Abstract

Several mathematical errors from Appl. Opt. 49, D69 (2010) are corrected in this erratum.

© 2010 Optical Society of America

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References

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  1. J. Sasian, “Theory of sixth-order wave aberrations,” Appl. Opt. 49, D69–D93 (2010).
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Equations (14)

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J ( H , ρ ) = y pupil 2 y pupil 2 · { 1 + Δ ρ h ρ h + Δ ρ i ρ i } = y pupil 2 y pupil 2 · { 1 + ρ Δ ρ } ,
J ( H , ρ ) = y pupil 2 y pupil 2 · { 1 + Δ ρ h ρ h + Δ ρ i ρ i + Δ ρ h ρ h Δ ρ i ρ i Δ ρ i ρ h Δ ρ h ρ i } .
ρ ( H W ¯ ( H , ρ ) ) = ρ h ( H W ¯ ( H , ρ ) · h ) + ρ i ( H W ¯ ( H , ρ ) · i ) = ρ H W ( H , ρ ) + 1 ρ · i ( H W ( H , ρ ) ) · i .
H W ¯ ( H , ρ ) = A H + B ρ .
ρ ( H W ¯ ( H , ρ ) ) = ρ h ( H W ¯ ( H , ρ ) · h ) + ρ i ( H W ¯ ( H , ρ ) · i ) = ρ h ( A H + B ρ h ) + ρ i B ρ i = H A ρ h + ρ h B ρ h + ρ i B ρ i + 2 B = H A ρ · ρ ρ h + 2 B + ρ h B ρ · ρ ρ h + ρ i B ρ · ρ ρ i = H A ρ · h + 2 B + ρ h B ρ · h + ρ i B ρ · i = A ρ · H + 2 B + B ρ · ρ = ρ ( A H + B ρ ) + ( A · H + B ρ ) · i ρ · i = ρ H W ¯ ( H , ρ ) + H W ¯ ( H , ρ ) · i ρ · i = ρ H W ¯ ( H , ρ ) + H W ¯ ( H , ρ ) · i ρ · i .
ρ ( B ρ ) = B ρ · ρ + B ρ ρ = B ρ · ρ + B .
ρ 2 W ( H , ρ ) = 2 W ( H , ρ ) ρ h 2 + 2 W ( H , ρ ) ρ i 2 = ρ ( ρ W ( H , ρ ) ) + 1 ρ · i ( ρ W ( H , ρ ) ) · i .
I 000 = 1 ,
I 020 ( ρ · ρ ) = 4 Ψ W ¯ 311 ( ρ · ρ ) ,
I 111 ( H · ρ ) = [ 4 Ψ W ¯ 220 + 6 Ψ W ¯ 222 ] ( H · ρ ) ,
I 200 ( H · H ) = 4 Ψ W ¯ 131 ( H · H ) .
Δ I ( H , ρ ) Δ Z 1 n · y P P · y pupil ρ 2 W ( H , ρ ) = 1 n · y P P · y pupil 16 W 040 ( ρ · ρ ) ,
Δ I ( H , ρ ) Δ Z n · y ¯ P P · y pupil 4 W ¯ 311 ( ρ · ρ ) = 4 Ψ W ¯ 311 ( ρ · ρ ) .
Δ H = 1 cos 3 ( θ ) 1 Ψ ρ W ( H , ρ ) .

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