Abstract

A closed-form solution for the shape of an aspheric mirror with a constant angular magnification is presented. The focal surface of such a mirror is derived. The advantages of the proposed design over the spherical mirror for application in the all-sky camera are discussed.

© 1992 Optical Society of America

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References

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  1. H. Betlem, “Braintank discussion: all-sky working group,” in Proceedings of the International Meteor Conference (W. A. Lanzing, Lupine-straat6, 7552 Hengelo, The Netherlands, 1988), p. 27.
  2. R. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, Cambridge, UK, 1980), p. 36.
  3. Ž. Andreić, “Simple 180° field of view F-theta all-sky camera,” in Innovative Optics and Phase Conjugate Optics, R. Ahlers, T. T. Tschudi, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1500, 293–304 (1991).
  4. C. Schur, “Experiments with all-sky photography,” Sky Telesc. 63, 621–624 (1982).

1982 (1)

C. Schur, “Experiments with all-sky photography,” Sky Telesc. 63, 621–624 (1982).

Andreic, Ž.

Ž. Andreić, “Simple 180° field of view F-theta all-sky camera,” in Innovative Optics and Phase Conjugate Optics, R. Ahlers, T. T. Tschudi, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1500, 293–304 (1991).

Betlem, H.

H. Betlem, “Braintank discussion: all-sky working group,” in Proceedings of the International Meteor Conference (W. A. Lanzing, Lupine-straat6, 7552 Hengelo, The Netherlands, 1988), p. 27.

Greenler, R.

R. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, Cambridge, UK, 1980), p. 36.

Schur, C.

C. Schur, “Experiments with all-sky photography,” Sky Telesc. 63, 621–624 (1982).

Sky Telesc. (1)

C. Schur, “Experiments with all-sky photography,” Sky Telesc. 63, 621–624 (1982).

Other (3)

H. Betlem, “Braintank discussion: all-sky working group,” in Proceedings of the International Meteor Conference (W. A. Lanzing, Lupine-straat6, 7552 Hengelo, The Netherlands, 1988), p. 27.

R. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, Cambridge, UK, 1980), p. 36.

Ž. Andreić, “Simple 180° field of view F-theta all-sky camera,” in Innovative Optics and Phase Conjugate Optics, R. Ahlers, T. T. Tschudi, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1500, 293–304 (1991).

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Figures (3)

Fig. 1
Fig. 1

Geometry of a simple all-sky camera. The angles α and β are defined to be positive.

Fig. 2
Fig. 2

Shape of the aspheric mirror with a FOV of 180° and M = 8. The profile of the focal surface is shown by the dashed curve, and the depth of the virtual light field along the reflected principal rays (incoming from quadrant I only) is bounded by thin solid lines. (Note that the left side of the drawing is truncated.)

Fig. 3
Fig. 3

Relative error [Eq. (7)] of the retrieved object angle β* for the spherical mirror with mirror paraxial angular magnification M as the parameter. The relative error of the α ≈ tan(α) approximation is also shown by a dashed curve.

Equations (8)

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d y / d x = - tan ( N arctan [ x / ( d - y ) ] ,
X = x / d , Y = y / d , Z = 1 - Y , U = X / Z .
d Z Z = tan [ N arctan ( U ) ] 1 - U tan [ N arctan ( U ) ] d U ,
x ( α ) = d sin ( α ) { cos [ ( N + 1 ) α ] } 1 / ( N + 1 ) , y ( α ) = d - d cos ( α ) { cos [ ( N + 1 ) α ] } 1 / ( N + 1 ) ,
x f ( α ) = M M - 1 x ( α ) , y f ( α ) = M M - 1 y ( α ) - d M - 1 .
f = d M - 1 .
β * = 2 arcsin [ ( M + 1 ) sin ( α ) / 2 ] - α .
RAD ( α ) = ( β * - β ) / β .

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