Static Star Simulator with Long Exit Pupil Distance

In order to improve the simulation accuracy of the static star simulator for the stars at infinity to meet the ground calibration requirements of the star sensor，an optical system design scheme of the static star simulator with long exit pupil distance is proposed. Firstly，according to the ground calibration requirements of the star sensor ，the technical indicators of the star simulator are obtained，so that the design parameters of the collimating optical system are calculated. Secondly，the Elfe eyepiece is selected as the initial structure. The design and optimization mainly constrains the distortion of the system through Zemax software. The final design results are got that the field of view is 6°, the focal length is 343.77 mm，the exit pupil distance is 1 000 mm，the distortion in the entire field of view is less than 0.027 6%，and the MTF is close to the diffraction limit. Combined with the tolerance analysis results，it shows that the system has high image quality and excellent stability. Finally, through calculating the position error of the star point，it is obtained that the starlight emission accuracy of the optical system is better than 6.16″，which achieves the high-precision simulation of the starry sky at infinity.

Star sensors are an important component of spacecraft attitude control systems, using stars as reference for attitude measurement to output their vector directions in star sensor coordinates, providing high-precision data information for spacecraft attitude control and astronomical navigation. With the rapid development of aerospace technology, higher requirements are put forward for the technology of star sensors. As an important equipment for calibration and testing on the ground, star simulators complement and are inseparable from the development of star sensors. Therefore, their accuracy needs to be correspondingly improved to meet the higher requirements of star sensors in ground calibration testing.

At present, the research on star simulators in China is developing towards high precision, large field of view, and lightweight, and the design of collimating optical systems is relatively mature. Currently, the exit pupil distance of the collimating optical system of star simulators is relatively short, but due to the deep entrance pupil of star sensors and the light shield outside the lens tube, the use space of the matching star simulators is limited, which requires the star simulator to have a large exit pupil distance, However, with the increase of the field of view, the diameter of the exit pupil of the collimating optical system with a long exit pupil distance increases, and the aberration also increases sharply accordingly.

This article designs a collimating optical system for a static star simulator with a long out of pupil distance to address this issue. It ensures that there is sufficient adjustable working distance between the star sensor and the star simulator to meet testing needs, and also ensures that the system has good imaging quality with a long out of pupil distance to achieve high-precision simulation of the infinitely distant star sky.

1. Principle and composition of static star simulator

Static star simulators, also known as calibrated star simulators, mainly simulate star maps in fixed sky regions, with high requirements for color temperature, magnitude, star point position, and star light emission accuracy. Due to the fixed star maps, if different sky region stars need to be simulated, the star point plate needs to be replaced, which is often used for performance testing of star sensors. The static star simulator mainly consists of a collimating optical system, a star point reticle, a filter, a light source, and an adjustment mechanism, as shown in Figure 1.

The principle is that a beam of light with uniform brightness is emitted from the light source, which is filtered and illuminated on the star point dividing plate. The beam passes through the transparent micropores on the star point plate to simulate the star point, and then passes through the collimating optical system to shoot out in parallel. The entire star map is projected and presented at the entrance pupil of the star sensor for observation and ground performance calibration testing. The light source is a star point dividing plate illumination, which can be controlled by a circuit to linearly adjust the current of the DC power supply to change its brightness to achieve simulation of different constant stars, etc; The function of the filter is to correct the light source spectrum to meet the technical specifications of the static star simulator; The star point dividing plate is placed on the focal plane of the collimating optical system, and several transparent micropores are engraved on it using laser direct writing technology; A collimating optical system is used to simulate the starlight of stars at infinity and generate a fixed celestial map.

The exit pupil distance of a star simulator refers to the distance from the vertex of the last lens of the collimating optical system to the intersection point of the image plane received by the star sensor and the optical axis. The entrance pupil position of the star sensor and the degree to which the star simulator is reliably close to the star sensor determine the exit pupil distance of the collimating optical system. To prevent the loss of light energy during the coupling process between the star simulator and the star sensor, resulting in insufficient utilization of light energy, the star simulator generally has an external exit pupil with a diameter slightly larger than the entrance pupil diameter of the star sensor. The two form a coaxial optical system and meet the principle of pupil connection, as shown in Figure 2.

2. Optical system design

The technical specifications of the collimating optical system of the star simulator are determined based on the requirements of the target star sensor, and the technical specifications of the static star simulator are shown in Table 1.

