Design and verification of optical system on very high-precision and miniature star sensor

  Objective  Very high-precision and miniature star sensor is applied to LEO or MEO satellites for resource exploration and commercial uses. It has characteristics of high accuracy, light weight, small volume, high reliability and short production cycle. To fulfill the design objectives according to the above mentioned characteristics, technical indicators requirements should be researched in the development phase. The existing literatures regarding the optical system design of star sensors determine the effective aperture commonly based on noise and the observed stars, and estimate working field through magnitude and star number. However, the information of color temperature and star database is lacked in the analysis of these literatures, which causes the deviation of analysis result and engineering practice. Also, the verification is less pointing at the encircled energy of diffused light spot and working band. The paper aims to study the key optical specifications of very high-precision and miniature star sensors, and to verify the indicators based on the characteristics of optical material and star point extraction algorithm.

  Methods  Taking measurement accuracy of the star sensor as breakthrough point, the paper demonstrates the verification of technical indicators of the optical system. The color temperature information of stars is presented based on the revised HipJ2000 star catalogue (Tab.1). Combining the manual of CDGM, the impacts on the absorptivity and refractivity of material in different wavelengths are analyzed and the operating band for light and small optics is confirmed accordingly. Based on the mathematical model of diffused light spot, the relationship between the accuracy and the radius of Gaussian beam is analyzed. And based on the light design features, the radius of Gaussian beam for centroid extraction of high accuracy is obtained (Fig.1-2). In view of the theoretical analysis of blackbody radiation law (Fig.3) and the given detector, the sensitivity of the system is analyzed and the aperture for extracting 6.5 magnitude star under different integration time is determined (Fig.4). According to the relationship between color temperature and star magnitude in Hipparcos catalogue, the working field of view of the star sensor is fixed by analyzing Monte Carlo method (Fig.5). The design indicators of the optical system for very high-precision and miniature star sensor is determined (Tab.2).

  Results and Discussions   The design of optical system is based on the requirement of design parameters in Tab.2. The optical lens is composed of six optics (Fig.6). To adapting to spacial environment, the first optic uses SiO₂ material, and the other optics uses ZF6, HZPK5 material. To further enhance the anti-radiation performance of the optical system, ZF6 material could be replaced by ZF506 material. The RMS deviation of diffused light spot is less than one pixel in full field of view, and the diffused light spot is close to circle with the biggest 11.281 μm at the edge of the field of view (Fig.7). The maximum centroid distortion is 1 μm (Fig.8). The geometric encircled energy under 0.9 field of view and 3 pixel×3 pixel is more than 90% (Fig.9). The lateral color of full field of view is less than 1.5 μm (Fig.10). Athermalization analysis is executed on the optical lens, and the sampling point is in steady state under temperature of −40 ℃ to 60 ℃. The variation of dimension of diffused light spot is less than 1 μm. Due to the relationship between RMS dimension and encircled energy, there is almost no change of encircled energy within this temperature range (Fig.11). Centroid shift of the diffused light spot is less than 0.05 μm (Fig.12). All design results conform with the standard in Tab.2. In the last part of the paper, the accuracy and reliability of the optical system is verified through calibration, out-field stargazing and anti-radiation test. According to the data calibration, by using the optical system in this paper, the calibration accuracy of 0.6″ (Fig.15) and measurement accuracy of 1.5″(3 \sigma )(Fig.17), could be realized. The limit detection of the star sensor is 6.51 magnitude star (Fig.18). After cumulative radiation of 60 krad (Si), 6.01 magnitude star could be detected (Fig.19-20).

  Conclusions  The measured data indicates that the analysis method of system indicators in this paper is effective. The optical system could be designed to extract stellar attitude of high accuracy. The analysis scheme of technical specifications of the optical mechanical system mentioned in this paper, the design method of optical system, as well as the measured data could be used as a reference for other photoelectric sensor designs.