Abstract

A general rule for the stability of plane reflecting surface systems is derived by use of the features of the reflection matrix. It is proved that only two directions can be stable: the forward direction and the backward direction (retroreflection). Examples for the application of this rule in the design of stable reflecting systems for optical communication are given.

© 1998 Optical Society of America

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References

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  1. R. Kingslake, Optical System Design (Academic, New York, 1983), pp. 153–154.
  2. L. Levi, Applied Optics (Wiley, New York, 1968), pp. 351, 363.
  3. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), p. 169.
  4. J. L. Synge, “Reflection in a corner formed by three plane mirrors,” Quart. Appl. Math. 4, 166–176 (1946).
  5. P. R. Yoder, “Study of light deviation errors in triple mirror and tetrahedral prisms,” J. Opt. Soc. Am. 48, 496–499 (1958).
    [CrossRef]
  6. K. N. Chandler, “On the effect of small errors in angles of corner-cube reflectors,” J. Opt. Soc. Am. 50, 203–206 (1960).
    [CrossRef]
  7. H. D. Eckhardt, “Simple model of corner reflector phenomena,” Appl. Opt. 10, 1559–1566 (1971).
    [CrossRef] [PubMed]
  8. M. Skop, D. Ben-Ezra, N. Schweitzer, “Adjustable stabilized reflector for optical communication,” Proceedings of the IEEE 19th Convention of Electrical and Electronics Engineers in Israel, (IEEE, New York, 1996), pp. 383–386.
    [CrossRef]
  9. J. S. Beggs, “Mirror-imaging kinematics,” J. Opt. Soc. Am. 50, 388–393 (1960).
    [CrossRef]

1971 (1)

1960 (2)

1958 (1)

1946 (1)

J. L. Synge, “Reflection in a corner formed by three plane mirrors,” Quart. Appl. Math. 4, 166–176 (1946).

Beggs, J. S.

Ben-Ezra, D.

M. Skop, D. Ben-Ezra, N. Schweitzer, “Adjustable stabilized reflector for optical communication,” Proceedings of the IEEE 19th Convention of Electrical and Electronics Engineers in Israel, (IEEE, New York, 1996), pp. 383–386.
[CrossRef]

Chandler, K. N.

Eckhardt, H. D.

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), p. 169.

Kingslake, R.

R. Kingslake, Optical System Design (Academic, New York, 1983), pp. 153–154.

Levi, L.

L. Levi, Applied Optics (Wiley, New York, 1968), pp. 351, 363.

Schweitzer, N.

M. Skop, D. Ben-Ezra, N. Schweitzer, “Adjustable stabilized reflector for optical communication,” Proceedings of the IEEE 19th Convention of Electrical and Electronics Engineers in Israel, (IEEE, New York, 1996), pp. 383–386.
[CrossRef]

Skop, M.

M. Skop, D. Ben-Ezra, N. Schweitzer, “Adjustable stabilized reflector for optical communication,” Proceedings of the IEEE 19th Convention of Electrical and Electronics Engineers in Israel, (IEEE, New York, 1996), pp. 383–386.
[CrossRef]

Synge, J. L.

J. L. Synge, “Reflection in a corner formed by three plane mirrors,” Quart. Appl. Math. 4, 166–176 (1946).

Yoder, P. R.

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

Quart. Appl. Math. (1)

J. L. Synge, “Reflection in a corner formed by three plane mirrors,” Quart. Appl. Math. 4, 166–176 (1946).

Other (4)

M. Skop, D. Ben-Ezra, N. Schweitzer, “Adjustable stabilized reflector for optical communication,” Proceedings of the IEEE 19th Convention of Electrical and Electronics Engineers in Israel, (IEEE, New York, 1996), pp. 383–386.
[CrossRef]

R. Kingslake, Optical System Design (Academic, New York, 1983), pp. 153–154.

L. Levi, Applied Optics (Wiley, New York, 1968), pp. 351, 363.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), p. 169.

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Figures (1)

Fig. 1
Fig. 1

Optical bypass: B, obstacle; 1, 2, 3, 4, plane mirrors.

Equations (2)

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

G X = 0   0 0 0   0 1 0 - 1 0     G Y =   0 0 1   0 0 0 - 1 0 0 ,
NS = sup R , r RA - AR r ,

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