To meet the principle of pupil to pupil connection and avoid energy loss, the exit pupil diameter of the star simulator is set to 70 mm; To ensure that there is no collision between the star sensor and the star simulator during the calibration testing process, and to have sufficient adjustable working distance, it is required that the exit pupil distance of the star simulator be greater than 1000 mm; To ensure accurate and clear imaging positions of star points in the field of view of the system’s simulated star map when the pupil distance is extended, it is required that the designed collimating optical system have the characteristics of small distortion, small field curvature, high energy concentration, and apochromatic aberration.

According to the usage requirements of the star sensor to be tested and a series of calculation results, the main parameter indicators of the optical system of the star simulator are shown in Table 2.

(1) Optical System Design and Optimization

The system places the star point reticle on the focal plane of the collimating optical system to simulate infinite starlight. Therefore, the system adopts an inverted design method, where the diaphragm surface is set at a distance of 1000 mm from the vertex of the first lens of the system, with a diameter of 70 mm.

In the selection of the initial structure, a transmissive collimating optical system that meets the requirements of achromatic aberration, sufficiently small distortion, and external exit pupil should be selected. Finally, the Elver eyepiece should be selected as the initial structure of the collimating optical system of the long exit pupil distance static star simulator. The layout diagram is shown in Figure 3, with a biconvex single lens inserted between two sets of double glued lenses, The symmetrical structural design ensures that the entire system has very small distortion and small chromatic aberration, resulting in good image quality.

In the lens group, each lens bears a certain deflection angle. The system has severe asymmetry due to the front diaphragm and long exit pupil distance. In the optimization process, to offset the influence of aberration, the two double glued lenses in the initial structure are separated, allowing the optical system to have more degrees of freedom and adding more variables to the system optimization. Add a flat convex lens in front of the exit pupil, and the curvature of the flat convex lens can balance the negative power generated by the negative lens behind it. Using a combination of positive and negative lenses is beneficial for reducing the system’s aberration and balancing chromatic aberration, as well as increasing the exit pupil distance.

In the optimization process, the curvature and thickness of all lenses are used as variables to adjust the air spacing between the lenses. As shown in the schematic diagram of Figure 1, a star plate needs to be installed after the optical system, and a space of about 8-10 mm needs to be reserved for the mechanical structure. The distance from the center of the last lens to the image plane is controlled through the combination of TTHI operands and OPGT. Finally, by viewing the Seidel diagram of the system, It was found that the contribution values of the 8th, 9th, 10th, and 11th faces of the system to distortion were relatively large. The maximum distortion DIMX operands and the contribution value DIST operands of a certain face to distortion were used as constraints to continue iterative optimization. Due to the large distance from the exit pupil, the impact of distortion cannot be balanced by optimizing lens curvature, thickness, and adjusting air spacing. Therefore, a positive lens was introduced to correct the distortion.

After optimization, the system consists of seven lenses, which significantly improves image quality. The entire process achieves correction and balance of spherical aberration, field curvature, distortion, and vertical chromatic aberration of the long exit pupil distance collimating optical system.

(2) Optical System Tolerance Analysis

The optical system belongs to the precision design and processing part, and after design optimization, there will inevitably be mechanical errors in the lens processing process. During experimental testing, there will be installation and adjustment errors in the placement of lens components and instruments, as well as parameter errors in lens materials and other aspects. Tolerance analysis can systematically analyze the impact of slight disturbances or color differences on system performance, and introduce them into optical systems to analyze whether system performance meets design requirements. Therefore, it is necessary to conduct tolerance analysis on the optical system after design is completed.

The MTF average value is used as the evaluation index for the long exit pupil distance collimation optical system. The Q5 processing level is used for Monte Carlo tolerance analysis, and the MTF spatial frequency is set to 50 lp/mm. The system is subjected to 50 cycles of Monte Carlo analysis to obtain the variation of the MTF average value. Through tolerance analysis of the long exit pupil distance collimation optical system, the results show that the system has good stability and meets the existing actual processing level.

(3) Conclusion

To meet the ground calibration requirements of high-precision star sensors, a static star simulator collimation optical system with an exit pupil distance of 1000 mm was designed using Zemax software. After design optimization, the image quality was evaluated. The distortion within the full field of view 6 ° range of the system was less than 0.027 6%, and the imaging quality was good. After Monte Carlo tolerance analysis, it was shown that the system has good stability. By calculating the star position error of the static star simulator, the theoretical value of the star light emission accuracy of the collimating optical system is obtained. The results show that the star light emission accuracy of the long pupil distance static star simulator collimating optical system is better than 6.16 “, meeting the requirements of star sensor calibration testing for high-precision simulation of stars.