Calibration of intrinsic parameters of a star tracker’s digital camera based on ground-based stars observations, taking into account atmospheric refraction and light aberration

Abstract

The mathematical model of a digital image contains a set of parameters called camera's intrinsic elements. The numerical values of the elements are unique and must be determined through the individual calibration. The paper considers the problem of fi ve intrinsic elements calibration: the focal length of the lens, two coordinates of the principial point of the image, and two second-order radial distortion coeffi cients. The stars observed by the calibrated camera from the Earth's surface are used as a calibration test pattern. The stellar coordinates are cataloged with very high accuracy, which makes it possible to get rid of complex calibration equipment and reduce the calibration problem to a particular problem of digital image processing. The positions of stars observed from the Earth's surface are distorted by a velocity aberration and atmospheric refraction. These effects are taken into account by introducing distortions into the direction vectors of stars taken from the star catalog. Two approaches to solving the calibration problem are considered, which take into account the unknown orientation of the calibrated camera relative to the Earth in different ways. It has been experimentally shown that both approaches lead to the same results. The discrepancy in calibration measurements after calibration decreases by a factor of 32, to a value on the order of the irremovable angular error in determining the apparent position of a star in a turbulent atmosphere. The results of individual calibration of the camera's intrinsic elements are used in the fi rmware of the star tracker to correct the systematic errors in attitude measurements.