The direction of the development for the star tracker is to realize the small size, high-precision, large field of view, multi-parameter, and high reliability. Thus, color temperature, as the secondary gist of the attitude discrimination of the star tracker, has been added into the research. This article focused on the definition of the star associated with the color temperature, and mainly researched achieving a wide range of adjustable, stable and reliable color temperature light source. In order to achieve this goal, based on analyzing the color science, photometric and radiometric studies, we improved the method of calculating the color addition, and built the entire experiment platform based on TMS320F2812 DSC and integrating sphere. Experimental results show that: the color temperature from 2 600 K to 10000 K continuous variation can be achieved through this method. Under the same conditions (outside ambient temperature), the stability and consistency of color temperature had been validated. Moreover, it is pointed out that the most important reasons affecting the stability of the color temperature is the ambient temperature.
In the detection and calibration of star sensors, it is usually necessary to provide a simulated star in order to detect and calibrate the star sensor in the laboratory, thereby reducing the impact of spatial atmospheric changes. We refer to devices that simulate stars as star simulators. According to their different functions, star simulators can be divided into two categories: the first category is called calibration devices. These devices typically simulate a single or limited number of star point images, simulating their size, luminosity, spectral characteristics, color temperature, etc; The second type is called functional detection equipment, which typically simulates the actual position of stars in the actual sky and their sky distribution. The adjustable standard color temperature light source discussed in this article belongs to the first category. It uses star simulators as the application background to simulate the color temperature of stars, providing standard light sources that can be adjusted within a wide range of color temperatures for star simulators.
In general, a single star simulator consists of three parts: 1) a light source system; 2) Filtering, attenuation, and collimation optical systems; 3) Mechanical interface and installation bracket structure. Figure 1 shows the various components of a single star simulator and their relationships with each other. The light emitted by the light source passes through the optical system and forms a point light source. Star points with different brightness (representing different magnitudes) or color temperatures (representing different surface temperatures of stars) pass through a light tube and generate simulated infinite parallel light at the entrance of the connected star sensor optical system, thus achieving the simulation of starlight.
Eternal stars are nouns used to indicate different levels of brightness of stars. In 1830, British scholar Herschel discovered when studying the brightness of stars that first-class stars were about 100 times brighter than sixth class stars, so the illumination ratio of adjacent stars was 2.512 times. As the benchmark for determining the illuminance of each magnitude, the illuminance of zero magnitude stars is specified as 2.65 × 10-6 lx. Stars that are brighter than zero magnitude stars have negative magnitudes and are designated as -1, -2, -3, etc., while the Sun has a magnitude of -26.7; Stars that are darker than zero magnitude stars have a positive magnitude and are designated as: 1st, 2nd, 3rd, etc. If there is an m-class star and an n-class star, and n>m, Em is the illuminance of the m-class star and En is the illuminance of the n-class star. The illuminance ratio of the two stars is Em/En=(2.512) ^ (n – m). Therefore, the illuminance of zero magnitude stars can be used to obtain the illuminance of other stars.
Due to differences in age, mass, pressure, and chemical composition of stars, the surface temperature of stars varies greatly, and the spectra formed by the emitted light also vary. The Harvard Observatory conducted spectral studies on 500000 stars and classified the occurrence of spectral lines in the stellar spectrum. The results showed that they were related to color, including blue O-type, blue white B-type, white A-type, yellow white F-type, yellow G-type, orange K-type, red M-type, and other main types. In addition, there are three additional types: R, N, and S. There is a gradual transition between each type, and each spectral type can be divided into 10 subtypes, represented by numbers 0-9, such as O0, O1,…, O9. Table 1 shows the relationship between the spectral types of all day navigation stars, surface temperature, and maximum radiation wavelength, which is one of the important basis for designing the optical system of the star simulator.
Blackbody, also known as an absolute blackbody (also known as a complete radiator), refers to an ideal object that, under radiation, neither reflects nor transmits, but can completely absorb the radiation energy falling on it. Stars are not truly blackbodies, but their radiation can be approximated by blackbody radiation at a certain temperature within a relatively narrow range of visible and near-infrared wavelengths. The maximum radiation wavelength of a star（ λ P) Conforming to Venn’s displacement law with the surface temperature of stars (T): λ P × T=2898 µ m Å K. Due to the maximum radiation wavelength of solar radiation being 0.48 µ m, the surface temperature of the sun, T=6037.5 K, can be calculated, resulting in a yellow color.
Adjustable standard color temperature light sources require color temperatures of different gears to simulate the color temperatures of most stars from M-type to A-type. According to the definition of color temperature, if the color of light emitted by a light source is the same as the color of light emitted by a blackbody at a certain temperature, the absolute temperature value of the blackbody is called the color temperature of the light source. In other words, the temperature of the blackbody can be represented by the color of the light source. Due to the fact that stellar radiation can be approximated by blackbody radiation at a certain color temperature, the surface temperature of stars can be simulated by the color of the light source.
