Abstract

A retroreflector (a device that reflects an incident beam of light through exactly 180°) constructed from a primary concave mirror and a small secondary mirror near its paraxial focus, the so-called cat’s-eye retroreflector, has been investigated. Ray-tracing of systems with both spherical and parabolic primaries suggests that the latter are considerably superior to the former and comparable to a cube-corner retroreflector. The investigation has also enabled mechanical tolerances for the construction of a cat’s-eye retroreflector to be deduced. The predicted tolerances may be much easier to attain than those for a cube-corner retroreflector.

© 1966 Optical Society of America

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References

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  1. P. Connes (private communication).
  2. P. Fellgett, J. Phys. Rad. 19, 237 (1958).
    [CrossRef]

1958

P. Fellgett, J. Phys. Rad. 19, 237 (1958).
[CrossRef]

Connes, P.

P. Connes (private communication).

Fellgett, P.

P. Fellgett, J. Phys. Rad. 19, 237 (1958).
[CrossRef]

J. Phys. Rad.

P. Fellgett, J. Phys. Rad. 19, 237 (1958).
[CrossRef]

Other

P. Connes (private communication).

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Figures (15)

Fig. 1
Fig. 1

The cat’s-eye retroreflector. Within the limitations of Gaussian optics, emergent rays are parallel to those incident.

Fig. 2
Fig. 2

Illustrations of the interference between two identical and parallel, but sheared and distorted, wavefronts. It is clear that in order to keep the variation in path difference across the interfering region minimal, the derivative of the wavefront function, as well as its absolute. value, should be a minimum. (a): Wavefronts plane parallel, no shear. Path difference = x0 across entire aperture. (b) Wavefronts plane parallel, shear = S introduced. Path difference = x0 across interfering region. (c) Wavefronts: parallel, distorted by maximum: value = d, shear = S introduced. Path difference variable across interfering region and mean path difference ≠ x0. (d) Wavefronts parallel, distorted by maximum: value = d with steeper slope than in (c), shear = S introduced. Path: difference more strongly variable across interfering region than in (c) but mean path difference almost: unchanged.

Fig. 3
Fig. 3

Parabolic primary, spherical secondary. Effect on wavefronts of changing the curvature of the secondary, narrow angle (1° field) case. Parameter δx = 0.

Fig. 4
Fig. 4

Parabolic primary, spherical secondary. Effect on wavefronts of changing the curvature of the secondary, wide angle (10° field) case. Parameter δx = 0.

Fig. 5
Fig. 5

Parabolic primary, spherical secondary. Effect on wavefronts of displacing the secondary from the primary focal point, narrow angle (1° field) case. Parameter R2 = −2.062F1.

Fig. 6
Fig. 6

Parabolic primary, spherical secondary. Effect on wavefronts of displacing the secondary from the primary focal point, wide-angle (10° field) case. Parameter R2 = −2.062F1.

Fig. 7
Fig. 7

Parabolic primary, spherical secondary. Wavefronts for angles of incidence 0° to 1° and parameters R2 = −2.062F1 and δx = 0.

Fig. 8
Fig. 8

Parabolic primary, spherical secondary. Wavefronts for angles of incidence 0° to 5° and parameters R2 = −2.062F1 and δx = 0.

Fig. 9
Fig. 9

Spherical primary, spherical secondary. Effect on wavefronts of changing the curvature of the secondary, narrow angle (1° field) case. Parameter δx = −0.0036A1.

Fig. 10
Fig. 10

Spherical primary, spherical secondary. Effect on wavefronts of changing the curvature of the secondary, compromise wide angle (7.6° field) case. Parameter δx = −0.025A1.

Fig. 11
Fig. 11

Spherical primary, spherical secondary. Effect on wavefronts of displacing the secondary about its optimum position, narrow angle (1° field) case. Parameter R2 = −1.00F1.

Fig. 12
Fig. 12

Spherical primary, spherical secondary. Effect on wavefronts of displacing the secondary about its optimum position, compromise wide angle (7.6° field) case. Parameter R2 = −1.00F1.

Fig. 13
Fig. 13

Spherical primary, spherical secondary. Wavefronts for angles of incidence 0° and 0.5° and parameters R2 = −1.00F1, δx = −0.0036A1.

Fig. 14
Fig. 14

Spherical primary, spherical secondary. Wavefronts for angles of incidence 0° to 5° and parameters R2 = −1.00F1, δx = −0.025A1.

Fig. 15
Fig. 15

Spherical primary, spherical secondary. Optimum secondary displacement against angle of incidence for f5 and f/10 over-all focal ratios.

Equations (1)

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[ wavefront slope as read directly from the figures ] × 10 2 = [ ray deviation in microradians ]

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