The internal structure of off-axis three-mirror system is commonly complex. The mirror installation error in assembly always affects the imaging line-of-sight and further degrades the image quality. Due to the complexity of the optical path in off-axis three-mirror optical system, the straightforward theoretical analysis on the variations of imaging line-of-sight is extremely difficult. In order to simplify the theoretical analysis, an equivalent single-mirror system is proposed and presented in this paper. In addition, the mathematical model of single-mirror system is established and the accurate expressions of imaging coordinate are derived. Utilizing the simulation software ZEMAX, off-axis three-mirror model and single-mirror model are both established. By adjusting the position of mirror and simulating the line-of-sight rotation of optical system, the variations of imaging coordinates are clearly observed. The final simulation results include: in off-axis three-mirror system, the varying sensitivity of the imaging coordinate to the rotation of line-of-sight is approximately 30 um/″; in single-mirror system, the varying sensitivity of the imaging coordinate to the rotation of line-of-sight is 31.5 um/″. Compared to the simulation results of the off-axis three-mirror model, the 5% relative error of single-mirror model analysis highly satisfies the requirement of equivalent analysis and also verifies its validity. This paper presents a new method to analyze the installation error of the mirror in the off-axis three-mirror system influencing on the imaging line-of-sight. Moreover, the off-axis three-mirror model is totally equivalent to the single-mirror model in theoretical analysis.
Space borne laser altimeter is able to measure the distance between satellite and land surface. Combining with the attitude, orbit and equipment placement information, the elevation of the measured area can be calculated, which can be used as an elevation control point in mapping. By the influence of satellite orbit height and laser spread angle, the footprint of laser on the land surface is in diameter of tens of meters. For the situation of a flat surface, every point has equal elevation and the central point of the footprint can be chosen as an elevation control point. For the situation of undulating surface, each point has different elevation, and there will be much error if the central point of the footprint is chosen as an elevation control point. Now, the point in latter situation is excluded which makes the efficiency of laser altimeter low. In this paper, the situation of undulating surface is considered, and new approaches of using DSM and image recognition are adopted, resulting in acquiring elevation control point in this situation and increasing the efficiency of laser altimeter.