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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 62, Iss. 12 — Dec. 1, 1972
  • pp: 1434–1438

Application of Fourier Techniques to Underwater Image Transmission: A Test of the Linear-Invariant Hypothesis

ROBERT T. HODGSON and DOUGLAS R. CALDWELL  »View Author Affiliations

JOSA, Vol. 62, Issue 12, pp. 1434-1438 (1972)

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The modulation transfer functions of some aqueous solutions were calculated in two ways: (a) by measuring the sine-wave response through observation of the contrast transmittance of a resolution grating, and (b) by computing the Fourier transform of the image of a line source. For linear-invariant systems, to which Fourier techniques are applicable, both schemes will yield the same result. In the experiments, significant differences were found, caused by small temperature fluctuations in the solutions. The indiscriminate application of Fourier techniques to image transmission in natural bodies of water is questioned.

ROBERT T. HODGSON and DOUGLAS R. CALDWELL, "Application of Fourier Techniques to Underwater Image Transmission: A Test of the Linear-Invariant Hypothesis," J. Opt. Soc. Am. 62, 1434-1438 (1972)

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  1. J. R. V. Zaneveld and G. F. Beardsley, Jr., J. Opt. Soc. Am. 59, 378 (1969).
  2. W. H. Wells, J. Opt. Soc. Am. 59, 686 (1969).
  3. R. C. Honey and G. P. Sorensen, in Electromagnetics of the Sea, AGARD Conference Proceedings No. 77 (NATO, Paris, 1970; NASA, Langley Field, Virginia, distr.), p. 39.
  4. H. T. Yura, Appl. Opt. 10, 114 (1971).
  5. The restriction of space invariance is usually removed by subdividing the image plane into isoplanatic patches in which the form of the point spread function is approximately uniform.
  6. G. B. Parrent, Jr. and B. J. Thompson, Physical Optics Notebook (Society of Photo-Optical Instrumentation Engineers, Redondo Beach, Calif., 1969).
  7. R. C. Jones, J. Opt. Soc. Am. 48, 934 (1958).
  8. L. Ochs, J. A. Baughman, and J. Ballance, OS-3 ARAND System: Documentation and Examples, Vol. 1 (Oregon State University, Corvallis, 1970).
  9. J. W. Coltman, J. Opt. Soc. Am. 44, 468 (1954). The use of this formula is justified for only linear systems with symmetric imaging errors.
  10. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
  11. S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. 53, 351 (1963).
  12. P. Lindberg, Opt. Acta 1, 80 (1954).
  13. E. L. O'Neill, Introduction to Statistical Optics (Addison—Wesley, Reading, Mass., 1963), p. 17.

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