In order to complete the calibration work of the star sensor, a high- precision collimating optical system with large field of view is designed. According to the static star simulator′ s working principle about cohesion between exit pupil of star simulator and entrance pupil of star sensor, the design principle and parameters of optical system is determined. The design results show that the field of view is Φ39°, distortion is less than 0.1%. A method of making star point board in accordance with aberrations of the optical system is put forward, to avoid process of repeatedly engraving star point board. Finally, the design of the system is tested. According to the testing results: simulated accuracy of the whole system reaches 15″ , the data can meet the using requirement of high accuracy with large field static star simulator.
When a space vehicle is operating in space, it uses space attitude measurement equipment to capture and measure its flight attitude information. Star sensor is a high-precision space attitude measurement instrument widely used in space vehicles. It extracts the attitude of the carrier body by identifying stars at different positions in the celestial sphere, with an accuracy of up to angular second level. With the development of space technology and the improvement of aircraft attitude positioning requirements, the technical specifications of star sensors are also becoming increasingly high. As a ground calibration equipment for star sensors, star simulators have also received increasing attention. It is urgent to develop a large field of view and high-precision star simulator that can meet the ground testing requirements of star sensors.
A static star simulator is an instrument that accurately simulates the position of stars in the sky on the ground. It mainly consists of five parts: driving circuit, light source, star point reticle, filter, and optical system. Among them, the performance of optical systems directly affects the technical indicators of star simulators, such as the simulated sky range and the accuracy of star position simulation. For the optical system of the star simulator, it is required to be able to interface well with the optical system of the star sensor. Considering the detection of the star sensor, the scattered spots in each field of view of the star simulator should be distributed within a specific range and have good symmetry, which determines the uniqueness of the optical design of the star simulator. An optical system with a wide band range, small distortion, and flat image field with high image quality will lay a solid foundation for providing accurate constant star map simulation for star simulation.
This article designs an optical system for a large field of view star simulator, which can reduce distortion and chromatic aberration by changing the asymmetric structure. The design results indicate that the focal length, distortion, and energy concentration meet the design requirements. A method for determining the position of star point marking was proposed, and the feasibility of the system application was verified by the experimental results obtained from its application.
(1) Design principles
The optical system is the core part of the static star simulator, and its main function is to emit parallel beams of light, imaging the star point reticle located at the focal plane of the system to simulate the position of the star at an infinite distance. At the same time, strict aberration correction is used to ensure the energy balance and position accuracy of the simulated star point. Therefore, the optical system design should choose a collimating optical system. The main basis for the design of a collimating optical system is to ensure that the light emitted by each star point in the full field of view is equal to the input pupil flux of the star sensor, and that the output pupil aperture of the star simulator matches the input pupil aperture parameters of the star sensor, achieving the transmission of all star map information of the star simulator to the star sensor. Due to the fact that the entrance pupil of the star sensor is located behind the optical system, it is required that the exit pupil of the static star simulator optical system be placed externally; According to the principle of pupil connection, it is necessary to ensure that the exit pupil position of the star simulator coincides with the entry pupil position of the star sensor during design, as shown in Figure 1.
(2) Design parameters
According to the ground calibration requirements of the star sensor, the design indicators of the optical system of the large field of view high-precision static star simulator are obtained, as shown in Table 1.
The aberration of optical systems directly affects the accuracy of star simulators, and four aspects are mainly considered in optical design:
1) To ensure that the simulated constant star points have high imaging position accuracy, which mainly depends on the system’s distortion. Therefore, according to the accuracy requirements of the large field of view star simulator, the relative distortion of the optical system should be strictly corrected to not exceed 0.1%;
2) The deviation between the energy center and the main ray is also a major cause of star position error. The distribution of points in the point chart can approximate the distribution of energy, and the concentration of these points can also determine the energy center of the imaging point. Therefore, the deviation between the system energy center and the main ray should be minimized as much as possible to improve the accuracy of emitting parallel light;
3) The optical system of the star simulator uses modulation transfer function (MTF) curves to measure the quality of collimation. Combined with the design requirements of the system’s flat image field, the design results do not only pursue high MTF, but also ensure that the geometric radii of the scattered spots in each field of view are not significantly different;
4) The vertical aberration of an optical system will increase due to the large distance from the pupil, and it is necessary to strictly control the coma, astigmatism, and magnification chromatic aberration that change with the height of the main ray projection.
Based on the above analysis results, a type of eyepiece system is selected as the initial structure of the optical system, as shown in Figure 2. The eyepiece consists of a flat convex lens and a set of triple bonded lenses. The system’s pupil is placed outside the front of the flat convex lens. Based on the characteristics of the single transparent mirror aberration, it is known that the flat convex lens will produce coma and astigmatism, and its aberration is corrected by the rear triple bonded lens set. In a triplex lens group, the power generated by the first curvature is equal to the total power of the eyepiece when combined with the convex lens. Therefore, the power of the entire eyepiece is borne by two closely connected thin lenses on the image plane, which is beneficial for reducing the field curvature and increasing the distance from the pupil. The last curvature is equivalent to the field lens and is used to adjust the position of the eyepiece’s pupil.
During the design process, in order to correct distortion and field area, the triplex mirror group is separated to increase the degree of freedom in the design. Due to the large distance from the exit pupil, changing the curvature, thickness, and air spacing of the lens still cannot effectively balance the residual aberration. Therefore, a lens is added to compensate and a negative lens is introduced to eliminate the field curvature; Select the combination of positive and negative lenses of H-FK61 and H-ZF62 to eliminate spherical and axial chromatic aberration. According to the technical specifications, the designed system has a focal length of 99.988 mm, an exit pupil diameter of 20 mm, and an exit pupil distance of 80 mm. The planned system optical path is shown in Figure 3.
The simulation accuracy of a star simulator is measured by the inter star angular distance error. For a static star simulator, the inter star angular distance mainly depends on the position of the star point on the star point reticle.
The general method for determining the position of a star is to know the single star position angle of the star, calculate the plane Cartesian coordinates of each constant star point on the star plate based on the designed focal length f ‘of the optical system of the star simulator, and then draw the star plate according to the corresponding coordinate values of each constant star point. This method usually results in test results exceeding the accuracy requirements due to the actual focal plane deviation after the optical system of the star simulator is installed and adjusted, and requires repeated measurement of the actual focal plane of the star simulator to calculate new star point positions and remake the star point plate. Additionally, due to the neglect of the influence of optical system distortion during each calculation of star point positions, it is difficult to further improve the accuracy of the simulator. Therefore, it is proposed to combine the distortion of the collimating optical system with the changes in image point positions when the front and rear defocuses reach the limit, and fit the positions of each star point along the radius direction on the star point reticle according to the normalized field of view and corresponding distortion.
After installing the star point reticle, the designed collimating optical system is applied to test the star point position on the star map. 105 sets of inter star angular distance error distribution maps for 15 test star points. The results show that the inter star angular distance error of all star points is less than 15 ″, which improves the calculation results of inter star angular distance error according to the optical system design and meets the accuracy requirements of the simulator.
A collimating optical system with a large exit pupil distance was designed using ZEMAX software to meet the ground calibration requirements of star sensors, and applied to high-precision static star simulators. This system has advantages such as large field of view, wide spectrum, and small distortion. The system has a compact structure, and the lens uses traditional surface shapes and commonly used optical materials, making it easy to process and apply. A method of first correcting the position of star points to create a star point reticle was proposed. A star map was tested using the designed star simulator, and good results were obtained. The angle error between all star points was less than 15 ″, which meets the requirements for ground calibration of star sensors.
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