Point and Beam Spread Functions of Seawater

摘要

The point spread function (PSF) describes response of a linear optical imaging system to a point light source (see Point spread function and imaging in turbid medium). This response includes the effects of both the image system itself (lens, mirror, recording media, etc.) and of the medium the optical signal lasses through (for example, seawater). By using the concept of the PSF, closely related to BSF, effects of different components of such a linear system can be separately modeled and multiplicatively accounted for in the spatial frequency domain. Mathematically, an image, g(x, y), of an object is the combination of the original signal (image), f (x, y), convolved with the PSF of the entire imaging system, h(x, y), and of the noise, n(x, y): g(x, y) = f (x, y) * h(x, y) + n(x, y) where coordinates x. y indicate a position in the image and the symbol * denotes the operation of convolution. If the PSF is shift invariant, the convolution of and h in the spatial domain corresponds to a simple multiplication of the Fourier transforms, fF and gF, of f and h, respectively. This is referred to a: the convolution theorem (for example http://mathworld. wolfram.com/Convolu tionTheorem.html).