# Design of Parabolic Off-Axis Reflector Optical System for Large Aperture Single Star Simulators
## 2 Principle and System Parameters
### Analysis of System Indexes and Determination of Main Parameters  
The operating spectral range of the optical system of the star sensitizer is jointly determined by the spectral range of the star to be detected and the spectral response range of the CCD [17]. Due to the long distance of the star, the wavelength of the light emitted  
Figure 1: Structure of the large caliber single star simulator system. is generally concentrated between 400 and 600 nm. Normally, the spectral range of the star sensitizer should cover the band of stellar light to ensure that the star sensitizer can effectively detect the light signal of the star, so the spectral range of the optical system of the star sensitizer is selected in the band of 450-850 nm [18]. Specifically for the single star simulator optical system designed in this paper, it is determined that its operating band is 450-850 nm, and the center wavelength is 632.8 nm. According to the principle of optical pupil articulation, the exit pupil of the star simulator optical system should coincide with the entry pupil of the star sensitizer optical system. If the exit pupil diameter of the star simulator optical system is smaller than the entry pupil diameter of the star sensitizer optical system, it will lead to energy loss [19]. Therefore, to minimize the energy loss, the aperture of the star simulator should be larger than the aperture of the star sensitizer. The aperture size of the star sensitizer needs to match the detection sensitivity of the selected sensor, and in general, increasing the aperture helps to increase the limiting magnitude of detection [20]. The aperture size of the optical system of a star sensor capable of detecting 15 magnitudes is 250 mm [21], and the aperture of the optical system needs to be larger if the star sensor is to detect higher magnitudes. To realize the ground simulation and test work of the star sensor with higher detection capability, combined with the development of single star simulators, this paper will design a single star simulator optical system with a larger aperture. Therefore, the aperture of the optical system designed in this paper is selected as 500 mm. The focal length of the optical system is calculated by Equation (1):  
\[F=\frac{f^{\prime}}{D} \tag{1}\]  
where \(F\) for the optical system F-number, \(D\) for the optical system aperture, \(f^{\prime}\) for the optical system focal length. The F-number determines the degree of difficulty of the optical system design [22]; after comprehensive consideration, the F-number is determined as 10. The aperture is selected as 500 mm by calculating the focal length of 5000 mm. According to the actual working requirements, this optical system's smaller field of view can meet the use requirements. To facilitate the installation and commissioning, the diameter of the simulated star point is selected as \(\varphi\)200 \(\upmu\)m, the diameter of the star point hole is selected as \(\varphi\)200 \(\upmu\)m, and the field of view of the optical system is calculated to be 0.01\({}^{\circ}\) by Equation (2) to meet the requirements. \[\theta=2\text{arctan}\left(\frac{d/2}{f^{\prime}}\right) \tag{2}\]  
From the Rayleigh criterion, when the maximum wave aberration in the optical system is less than or equal to \(1/4\lambda\), it can be considered that the imaging quality of the optical system reaches the ideal level [16]. Therefore, the smaller the wave aberration of the optical system is, the better the imaging quality of the optical system is. The better the imaging quality of the optical system of the single star simulator, the closer the simulated star point is to the real star. The test and calibration of the star sensitizer are more accurate. Combined with the current development of single star simulators, the optical system designed in this paper is required to have a wave aberration of less than \(1/25\lambda\).