Abstract

A beam of laser light enters the camera. The light diffusely reflected by the film re-emerges, and the speckle pattern formed at the plane of the lens diaphragm is observed. A traversing lens produces slight movements of the light spot at the film plane. If the camera is out of focus these cause bodily movements of the speckle pattern. As the focal position is approached the speckle size and rate of movement increase and finally give way to a random change of structure. The focal position can be estimated to within 0.1 or less of the Rayleigh limit. Using this it is possible to measure all the primary and secondary aberrations (other than distortion) of the camera, including any errors of film position.

© 1974 Optical Society of America

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References

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  1. l. I. Goldfischer, J. Opt. Soc. Am. 55, 247 (1965).
    [CrossRef]
  2. J. M. Burch, in Optical Instruments and Techniques, 1969J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).
  3. G. Groh, in The Engineering Uses of Holography, Ed., E. R. Robertson, J. M. Harvey, eds. (1970).
  4. E. Archbold, A. E. Ennos, P. A. Taylor, in Optical Instruments and Techniques, 1969, J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).
  5. J. A. Leendertz, in Optical Instruments and Techniques, 1969, J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).
  6. H. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).
  8. H. H. Hopkins, 1950, Wave Theory of Aberrations (Clarendon Press, Oxford, 1950).

1966 (1)

1965 (1)

Archbold, E.

E. Archbold, A. E. Ennos, P. A. Taylor, in Optical Instruments and Techniques, 1969, J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Burch, J. M.

J. M. Burch, in Optical Instruments and Techniques, 1969J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).

Ennos, A. E.

E. Archbold, A. E. Ennos, P. A. Taylor, in Optical Instruments and Techniques, 1969, J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).

Goldfischer, l. I.

Groh, G.

G. Groh, in The Engineering Uses of Holography, Ed., E. R. Robertson, J. M. Harvey, eds. (1970).

Hopkins, H. H.

H. H. Hopkins, 1950, Wave Theory of Aberrations (Clarendon Press, Oxford, 1950).

Kogelnik, H.

Leendertz, J. A.

J. A. Leendertz, in Optical Instruments and Techniques, 1969, J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).

Li, T.

Taylor, P. A.

E. Archbold, A. E. Ennos, P. A. Taylor, in Optical Instruments and Techniques, 1969, J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Other (6)

J. M. Burch, in Optical Instruments and Techniques, 1969J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).

G. Groh, in The Engineering Uses of Holography, Ed., E. R. Robertson, J. M. Harvey, eds. (1970).

E. Archbold, A. E. Ennos, P. A. Taylor, in Optical Instruments and Techniques, 1969, J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).

J. A. Leendertz, in Optical Instruments and Techniques, 1969, J. Home Dickson, Ed. (Oriel Press, Newcastle upon Tyne, England, 1970).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

H. H. Hopkins, 1950, Wave Theory of Aberrations (Clarendon Press, Oxford, 1950).

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Figures (11)

Fig. 1
Fig. 1

Formation of speckle pattern by diffuse reflection.

Fig. 2
Fig. 2

Diagram of Gaussian beam waist, showing notation.

Fig. 3
Fig. 3

Astigmatic beam.

Fig. 4
Fig. 4

Diagram showing notation for aberrations.

Fig. 5
Fig. 5

Arrangement of experimental apparatus.

Fig. 6
Fig. 6

(a) Focal position variation for L2 vs x′ for σ = 0 showing spherical aberration. (b) Means for positive and negative x′ from (a) compared with best fitting quartics.

Fig. 7
Fig. 7

Focal position variation vs x′ for equal positive and negative values of σ. The curves for negative σ have been laterally reversed for comparison. (a) σ = ±0.5 (field angle ±9.5°); (b) σ = ±1 (field angle ±19°); (c) means for positive and negative x′ for the horizontal direction from (a) and (b) compared with a best fitting parabola; (d) means for positive and negative x′ for the vertical direction from (a) and (b) compared with a best fitting parabola and with a parabola obtained from the y-axis results.

