Abstract

The cat's-eye retroreflector is a passive optical system consisting of a secondary mirror placed at the focal point of a primary lens. We analyze the cat's eye using the paraxial ray matrix approach. The position of the equivalent reflecting surface and the angular field of view of a realizable cat's eye are functions of the radius of curvature of the secondary mirror. The field of view is maximum for a secondary mirror with a concave radius of curvature equal to the focal length of the primary lens. We further derive the general dependence of retroreflection errors on misadjustment of the secondary mirror.

© 1975 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. F. Chang, D. G. Currie, C. O. Alley, M. E. Pittman, J. Opt. Soc. Am. 61, 431 (1971).
    [CrossRef]
  2. H. D. Eckhardt, Appl. Opt. 10, 1559 (1971).
    [CrossRef] [PubMed]
  3. F. Stenman, Comment. Physico-Mathematicae 42, 39 (1972).
  4. R. Beer, D. Marjaniemi, Appl. Opt. 5, 1191 (1966).
    [CrossRef] [PubMed]
  5. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1971), pp. 18–49 and references therein.
  6. H. Kogelnik, Appl. Opt. 4, 1562 (1965).
    [CrossRef]
  7. In fact, lens aberration (which we do not consider here) or the secondary mirror diameter would limit the effective field of view of the optimized cat's eye.

1972

F. Stenman, Comment. Physico-Mathematicae 42, 39 (1972).

1971

1966

1965

Appl. Opt.

Comment. Physico-Mathematicae

F. Stenman, Comment. Physico-Mathematicae 42, 39 (1972).

J. Opt. Soc. Am.

Other

In fact, lens aberration (which we do not consider here) or the secondary mirror diameter would limit the effective field of view of the optimized cat's eye.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1971), pp. 18–49 and references therein.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Retroreflectors: (a) corner cube; (b) cat's eye with primary lens; (c) cat's eye with primary mirror. (b) and (c) are formally equivalent in the paraxial approximation.

Fig. 2
Fig. 2

Optical system: (a) The primary lens of focal length f is separated from the secondary mirror of radius R by a distance d. At the lens surface the input ray of height ri and slope ri is transformed by the system into the output ray of height r0 and slope r0. (b) The cat's-eye configuration. The mirror is located at a distance d = f from the primary lens.

Fig. 3
Fig. 3

The effect of tilt of the secondary mirror. The slope of the intermediate ray | r r |is changed by 2α (dashed line) if the mirror is tilted by α. For simplicity, a plane secondary mirror is shown.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

[ A B C D ] .
| r 0 r 0 | = [ A B C D ] | r i r i | ,
q 0 = A q i + B C q i + D ,
1 q = 1 R i λ π ω 2 .
[ 1 d 0 1 ] ,
[ 1 0 ( 1 / f ) 1 ] .
[ 1 0 ( 2 / R ) 1 ] .
[ 1 0 0 1 ] .
[ A B C D ] = [ 1 0 1 / f 1 ] [ 1 d 0 1 ] [ 1 0 2 / R 1 ] [ 1 d 0 1 ] [ 1 0 1 / f 1 ] .
A = 1 2 d R 2 d f + 2 d 2 f R B = 2 d 2 d 2 R C = 2 f 2 R + 4 d f R + 2 d f 2 2 d 2 f 2 R D = 1 2 d f 2 d R + 2 d 2 f R } .
r 0 = r i ,
C = 0 D = 1 } .
d = f ,
[ A B C D ] = [ 1 , 2 d 2 d 2 R 0 , 1 ] .
B 2 = d 2 R d .
| r r |
| r 0 r 0 | = [ 1 , d 1 / f , 1 d / f ] | r r | .
r 0 = 2 α ( 1 d f ) + C r i + D r i ,
r 0 d | d = f = 2 α f + 2 r i f 2 + ( 2 R 2 f ) r i .
Δ r 0 | d f = [ 2 α f + 2 r i f 2 + 2 r i ( 1 R 1 f ) ] Δ d .
[ 1 0 0 1 ] ,
Δ r 0 | d = R f = ( 2 α f + 2 r i f 2 ) Δ d .
| Δ d | 3.84 μ m .
| α | max 1.25 × 10 3 .
| r i | max 1.25 × 10 3 .
| r r |

Metrics