Multi-color temperature simulation for star simulator

Aiming at the simulation requirement for multiple color temperatures of a star simulator，a simulation method of multiple color temperatures for a star simulator is put forward． Then，the influence of data and bandwidth data of different wave bands on color temperatures is analyzed with a combination of a broadband spectroscopic light source lamp array which is consisted of xenon lamps and halogen tungsten lamps． On the basis of polynomial fitting method，feedback control of color temperature simulation is realized by utilizing genetic algorithm． Therefore，spectrum simulation of 3900 K，4800 K and 6500 K color temperature within the spectral region between 350 nm and 900 nm is realized，which satisfies the simulation requirement for multiple color temperatures of a star simulator.

Star sensors mainly use charge coupled devices (CCD) or complementary metal oxide semiconductors (CMOS) to receive the light emitted by stars through optical systems, and process the data into observation star maps and navigation star maps stored in the database for comparison to obtain the position and attitude of spacecraft in the starry sky. A crucial aspect in star sensor technology is the reception of light emitted by stars, so the calibration of star sensors is particularly important. The commonly used calibration methods can be divided into in orbit calibration and ground calibration. Although in orbit calibration has the same accuracy as the real space environment, it is extremely expensive, and compared to ground calibration equipment, in orbit calibration equipment has poor maintainability. Therefore, it is imperative to develop high-precision and high-performance ground calibration equipment.

Due to the varying temperature and radiation spectrum distribution of stars in the universe, as well as the varying response intervals and curves of receivers for different types of star sensors, it is necessary to match the color temperature of the star sensor calibration equipment with the color temperature of the detected star, thereby reducing the calibration error caused by color temperature mismatch. In response to the above situation, domestic and foreign researchers have conducted research on color temperature simulation.

Although the LED light sources commonly used in color temperature simulation methods for LED hybrid light sources have a series of advantages such as small size, long lifespan, high luminous efficiency, and stable luminous intensity, variable current driven LEDs can cause changes in the full width at half peak and drift in peak wavelength, and some band LEDs are difficult to match, reducing the efficiency and accuracy of spectral matching algorithms. Therefore, in response to the above situation, based on the study of the spectra of stars in the universe, a color temperature simulation lighting system mixed with xenon and halogen tungsten lamps was designed to achieve the calibration of the wide spectrum and high accuracy spectral detection ability of star sensors, solve the impact of spectral mismatch on the accuracy of star sensor optical signal calibration during ground calibration experiments, and improve the calibration accuracy of star sensors.

1. Design of color temperature simulation lighting system

The multi color temperature multi star simulator mainly consists of a collimating optical system, a star map display system, a color temperature simulation lighting system, and a multi-dimensional optical adjustment frame. The main components of the multi color temperature multi star simulator are shown in Figure 1.

Fig.1 Composition of multi color temperature star simulator

The collimating optical system is used to simulate the emission characteristics of stars at infinity, the star map display system is used to provide the star position information required by the star sensor, the color temperature simulation lighting system is used to provide the star color temperature information required by the star sensor, and the multi-dimensional optical adjustment frame is used to adjust the position relationship between the star simulator and the star sensor.

The requirement for spectral matching in a multi color temperature star simulator is to simulate the spectra of three typical color temperatures of 3900 K, 4800 K, and 6500 K within the spectral range of 350-900 nm, with a simulation accuracy of better than 10%.

The color temperature simulation lighting system consists of a wide spectral light source array, a color temperature simulation and control module, an integrating sphere, and a spectral radiometer. The wide spectral light source array is the core component of the color temperature simulation lighting system. The wide spectral light source array provides light radiation flux for the entire multicolor temperature star simulator; Simultaneously provide a spectral distribution that is close to the simulated star map. Due to the color temperature simulation lighting system covering a wavelength range of 360~900 nm, halogen tungsten lamps have strong luminous intensity, good stability, and relatively long service life within this wavelength range. However, halogen tungsten lamps have relatively low energy in the short wave band and cannot meet the requirements when used alone. The spectral distribution curve is shown in Figure 2; The optical and electrical parameters of xenon lamps have good consistency, and the spectral energy distribution remains almost unchanged during their lifespan. The working state is less affected by changes in external conditions, and the radiation spectral energy distribution is similar to that of sunlight. However, xenon lamps are unstable around 700-820 nm and cannot meet the requirements when used alone.

