ABSTRACT
Investigations of scientific teams in France, Israel, Belarus, the United States, Russia, and some other countries have been devoted to the development of modern theory of vision in scattering media. It is possible to consider that by the present time, mechanisms of imaging and special features of influencing scattering media on the quality of image of objects have been studied in ample details, and accumulated knowledge has allowed the researchers to pass to solving higher-level problems, for example, problems of correction of hyperspectral satellite images for the distorting effect of the atmosphere.
Nevertheless, until recently, there have been a number of general theoretical problems demanding unambiguous interpretation; the present work is devoted exactly to this subject. The first of these problems is formulated as follows. Is it possible and how to determine the optical transfer function (pulse response, point spread function, or influence function) of a scattering medium or an imaging channel in the scattering medium independent of any properties of objects under observation and characteristics of let even ideal optical systems that allow the image of any objects to be restored using these characteristics? Or differently, is it possible to determine the general transfer properties inherent in a concrete scattering medium (by analogy to its optical characteristics) that can subsequently be used for imaging of objects with arbitrary optical properties and any characteristics of let even ideal optical systems? In this chapter, we will try to illuminate these problems and to present the corresponding models giving comprehensive answer on the imaginary problems arisen in the irregular atmosphere.
One more problem arises due to the fact that the pulsed response or the point spread function (PSF) used in vision theory is not an image of a point object, as in theory of optical systems (though in the literature devoted to vision theory they are sometimes identified). However, if the PSF is not a point image, how can the point image be constructed in the context of linear systems theory?
Having solved this problem, we will simultaneously answer the question on how many optical transfer functions or PSFs are required to be determined in order that to restore or to filter out wide-angle images of objects observed through scattering media (for example, to perform the atmospheric correction)?
Answers to these questions and problems of constructing the PSF connected with them for spherical models of the system atmosphere—Earth's surface—are considered in this chapter.
