Abstract

We derive equations for defocus and primary spherical wave aberration coefficients caused by a shift in image plane of a perfect optical system. The spherical aberration equation is accurate at describing changes in the spherical aberration of an aberrated schematic eye.

© 2006 Optical Society of America

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References

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  1. D. A. Atchison and W. N. Charman, "The influences of reference plane and direction of measurement on eye aberration measurement," J. Opt. Soc. Am. A 22, 2589-2597 (2005).
    [CrossRef]
  2. H. H. Hopkins and M. J. Yzuel, "The computation of diffraction patterns in the presence of aberrations," Opt. Acta 17, 157-182 (1970).
    [CrossRef]
  3. R. Navarro, J. Santamaría, and J. Bescós, "Accommodation-dependent model of the human eye with aspherics," J. Opt. Soc. Am. A 2, 1273-1281 (1985).
    [CrossRef] [PubMed]

2005

1985

1970

H. H. Hopkins and M. J. Yzuel, "The computation of diffraction patterns in the presence of aberrations," Opt. Acta 17, 157-182 (1970).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

General case of an optical system imaging a point Q (not shown) to the point Q .

Fig. 2
Fig. 2

Schema for calculation of wave aberration coefficients.

Fig. 3
Fig. 3

Change in spherical aberration coefficient as a function of shift in focal plane for into-the-eye ray tracing with the Navarro model eye.

Tables (2)

Tables Icon

Table 1 Into-the-Eye Ray-Trace Results for the Focused and Defocused ( Δ Z = + 5 mm ) Navarro Model Eye

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Table 2 Wave Aberration Coefficients for the Focused and Defocused ( Δ Z = 5 mm ) Navarro Model Eye a

Equations (20)

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Wave aberration ( W ) = [ B B ] ,
Δ Z = R R
Y Y = Δ Y = S sin ( α ) .
( R + S ) 2 = R 2 + Δ Z 2 2 R Δ Z cos ( β ) ,
S = R 2 + Δ Z 2 2 R Δ Z cos ( β ) R ,
cos ( β ) = 1 Y 2 R 2 = 1 ( 1 2 ) Y 2 R 2 ( 1 8 ) Y 4 R 4 + .
S = { R 2 + Δ Z 2 2 R Δ Z [ 1 ( 1 2 ) Y 2 R 2 ( 1 8 ) Y 4 R 4 + ] } 1 2 R = { R 2 + Δ Z 2 2 R Δ Z + 2 R Δ Z [ ( 1 2 ) Y 2 R 2 + ( 1 8 ) Y 4 R 4 + ] } 1 2 R ,
R 2 + Δ Z 2 2 R Δ Z = R 2 ,
S = { R 2 + 2 R Δ Z [ ( 1 2 ) Y 2 R 2 + ( 1 8 ) Y 4 R 4 + ] } 1 2 R = R { 1 + [ 2 R Δ Z R 2 ] [ ( 1 2 ) Y 2 R 2 + ( 1 8 ) Y 4 R 4 + ] } 1 2 R .
S = ( 1 2 ) R ( R Δ Z R 2 ) [ Y 2 R 2 + ( 1 4 ) Y 4 R 4 + ] ( 1 8 ) R ( R Δ Z R 2 ) 2 [ Y 2 R 2 + ( 1 4 ) Y 4 R 4 + ] 2 .
S = ( 1 2 ) ( 1 R 1 R ) Y 2 + ( 1 8 ) ( 1 R 3 ) [ 2 ( R R ) ( R R ) 3 1 ] Y 4 + ,
W = n S = W 2 , 0 Y 2 + W 4 , 0 Y 4 + ,
W 2 , 0 = n ( 1 2 ) ( 1 R 1 R ) ,
W 4 , 0 = n ( 1 8 ) ( 1 R 3 ) [ 2 ( R R ) ( R R ) 3 1 ] .
Δ W 4 , 0 = n ( 1 8 ) ( 1 R 3 ) [ 2 ( R R ) ( R R ) 3 1 ] .
Δ W 4 , 0 = n ( 1 8 ) ( 1 R 2 ) ( 1 R 1 R ) .
R = R ( 1 + h ) or h = ( R R ) R ,
Δ W 4 , 0 = n ( 1 8 ) ( 1 R 2 ) [ 2 R R 2 R 3 1 R ] = n ( 1 8 ) ( 1 R 2 ) { 2 R R 2 [ R 2 R ( 1 + h ) 2 ] 1 R } = n ( 1 8 ) ( 1 R 2 ) [ 2 R ( 1 + h ) 2 R 1 R ] .
Δ W 4 , 0 = n ( 1 8 ) ( 1 R 2 ) [ 2 R ( 1 2 h ) R 1 R ] = n ( 1 8 ) ( 1 R 2 ) { 2 R [ 1 2 ( R R ) R ] R 1 R } = n ( 1 8 ) ( 1 R 2 ) ( 1 R 1 R ) ,
Δ W 4 , 0 = ( 1 8 ) R 3 or ( 1 8 ) R x 3 ,

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