THE IMAGE SPEED DURING THE OPTICAL-ELECTRONIC SURFACING THE PLANET

Abstract

In this paper, a formula is obtained for calculating the velocity of an image in the plane of image fixation during a space survey of the planet's surface with the aid of an on-oard optoelectronic device. The ideal task is considered: the Earth is modeled by an absolutely rigid homogeneous ball, rotating uniformly around the fixed axis, and the satellite's center of mass describes a fixed Keplerian orbit, in one of the focal points of which the center of the Earth is located. The axis of sight has a direction in the nadir, i.e. passes through the center of the Earth. The main focus of the "cosmic camera" is in the center of mass of the satellite P, and the plane of fixation of the images is perpendicular to the viewing axis and is located at the focal distance d behind the point P. The obtained analytical formula for calculating the velocity field of motion of image points in the model problem under consideration when shooting in a nadir is of fundamental importance for solving the inverse problem when reconstructing a "blurred" image. The formula is important for calculating and optimizing the parameters of the compensators used in practice to "smear" the image. In addition, the resulting formula is useful for verifying numerical algorithms that model the "smear" effect. It can be used in planning work programs for remote sensing of the Earth.