Abstract

Communications are short papers. Appropriate material for this section includes reports of incidental research results, comments on papers previously published, and short descriptions of theoretical and experimental techniques. Communications are handled much the same as regular papers. Proofs are provided.

The rotational properties of Zernike polynomials allow for an easy generation of variable amounts of aberration using two rotated phase plates, each one encoding one or several Zernike modes. This effect may be used to build variable aberration generators useful for calibrating different kinds of aberrometer.

© 2005 Optical Society of America

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References

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    [PubMed]
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2003 (1)

2002 (2)

J. Schwiegerling, “Scaling Zernike expansion coefficients to different pupil sizes,” J. Opt. Soc. Am. A 19, 1937–1945 (2002).
[CrossRef]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–S660 (2002).
[PubMed]

2001 (1)

2000 (1)

1999 (1)

1998 (1)

1997 (2)

1991 (1)

1967 (1)

Alvarez, L. W.

L. W. Alvarez, W. E. Humphrey, “Variable power lens and system,” U.S. patent 3,507,565 (April 21, 1970).

L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent 3,305,294 (February 21, 1967).

Applegate, R.

Applegate, R. A.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–S660 (2002).
[PubMed]

Bará, S.

Campbell, C. E.

Charman, N.

Cox, I. G.

Greivenkamp, J. E.

Guirao, A.

Howland, H. C.

Humphrey, W. E.

L. W. Alvarez, W. E. Humphrey, “Variable power lens and system,” U.S. patent 3,507,565 (April 21, 1970).

Jaroszewicz, Z.

Kolodziejczyk, A.

Liang, J.

Lohmann, A. W.

López-Gil, N.

Love, G. D.

Mancebo, T.

Miller, D. T.

Moreno, V.

Moreno-Barriuso, E.

Palusinski, I. A.

Paris, D. P.

Sasián, J. M.

Schwiegerling, J.

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–S660 (2002).
[PubMed]

Thibos, L. N.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–S660 (2002).
[PubMed]

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–S660 (2002).
[PubMed]

Williams, D. R.

Appl. Opt. (5)

J. Opt. Soc. Am. A (5)

J. Refract. Surg. (1)

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–S660 (2002).
[PubMed]

Other (2)

L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent 3,305,294 (February 21, 1967).

L. W. Alvarez, W. E. Humphrey, “Variable power lens and system,” U.S. patent 3,507,565 (April 21, 1970).

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Figures (2)

Fig. 1
Fig. 1

Adding the phases of two counterrotated coma plates corresponding to the Zernike term Z 3 + 1 with normalized coefficients of the same magnitude ( 0.20 μ m ) but opposite sign gives rise to variable amounts of the Z 3 1 term, as described by Eq. (5). For a better visualization the phase plots are wrapped, with gray levels from 0 (black) to 1 (white), spanning a range of 0.633 μ m . This figure can also be interpreted (reading it from bottom to top) as corresponding to the sum of two counterrotated Z 3 1 terms with coefficients of the same magnitude and sign (see text).

Fig. 2
Fig. 2

Two phases ± c θ Z 4 0 ( r ) are used to produce a variable amount of spherical aberration Z 4 0 ( r ) . Note that two distinct angular sectors are produced, and both the amount of aberration and the size of each sector depend on the rotation angle (see text for details).

Equations (5)

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( a ̂ n m a ̂ n m ) = R ( m α ) ( a n m a n m ) = [ cos ( m α ) sin ( m α ) sin ( m α ) cos ( m α ) ] ( a n m a n m ) .
( a ̂ + a ̂ ) = R ( m α ) ( a 1 + a 1 ) + R ( m α ) ( a 2 + a 2 ) = ( [ a 1 + + a 2 + ] cos ( m α ) + [ a 1 a 2 ] sin ( m α ) [ a 1 + a 2 + ] sin ( m α ) + [ a 1 + a 2 ] cos ( m α ) ) .
( a ̂ + a ̂ ) = ( [ a 1 + + a 2 + ] cos ( m α ) [ a 1 + a 2 + ] sin ( m α ) ) .
( a ̂ + a ̂ ) = ( 2 a + cos ( m α ) 0 ) ,
( a ̂ + a ̂ ) = ( 0 2 a + sin ( m α ) ) .

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