Fig. 8
Fig. 8

Focal position variation versus σ for x′ = 0, for the sagittal direction, showing field curvature and film position error. Difference between tangential and sagittal foci showing astigmatism.

Fig. 9
Fig. 9

Film position variations for twelve successive frames, with x′ = σ = 0.

Fig. 10
Fig. 10

Differences between positive and negative x′ values obtained from Figs. 7(a) and (b), after subtraction of the cubic term. (a) Horizontal direction; (b) vertical direction.

Fig. 11
Fig. 11

Focal position variation (mean values for positive and negative y′) vs y′ for σ = 1, compared with best fitting quartics.

Equations (19)

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tan 2 α = 2 ( 2 W / x y ) ( 2 W / x 2 ) ( 2 W / y 2 ) .
2 W ξ 2 2 W η 2 = [ ( 2 W x 2 2 W y 2 ) 2 + 4 ( 2 W x y ) 2 ] 1 / 2 .
1 2 ( 2 W ξ 2 + 2 W η 2 ) = 1 2 ( 2 W x 2 + 2 W y 2 )
W = 2 C 20 σ 2 r 2 + 2 C 22 σ 2 x 2 + 1 C 31 σ r 2 x + 0 C 40 r 4
C 20 σ 4 r 2 + 4 C 22 σ 4 r 2 x 2 + 3 C 31 σ 3 r 2 x + 3 C 33 σ 3 x 3 + 2 C 40 σ 2 r 4 + 2 C 42 σ 2 r 2 x 2 + 1 C 51 σ r 4 x + 0 C 60 r 6
2 [ C 20 + 2 C 22 ] σ 2 + 6 1 C 31 x σ + 12 0 C 40 x 2
2 [ C 20 + 4 C 22 ] σ 4 + 6 [ C 31 + 3 C 33 ] x σ 3 + 12 [ C 40 + 2 C 42 ] x 2 σ 2 + 20 1 C 51 x 3 σ + 30 0 C 60 x 4
2 2 C 20 σ 2 + 2 1 C 31 x σ + 4 0 C 40 x 2
2 4 C 20 σ 4 + 2 3 C 31 x σ 3 + 4 [ C 40 + 1 2 2 C 42 ] x 2 σ 2 + 4 1 C 51 x 3 σ + 6 0 C 60 x 4
0 C 40 = ( 1 / 12 ) ρ m 2 A / F 2 2 = 5.24 μ m 0 C 60 = ( 1 / 30 ) ρ m 2 B / F 2 2 = 3.87 μ m .
2 C 22 = 1 2 ρ m 2 / F 2 2 × 11.4 = 4.50 μ m . 4 C 22 = + ρ m 2 / F 2 2 × 9.4 = + 3.82 μ m .
1 C 31 = ( 1 / 12 ) ( ρ m 2 / F 2 2 ) × 120.6 = + 7.92 μ m . 3 C 31 + 3 C 33 = ( 1 / 12 ) ( ρ m 2 / F 2 2 ) × 53 = 3.49 μ m . 1 C 51 = ( 1 / 40 ) ( ρ m 2 / F 2 2 ) × 425 = 8.40 μ m .
2 [ 2 C 20 + 2 C 22 ] σ 2 + 4 0 C 40 y 2
2 [ 4 C 20 + 4 C 22 ] σ 4 + 4 [ 2 C 40 + 1 2 2 C 42 ] y 2 σ 2 + 6 0 C 60 y 4
2 2 C 20 σ 2 + 12 0 C 40 y 2
2 4 C 20 σ 4 + 12 2 C 40 y 2 σ 2 + 30 0 C 60 y 4
2 1 C 31 y σ
2 3 C 31 y σ 3 + 4 1 C 51 y 3 σ
0 C 40 + 2 C 40 = ( 1 / 12 ) ( ρ m 2 / F 2 2 ) × 5.75 = 0.39 μ m . 0 C 60 = ( 1 / 30 ) ( ρ m 2 / F 2 2 ) × 199 = 5.24 μ m .

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