Abstract

The correction of lens aberrations using a hologram made with a collimated reference is discussed. Two geometries in which the theoretical third-order hologram aberrations may be avoided are demonstrated. The results of experiments which demonstrate the aberration correction using the Ronchi and DeVany tests are presented.

© 1971 Optical Society of America

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References

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  1. The hologram may be thought of as a synthetic aperture for the optical system which has been designed to cancel the aberrations. The technique is also similar to that used in the Vander Lugt matched filter synthesis.
  2. J. Upatnieks, A. Vander Lugt, E. Leith, Appl. Opt. 5, 589 (1966).
    [Crossref] [PubMed]
  3. See p. 151 of Ref. 12 for an explanation of this curve.
  4. J. H. Altman, Appl. Opt. 5, 1689 (1966).
    [Crossref] [PubMed]
  5. L. F. Collins, Appl. Opt. 7, 1236 (1968).
    [Crossref] [PubMed]
  6. J. E. Ward, D. C. Auth, F. P. Carlson, “Holographic Aberration Correction,” U. of Washington, Tech. Rep. TR 138 (April1970).
  7. R. W. Meier, J. Opt. Soc. Amer. 55, 987 (1965).
  8. See Ref. 7, Eqs. (20), (22), (25), (29), and (31).
  9. V. Ronchi, Appl. Opt. 3, 437 (1964).
    [Crossref]
  10. A. S. DeVany, Appl. Opt. 6, 1073 (1967).
    [Crossref] [PubMed]
  11. V. Russo, S. Sottini, Appl. Opt. 7, 202 (1968).
    [Crossref] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

1968 (2)

1967 (1)

1966 (2)

1965 (1)

R. W. Meier, J. Opt. Soc. Amer. 55, 987 (1965).

1964 (1)

Altman, J. H.

Auth, D. C.

J. E. Ward, D. C. Auth, F. P. Carlson, “Holographic Aberration Correction,” U. of Washington, Tech. Rep. TR 138 (April1970).

Carlson, F. P.

J. E. Ward, D. C. Auth, F. P. Carlson, “Holographic Aberration Correction,” U. of Washington, Tech. Rep. TR 138 (April1970).

Collins, L. F.

DeVany, A. S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Leith, E.

Meier, R. W.

R. W. Meier, J. Opt. Soc. Amer. 55, 987 (1965).

Ronchi, V.

Russo, V.

Sottini, S.

Upatnieks, J.

Vander Lugt, A.

Ward, J. E.

J. E. Ward, D. C. Auth, F. P. Carlson, “Holographic Aberration Correction,” U. of Washington, Tech. Rep. TR 138 (April1970).

Appl. Opt. (6)

J. Opt. Soc. Amer. (1)

R. W. Meier, J. Opt. Soc. Amer. 55, 987 (1965).

Other (5)

See Ref. 7, Eqs. (20), (22), (25), (29), and (31).

The hologram may be thought of as a synthetic aperture for the optical system which has been designed to cancel the aberrations. The technique is also similar to that used in the Vander Lugt matched filter synthesis.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

J. E. Ward, D. C. Auth, F. P. Carlson, “Holographic Aberration Correction,” U. of Washington, Tech. Rep. TR 138 (April1970).

See p. 151 of Ref. 12 for an explanation of this curve.

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Figures (5)

Fig. 1
Fig. 1

(a) Geometry for making symmetric hologram. (b) Conjugate wave produced by back illumination. (c) Conjugate wave produced by front illumination.

Fig. 2
Fig. 2

(a) Collimated reconstructing beam produces a beam containing conjugate aberrations which cancel as beam passes through the aberrated lens. Theoretical third-order hologram aberrations are zero. (b) Aberrated wavefront from the lens used to reconstruct the hologram. The aberrations are canceled. Again the theoretical hologram aberrations vanish. The unaberrated, collimated wave produced may be used to provide the collimated reconstructing beam necessary in (a).

Fig. 3
Fig. 3

(a) The Hurler-Driffield curve for Kodak 649-F developed in D-19 for 2 min at 20°C. A normalized exposure value of 1.0 corresponds to the maximum exposure of the experimental hologram. (b) A linear relationship exists between photographic density and normalized exposure, for the exposure range of (a).

Fig. 4
Fig. 4

DeVany double-wire test. The uncorrected results in the top row of photographs show spherical aberration. In the corresponding photos below, the corrected beam projected the image of the wires undistorted. From left to right, the double-wire apparatus intersected the left, center, and right portions of the beam.

Fig. 5
Fig. 5

The Ronchi test. From left to right, (a, b, c, see text), the grating was placed behind the focus, slightly in front of the focus, and in front of the focus. The uncorrected version above shows the expected cubic curves due to spherical aberration, while the corresponding results below show the shadow fringes projected nearly undistorted.

Equations (9)

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O = O exp [ j Φ ( x , y ) ] exp [ j ( k y y - k z z ) ] ,
A = A exp [ - j ( k y y + k z z ) ] .
θ = tan - 1 ( k y / k z ) ,
I ( x , y ) = A 2 + O 2 + 2 A O cos [ 2 k y y - Φ ( x , y ) ] .
t 1 ( x , y ) = J 1 ( α ) exp { j [ 2 k y y - Φ ( x , y ) ] } ,
w ( x 1 , y 1 , z 1 ) = 1 / z 1 u ( x , y ) t 1 ( x , y ) × exp { - j π [ ( x 1 - x ) 2 + ( y 1 - y ) 2 / λ z 1 ] } d x d y .
u ( x , y ) t 1 ( x , y ) = u ( x , y ) f ( α , y )
lim y c z c + / z c = lim y r z r - / z r
y 0 / z 0 = y c / z c = - lim y r z r - / z r .

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