Abstract

A method for reconstructing wavefront aberrations from intensity measurements in the focal plane of a focusing optic is presented. This reconstruction method is simple, fast, and accurate in reconstructing wavefront aberrations because it uses the inverse Fourier transform of an intensity distribution in the focal plane with a reference electric field. The validity of the reconstruction method is demonstrated by computing a wavefront aberration from the intensity distributions in the focal plane.

© 2007 Optical Society of America

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References

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  1. D. Malacara, Optical Shop Testing (Wiley-Interscience, 1992), Chap. 5.
  2. R. Tyson, Principles of Adaptive Optics (Academic, 1997), Chap. 5.
  3. J. R. Fienup, Appl. Opt. 21, 2758 (1982).
    [CrossRef] [PubMed]
  4. F. Roddier, Appl. Opt. 27, 1223 (1988).
    [CrossRef] [PubMed]
  5. R. G. Paxman, T. J. Schulz, and J. R. Fienup, J. Opt. Soc. Am. A 9, 1072 (1992).
    [CrossRef]
  6. "Methods for reporting optical aberrations of eyes," ANSI Z80.28-2004 (American National Standards Institute, 2004).
  7. T. M. Jeong, D.-K. Ko, and J. Lee, Opt. Lett. 32, 232 (2007).
    [CrossRef] [PubMed]

2007 (1)

1992 (1)

1988 (1)

1982 (1)

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Other (3)

D. Malacara, Optical Shop Testing (Wiley-Interscience, 1992), Chap. 5.

R. Tyson, Principles of Adaptive Optics (Academic, 1997), Chap. 5.

"Methods for reporting optical aberrations of eyes," ANSI Z80.28-2004 (American National Standards Institute, 2004).

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Figures (2)

Fig. 1
Fig. 1

Optical layout for reconstructing wavefront aberrations from the intensity measurement.

Fig. 2
Fig. 2

(a) Wavefront aberration map of the whole incoming electric field and (b) its intensity distribution in the focal plane. (c) Wavefront aberration map of the inner aberrated electric field and (d) its intensity distribution in the focal plane. (e) Test and (f) reconstructed wavefront aberrations. In (a) and (c), the size of the map was 25 mm × 25 mm with 128 × 128 sections. Thus, r i and r o were 10.4 and 11.5 mm , respectively. In (b) and (d), the size of the map was 1.6 mm × 1.6 mm with 200 × 200 sections.

Equations (7)

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E 2 ( x 2 , y 2 ) E 1 ( x 1 , y 1 ) P ( x 1 , y 1 ) exp [ i k W ( x 1 , y 1 ) ] exp [ i k f ( x 1 x 2 + y 1 y 2 ) ] d x 1 d y 1 .
E 2 ( x 2 , y 2 ) r = 0 r = r i E 1 ( x 1 , y 1 ) exp [ i k W ( x 1 , y 1 ) ] exp [ i k f ( x 1 x 2 + y 1 y 2 ) ] d x 1 d y 1 + exp ( i ϕ 0 ) r = r i r = r o E 1 ( x 1 , y 1 ) exp [ i k f ( x 1 x 2 + y 1 y 2 ) ] d x 1 d y 1 = A ( x 2 , y 2 ) exp [ i ϕ ( x 2 , y 2 ) ] + R ( x 2 , y 2 ) exp [ i { ϕ r ( x 2 , y 2 ) + ϕ 0 } ] .
I 2 ( x 2 , y 2 ) = A ( x 2 , y 2 ) 2 + R ( x 2 , y 2 ) 2 + 2 A ( x 2 , y 2 ) R ( x 2 , y 2 ) cos [ ϕ ( x 2 , y 2 ) ϕ r ( x 2 , y 2 ) ϕ 0 ] .
ϕ ( x 2 , y 2 ) = ϕ r ( x 2 , y 2 ) + ϕ 0 + cos 1 [ D ( x 2 , y 2 ) ] ,
D ( x 2 , y 2 ) = I 2 ( x 2 , y 2 ) A ( x 2 , y 2 ) 2 R ( x 2 , y 2 ) 2 2 A ( x 2 , y 2 ) R ( x 2 , y 2 ) .
E 1 ( x 1 , y 1 ) P ( x 1 , y 1 ) exp [ i k W ( x 1 , y 1 ) ] exp [ i k f ( x 1 x 2 + y 1 y 2 ) ] d x 1 d y 1 = A ( x 2 , y 2 ) exp [ i { ϕ r ( x 2 , y 2 ) + ϕ 0 + cos 1 D ( x 2 , y 2 ) } ] .
E 1 ( x 1 , y 1 ) P ( x 1 , y 1 ) exp [ i k W ( x 1 , y 1 ) ] exp ( i ϕ 0 ) = F 1 [ A ( x 2 , y 2 ) exp [ i { ϕ r ( x 2 , y 2 ) + cos 1 D ( x 2 , y 2 ) } ] ] = B ( x 1 , y 1 ) exp [ i ϕ i n v ( x 1 , y 1 ) ] .

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