A Light Source System of Multi-star Simulator with Adjustable Background and Controllable Magnitude

A light source of multi-star simulator capable of background adjustment and magnitude control has been designed. Two integrating spheres are employed as the star-point light source and the background light source respectively. A beam splitter prism has been designed to serve as the beam combiner for the star-point and the background light sources, and a mathematical model has been constructed respectively to compute the light ﬂux of the two integrating spheres. A magnitude testing system and a background testing system have been created using low-light illuminometer, luminance meter, and testing instruments to measure the star-point magnitude and the background luminance of the multi-star simulator. The test results suggest that the star-point magnitude is adjustable from 0 to +5 m v , with a simulation precision superior to ± 0.026 m v . The maximum background luminance is 3.8 × 10 5 cd · m − 2 , and the minimum background luminance is6.4 × 10 − 2 cd · m − 2 . The designed light source system can meet the requirements for simulating the stellar map with a sky background.


Introduction
A star sensor is an important component for spacecraft attitude control.It relies on its optical system to capture and send the image of stars in different sky regions to the CCD receiver.Stellar images corresponding to various moments are generated by different stellar map extraction and recognition algorithm, and are then compared with the on-board pre-stored navigation stellar map for characteristics matching so that the spacecraft attitude can be determined for that particular moment [1−3] .For this reason, a lot of observation is needed to validate the star sensor system once it has been designed and built, particularly with the software module, which needs continual testing, calibration, and improvement to better the dynamic performance of the star sensor system as a whole.Observation of the true starry sky is never-theless restrained by natural condition.Hence, a star simulator is desirable that is capable of simulating the true starry sky so that it is possible to be completed in the laboratory linked ground closed-loop star attitude testing on the star sensor system [4−7] .
The star simulator, as an important component in ground closed-loop linked testing of star sensors, is either a static or a dynamic simulator depending on the simulating method of the stellar image [8−10] .A static star simulator is more compact and also lighter due to the absence of complicated control computer and display instruments, so it is more convenient to use.A traditional static star simulator incorporates a star-point reticule as the stellar map display element.
After imaging by its collimation optical system, the simulator produces parallel multi-star light.Owing to the fabrication process limitation of star-point reticules, the existing static star simulator cannot simulate the background in the star image, which leading to lack of background simulation information.
In order to simulate the star sensor on-orbit working environment, a light source system of multi-star simulator with adjustable background and controllable magnitude is designed.A beam splitter prism is employed to superimpose the sky background on the stellar image, and an electrical control system is used to control separately the simulated magnitude of the star-points and the simulated range of the background luminance.This makes it possible to simulate the daytime or the nighttime sky to be observed by the star sensor in the laboratory, so that the testing and calibration precision of the star sensor software may be enhanced and the dynamic performance of the sensor will be bettered.

System Composition
The light source system of multi-star simulator with adjustable background and controllable magnitude, as one of the important components in a multi-star simulator, has the main function to provide the light source for the star-point reticule and the background reticule in order to support the collimation optical system and the beam splitting prism.The working principle diagram of a multi-star simulator is shown in Figure 1.
To meet the ground calibration requirements of navigation sensors, the star-point magnitude on the emergence plane of the optical system of a multi-star simulator have a simulation range from 0 to +5 m v , with a simulation precision better than ±0.3 m v and a uniformity better than 5%, and the magnitude and the luminance will be continuously adjustable ( Here, D 1 is the opening diameter of integrating sphere I. D 2 is the aperture of the optical system.By calculating, the light flux of integrating sphere I is found to be 1026 lm, so a 30 W halogen tungsten lamp is chosen.Because of extra require-ment for color temperature simulation, a 30 W xenon lamp is used along with the halogen tungsten lamp to build a composite light source.

Background Light Source
According to astronomy handbooks and technical literatures, a clear daytime sky has a luminance of ( Here, L emerg is the luminance of integrating sphere II on the emergence plane in the optical system; α is the

Test Validation
To test the star magnitude, background and reduce the test error in actual test results, all test results are averaged.

Magnitude Test System and Test Results
The magnitude test system, consisting of a low-light illuminometer and star-point test instruments, measures the star-points on the emergence plane of the optical system, as shown in Figure 5.
The luminance and proportion of the xenon and the halogen tungsten lamps are adjusted by use of the star-point light source controller when simulating stars with appropriate magnitude.The low-light illuminometer monitors the current luminance in real time, which are then compared with the theoretical magnitude value to obtain the simulation errors.The above parameters are presented in Table 1.
The measurement results indicate that the magnitude light source satisfies the requirements for ground calibration of navigation sensors and has a simulation precision superior to ±0.026 m v .

Background Test System and Test Results
The background test system, consisting of a luminance meter and background test instruments, measures the background luminance and uniformity on the emergence plane of the optical system, as shown   2.
The maximum luminance value in the effective working zone is taken as the current luminance simu-  .
The measurement results demonstrate that the background light source is capable of simulating a clear daytime sky since it produces a luminance up to 3.8×10 5 cd•m −2 , with a luminance uniformity better than 2.78%.It is able to meet the requirements for ground calibration of navigation sensors.

Conclusion
In consideration of the requirements for stellar map simulation in the sky background, a light source system of multi-star simulator capable of background adjustment and magnitude control is designed.Firstly, the composition and working principle of the light source are described, and two integrating spheres are employed to construct the star-point light source and the background light source respectively.Secondly, a beam splitting prism is designed to materialize the superimposition of star-points on the background ima- Fig. 1 System principle of the multi-star simulator

Fig. 3
Fig. 3 Schematic diagram of star-point light source transmission

φ 2
is the light flux at the star-point reticule, and star-points are treated as elementary light pipes without energy loss.φ 2 is the light flux of the optical system.Ω 2 is the solid angle subtended by the clear aperture relative to the star-point, Ω 2 is the solid angle of the exiting light of the star-point, τ split is the transmissibility of the splitting prism, and τ opt is the transmissibility of the optical system.

3 × 10 5 2 ap 4 2π( 1 −
cd•m −2 .From the composition and working principle of the described multi-star simulator, an operational model of the background light source is constructed.It is different from the star-point light source model mainly in the opening area of the reticule, i.e., the background reticule has an effective working surface of 53 mm in diameter.Energy loss occurs likewise in the transmission from the object plane to the image plane, and the major loss occurring in the collimation optical system, as shown in Figure 4. Considering the background luminance required by the emergence plane of the optical system, that is 3×10 5 cd•m −2 for a clear sky.With the design results of the optical system, a mathematical model represented by Eq. (2) is built to evaluate the light flux φ emerg of the background light source, i.e., integrating sphere II on the emergence plane in the optical system, the incident light flux φ inc of the background reticule, and the light flux φ int of integrating sphere II.⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ φ emerg = L emerg πD cos α), φ inc = S 2π 0 dϕS θ1 0 L sin θ cos θdθds, φ int = 2πL bg ds τ split .

Fig. 4 4 ;L
Fig. 4 Schematic diagram of background light source transmission

Fig. 5
Fig. 5 Test system of magnitude 5 cd•m −2 minimum luminance 6.4×10 −2 cd•m −2 lation quantity.33 characteristic points arranged in arrays are taken and measured using a luminance meter.The measurement results are illustrated in Figure 7.The effective working zone is calculated for its luminance uniformity using Eq.(3)

Fig. 7
Fig. 7 Uniformity test data for background