Abstract

Distortion can be corrected in an image by placing a fourth-order aspheric optical element near the image plane. Moving the aspheric surface longitudinally changes the amount of distortion that is added by the aspheric surface without changing the paraxial image. Third-order astigmatism limits the performance of distortion correctors and may be eliminated by adding another fourth-order aspheric surface. Example elements were fabricated by diamond turning and were shown to introduce distortion without significantly degrading image quality. Three arrangements of distortion correctors are discussed: a single-element planoaspheric arrangement, an antisymmetric two-element arrangement, and a bi-aspheric arrangement in which distortion is not adjustable.

© 1992 Optical Society of America

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References

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  1. J. Meiron, “On the design of optical systems containing aspheric surfaces,” J. Opt. Soc. Am. 46, 288–292 (1956).
    [CrossRef]
  2. C. G. Wynne, “Field correctors for large telescopes,” Appl. Opt. 4, 1185–1192 (1965).
    [CrossRef]
  3. R. T. Jones, “Wide angle lenses with aspheric correcting surfaces,” Appl. Opt. 5, 1846–1849 (1966).
    [CrossRef] [PubMed]
  4. W. T. Plummer, “Unusual optics of the Polaroid SX-70 Land camera,” Appl. Opt. 21, 196–202 (1982).
    [CrossRef] [PubMed]
  5. J. Kross, F. W. Oertmann, R. Schuhmann, “On aspherics in optical systems,” in Optical System Design, Analysis, and Production for Advanced Technology Systems, R. E. Fisher, P. J. Rogers, eds. Proc. Soc. Photo-Opt. Instrum. Eng.655, 98–106 (1988).
  6. R. R. Shannon, “Aspheric surfaces,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1980), Vol. 8, pp. 55–85.
  7. K. M. Bystricky, P. R. Yoder, “Catadioptric lens with aberrations balanced by aspherizing one surface,” Appl. Opt. 24, 1206–1208 (1985).
    [CrossRef] [PubMed]
  8. M. Katz, “Aspheric surfaces used to minimize oblique astigmatic error, power error, and distortion of some high positive and negative power opthalmic lenses,” Appl. Opt. 21, 2982–2991 (1982).
    [CrossRef] [PubMed]
  9. A. B. Meinel, M. P. Meinel, J. E. Stacy, T. T. Saito, S. R. Patterson, “Wavefront correctors by diamond turning,” Appl. Opt. 25, 824–825 (1986).
    [CrossRef] [PubMed]
  10. W. T. Welford, Aberrations of Optical Systems (Hilger, Philadelphia, Pa., 1986).
  11. CODE V (Optical Research Associates, Pasadena, Calif., 1990).

1986 (1)

1985 (1)

1982 (2)

1966 (1)

1965 (1)

1956 (1)

Bystricky, K. M.

Jones, R. T.

Katz, M.

Kross, J.

J. Kross, F. W. Oertmann, R. Schuhmann, “On aspherics in optical systems,” in Optical System Design, Analysis, and Production for Advanced Technology Systems, R. E. Fisher, P. J. Rogers, eds. Proc. Soc. Photo-Opt. Instrum. Eng.655, 98–106 (1988).

Meinel, A. B.

Meinel, M. P.

Meiron, J.

Oertmann, F. W.

J. Kross, F. W. Oertmann, R. Schuhmann, “On aspherics in optical systems,” in Optical System Design, Analysis, and Production for Advanced Technology Systems, R. E. Fisher, P. J. Rogers, eds. Proc. Soc. Photo-Opt. Instrum. Eng.655, 98–106 (1988).

Patterson, S. R.

Plummer, W. T.

Saito, T. T.

Schuhmann, R.

J. Kross, F. W. Oertmann, R. Schuhmann, “On aspherics in optical systems,” in Optical System Design, Analysis, and Production for Advanced Technology Systems, R. E. Fisher, P. J. Rogers, eds. Proc. Soc. Photo-Opt. Instrum. Eng.655, 98–106 (1988).

Shannon, R. R.

R. R. Shannon, “Aspheric surfaces,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1980), Vol. 8, pp. 55–85.

Stacy, J. E.

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilger, Philadelphia, Pa., 1986).

Wynne, C. G.

Yoder, P. R.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

Other (4)

W. T. Welford, Aberrations of Optical Systems (Hilger, Philadelphia, Pa., 1986).

CODE V (Optical Research Associates, Pasadena, Calif., 1990).

J. Kross, F. W. Oertmann, R. Schuhmann, “On aspherics in optical systems,” in Optical System Design, Analysis, and Production for Advanced Technology Systems, R. E. Fisher, P. J. Rogers, eds. Proc. Soc. Photo-Opt. Instrum. Eng.655, 98–106 (1988).

R. R. Shannon, “Aspheric surfaces,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1980), Vol. 8, pp. 55–85.

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Figures (12)

Fig. 1
Fig. 1

Planoaspheric distortion corrector near a telecentric image plane. Distortion appears as a deviation in chief-ray height from its paraxial value. This deviation varies with the cube of image height for third-order distortion.

