Abstract

Formulas are developed for the precise calculation of optimum stray-light baffles for Cassegrain optical systems, including systems having extreme optical curvatures such as those in infrared missile guidance systems. Minimum diffraction and maximum optical efficiency are the primary considerations.

© 1992 Optical Society of America

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References

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  1. T. R. Stoever, Genesee Optics Software, Inc., 3136 Winton Road S., Rochester, N.Y. 14623 (personal communication, 1991).
  2. A. T. Young, “Design of Cassegrain light shields,” Appl. Opt. 6, 1063–1067 (1967).
    [CrossRef] [PubMed]
  3. H. L. Pearson, “Formulas from algebra, trigonometry and analytic geometry,” in Handbook of Applied Mathematics, 2nd ed., C. E. Pearson, ed. (Van Nostrand Reinhold, New York, 1983), p. 14.

1967 (1)

Pearson, H. L.

H. L. Pearson, “Formulas from algebra, trigonometry and analytic geometry,” in Handbook of Applied Mathematics, 2nd ed., C. E. Pearson, ed. (Van Nostrand Reinhold, New York, 1983), p. 14.

Stoever, T. R.

T. R. Stoever, Genesee Optics Software, Inc., 3136 Winton Road S., Rochester, N.Y. 14623 (personal communication, 1991).

Young, A. T.

Appl. Opt. (1)

Other (2)

T. R. Stoever, Genesee Optics Software, Inc., 3136 Winton Road S., Rochester, N.Y. 14623 (personal communication, 1991).

H. L. Pearson, “Formulas from algebra, trigonometry and analytic geometry,” in Handbook of Applied Mathematics, 2nd ed., C. E. Pearson, ed. (Van Nostrand Reinhold, New York, 1983), p. 14.

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Figures (2)

Fig. 1
Fig. 1

Relative obstruction of matched primary and secondary baffles in an f/10 Cassegrain having an f/2 primary mirror and a typical field of view shielded from stray light.

Fig. 2
Fig. 2

Optical layout of a baffled Cassegrain having the primary and secondary baffles terminated at (x4, y4) and x2, y2) [labeled (x4, y4) and (x2, y2)], respectively.

Equations (25)

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x 1 = R 1 - ( R 1 2 - y 1 2 ) 1 / 2 ,
x 8 = R 1 2 ,             y 8 = I 2 M ,
Y = A 1 X + B 1 ,
A 1 = 2 y 1 - I M 2 x 1 - R 1 ,             B 1 = I x 1 M - y 1 R 1 2 x 1 - R 1 .
Y = A 2 X + B 2 ,
A 2 = y 5 - y 3 x 5 - x 3 ,             B 2 = y 3 x 5 - y 5 x 3 x 5 - x 3 .
x 3 = - E - ( E 2 - 4 D F ) 1 / 2 2 D ,
D = A 1 2 + 1 , E = 2 ( A 1 B 1 - h ) , F = B 1 2 - R 2 2 + h 2 .
Y = A 4 X + B 4 ,
A 4 = y 7 - y 4 x 7 - x 4 ,             B 4 = y 4 x 7 - y 7 x 4 x 7 - x 4 .
y 2 = A 1 B 4 - A 4 B 1 A 1 - A 4 .
y 2 = A 1 ( y 4 x 7 - y 7 x 4 x 7 - x 4 ) - B 1 ( y 7 - y 4 x 7 - x 4 ) A 1 - ( y 7 - y 4 x 7 - x 4 ) .
y 2 = A 1 [ ( A 2 x 4 + B 2 ) x 7 - y 7 x 4 ] - ( y 7 - A 2 x 4 - B 2 ) B 1 A 1 ( x 7 - x 4 ) - ( y 7 - A 2 x 4 - B 2 ) .
Y = A 3 X + B 3 ,
A 3 = - 2 y 4 R 1 - 2 x 4 ,             B 3 = - A 3 R 1 2 .
y 2 = y 6 = ( - 2 y 4 R 1 - 2 x 4 ) ( x 6 - R 1 2 ) .
x 6 = R 1 - ( R 1 2 - y 2 2 ) 1 / 2 .
y 2 + y 4 R 1 R 1 - 2 x 4 = 2 y 4 ( R 1 2 - y 2 2 ) 1 / 2 R 1 - 2 x 4 .
[ ( R 1 - 2 x 4 ) 2 + 4 y 4 2 ] × y 2 2 + 2 y 4 R 1 ( R 1 - 2 x 4 ) y 2 - 3 y 4 2 R 1 2 = 0.
[ ( R 1 - 2 x 4 ) 2 + 4 ( A 2 x 4 + B 2 ) 2 ] × y 2 2 + 2 ( A 2 x 4 + B 2 ) R 1 ( R 1 - 2 x 4 ) × y 2 - 3 ( A 2 x 4 + B 2 ) 2 R 1 2 = 0
F x 4 4 + G x 4 3 + H x 4 2 + J x 4 + L = 0 ,
F = K 1 K 10 2 + K 4 K 10 K 12 + K 12 2 K 7 , G = K 2 K 10 2 + 2 K 1 K 10 K 11 + K 5 K 10 K 12 + K 4 ( K 11 K 12 + K 10 K 13 ) + K 12 2 K 8 + 2 K 7 K 12 K 13 , H = K 3 K 10 2 + 2 K 2 K 10 K 11 + K 1 K 11 2 + K 6 K 10 K 12 + K 5 ( K 11 K 12 + K 10 K 13 ) + K 4 K 11 K 13 + K 12 2 K 9 + 2 K 8 K 12 K 13 + K 13 2 K 7 , J = 2 K 3 K 10 K 11 + K 2 K 11 2 + K 6 ( K 11 K 12 + K 10 K 13 ) + K 5 K 11 K 13 + 2 K 9 K 12 K 13 + K 8 K 13 2 , L = K 3 K 11 2 + K 6 K 11 K 13 + K 9 K 13 2 .
K 1 = 4 ( A 2 2 + 1 ) , K 2 = 4 ( 2 A 2 B 2 - R 1 ) , K 3 = R 1 2 + 4 B 2 2 , K 4 = - 4 A 2 R 1 , K 5 = 2 ( A 2 R 1 2 - 2 B 2 R 1 ) , K 6 = 2 B 2 R 1 2 , K 7 = - 3 A 2 2 R 1 2 , K 8 = - 6 A 2 B 2 R 1 2 , K 9 = - 3 B 2 2 R 1 2 , K 10 = A 1 A 2 x 7 - A 1 y 7 + B 1 A 2 , K 11 = A 1 B 2 x 7 - B 1 y 7 + B 1 B 2 , K 12 = A 2 - A 1 , K 13 = A 1 x 7 - y 7 + B 2 .
x 4 j + 1 x 4 j - f ( x 4 j ) f ( x 4 j )
x 2 = y 2 - B 1 A 1 .

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