Introduction to the Theory of Star Simulator

This chapter first introduces the working principle of a large field of view multi star simulator and the relevant theories of star simulators, introduces constant stars and spectral types, elaborates on the theory of color temperature, and proposes the technical specifications of a large field of view multi star simulator.

1. Constant stars and their spectral types

Spherical or quasi spherical celestial bodies that can emit light themselves are collectively referred to as stars. Usually, on moonless nights, more than 3000 stars can be observed, but at this moment, only half of the celestial sphere is visible. Therefore, in a day, people should be able to see about 6000 stars. If the environment is ideal on that day, ten thousand or even more stars may be observed. In ancient times, people believed that the distance between stars remained constant, so they named them stars. With the rapid development of science and technology, although people continue to use the title of “star”, it is already understood that every star is a large sphere that emits light and heat like the sun.

In order to represent the brightness of different stars, in photometry, the radiance of stars received outside the Earth’s atmosphere is used to measure the brightness and darkness of stars. The larger the magnitude value, the darker the brightness of the star, and vice versa. British scholars have found that there is a brightness difference of about 100 times between first-class and sixth-class stars, indicating an illuminance ratio of 2.512 for adjacent stars. So, with an illumination of 2.65 on a zero magnitude star × 10 ^ -6 lx to determine the illuminance of each magnitude. Those brighter than zero magnitude stars are defined as negative magnitudes, while those darker than zero magnitude stars are defined as positive magnitudes.

The magnitudes measured by receivers with different spectral response characteristics are different, so there are different classifications for constellations. There are several common types:

(1) Visual magnitude: The magnitude measured by a receiver with spectral characteristics similar to vision, which is the most commonly used type of magnitude, represented by Mv.

(2) Absolute magnitude: Observing the brightness value of a star at the same distance. Placing a star at a distance of 32.62 light-years from Earth yields an absolute magnitude value, which allows for the comparison of the actual luminous abilities of different celestial bodies.

(3) Radiant magnitude: Using radiometers, thermocouples, etc. that have no spectral selectivity as receivers, the star’s thermal radiation energy is detected to determine the star’s equivalent.

(4) Hot magnitude: The magnitude measured by a full spectrum receiver, representing the total radiation of a star reaching the Earth’s atmosphere. The determination of thermal magnitude is not related to the spectral response rate of the receiver, so detector devices with different spectral response rates can be used to eliminate differences in thermal magnitude to obtain the required magnitude.

(5) Instrument magnitude: The spectral response characteristics of the receiver determine the instrument magnitude.

The value of instrument magnitude (such as star sensors) depends on the spectral response of the detector and the spectral distribution of the stars. Usually, the instrument magnitude is analyzed and calculated based on the apparent magnitude. For most stars, their instrument (CCD) magnitude is almost the same as the apparent magnitude. In practical work, CCD is usually used to receive and determine the magnitude that the star simulator can achieve by observing the brightness corresponding to its response curve. Therefore, for the convenience of experimental research, the brightness of the star simulator is calculated based on the apparent magnitude.

Star simulators not only need to simulate the magnitude of stellar light, but also sometimes their spectral characteristics. The radiation spectrum of a star is related to its surface temperature, which in turn varies with the age, mass, pressure, and chemical composition of the star. American scholars conducted spectral studies on nearly 500000 stars in the late 19th century, discovering that the spectra of stars were related to their colors, and proposed a spectral classification system. Divide the stellar spectrum into spectral types such as M, K, G, F, A, B, O, and add three additional types. There is a transition between various types, and each spectral type can be subdivided into 10 subtypes, represented by a subscript of 0-9. Table 2.1 shows the spectral types of stars.

2. About Blackbody and Color Temperature

Blackbody is a substance that neither reflects nor transmits at any temperature, but absorbs all the energy of any wavelength radiating onto its surface, that is, the spectral absorption rate of blackbody α B=1, strictly speaking, blackbodies do not exist, nor do stars. However, in the visible and near-infrared bands, their radiation can be approximated as blackbody radiation at a certain temperature.

When the color of the light emitted by the light source is the same as the color radiated by the blackbody at a certain temperature, the temperature of the blackbody is called the color temperature Tc of the light source, represented by an absolute temperature scale. As shown in Figure 2.2, the spectra of M-type, G-type, and A-type stars at color temperatures of 3000K, 5800K, and 10000K are presented.

The blackbody radiation energy curves of stars under different color temperatures are shown in Figure 2.3. From Figure 2.3, it can be seen that the stronger the energy of blackbody radiation in the ultraviolet band, the greater the color temperature, and there is a radiation peak at each color temperature. The blackbody radiation curve can be used to calculate the total radiation energy of blackbody at a specific color temperature within any band range.

3. Overall technical indicators of the star simulator

1) Simulate the relative positions and magnitudes of stars within the range of ± 10 ° declination and ± 20 ° declination, centered around the HIP3821 star. The required simulated star positions and magnitudes are shown in Appendix A. The lowest magnitude in Appendix A is about 7Mv, the minimum angle between stars is about 2.5 °, the number of stars is 65, and the distribution field of view is 20 ° × 40 °;

2) The simulation accuracy of the positions of all star points in the simulated sky area relative to the HIP3821 star is not greater than 2.5 “in both the right ascension and declination directions;

3) Using the data in Appendix A as the comparison benchmark, the magnitude illumination error shall not exceed 5%; Each simulated star is based on its own nominal magnitude, which is adjustable within the range of ± 1.5Mv, with an adjustment interval of no more than 0.05Mv;

4) The simulated star uses a white light source, with a spectral range of 450nm~750nm and a central wavelength of 550nm ± 50nm;

5) The parallelism of simulated stars is better than 2 “;

6) Under the specified environmental conditions, continuously work for 4 hours, and the illumination change of the simulated star shall not exceed 10%;

7) The design ensures that the star point angle is not greater than 15 “.