Fig. 2
Fig. 2

Distortion, field curvature, astigmatism, coma, and spherical aberration as a function of the distance from the planoaspheric distortion corrector to a telecentric image plane. For this range of image distance, distortion dominates over all other aberrations, except FFC when the distortion corrector is near the image plane.

Fig. 3
Fig. 3

Merit function for a family of planoaspheric distortion correctors that provide a constant value of distortion. The merit function contains terms of astigmatism, loss of telecentricity, and FFC. For the distortion corrector near the image, astigmatism is small, but field curvature and loss of telecentricity are correspondingly large. Conversely, for the distortion corrector far from the image, astigmatism is large, while field curvature and loss of telecentricity are small. The minimum represents a balance among these three parameters.

Fig. 4
Fig. 4

Three configurations of distortion correctors that provide the same amount of distortion: a, astigmatism is small, but field curvature and loss of telecentricity are large: c, field curvature and loss of telecentricity are small, but astigmatism and spherical aberration are large; b, a reasonable balance between these extremes.

Fig. 5
Fig. 5

Field aberration curves of a planoaspheric distortion corrector in image space with u = −0.15. Distortion is significantly greater than the transverse ray aberration because of astigmatism. Both distortion and tangential astigmatism are reduced at full field by fifth-order terms, which cause the aberration curves to appear linear near full field.

Fig. 6
Fig. 6

Spot diagram for the planoaspheric distortion corrector. Fourth-order field curvature appears as a defocus that varies as the fourth power in image height. Astigmatism appears as the oblique shape of the spots.

Fig. 7
Fig. 7

Antisymmetric arrangement for correcting distortion in intermediate images. This arrangement adds no fourth-order field curvature or third-order astigmatism, and it introduces twice the distortion of a single-element arrangement while maintaining telecentricity. Following the final surface, the real rays are drawn to the right, and the virtual rays are drawn to the left to indicate the virtual images formed.

Fig. 8
Fig. 8

Field aberration curves of the antisymmetric distortion corrector. Astigmatism and field curvature have been drastically reduced, and distortion has doubled. Astigmatism is now dominated by higher-order terms.

Fig. 9
Fig. 9

Spot diagrams in the paraxial image plane for the antisymmetric distortion corrector. The spot size is much smaller than that of the single-element distortion corrector. The defocus patterns that are indicative of field curvature have been supplanted by comet patterns that are indicative of coma. The field of view is twice as large as in Fig. 5.

Fig. 10
Fig. 10

Biaspheric distortion corrector. This type of distortion corrector can be corrected for astigmatism, but then the distortion cannot be adjusted.

Fig. 11
Fig. 11

Field aberrations of an example biaspheric distortion corrector. Third-order astigmatism is well corrected, although higher-order terms remain. Higher-order distortion reduces total distortion at full field.

Fig. 12
Fig. 12

Spot diagrams in the paraxial image plane for a biaspheric distortion corrector. The field of view has increased by a factor of 2 from Fig. 6. Defocus from the paraxial image plane would further improve image quality.

Equations (21)

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z = a h 4 ,
u ¯ = 4 a ( n - 1 ) h 3
Δ η = 4 a ( n - 1 ) η 3 d ,
SPH = - 4 a ( n - 1 ) u 3 d 4 ,
CMA = 12 a ( n - 1 ) u 2 ( η - d u ¯ ) d 3 ,
AST = - 12 a ( n - 1 ) u ( η - d u ¯ ) 2 d 2 ,
DST = 4 a ( n - 1 ) ( η - d u ¯ ) 3 d .
FFC = a ( n - 1 ) u ( η - d u ¯ ) 4 .
- ( η - d u ¯ ) 3 u < d < ( η - d u ¯ ) 3 u .
u ¯ = 4 a ( n - 1 ) η 3 = DST / d .
M ( d ) = AST + FFC + u ¯ = 3 DST ( d η ) + DST 4 η d + DST d ,
AST = AST 1 + AST 2 ,
DST = DST 1 + DST 2 ,
AST = - 12 ( n - 1 ) u η 2 ( - a 1 d 1 2 + a 2 d 2 2 )
DST = 4 ( n - 1 ) η 3 a 1 d 1 ( d 1 / d 2 - 1 ) .
SPH = - 4 n ( n - 1 ) u 3 [ a 1 ( d 2 + t n ) 4 - a 2 d 2 4 ] ,
CMA = 12 ( n - 1 ) u 2 η [ a 2 d 2 3 - a 1 ( d 2 + t n ) 3 ] ,
AST = - 12 ( n - 1 ) u η 2 [ d 2 2 ( a 1 - a 2 ) + 2 d 2 a 1 t n + a 1 ( t n ) 2 ] ,
DST = 4 ( n - 1 ) η 3 [ d 2 ( a 1 - a 2 ) + a 1 ( t n ) ] ,
FFC = ( n - 1 ) η 4 ( a 1 - a 2 ) ,
d 2 = ( t n ) a 1 + a 1 a 2 a 1 - a 2 .

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