Abstract

Spherical fits to an aspheric surface provide a measure of the raw asphericity, give an easily generated starting point for its fabrication, and show the amount of aberration to be expected in a center of curvature test. Conicoidal fits have similar uses. We have previously shown that a conicoidal fit can be substantially closer than a spherical fit. In this paper we include fits to sections of plane symmetric surfaces that have no symmetry and give examples of such fits to surfaces of a completely asymmetric lens.

© 1989 Optical Society of America

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References

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  1. B. Tatian, “Testing an Unusual Optical Surface,” Proc. Soc. Photo-Opt. Instrum. Eng. 554, 139–147 (1985).
  2. O. Cardona-Nunez, A. Cornejo-Rodriguez, J. R. Diaz-Uribe, A. Cordero-Davila, J. Pedraza-Contreras, “Comparison Between Toroidal and Conic Surfaces that Best Fit an Off-Axis Conic Section,” Appl. Opt. 26, 4832–4834 (1987).
    [CrossRef] [PubMed]
  3. This was the result of a suggestion from K. P. Thompson of Optical Research Associates.
  4. B. Tatian, “First Look at the Computer Design of Optical Systems Without Any Symmetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 766, 38–47 (1985).
  5. G. Spencer, M. Murty, “General Ray-Tracing Procedure,” J. Opt. Soc. Am. 52, 672–678 (1962).
    [CrossRef]

1987 (1)

1985 (2)

B. Tatian, “First Look at the Computer Design of Optical Systems Without Any Symmetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 766, 38–47 (1985).

B. Tatian, “Testing an Unusual Optical Surface,” Proc. Soc. Photo-Opt. Instrum. Eng. 554, 139–147 (1985).

1962 (1)

Cardona-Nunez, O.

Cordero-Davila, A.

Cornejo-Rodriguez, A.

Diaz-Uribe, J. R.

Murty, M.

Pedraza-Contreras, J.

Spencer, G.

Tatian, B.

B. Tatian, “Testing an Unusual Optical Surface,” Proc. Soc. Photo-Opt. Instrum. Eng. 554, 139–147 (1985).

B. Tatian, “First Look at the Computer Design of Optical Systems Without Any Symmetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 766, 38–47 (1985).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

B. Tatian, “Testing an Unusual Optical Surface,” Proc. Soc. Photo-Opt. Instrum. Eng. 554, 139–147 (1985).

B. Tatian, “First Look at the Computer Design of Optical Systems Without Any Symmetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 766, 38–47 (1985).

Other (1)

This was the result of a suggestion from K. P. Thompson of Optical Research Associates.

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Figures (16)

Fig. 1
Fig. 1

Three types of fit related to null tests.

Fig. 2
Fig. 2

Geometry of an asymmetric aspheric surface.

Fig. 3
Fig. 3

Two surface sections on a conicoid used in fitting an aspheric surface.

Fig. 4
Fig. 4

Three-dimensional and side views of an asymmetric unobstructed mirror system.

Fig. 5
Fig. 5

Departure of the primary mirror from a sphere.

Fig. 6
Fig. 6

Departure of the secondary mirror from a sphere.

Fig. 7
Fig. 7

Departure of the tertiary mirror from a sphere.

Fig. 8
Fig. 8

Departure of the primary mirror from a sphere plus astigmatism.

Fig. 9
Fig. 9

Departure of the secondary mirror from a sphere plus astigmatism.

Fig. 10
Fig. 10

Departure of the tertiary mirror from a sphere plus astigmatism.

Fig. 11
Fig. 11

Departure of the secondary mirror from an ellipsoid.

Fig. 12
Fig. 12

Departure of the tertiary mirror from an oblate spheroid.

Fig. 13
Fig. 13

Departure of the tertiary mirror from an ellipsoid.

Fig. 14
Fig. 14

Departure of the secondary mirror from an ellipsoid plus astigmatism.

Fig. 15
Fig. 15

Departure of the tertiary mirror from an oblate spheroid plus astigmatism.

Fig. 16
Fig. 16

Departure of the tertiary mirror from an ellipsoid plus astigmatism.

Tables (4)

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Table I Magnitudes of Orthogonalized Derivative Vectors

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Table II Lens Specifications

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Table III Unusual Surface Coefficients

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Table IV Gut Ray Trace

Equations (10)

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c ( ξ 2 + η 2 + ζ 2 ) 2 ζ + c κ ζ 2 = 0 , P = R ( ϕ Q ) , ϕ = ( ξ , η , ζ ) T , P = ( x , y , z ) T , Q = ( x d , y d , z d ) T ,
a ( y 2 x 2 ) + bxy .
tan α = z x tan β = z y / ( 1 + z x 2 ) 1 / 2 ,
z x x = z x x / ( A B ) , z x y = [ z x z y z x x / A + z x y ] / B 2 , z y y = [ z x 2 z y 2 z x x / A 2 z x z y z x y + A z y y ] / B 3 ,
A = 1 + z x 2 , B = ( 1 + z x 2 + z y 2 ) 1 / 2 .
z x y λ 2 + ( z y y z x x ) λ + z x y = 0 , S = z x x + z x y λ 1 , T = z x x + z x y λ 2 ,
S = c / D , T = c / D 3 ,
κ y 2 = ( T S ) / S 3 ,
c = ( S 3 / T ) 1 / 2 .
R = R s 1 R c , Q = Q c R 1 Q s .

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