Abstract

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.

© 1972 Optical Society of America

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References

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  1. J. R. V. Zaneveld and G. F. Beardsley, J. Opt. Soc. Am. 59, 378 (1969).
    [Crossref]
  2. W. H. Wells, J. Opt. Soc. Am. 59, 686 (1969).
    [Crossref]
  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).
    [Crossref] [PubMed]
  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 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).
    [Crossref]
  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.
    [Crossref]
  10. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
    [Crossref]
  11. S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. 53, 351 (1963).
    [Crossref]
  12. P. Lindberg, Opt. Acta 1, 80 (1954).
    [Crossref]
  13. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 17.

1971 (1)

1969 (2)

1964 (1)

1963 (1)

1958 (1)

1954 (2)

Ballance, J.

L. Ochs, J. A. Baughman, and J. Ballance, OS-3 ARAND System: Documentation and Examples, Vol. 1 (Oregon State University, Corvallis, 1970).

Baughman, J. A.

L. Ochs, J. A. Baughman, and J. Ballance, OS-3 ARAND System: Documentation and Examples, Vol. 1 (Oregon State University, Corvallis, 1970).

Beardsley, G. F.

Coltman, J. W.

Culver, W. H.

Duntley, S. Q.

Honey, R. C.

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.

Hufnagel, R. E.

Jones, R. C.

Lindberg, P.

P. Lindberg, Opt. Acta 1, 80 (1954).
[Crossref]

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 17.

Ochs, L.

L. Ochs, J. A. Baughman, and J. Ballance, OS-3 ARAND System: Documentation and Examples, Vol. 1 (Oregon State University, Corvallis, 1970).

Parrent, G. B.

G. B. Parrent and B. J. Thompson, Physical Optics Notebook (Society of Photo-Optical Instrumentation Engineers, Redondo Beach, Calif., 1969).

Preisendorfer, R. W.

Richey, F.

Sorensen, G. P.

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.

Stanley, N. R.

Thompson, B. J.

G. B. Parrent and B. J. Thompson, Physical Optics Notebook (Society of Photo-Optical Instrumentation Engineers, Redondo Beach, Calif., 1969).

Wells, W. H.

Yura, H. T.

Zaneveld, J. R. V.

Appl. Opt. (1)

J. Opt. Soc. Am. (6)

Opt. Acta (1)

P. Lindberg, Opt. Acta 1, 80 (1954).
[Crossref]

Other (5)

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 17.

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.

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.

G. B. Parrent and B. J. Thompson, Physical Optics Notebook (Society of Photo-Optical Instrumentation Engineers, Redondo Beach, Calif., 1969).

L. Ochs, J. A. Baughman, and J. Ballance, OS-3 ARAND System: Documentation and Examples, Vol. 1 (Oregon State University, Corvallis, 1970).

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Figures (6)

F. 1
F. 1

Schematic illustration of experimental apparatus. A short-arc lamp (1), followed by a narrow band-pass filter (2), illuminates the optical target (3). The object illumination passes through the water (4) and is received by the Questar (5). The image irradiance is monitored by a microscope (6), connected to a linear photometer (7). An x, y recorder (8) records the image irradiance (y axis) as a function of object displacement (x axis).

F. 2
F. 2

Image wave number vs object wave number. The data were collected at various ranges in water with differing scattering characteristics. Open circles, Phytoplankton, 1 m. Open squares, Phytoplankton, 2 m. Open triangles, Phytoplankton, 3 m. Open hexagons, clay sediment, 2 m. The units of Ω are in cycles/mrad.

F. 3
F. 3

Optical-system calibration in air. The circles represent the SWR. The SWR multiplied by the normalized source spectrum is shown by the squares. This is the predicted spectrum, S1(Ω), which is to be compared with the normalized spectrum of the line spread function, S2(Ω), represented by triangles. The units of Ω are in cycles/mrad.

F. 4
F. 4

Hydrological data taken when the water was well mixed to reduce thermal fluctuations. The notation is the same as in Fig. 3, except that the in-air SWR is included in the upper right-hand corner. The temperature history during the test is shown in the enclosed box.

F. 5
F. 5

Hydrological data taken when the water was left standing undisturbed, to encourage thermal fluctuations. The notation is the same as that in Figs. 3 and 4.

F. 6
F. 6

Average spectral error as a function of rms temperature fluctuations. The data were collected over a week, while the water was cooling down to laboratory temperature. Note that, for each pair of data points (shown by similar symbols), the lesser spectral error corresponds to the smaller rms temperature fluctuation. Open circles, 26 October. Open squares, 27 October. Open triangles, 1 November. Cross, air calibration.

Equations (8)

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

s i ( x , y ) = h ( x ξ , y η ) s 0 ( ξ , η ) d ξ d η ,
S i ( k , l ) = H ( k , l ) S 0 ( k , l ) .
r = ( x 2 + y 2 ) 1 2 and θ = tan 1 y / x .
s i ( r ) = h ( r ζ ) s 0 ( ζ ) d ζ
S i ( n ) = H ( n ) S 0 ( n ) , n = ( k 2 + l 2 ) 1 2 .
S 0 = sin π δ Ω π δ Ω ,
E ( Ω ) = | S 1 ( Ω ) S 2 ( Ω ) |
Ē = 1 6 j = 1 6 E ( j Ω 0 ) , Ω 0 = 5 cycles / mrad .