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References

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  1. D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Appendix 3.
  2. R. Kingslake, Trans. Opt. Soc. 27, 94 (1925–26).
  3. H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950), p. 48.
  4. F. Zernike, Physics 1, 689 (1934).

1934 (1)

F. Zernike, Physics 1, 689 (1934).

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950), p. 48.

Kingslake, R.

R. Kingslake, Trans. Opt. Soc. 27, 94 (1925–26).

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Appendix 3.

Zernike, F.

F. Zernike, Physics 1, 689 (1934).

Physics (1)

F. Zernike, Physics 1, 689 (1934).

Trans. Opt. Soc. (1)

R. Kingslake, Trans. Opt. Soc. 27, 94 (1925–26).

Other (2)

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950), p. 48.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Appendix 3.

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Equations (13)

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W ( x , y ) = A ( x 2 + y 2 ) 2 + B y ( x 2 + y 2 ) + C ( x 2 + 3 y 2 ) + D ( x 2 + y 2 ) + E y + F x ,
W ( x , y ) = A 1 U 00 constant + A 2 ( U 10 sin ϕ 2 + U 11 cos ϕ 2 ) wave front tilt + A 3 U 21 defousing + A 4 ( U 20 sin 2 ϕ 4 + U 22 cos 2 ϕ 4 ) third-order astigmatism + A 5 ( U 31 sin ϕ 5 + U 32 cos ϕ 5 ) coma + A 6 ( U 30 sin 3 ϕ 6 + U 33 cos 3 ϕ 6 ) triangular astigmatism + A 7 U 42 spherical aberration + A 8 ( U 40 sin 4 ϕ 8 + U 44 cos 4 ϕ 8 ) quadratic astigmatism + A 9 ( U 41 sin 2 ϕ 9 + U 43 cos 2 ϕ 9 ) fifth-order astigmatism ,
W ( x , y ) = A 1 + A 2 ρ cos ( θ + ϕ 2 ) + A 3 ( 2 ρ 2 1 ) + A 4 ρ 2 cos 2 ( θ ϕ 4 ) + A 5 ( 3 ρ 3 2 ρ ) cos ( θ ϕ 5 ) + A 6 ρ 3 cos 3 ( θ ϕ 6 ) + A 7 ( 6 ρ 4 6 ρ 2 + 1 ) + A 8 ρ 4 cos 4 ( θ ϕ 8 ) + A 9 ( 4 ρ 4 3 ρ 2 ) cos 2 ( θ ϕ 9 ) ,
W ( x , y ) = a 1 + a 2 y + a 3 x + a 4 y 2 + a 5 x y + a 6 x 2 + a 7 y 3 + a 8 x y 2 + a 9 x 2 y + a 10 x 3 + a 11 y 4 + a 12 x y 3 + a 13 x 2 y 2 + a 14 x 3 y + a 15 x 4 .
A 1 = a 1 + a 4 4 + a 6 4 + 7 a 11 48 + 5 a 15 48 + a 13 24 .
tan ϕ 2 = 6 a 3 + a 8 + 3 a 10 6 a 2 + a 9 + 3 a 7 , A 2 = 6 a 3 + a 8 + 3 a 10 6 sin ϕ 2 ; ( tan ϕ 2 0 ) , A 2 = 6 a 2 + a 9 + 3 a 7 6 cos ϕ 2 ; ( tan ϕ 2 ) .
A 3 = 1 4 ( a 4 + a 6 + 7 a 11 8 + a 13 4 + 5 a 15 8 ) .
tan 2 ϕ 4 = 8 a 5 + 3 a 12 + 3 a 14 8 a 4 8 a 6 + 6 a 11 6 a 15 , A 4 = 8 a 5 + 3 a 12 + 3 a 14 16 sin 2 ϕ 4 ; ( tan 2 ϕ 4 0 ) , A 4 = 4 a 4 4 a 6 + 3 a 11 3 a 15 8 cos 2 ϕ 4 ; ( tan 2 ϕ 4 ) .
tan ϕ 5 = a 8 + 3 a 10 a 9 + 3 a 7 , A 5 = a 8 + 3 a 10 12 sin ϕ 5 ; ( tan ϕ 5 0 ) , A 5 = a 9 + 3 a 7 12 cos ϕ 5 ; ( tan ϕ 5 ) .
tan 3 ϕ 6 = a 8 a 10 a 7 a 9 , A 6 = a 8 a 10 4 sin 3 ϕ 6 ; ( tan 3 ϕ 6 0 ) , A 6 = a 7 a 9 4 cos 3 ϕ 6 ; ( tan 3 ϕ 6 ) .
A 7 = 1 48 ( 7 a 11 2 + 5 a 15 2 + a 13 ) .
tan 4 ϕ 8 = 2 ( a 12 a 14 ) a 11 + 3 a 15 2 a 13 , A 8 = a 12 a 14 8 sin 4 ϕ 8 ; ( tan 4 ϕ 8 0 ) , A 8 = a 11 3 a 15 2 a 13 16 cos 4 ϕ 8 ; ( tan 4 ϕ 8 ) .
tan 2 ϕ 9 = a 12 + a 14 2 ( a 11 a 15 ) , A 9 = a 12 + a 14 16 sin 2 ϕ 9 ; ( tan 2 ϕ 9 0 ) , A 9 = a 11 a 15 8 cos 2 ϕ 9 ; ( tan 2 ϕ 9 ) .

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