Earth-moon space optical observation target apparent magnitude calculation method

Abstract

The invention discloses an earth-moon space optical observation target apparent magnitude calculation method, and solves the problem of how to improve the earth-moon space target observation apparent magnitude calculation accuracy. Belongs to the field of apparent magnitude calculation. Comprising the following steps: simulating target characteristics by using a Lambert sphere with mirror reflection and diffuse reflection at the same time, constructing a target apparent magnitude model based on the relationship between irradiance and apparent magnitude, and calculating the target apparent magnitude according to the irradiance of direct solar radiation to the target, the irradiance of earth reflection to the target and the irradiance of moonlight to the target. Respectively obtaining a target first irradiance when sunlight is used as a light source, a target second irradiance when earth reflection light is used as a light source and a target third irradiance when moonlight is used as a light source; summing the target first irradiance, the target second irradiance and the target third irradiance to obtain the irradiance of the target reflected light received by the sensor, and obtaining the magnitude of the earth-moon space optical observation target based on a target magnitude model; according to the invention, the accuracy of earth-moon space target observation brightness estimation is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of apparent magnitude calculation, and relates to a method for calculating the apparent magnitude of an optical observation target in Earth-Moon space. Background Art

[0002] With the continuous improvement of space technology capabilities, countries are competing to focus their space development on the cislunar space.

[0003] Space situational awareness can be defined as "the identification, characterization, and understanding of any factors related to the space domain, whether passive or active." Its significance lies in maintaining the safe operation of spacecraft on orbit, providing early warning of potential collisions, and detecting, identifying, and cataloging unknown spacecraft.

[0004] With increasing human activity in cis-lunar space, the need for optical observation capabilities in cis-lunar space is becoming increasingly urgent. Current detection capabilities are unable to cover the vast expanse of cis-lunar space. Currently, situational awareness equipment is primarily used by spacecraft in low-, medium-, and geostationary orbits. However, given the distant Moon and the vast expanse of cis-lunar space, relying solely on ground-based observation equipment will be insufficient to meet the growing demand for situational awareness in cis-lunar space. Detecting targets in cis-lunar space presents challenges such as a large observation volume, a short observation arc, high error sensitivity, and slow orbit determination convergence. Deploying space-based observation platforms to patrol cis-lunar space can effectively increase the observation volume and arc length, thereby enhancing situational awareness capabilities in cis-lunar space.

[0005] To evaluate observational performance, the most common method is to calculate the apparent magnitude using sunlight. For example, the method used in the application with the following number: 202011292546.0, publication number: CN112417670A, and invention title: A GEO target photometric characteristic calculation model considering the sailboard offset effect. The apparent magnitude calculation method only considers the solar irradiance on the target. This is feasible for GEO targets, but targets in cislunar space are closer to the moon, so calculating the apparent magnitude using only the sun as the light source is still not accurate enough. Furthermore, by only calculating the solar irradiance on the target, it is impossible to determine the contributions of the moon and earth to the irradiance of the target. Summary of the Invention

[0006] In order to solve the technical problem of how to improve the accuracy of calculating the apparent magnitude of targets observed in Earth-Moon space, the present invention takes into account the conditions of sunlight, moonlight, and earth reflection, and proposes a method for calculating the apparent magnitude of targets for optical observation in Earth-Moon space. The moon and the earth are also included in the scope of light source calculation, that is, the contribution of sunlight, moonlight, and earth reflection to the irradiance of the target is calculated at the same time, and a more accurate target apparent magnitude calculation result is obtained. This solves the problem that the target apparent magnitude cannot be accurately obtained without considering the influence of moonlight and earth reflection, and the target apparent magnitude cannot be calculated in the absence of sunlight. Through the optimized scheme, the contribution rate of moonlight and earth reflection to the target brightness is effectively evaluated, the influence of moonlight and earth reflection on space-based optical observation in Earth-Moon space is effectively determined, and the accuracy of brightness estimation of target observation in Earth-Moon space is improved.

