# Line of Sight and Image Motion Compensation for Step and Stare Imaging System
## 1 Introduction  
In recent years, electro-optic/infrared imaging systems with high resolution, wide area, and accurate geo-positioning characteristics are required for search and rescue, border and coastal patrol, and other applications. For the above requirements, the system should have a long focal length, high imaging frame frequency, and high geo-locating accuracy. Such systems have three imaging patterns: linear array scanning, step and stare, and scan stare imaging patterns [1]. Step and stare imaging pattern in which the line of sight (LOS) is stepped to a position and held for some time and then stepped to a new position. This type of scan is often used when a pattern of several small images are to be stitched together in a mosaic to form a larger image and should be preferred when more accurate geo-location is required [2].  
There are two primary architectures for the step and stare imaging system: two-axis gimbaled systems and two-axis gimbaled systems with steering mirrors. Two-axis gimbaled systems are switched to perform LOS pointing and motion compensation. They are the simplest and lowest cost. However, they are not suitable for high frame frequency applications because of the larger payload. Two-axis gimbaled systems with steering mirrors provide more stability but with greater cost and complexity [3]. This architecture can choose two single-axis steering mirrors and one two-axis steering mirror. Considering the nonlinear coupling and complexity of control, one two-axis steering mirroris generally only used in limited space. If the space allowed, two single-axis steering mirrors can be preferred. The description is detailed in Table 1. The system described in this paper has a suitable space, so it chooses the architecture of a two-axis gimbal with two single-axis steering mirrors.  
The step and stare imaging system needs to focus on how to achieve an accurate line of sight or image motion compensation. The way of using two-axis or multi-axis gimbals to achieve stabilization of the LOS is described in many early documents [4; 5; 6; 7; 8; 9].With the emergence and development of fast steering mirrors, the literature began to use the fast steering mirrors(FSMs) with two-axis gimbals to realize the composite systems to achieve more accurate and fast stabilization of LOS. Most of these systems focus on the tracking system and pay more attention to the stabilization accuracy of the LOS of the system rather than the imaging resolution [10; 11; 12; 13]. The above literature does not combine the LOS and image motion compensation. The system described in this article needs to achieve high-resolution images while achieving LOS stability. That means, to reach the LOS pointing position before the imaging exposure, and to carry out image motion compensation during the exposure. Thus, we will focus this paper on LOS and image motion compensation for step and stare imaging system which uses two-axis gimbal with two single-axis steering mirrors.  
The layout of the rest of this paper is as follows. The second part of this article describes the composition, working principle, and imaging optical path. In the third part, the LOS and motion compensation kinematics and algorithm are described. The method proposed in this paper is verified by ground and flight tests in the fourth part, and the conclusions got from the tests are expounded. The test results are discussed and summarized in Section 5.