According to Glassman’s law of color mixing, in a mixed color composed of two components, if one component changes continuously, the appearance of the mixed color also changes continuously. If two components are complementary colors to each other and mixed in a certain proportion, they will produce white or gray. If mixed in other proportions, they will produce unsaturated colors with approximately significant color components; If any two non complementary colors are mixed, a middle color is generated, and the hue and saturation of the middle color vary with the hue and relative quantity of these two colors.
Based on the above principles, calculate the brightness coefficient of the excellent temperature from 2600 K to 10000 K, and use digital dimming method to adjust the light source to achieve adjustable standard color temperature light source. The basic working method of an adjustable standard color temperature light source is: the user inputs the desired color temperature from the input interface, and the processor calculates the corresponding tristimulus value based on the input color temperature value, generating the corresponding pulse square wave to control the light source driver to drive the tristimulus light source.
By utilizing the diffuse reflection characteristics of the integrating sphere to mix the three primary colors of light, the desired color temperature is generated. The color sensor collects the mixed light of three primary colors, which is filtered, amplified, and converted into A/D before being sent to the processor. The processor corrects the power parameters provided to the light source driver, thereby achieving closed-loop control of the color temperature stability of the light source [7-10], reducing color errors caused by various reasons.
The adjustable standard color temperature light source mainly includes two parts: the control part and the mixed light path part. The control part mainly includes: main control circuit, driving circuit, and feedback circuit; The mixed light path mainly uses an integrating sphere to mix the three primary colors. The main function of the main control circuit is to recognize the input color temperature value when a certain color temperature value is input; Calculate the tristimulus values and brightness coefficients of the three primary colors at a certain color temperature; Generate corresponding pulse width modulation signals based on the brightness coefficients of the three primary colors; Perform A/D conversion on the signal detected by the feedback circuit; Correct the pulse signal to reduce color error. Among them, the main control chip selects tms320f2812 as the core of control operations. The main function of the driving circuit is to respond to the input of the control circuit control signal, amplify its power, and use digital dimming to drive the light source. Here, we choose 3 W full color LED as the luminous light source. The main function of the feedback circuit is to monitor the luminescence of the mixed light source in the integrating sphere, real-time monitor the tristimulus signal of the mixed light, sample and output the monitoring signal, filter and amplify the signal, and provide it to the control circuit A/D converter for use. The color sensor uses Agilent’s color sensing unit. The main function of the mixed light path is to use an integrating sphere to mix the three primary colors of light, ensuring that the mixed light can be uniform and facilitating the calibration of the light source using a colorimeter. The integrating sphere is customized according to the selected colorimeter, the installation device of the light source, and the color sensor.
Figure 3 shows the state diagram of the machine control software on the colorimeter continuously sampling 2600 K. The left area in the figure represents the chromaticity coordinates of the colorimeter for the mixed light in the integrating sphere
The variation trend of (x, y), (u, v), color temperature, and vertical illumination sampled continuously for 5 hours. We can see that the variation amplitude of each parameter is almost on a straight line. The area on the right side of the graph is the chromaticity map, where the red intersection represents the position of the mixed light in the integrating sphere in the chromaticity map, and the black intersection represents the position of the standard white light. From the position of the red intersection, we can see that the chromaticity coordinates of the mixed light are already very close to the color coordinate point of 2600 K on the blackbody trajectory. Multiple measurements were taken at different times for color temperature ranging from 2600 to 10 000K, divided into 8 groups and measured 10 times each at different times. The above experimental data was processed according to the theory of random error. Due to different environmental conditions at different times, the measurement conditions are not constant. Therefore, the above experimental data is processed according to the unequal precision measurement theory to obtain some of the experimental data processing results shown in Table 2.
By sampling 2600 K to 10000 K ten times during different time periods on March 19, 20, and 21, 2010, we can know that the color temperature changes slightly during a certain time period of the day, but from morning to afternoon and then to evening (the temperature gradually increases and then decreases), the color temperature of the light source changes to a certain extent with changes in external temperature. In areas with low color temperature, the degree of influence from environmental temperature is greater, High color temperature areas are less affected by environmental temperature. By conducting long-term sampling on three color temperature values of 2600 K, 5200 K, and 10000 K at different dates and time periods, a specific color temperature was measured at the same time period on different dates with similar temperatures. The change in color temperature was relatively small, but if the color temperature was compared at different time periods (with different temperatures) on different dates, the color temperature still increased with the increase of environmental temperature.
This article takes star simulators as the application background, with the main goal of simulating the color temperature of stellar bodies, and designs and implements an adjustable standard color temperature light source for star simulators. Through experimental analysis, we can draw the following conclusion: according to the method in the article, continuous adjustable color temperature from 2600 to 10000 K can be achieved; It can ensure the stability and consistency of color temperature under the same external environmental temperature conditions; Environmental temperature is an important factor affecting color temperature stability; High color temperature areas are less affected by environmental temperature compared to low color temperature areas.
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