[0007] The purpose of the present invention is specifically achieved through the following technical solutions:

[0008] The present invention discloses a method for calculating the apparent magnitude of an optical observation target in Earth-Moon space, comprising:

[0009] Step 1: Integrate the solar irradiance in the visible light band to obtain the irradiance of the solar visible light reaching the earth; the irradiance of the solar visible light reaching the earth is used as the irradiance of the solar direct light reaching the target;

[0010] Step 2: Simplify the earth into a diffuse reflecting Lambertian sphere with a completely diffuse reflecting surface, and obtain the irradiance of the light reflected from the earth reaching the target through the Lambertian body reflection law;

[0011] Step 3: Integrate the irradiance of the moon's reflected light reaching the target in the visible light band to obtain the irradiance of the moonlight reaching the target;

[0012] Step 4: Use a Lambertian sphere with both specular and diffuse reflection to simulate target characteristics, and construct a target magnitude model based on the relationship between irradiance and magnitude.

[0013] Step 5: Based on the target apparent magnitude model, the first irradiance of the target when sunlight is the light source is obtained by the irradiance of direct sunlight reaching the target, the second irradiance of the target when earth reflected light is the light source is obtained by the irradiance of earth reflected light reaching the target, and the third irradiance of the target when moonlight is the light source is obtained by the irradiance of moonlight reaching the target;

[0014] Step six, summing the first target irradiance, the second target irradiance, and the third target irradiance to obtain the irradiance of the target reflected light received by the sensor. Based on the target apparent magnitude model, the apparent magnitude of the target in the Earth-Moon space optical observation is obtained from the irradiance of the target reflected light received by the sensor.

[0015] In step 1, the calculation method for the irradiance of direct sunlight reaching the target is:

[0016] ;

[0017] Where, is the irradiance of direct sunlight reaching the target, is the irradiance of the sun’s visible light reaching the Earth, is the radius of the sun, is the average distance between the Earth and the Sun, is Planck's constant, is the speed of light in vacuum, is the wavelength of light, is a natural constant, is the Boltzmann constant, is the absolute temperature of the solar blackbody.

[0018] In step 2, the irradiance of the earth's reflected light reaching the target is calculated as follows:

[0019] ;

[0020] Where, is the irradiance of the earth's reflected light reaching the target, is the angle between the sun, the earth and the target, is the radius of the Earth, is the distance between the Earth and the target, is the Earth's reflectivity.

[0021] In step 3, the irradiance of moonlight reaching the target is calculated as:

[0022] ;

[0023] Where, is the irradiance of moonlight reaching the target, is the lunar reflectivity, is the radius of the moon, is the distance from the moon to the target, is the moon phase function, is the moon magnitude phase function in Replace with obtained; among them, is the angle between the sun, moon and target, is the lunar phase angle observed at the top of the Earth's atmosphere.

[0024] In step 3, the irradiance of the moon's reflected light reaching the target is calculated as follows:

[0025] ;

[0026] Where, is the irradiance of the moon's reflected light reaching the target, The wavelength is The irradiance of sunlight reaching the moon.

[0027] In step 3, the method for constructing the lunar magnitude phase function is:

[0028] ;

[0029] Where, is the lunar magnitude, ; is the first fitting coefficient of the phase angle, is the second fitting coefficient of the phase angle.

[0030] In step 4, the target apparent magnitude model is:

[0031] ;

[0032] Where, is the target apparent magnitude, is the apparent magnitude of the Sun, is the irradiance of the target reflected light reaching the sensor, is the irradiance of direct sunlight reaching the target.

[0033] In step 5, the calculation method of the target first irradiance is:

[0034] ;

[0035] The calculation method of the target second irradiance is:

[0036] ;

[0037] The calculation method of the target third irradiance is:

[0038] ;

[0039] Where, is the first irradiance of the target, is the target second irradiance, is the target third irradiance; is the average reflectivity, is the cross-sectional area of ​​the Lambertian sphere, is the target observation distance, is the proportional coefficient of target diffuse reflection and specular reflection;

[0040] is the first diffuse reflection phase angle function, is the first specular reflection phase angle function, is the solar phase angle formed by the sensor and the target relative to the sun;

[0041] is the second diffuse reflection phase angle function, is the second mirror reflection phase angle function, is the earth phase angle formed by the sensor and the target relative to the earth;

[0042] is the third diffuse reflection phase angle function, is the third mirror reflection phase angle function, is the lunar phase angle of the sensor and target relative to the moon.

[0043] In step 6, the calculation method of the irradiance of the target reflected light received by the sensor is:

[0044] ;

[0045] Where, is the irradiance of the target reflected light received by the sensor, is the distance between the target and the sensor.

