Abstract

The characteristic fringes of hologram interferometry can be analyzed by the use of density functions, i.e., functions that specify what fraction of the exposure time an object point spends in any one place. In many cases, this method of analysis avoids cumbersome series solutions for fringe functions; in this paper the method is applied to nonlinear vibrations and to combinations of sinusoidal oscillations whose frequencies are related by rational numbers. For nonlinear vibrations, results are obtained that allow direct calculation of nonlinear spring functions, without presumption of a solution to the nonlinear differential equation of motion.

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  1. R. L. Powell, in The Engineering Uses of Holography, edited by E. R. Robertson and J. M. Harvey (Cambridge U. P., Cambridge, 1970), pp. 333–340.
  2. A. D. Wilson, J. Opt. Soc. Am. 60, 1068 (1970).
  3. A. D. Wilson and D. H. Strope, J. Opt. Soc. Am. 60, 1162 (1970).
  4. K. A. Stetson, J. Opt. Soc. Am. 60, 1378 (1970).
  5. R. L. Powell and K. A. Stetson, J. Opt. Soc. Am. 55, 1593 (1965).
  6. A. Kozma, private communication.
  7. K. A. Stetson, Optik 29, 386 (1969).
  8. H. Cramer, The Elements of Probability Theory (Wiley, New York, 1958), Ch. 5, pp. 57–86.
  9. E. M. Hofstetter, in Matheematics of Physics and Chemnistry Vol. II, edited by H. Margenau and G. M. Murphy (Van Nostrand, Princeton, New Jersey, 1964), Ch. 3.
  10. K. A. Stetson, Optik 31, 576 (1970).
  11. W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), Ch. 4, Sec. 3, p. 67.
  12. J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems (Wiley-Interscience, New York and London, 1950), Ch. 2, p. 18.
  13. Reference 12, Ch. 4, pp. 83–90.
  14. Reference 8, Ch. 9, p. 136.
  15. Reference 8, Ch. 3, p. 37, and Ref. 11, p. 43.

Cramer, H.

H. Cramer, The Elements of Probability Theory (Wiley, New York, 1958), Ch. 5, pp. 57–86.

Davenport, W. B.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), Ch. 4, Sec. 3, p. 67.

Hofstetter, E. M.

E. M. Hofstetter, in Matheematics of Physics and Chemnistry Vol. II, edited by H. Margenau and G. M. Murphy (Van Nostrand, Princeton, New Jersey, 1964), Ch. 3.

Kozma, A.

A. Kozma, private communication.

Powell, R. L.

R. L. Powell and K. A. Stetson, J. Opt. Soc. Am. 55, 1593 (1965).

R. L. Powell, in The Engineering Uses of Holography, edited by E. R. Robertson and J. M. Harvey (Cambridge U. P., Cambridge, 1970), pp. 333–340.

Root, W. L.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), Ch. 4, Sec. 3, p. 67.

Stetson, K. A.

K. A. Stetson, J. Opt. Soc. Am. 60, 1378 (1970).

K. A. Stetson, Optik 29, 386 (1969).

K. A. Stetson, Optik 31, 576 (1970).

R. L. Powell and K. A. Stetson, J. Opt. Soc. Am. 55, 1593 (1965).

Stoker, J. J.

J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems (Wiley-Interscience, New York and London, 1950), Ch. 2, p. 18.

Strope, D. H.

A. D. Wilson and D. H. Strope, J. Opt. Soc. Am. 60, 1162 (1970).

Wilson, A. D.

A. D. Wilson and D. H. Strope, J. Opt. Soc. Am. 60, 1162 (1970).

A. D. Wilson, J. Opt. Soc. Am. 60, 1068 (1970).

Other (15)

R. L. Powell, in The Engineering Uses of Holography, edited by E. R. Robertson and J. M. Harvey (Cambridge U. P., Cambridge, 1970), pp. 333–340.

A. D. Wilson, J. Opt. Soc. Am. 60, 1068 (1970).

A. D. Wilson and D. H. Strope, J. Opt. Soc. Am. 60, 1162 (1970).

K. A. Stetson, J. Opt. Soc. Am. 60, 1378 (1970).

R. L. Powell and K. A. Stetson, J. Opt. Soc. Am. 55, 1593 (1965).

A. Kozma, private communication.

K. A. Stetson, Optik 29, 386 (1969).

H. Cramer, The Elements of Probability Theory (Wiley, New York, 1958), Ch. 5, pp. 57–86.

E. M. Hofstetter, in Matheematics of Physics and Chemnistry Vol. II, edited by H. Margenau and G. M. Murphy (Van Nostrand, Princeton, New Jersey, 1964), Ch. 3.

K. A. Stetson, Optik 31, 576 (1970).

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), Ch. 4, Sec. 3, p. 67.

J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems (Wiley-Interscience, New York and London, 1950), Ch. 2, p. 18.

Reference 12, Ch. 4, pp. 83–90.

Reference 8, Ch. 9, p. 136.

Reference 8, Ch. 3, p. 37, and Ref. 11, p. 43.

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