Temporal metric spaces in radiative transfer theory. IV. Temporal diameters

SIO Reference 59-17. When a steady point source of radiant energy is turned on in optical medium such as a cloud, a lake, or some given region of an ocean, there is a small yet finite period of time in which the light field produced by the source is in the process of building up to a steady state. During this period the radiant energy from the source is transmitted at the speed of light to the farthest reaches of the medium while simultaneously being diffused and rediffused within the characteristic spheroid (the interior of the region defined by the wavefront and the boundaries of the medium). Even though this transmission, diffusion, and final attainment of the steady state configuration of the light field take place in a relatively small interval of time, an enormous collection of complex radiometric events takes place.In this note we systematically isolate some of these radiometric events and show that they may be arrayed in orderly and informative sequence in time and space. The results of such a painfully detailed analysis of apparently imperceptible transient phenomena are immediately applicable to all radiative transfer processes, including those in the so-called steady state, since these are viewable as superpositions of instantaneous transient states. Furthermore, the approach to the time-dependent problem presented here requires no explicit model of the light field such as that represented by the equation of transfer. Specifically, the approach of the present paper is based on the idea of the n-ary temporal diameter of an optical medium