Objective  Target detection with earthlimb and deep space background is an important imaging method for spaceborne optical remote sensors, which can effectively reduce the impact of earth stray radiation. It is widely used in weak target detection, such as mid-course warning of ballistic missile, space target monitoring, and astronomical detection. Usually, the earth is controlled outside the field of view of sensors, but the earth stray light will still reach the focal plane through the non-imaging optical path, which will affect the detection of targets. The earth radiation received by a remote sensor includes earth surface energy through the atmosphere, atmospheric spontaneous radiation energy and atmospheric backscattering energy of solar radiation. The earth radiation is related to the types of ground objects, atmospheric conditions, observational geometry, and the geometry of the sun. Due to its complexity, the stray light analysis software has not been able to accurately analyze the influence of earth stray light. In order to evaluate the influence of the earth stray radiation and guide the stray light suppression design of remote sensors, the earth stray radiation is modeled and analyzed.

  Methods  Based on the radiation theory, the radiation model of earth spherical crown is established, and the spherical cap region that contributes to its optical payload stray light at any satellite position is given. The total stray radiation of earth is solved using the method of region meshing and small facet integration (Fig.1). The radiation energy of a small facet includes surface energy passing through the atmosphere, atmospheric spontaneous radiation energy, and atmospheric backscattered energy of solar radiation. For accurate characterization, a latitude longitude model and a solar vector model of small facets are established based on satellite parameters to calculate their solar irradiation geometry (Fig.3-4). Combined with the satellite observation geometry, surface parameters and atmospheric parameters, etc., the radiance is obtained using the atmospheric radiation transfer model.

  Results and Discussions   Taking the visible and long wave infrared band of a spaceborne remote sensor as an example, the comparative analysis of the earth stray radiation is carried out in terms of the nadir location, time and sensor boresight direction (Fig.8-9).The earth stray radiation changes periodically with time. The fluctuation in the visible light band is nearly 10 times at different times and in the long wave infrared band can be ignored. The earth stray radiation is sensitive to the change of boresight elevation angle. There are seven orders of magnitude fluctuations in the visible light band and two orders of magnitude fluctuations in the long wave infrared band when the elevation angle changes 25°. The boresight azimuth angle has an influence on the earth stray radiation in the visible light band and can be ignored in the long wave infrared band. It has nearly five times of fluctuations varying with different azimuth angles. The geographical latitude has an influence on the earth stray radiation in the visible light band and can be ignored in the long wave infrared band. The lower the latitude is, the greater the influence of stray radiation is.

  Conclusions  In order to solve the problem that the earth stray radiation can not be accurately simulated for the spaceborne optical remote sensor used for earthlimb and deep space background target detection, the mathematical model of earth spherical crown stray radiation is established. The visible and long wave infrared band of a spaceborne remote sensor is taken as an example to simulate the earth stray radiation from various dimensions such as the position of the satellite nadir, time and the direction of the payload's line of sight. The research results can be widely used in stray light suppression design of spaceborne remote sensors with earthlimb and deep space background.