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)