Abstract

Two general theorems in the theory of mirrors are presented. The first one asserts that a mirror that reflects a parallel beam into a beam with zero mean curvature must be harmonic. The second one provides a universal characterization of the spot diagram of rays from a reflected parallel beam as they intersect a plane orthogonal to their direction of propagation.

© 2002 Optical Society of America

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References

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  1. J. A. Kneisly, “Local curvature of a wave front in an optical system,” J. Opt. Soc. Am. 54, 229–235 (1964).
    [CrossRef]
  2. O. N. Stavroudis, The Optics of Rays, Wavefronts and Caustics (Academic, New York, 1972).
  3. J. B. Keller, H. B. Keller, “Determination of reflected and transmitted fields by geometrical optics,” J. Opt. Soc. Am. 40, 48–52 (1950).
    [CrossRef]
  4. J. Rubinstein, G. Wolansky, “A class of elliptic differential equations related to optical design,” available as preprint.
  5. J. Rubinstein, G. Wolansky, “Reconstruction of optical surfaces from ray deflections,” Opt. Rev. (to be published).

1964 (1)

1950 (1)

Keller, H. B.

Keller, J. B.

Kneisly, J. A.

Rubinstein, J.

J. Rubinstein, G. Wolansky, “Reconstruction of optical surfaces from ray deflections,” Opt. Rev. (to be published).

J. Rubinstein, G. Wolansky, “A class of elliptic differential equations related to optical design,” available as preprint.

Stavroudis, O. N.

O. N. Stavroudis, The Optics of Rays, Wavefronts and Caustics (Academic, New York, 1972).

Wolansky, G.

J. Rubinstein, G. Wolansky, “Reconstruction of optical surfaces from ray deflections,” Opt. Rev. (to be published).

J. Rubinstein, G. Wolansky, “A class of elliptic differential equations related to optical design,” available as preprint.

J. Opt. Soc. Am. (2)

Other (3)

J. Rubinstein, G. Wolansky, “A class of elliptic differential equations related to optical design,” available as preprint.

J. Rubinstein, G. Wolansky, “Reconstruction of optical surfaces from ray deflections,” Opt. Rev. (to be published).

O. N. Stavroudis, The Optics of Rays, Wavefronts and Caustics (Academic, New York, 1972).

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Figures (1)

Fig. 1
Fig. 1

Deflection of a reflected beam.

Equations (13)

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Hr=2Hs,
u(1+|u|2)1/2=Hr.
Hr=cos iκ1+1cos2 i κ2.
κ1=uyy(1+ux2)1/2.
κ2=uxx(1+ux2)3/2.
Δu=(1+|u|2)Hr.
δ(x, y)=ξ-x,(x, y)=η-y.
a=δ/D,b=/D,c=-u/D,
D=(δ2+2+u2)1/2.
w1-w2=sN,
ux=δD+u,uy=D+u.
D(D+u)(δy-x)=δ2δy-2x+δ(y-δx).
ψx2ψxy+ψxψy(ψyy-ψxx)-ψy2ψxy=0.

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