Abstract

We present a general form for aberration coefficients of any order in holographic imaging. The form has the advantage of being easily written and remembered and of classifying aberrations according to the values of two integer parameters.

© 1984 Optical Society of America

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References

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  1. R. W. Meier, “Magnification and third-order aberrations in holography,” J. Opt. Soc. Am. 55, 987–992 (1965).
  2. E. B. Champagne, “Non-paraxial imaging, magnification and aberration properties in holography,” J. Opt. Soc. Am. 57, 51–55 (1967).
    [CrossRef]
  3. J. N. Latta, “Computer-based analysis of hologram imagery and aberrations. I. Hologram types and their nonchromatic aberrations,” Appl. Opt. 10, 599–608 (1971); “II. Aberrations induced by a wavelength shift,” Appl. Opt. 10, 609–618 (1971).
    [CrossRef] [PubMed]
  4. J. N. Latta, “Fifth-order hologram aberrations,” Appl. Opt. 10, 666–667 (1971).
    [CrossRef] [PubMed]
  5. P. C. Mehta, K. Syam, Sunder Rao, R. Hradaynath, “Higher-order aberrations in holographic lenses,” Appl. Opt. 21, 4553–4558 (1982).
    [CrossRef] [PubMed]
  6. J. M. Rebordão, M. Grosmann, “Refraction on spherical surfaces. I. An exact algebraic approach,” J. Opt. Soc. Am. A 1, 51–61 (1984).
    [CrossRef]
  7. J. M. Rebordão, “Conception et évaluation d’élements et de systémes optiques: nouvelle approche algébrique libérée des contraintes de symétrie,” Ph.D. Dissertation (Université de Strasbourg, Strasbourg, France, 1983).
  8. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic Press, New York, 1971).

1984 (1)

1982 (1)

1971 (2)

1967 (1)

1965 (1)

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic Press, New York, 1971).

Champagne, E. B.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic Press, New York, 1971).

Grosmann, M.

Hradaynath, R.

Latta, J. N.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic Press, New York, 1971).

Mehta, P. C.

Meier, R. W.

Rao, Sunder

Rebordão, J. M.

J. M. Rebordão, M. Grosmann, “Refraction on spherical surfaces. I. An exact algebraic approach,” J. Opt. Soc. Am. A 1, 51–61 (1984).
[CrossRef]

J. M. Rebordão, “Conception et évaluation d’élements et de systémes optiques: nouvelle approche algébrique libérée des contraintes de symétrie,” Ph.D. Dissertation (Université de Strasbourg, Strasbourg, France, 1983).

Syam, K.

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Equations (25)

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R C O R = R C + μ ( R O - R R ) ,
μ = n λ C λ O ,
w i = x i x + y i y .
R i = Q i ( 1 + χ ) 1 / 2 ,
χ = r 2 - 2 w i Q i 2 ,             r 2 = x 2 + y 2 .
( 1 + χ ) 1 / 2 = 1 + n = 1 a n χ n ,
a n = 1 2 n n ! i = 1 n ( 3 - 2 i ) = ( - 1 ) n - 1 1 2 2 n - 1 [ 2 ( n - 1 ) ] ! n ! ( n - 1 ) ! .
χ n = 1 Q i 2 n ( r 2 - 2 w i ) n = 1 Q i 2 n k = 0 n ( - 2 ) n - k ( n k ) r 2 k w i n - k .
R i = Q i + n = 1 k = 0 n b n k r 2 k w i n - k Q i 2 n - 1 ,
b n k = ( - 1 ) k + 1 [ 2 ( n - 1 ) ] ! 2 n + k - 1 k ! ( n - k ) ! ( n - 1 ) ! .
S = Q C + μ ( Q O - Q R ) ,
A i j n = x C i y C j Q C n + μ ( x O i y O j Q O n - x R i y R j Q R n ) ,
B k n = w C n Q C k + μ ( w O n Q O k - w R n Q R k ) ,
B k n = j = 0 n ( n j ) A j , n - j k x j y n - j ,
R C O R = S + n = 1 k = 0 n b n k B 2 n - 1 n - k r 2 k ,
R I = Q I + n = 1 k = 0 n b n k w I n - k Q I 2 n - 1 r 2 k .
R C O R - R I = ( S - Q I ) + n = 1 k = 0 n b n k ( B 2 n - 1 n - k - w I n - k Q I 2 n - 1 ) r 2 k .
Δ ϕ = 2 π λ C ( R C O R - R I ) .
- ( A 10 1 - x I Q I ) x - ( A 01 1 - y I Q I ) y + 1 2 ( A 00 1 - 1 Q I ) r 2
x I Q I = A 10 1 = x C Q C + μ ( x O Q O - x R Q R ) , y I Q I = A 01 1 = y C Q C + μ ( y O Q O - y R Q R ) , 1 Q I = A 00 1 = 1 Q C + μ ( 1 Q O - 1 Q R ) .
b n n = ( - 1 ) n + 1 [ 2 ( n - 1 ) ] ! 2 2 n - 1 n ! ( n - 1 ) ! .
b n 0 = - [ 2 ( n - 1 ) ] ! 2 n - 1 n ! ( n - 1 ) ! .
A i j n = x C i y C j Q c n + μ m i + j + n ( x O j y O i Q O n - x R i y R j Q R n ) ,
B k n = w C n Q C k + μ m n + k ( w O n Q O k - w R n Q R k ) ,
A i j n - x I i y I j Q I n .

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