Abstract

In 2003 Woods and Greenaway [J. Opt. Soc. Am. A 20, 508 (2003)] published the mathematical details of their method for wavefront sensing by use of a Green’s function solution to the intensity transport equation. Upon reviewing this work I have found that there does not seem to be sufficient information in the data they collect to fully characterize all types of aberrations expected in a wavefront. This I will demonstrate.

© 2007 Optical Society of America

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References

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  1. S. C. Woods and A. H. Greenaway, "Wave-front sensing by use of a Green's function solution to the intensity transport equation," J. Opt. Soc. Am. A 20, 508-512 (2003).
    [CrossRef]
  2. F. Roddier, M. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared application," Publ. Astron. Soc. Jpn. 103, 131-149 (1991).
    [CrossRef]
  3. ANSI Z80.28-2004 Methods for Reporting Optical Abberations of Eyes (American National Standards Institute, 2004).

2003

1991

F. Roddier, M. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared application," Publ. Astron. Soc. Jpn. 103, 131-149 (1991).
[CrossRef]

Graves, J. E.

F. Roddier, M. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared application," Publ. Astron. Soc. Jpn. 103, 131-149 (1991).
[CrossRef]

Greenaway, A. H.

Northcott, M.

F. Roddier, M. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared application," Publ. Astron. Soc. Jpn. 103, 131-149 (1991).
[CrossRef]

Roddier, F.

F. Roddier, M. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared application," Publ. Astron. Soc. Jpn. 103, 131-149 (1991).
[CrossRef]

Woods, S. C.

J. Opt. Soc. Am. A

Publ. Astron. Soc. Jpn.

F. Roddier, M. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared application," Publ. Astron. Soc. Jpn. 103, 131-149 (1991).
[CrossRef]

Other

ANSI Z80.28-2004 Methods for Reporting Optical Abberations of Eyes (American National Standards Institute, 2004).

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Equations (24)

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S ( r ) = k I 0 I z ( r ) z .
k I I z = 2 ϕ ,
S ( r ) = 2 ϕ .
ϕ = c n m Z n m ,
2 ϕ = c n m 2 Z n m ,
k I Z z = c n m 2 Z n m .
Z n m ( ρ , θ ) = N n m R n m ( ρ ) M ( m θ ) ,
N n m = ( 2 δ 0 , m ) ( n + 1 ) ,
δ 0 , m = 1 if m = 0 , δ 0 , m = 0 if m is not 0 .
R n m ( ρ ) = s = 0 0.5 ( n m ) ( 1 ) s ( n s ) ! s ! [ 0.5 ( n + m ) s ] ! [ 0.5 ( n m ) s ] ! ρ n 2 s ,
with s an integer summation index incremented by one unit ;
M ( m θ ) = cos ( m θ ) if m = 0 ,
M ( m θ ) = sin ( m θ ) if m < 0 .
2 f ( r , θ ) = 2 f r 2 + 1 r f r + 1 r 2 2 f θ 2 .
2 Z ( r , θ ) = N [ 2 R ( r ) M ( m θ ) r 2 + 1 r R ( r ) M ( m θ ) r + 1 r 2 2 R ( r ) M ( m θ ) θ 2 ]
2 Z ( r , θ ) = N [ 2 R ( r ) r 2 + 1 r R ( r ) r ] M ( m θ ) + N R ( r ) r 2 2 M ( m θ ) θ 2 .
2 M ( θ ) θ 2 = 2 cos ( m θ ) θ 2 = m 2 cos ( m θ ) = m 2 M ( m θ )
2 M ( θ ) θ 2 = 2 sin ( m θ ) θ 2 = m 2 sin ( m θ ) = m 2 M ( m θ ) .
2 Z ( r , θ ) = [ 2 R ( r ) r 2 + 1 r R ( r ) r ] M ( m θ ) m 2 R ( r ) M ( m θ ) r 2 2 Z ( r , θ ) = [ 2 R ( r ) r 2 + 1 r R ( r ) r m 2 R ( r ) r 2 ] M ( m θ ) .
R n m ( r ) = s = 0 0.5 ( n m ) ( 1 ) s ( n s ) ! s ! [ 0.5 ( n + m ) s ] ! [ 0.5 ( n m ) s ] ! r n 2 s ,
R n n ( r ) = r n .
2 R ( r ) r 2 = n ( n 1 ) r n 2 , 1 r R ( r ) r = n r n 2 ,
m 2 r 2 R ( r ) = n 2 r n 2 ,
2 Z n ± n ( r , θ ) = [ n ( n 1 ) r n 2 + n r n 2 n 2 r n 2 ] M ( n θ ) = 0 .

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