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References

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  1. D. Malacara, Ed., Optical Shop Testing (Wiley, New York, 1978), Appendix 1.
  2. M. Lipschuts, Differential Geometry (McGraw-Hill, New York, 1980), Chap. 4.
  3. G. Smith, D. A. Atchison, “Construction, Specification, and Mathematical Description of Aspherical Surfaces,” Am. J. Opt. Phys. Opt. 60, 216 (1982).
    [CrossRef]

1982 (1)

G. Smith, D. A. Atchison, “Construction, Specification, and Mathematical Description of Aspherical Surfaces,” Am. J. Opt. Phys. Opt. 60, 216 (1982).
[CrossRef]

Atchison, D. A.

G. Smith, D. A. Atchison, “Construction, Specification, and Mathematical Description of Aspherical Surfaces,” Am. J. Opt. Phys. Opt. 60, 216 (1982).
[CrossRef]

Lipschuts, M.

M. Lipschuts, Differential Geometry (McGraw-Hill, New York, 1980), Chap. 4.

Smith, G.

G. Smith, D. A. Atchison, “Construction, Specification, and Mathematical Description of Aspherical Surfaces,” Am. J. Opt. Phys. Opt. 60, 216 (1982).
[CrossRef]

Am. J. Opt. Phys. Opt. (1)

G. Smith, D. A. Atchison, “Construction, Specification, and Mathematical Description of Aspherical Surfaces,” Am. J. Opt. Phys. Opt. 60, 216 (1982).
[CrossRef]

Other (2)

D. Malacara, Ed., Optical Shop Testing (Wiley, New York, 1978), Appendix 1.

M. Lipschuts, Differential Geometry (McGraw-Hill, New York, 1980), Chap. 4.

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Figures (4)

Fig. 1
Fig. 1

Off-axis paraboloid.

Fig. 2
Fig. 2

Symmetrical optical system formed by two identical spherocylindrical surfaces.

Fig. 3
Fig. 3

Conic surface whose curvatures are to be evaluated.

Fig. 4
Fig. 4

Calculation of the sagittal curvature of a conic surface.

Equations (20)

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Z = c S 2 1 + 1 - ( K + 1 ) c 2 S 2 ,
Z = c X 2 1 + 1 - ( K + 1 ) c 2 X 2 .
R t = { 1 + ( d Z d X | ( S 0 , Z 0 ) ) 2 } d 2 Z d X 2 | ( S 0 , Z 0 ) .
R t = ( 1 - c 2 K X 2 ) 3 / 2 c .
Z s = Z plane ,
r = X i + Y j ¯ + Z k ,
n = i + c S 0 [ 1 - ( K + 1 ) c 2 S 2 ] 1 / 2 k ¯ ,
n · [ ( X - X 0 ) i + Y j ¯ + ( Z - Z 0 ) k ¯ ] = 0.
Z plane = - a X + b
a = [ 1 - ( K + 1 ) c 2 X 0 2 ] 1 / 2 c X 0 ,
b = Z 0 + a X 0 .
Y = t
X = a ( d b - c ) c 2 + d a 2 + [ E - c 2 t 2 ( c 2 + d a 2 ) ] 1 / 2 c 2 + d a 2 ,
Z = c ( t 2 + X 2 ) 1 + 1 - d ( t 2 + X 2 ) ,
E = ( K c 2 X 2 - 1 ) 2 X 2 ,
d = ( K + 1 ) c 2 .
R s = [ ( d 2 X d t 2 | t = 0 ) 2 + ( d 2 Y d t 2 | t = 0 ) 2 + ( d 2 Z d t 2 | t = 0 ) 2 ] - 1 / 2 .
R s = [ c 4 E + c 2 ( E 1 / 2 - c X 0 ) 2 E ( 1 - d X 0 ) ] - 1 / 2 ,
R s = ( 1 - K c 2 X 2 ) 1 / 2 c .
c s 3 = c 2 c t .

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