[CrossRef]

2000 (3)

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 16, S654 (2000).
[PubMed]

C. Paterson and J. C. Dainty, Opt. Lett. 25, 1687 (2000).
[CrossRef]

1998 (1)

R. K. Tyson, Principles of Adaptive Optics (Academic, 1998).

1983 (1)

1911 (1)

A. Sommerfeld and J. I. Runge, Ann. Phys. 35, 277 (1911).
[CrossRef]

Applegate, R. A.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 16, S654 (2000).
[PubMed]

Atchison, D. A.

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

Bara, S.

Barbero, S.

S. Barbero and L. N. Thibos, ''Error analysis and correction in wavefront reconstruction from Transport-of-Intensity-Equation,'' Opt. Eng. (to be published).

Dainty, J. C.

Gureyev, T. E.

K. A. Nugent, D. Paganin, and T. E. Gureyev, Phys. Today 54, 27 (2001).
[CrossRef]

Nugent, K. A.

K. A. Nugent, D. Paganin, and T. E. Gureyev, Phys. Today 54, 27 (2001).
[CrossRef]

Paganin, D.

K. A. Nugent, D. Paganin, and T. E. Gureyev, Phys. Today 54, 27 (2001).
[CrossRef]

Paterson, C.

Pinchover, Y.

Y. Pinchover and J. Rubinstein, Introduction to Partial Differential Equations (Cambridge U. Press, 2005).
[CrossRef]

Rubinstein, J.

Y. Pinchover and J. Rubinstein, Introduction to Partial Differential Equations (Cambridge U. Press, 2005).
[CrossRef]

Runge, J. I.

A. Sommerfeld and J. I. Runge, Ann. Phys. 35, 277 (1911).
[CrossRef]

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 16, S654 (2000).
[PubMed]

Smith, G.

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

Sommerfeld, A.

A. Sommerfeld and J. I. Runge, Ann. Phys. 35, 277 (1911).
[CrossRef]

Teague, M. R.

Thibos, L. N.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 16, S654 (2000).
[PubMed]

S. Barbero and L. N. Thibos, ''Error analysis and correction in wavefront reconstruction from Transport-of-Intensity-Equation,'' Opt. Eng. (to be published).

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, 1998).

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 16, S654 (2000).
[PubMed]

Ann. Phys. (1)

A. Sommerfeld and J. I. Runge, Ann. Phys. 35, 277 (1911).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Refract. Surg. (1)

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 16, S654 (2000).
[PubMed]

Opt. Lett. (1)

Phys. Today (1)

K. A. Nugent, D. Paganin, and T. E. Gureyev, Phys. Today 54, 27 (2001).
[CrossRef]

Other (4)

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

S. Barbero and L. N. Thibos, ''Error analysis and correction in wavefront reconstruction from Transport-of-Intensity-Equation,'' Opt. Eng. (to be published).

Y. Pinchover and J. Rubinstein, Introduction to Partial Differential Equations (Cambridge U. Press, 2005).
[CrossRef]

R. K. Tyson, Principles of Adaptive Optics (Academic, 1998).

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Figures (2)

Fig. 1
Fig. 1

(a), (b) Two H–S images are taken in two axial locations in the optical axis. The energy contained in each spot of the H–S images is computed to generate (c), (d) two spot energy maps. The difference between energy maps (d) and (c) is (e) the energy map necessary to compute Eq. (1).

Fig. 2
Fig. 2

Error in the wavefront reconstruction rms for different levels of simulated noise in the Laplacian data and values of the weight factor w. The FEM solver used 6000 mesh points. Symbols indicate different noise levels: triangles, level A; squares, level B; circles, level C.

Equations (10)

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

Δ u = ( I z ) I .
min K ( u ) min D ( w u f 2 + Δ u g 2 ) d x d y .
w ( f Δ u ) + ( Δ 2 u Δ g ) = 0 .
w n u n ( Δ u ) = w f n ̂ n g ,
Δ u = g ,
Δ v w v = Δ g w f ,
boundary condition v = g ,
Δ u = v ,
boundary condition w n u = w f n ̂ n g + n v .
U ( l , m ) = w k 2 G ( l 2 + m 2 ) k ( l F x + m F y ) w k 4 ( l 2 + m 2 ) 2 k 2 ( l 2 + m 2 ) ,

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