2. Research on Color Temperature Simulation and Control Technology

In order to achieve the requirements of color temperature simulation, it is necessary to reasonably divide the spectral range of the wide spectral light source lamp array light source, study the control method of small band light intensity, and then achieve the requirements of multi color temperature simulation for the star simulator.

Due to the different effects of spectral data changes in different bands on color temperature calculation, more precise control is needed for positions with larger weights, and the accuracy requirements for positions with smaller weights are relatively low. In order to better divide the spectral intervals corresponding to each group of lamps, the following simulation simulates the impact of different band data and bandwidth changes on color temperature. The ideal blackbody radiation data is changed at four bandwidths of 1 nm, 5 nm, 10 nm, and 20 nm. Except for the 1 nm resolution data, all other bandwidths are linearly interpolated to 1 nm resolution before color temperature calculation. Four scenarios of 1%, 2%, 5%, and 10% increase in spectral energy change resolution are considered at once.

Take the ideal blackbody radiation with a color temperature of 6500 K as an example for detailed analysis. Firstly, the impact of different spectral energy increases of 1% on the color coordinates of 6500 K ideal blackbody radiance under four different bandwidths is analyzed. The results show that the increase in bandwidth also increases the impact on color temperature, which is basically linear, indicating that bandwidth is the accumulation of the effects of a single wavelength.

The light emitted by the wide spectral light source array is filtered by a filter group, and then adjusted by an electrically controlled variable aperture group to adjust its luminous flux. After passing through the integrating sphere, the spectral curve is input into the collimation optical system of the star simulator. Due to the uncertainty of the transmission coefficient error of the variable aperture, a genetic algorithm is introduced as the color temperature matching algorithm. Based on the least squares solution, set the solution range for the transmission coefficient of the variable aperture in each small spectral interval. The solving steps based on genetic algorithm are:

(1) Using the least squares method to solve the non negative least squares solution of the color temperature matching transmittance coefficient of the multi color temperature multi star simulator, as the initial population of the genetic algorithm;

(2) Determine the value range of the transmittance coefficient based on the non negative least squares solution;

(3) Taking the sum of squares of the least squares residuals as the objective, a moderate function is established. The genetic algorithm selects a set of solutions based on the magnitude of the moderate function value. The larger the moderate function, the greater the possibility of selecting solutions with larger objective values, and the better the quality of the corresponding solutions;

(4) On the basis of the moderate function, repeatedly perform cross combination and mutation operations on the population, and finally obtain the optimal combination of transmission coefficients.

3. Multicolor Temperature Star Simulator Experiment

The spectral radiometer needs to be calibrated before using a multi color temperature simulator to detect spectral distribution by placing it inside an integrating sphere. In order to verify whether the simulated spectral curve of the star simulator meets the accuracy requirements, the spectral curve of the multi color temperature multi star simulator simulated at a color temperature of 3900 K is drawn to meet the requirement of 10% curve simulation accuracy.

In order to further verify the simulation of spectra by multi color temperature and multi star simulators, according to the commonly used evaluation method of relative area method, which describes the degree of deviation of the spectral curve, the standard blackbody color temperature curve is surrounded by an area of S1 and the minimum deviation of the spectral curve of the star simulator from the standard blackbody color temperature curve is surrounded by an area of S2. Therefore, the simulation error is Δ =  S2/S1.

This article designs a color temperature simulation lighting system based on the requirements of star simulators for multi color temperature simulation and the working principle of star simulators, with a wide spectrum light source array composed of xenon lamps and halogen tungsten lamps as the core. It analyzes the impact of different band data and bandwidth data changes on color temperature, and solves polynomial solutions for each band of the wide spectrum light source array. Then, feedback control of color temperature simulation is achieved through genetic algorithm, Realized spectral simulation of 3900 K, 4800 K, and 6500 K color temperatures in the spectral range of 350-900 nm.