Abstract

A method is proposed for designing an arbitrary continuous refracting surface that can realize conversion between two specified distributions of wavefront. Optimization technique is avoided by solving a partial differential equation governing the surface-profile function. This equation is obtained using the property of congruence and the law of refraction, and its solution in this special case is found to be the same as that obtained in wavefront conjugation. A method based on finding the local coefficients of the surface is developed to solve the equation numerically, and an example is given to illustrate its feasibility.

© 2007 Optical Society of America

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References

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2005 (2)

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2003 (1)

2002 (3)

2001 (1)

2000 (1)

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1964 (1)

1950 (1)

Angel, J. R. P.

Applegate, R. A.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 18, S652 (2002).
[PubMed]

Atchison, D. A.

Avudainayagam, C.

Avudainayagam, K.

Bará, S.

Born, M.

M. Born and E. Wolf, Principles of Optics (Academic, 1999).

Campbell, C. E.

Chernyak, D. A.

Cox, I. G.

Cox, M. J.

Dietze, H. H.

Guirao, A.

Jeong, T. M.

Keller, H. B.

Keller, J. B.

Kneisly, J. A.

Landgrave, J. E. A.

Mancebo, T.

Menon, M.

Moreno-Barriuso, E.

Moya-Cessa, J. R.

Navarro, R.

Porter, J.

Raasch, T. W.

Rhoadarmer, T. A.

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 18, S652 (2002).
[PubMed]

Smith, G.

Thibos, L. N.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 18, S652 (2002).
[PubMed]

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, J. Refract. Surg. 18, S652 (2002).
[PubMed]

Williams, D. R.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Academic, 1999).

Yi, A. Y.

Yoon, G.

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Figures (2)

Fig. 1
Fig. 1

Notation relating to a wavefront conversion.

Fig. 2
Fig. 2

Designed refracting surface.

Equations (11)

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

( ρ u ) ( z z 0 ) = p ( u ) κ 0 ( u ) ,
( ρ v ) ( z z 1 ) = q ( v ) κ 1 ( v ) ,
n = ( p ( u ) q ( v ) ) κ ,
ρ f = n ( ρ , f ( ρ ) ) ,
f ( ρ ) = z in ρ in ρ n d s .
f = z ¯ n ¯ δ ρ + c 4 ( δ ρ ) 2 + c 3 δ x δ y + c 5 ( ( δ x ) 2 ( δ y ) 2 ) .
( c ¯ x x c ¯ x z n ¯ x + 2 ( c 5 + c 4 ) ) δ x + ( c ¯ x y c ¯ x z n ¯ y + c 3 ) δ y = 0 ,
( c ¯ x y c ¯ x z n ¯ y + c 3 ) δ x + ( c ¯ y y c ¯ y z n ¯ y + 2 ( c 4 c 5 ) ) δ y = 0 .
c 3 = c ¯ x z n ¯ y c ¯ x y ,
c 4 = { ( c ¯ x z n ¯ x c ¯ x x ) + ( c ¯ y z n ¯ y c ¯ y y ) } 4 ,
c 5 = { ( c ¯ x z n ¯ x c ¯ x x ) ( c ¯ y z n ¯ y c ¯ y y ) } 4 .

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