Abstract

Thin flat mirrors are often used in designing various optical measurement systems. Such mirrors are generally deformed by environmental conditions during measurements. A detailed theory of deformation of a thin flat mirror that oscillates harmonically in the direction of the normal to its surface is introduced in our work. The mirror is treated as a vibrating membrane, and the time-dependent effect of the mirror deformation on the properties of reflected light is studied. A relation is derived for a dynamic wave aberration. On the basis of this relation, calculation of the Strehl definition of the deformed mirror is performed both by exact integration and by approximation. The results obtained can be used for analysis of the influence of mechanical vibrations on the accuracy of optical measurement systems in various practical applications where thin flat mirrors are used.

© 2004 Optical Society of America

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  1. L. D. Landau, E. M. Lifshitz, Theory of Elasticity. Course in Theoretical Physics, Vol. 7 (Pergamon, Oxford, UK, 1970).
  2. K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering (Cambridge U. Press, Cambridge, UK, 2002).
  3. A. P. S. Selvadurai, Partial Differential Equations in Mechanics, Vol. 1 (Springer, Berlin, 2000).
  4. A. P. S. Selvadurai, Partial Differential Equations in Mechanics, Vol. 2 (Springer, Berlin, 2000).
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1968).
  6. A. Miks, “Dependence of the wave-front aberration on the radius of the reference sphere,” J. Opt. Soc. Am. A 19, 1187–1190 (2002).
    [CrossRef]
  7. A. Miks, Applied Optics (Czech Technical University Press, Prague, 2000).
  8. C. Lanczos, Applied Analysis (Prentice Hall, New York, 1956).
  9. G. Meinardus, Approximation von Funktionen und ihre numerische Behandlung (Springer, Berlin, 1964).
  10. Melles Griot Catalogue 2003, Chap. 36.2.

2002 (1)

Bence, S. J.

K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering (Cambridge U. Press, Cambridge, UK, 2002).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1968).

Hobson, M. P.

K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering (Cambridge U. Press, Cambridge, UK, 2002).

Lanczos, C.

C. Lanczos, Applied Analysis (Prentice Hall, New York, 1956).

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Theory of Elasticity. Course in Theoretical Physics, Vol. 7 (Pergamon, Oxford, UK, 1970).

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Theory of Elasticity. Course in Theoretical Physics, Vol. 7 (Pergamon, Oxford, UK, 1970).

Meinardus, G.

G. Meinardus, Approximation von Funktionen und ihre numerische Behandlung (Springer, Berlin, 1964).

Miks, A.

Riley, K. F.

K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering (Cambridge U. Press, Cambridge, UK, 2002).

Selvadurai, A. P. S.

A. P. S. Selvadurai, Partial Differential Equations in Mechanics, Vol. 1 (Springer, Berlin, 2000).

A. P. S. Selvadurai, Partial Differential Equations in Mechanics, Vol. 2 (Springer, Berlin, 2000).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1968).

J. Opt. Soc. Am. A (1)

Other (9)

L. D. Landau, E. M. Lifshitz, Theory of Elasticity. Course in Theoretical Physics, Vol. 7 (Pergamon, Oxford, UK, 1970).

K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering (Cambridge U. Press, Cambridge, UK, 2002).

A. P. S. Selvadurai, Partial Differential Equations in Mechanics, Vol. 1 (Springer, Berlin, 2000).

A. P. S. Selvadurai, Partial Differential Equations in Mechanics, Vol. 2 (Springer, Berlin, 2000).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1968).

A. Miks, Applied Optics (Czech Technical University Press, Prague, 2000).

C. Lanczos, Applied Analysis (Prentice Hall, New York, 1956).

G. Meinardus, Approximation von Funktionen und ihre numerische Behandlung (Springer, Berlin, 1964).

Melles Griot Catalogue 2003, Chap. 36.2.

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