fine structure suitable for all types of specular surfaces utilizes a theoretical 3 model prepared earlier for another application. The specular surface is assumed to be simulated by a mosaic of microscopic specular areas 6a which are optically flat to X/l0 where x is a characteristic wavelength. The coherent reflection which is produced by each element 6a has an angular diameter given approximately by the diffraction limit p2 X/d where d is a characteristic scale size for 6a. Any angular deviation between the planes of the area elements will spread the solar image cone. This is treated by assuming that the surface normals of the elements are distributed randomly over an angular diameter e, i.e., their distribution is rectangular. If, in addition, the reflector consists of an array of small mirrors, the distribution of their principal normals is characterized by an angular diameter n. The combined effect of these deviations produces a solar image divergence which has a total angular diameter t = 2(e + q). The brightness of the solar image cone is readily derived for these reflector characteristics. The light that is emitted by the Sun is conveniently described for this application by an average visual ctufc radiance N0 (2.0 x 10 watts/ster m ). If the spacecraft is located a distance S from the Sun, the radiant flux on a reflector element 6a from an infinitesimal area dA on the solar disk is given by N@dA 6a cos(a/2)/S where a is the "phase" angle at the spacecraft between the Sun and the Earth. The reflected intensity of this parallel beam is diminished by the specular reflectance rg of the surface and by the divergence of the light rays into a narrow cone of diameter p which is assumed to be uniformly illuminated. Thus, the differential irradiance at Earth neglecting atmospheric effects is N0dArs6a cos(a/2)/s2(irp2R2/4) where R is the spacecraft range from Earth. Integration over the solar disk which subtends an angle a yields an irradiance N@o2rs6a cos(a/2)/(p + a)2R2 over an image cone p + a. Integration over the reflector introduces the divergence due to deviations in the surface, and the total irradiance from the reflector is N0o2rsa cos(a/2)/(p + a + t)2R2 above the atmosphere. At the surface of the Earth the irradiance is degraded further by atmospheric extinction and the optical response of the instrument which are denoted by the factor k. Thus the complete expression for the irradiance is
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