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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 61, Iss. 10 — Oct. 1, 1971
  • pp: 1359–1362

Hologram Interferometry of Nonsinusoidal Vibrations Analyzed by Density Functions

KARL A. STETSON  »View Author Affiliations


JOSA, Vol. 61, Issue 10, pp. 1359-1362 (1971)
http://dx.doi.org/10.1364/JOSA.61.001359


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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.

Citation
KARL A. STETSON, "Hologram Interferometry of Nonsinusoidal Vibrations Analyzed by Density Functions," J. Opt. Soc. Am. 61, 1359-1362 (1971)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-61-10-1359


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References

  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.

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