[0046] In step 6, the calculation method for the apparent magnitude of the optical observation target in the Earth-Moon space is:

[0047] ;

[0048] Where, is the apparent magnitude of the target in optical observation in Earth-Moon space, is the radius of the Lambertian sphere, is the phase function, that is, the angle function formed by the sun, the earth and the target.

[0049] The beneficial effects of the present invention are:

[0050] 1. To simplify the calculation, the present invention integrates the solar irradiance within the visible light band to obtain the irradiance of the sun's visible light reaching the Earth. Since the average distance from the Earth to the Moon is much smaller than the average distance between the Sun and the Earth, the present invention uses the irradiance of the sun's visible light reaching the Earth as the irradiance of the sun's direct light reaching the target.

[0051] 2. During remote sensing observations of the Earth, the Earth itself exhibits different reflectivities due to different surface covers. However, in the present invention, the target is very far away from the Earth, and the impact of different surface covers on the reflectivity is very limited. Simplifying the Earth into a diffusely reflecting Lambertian sphere with a completely diffusely reflecting surface can effectively simulate the Earth's reflected light at a longer distance scale. The irradiance of the Earth's reflected light reaching the target can be quickly obtained through the Lambertian body reflection law.

[0052] 3. After sunlight directly hits the surface of the moon, it is reflected into space to form moonlight. By referring to the fitting coefficient of the lunar phase function, the irradiance of the moon's reflected light reaching the target is integrated in the visible light band to obtain a more accurate irradiance of the moonlight reaching the target.

[0053] 4. Space debris is an object that has both specular reflection and diffuse reflection properties. Therefore, the present invention uses a Lambertian sphere that has both specular reflection and diffuse reflection to better simulate the characteristics of space debris, thereby constructing a target apparent magnitude model based on the relationship between irradiance and apparent magnitude.

[0054] 5. The irradiance of the target reflected light reaching the sensor in the target apparent magnitude model constructed by the present invention takes into account the irradiance contributions of sunlight, earth reflected light, and moonlight. Compared with the second apparent magnitude model in the prior art that only considers the irradiance contribution of sunlight, the calculation results of the target apparent magnitude model constructed by the present invention are more accurate.

[0055] 6. The present invention takes into account the conditions of sunlight, moonlight, and earth reflection light, and also includes the moon and the earth in the scope of light source calculation, that is, the irradiance of sunlight, moonlight, and earth reflection light is calculated at the same time. Based on the target apparent magnitude model, the irradiance of direct sunlight reaching the target is used to obtain the first irradiance of the target when sunlight is the light source, the irradiance of earth reflection light reaching the target is used to obtain the second irradiance of the target when earth reflection light is the light source, and the irradiance of moonlight reaching the target is used to obtain the third irradiance of the target when moonlight is the light source; since the irradiances of sunlight, moonlight, and earth reflection light are calculated separately, the contribution rates of moonlight and earth reflection light to the target brightness can be evaluated. This optimization scheme effectively determines the impact of moonlight and earth reflection light on space-based optical observations in the Earth-Moon space.

[0056] 7. The irradiance of the target's first, second, and third irradiances are summed to obtain the irradiance of the target's reflected light received by the sensor. Based on the target apparent magnitude model, the apparent magnitude of the target observed in the Earth-Moon space obtained from the irradiance of the target's reflected light received by the sensor is a more accurate calculation result of the target's apparent magnitude. This solves the problem of being unable to accurately obtain the target's apparent magnitude without considering the influence of moonlight and earth reflection light, and the problem of being unable to calculate the target's apparent magnitude in the absence of sunlight, thereby improving the accuracy of the brightness estimation of the target observed in the Earth-Moon space.

[0057] 8. When the sun is blocked or other unfavorable observation conditions are present, the feasibility of using moonlight and earth reflection to observe the target can be determined by the calculation results of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0059] Figure 1 A schematic diagram of the relative position relationship of the sun, earth, moon, target, and sensor provided in an embodiment of the present invention.

[0060] Figure 2 A schematic diagram of the relative position relationship of the sun, moon, target, and sensor provided in an embodiment of the present invention.

[0061] Figure 3 A schematic diagram of the relative position relationship of the sun, earth, target, and sensor provided in an embodiment of the present invention.

[0062] Figure 4 A schematic diagram of the relative position relationship between the sun, target, and sensor provided in an embodiment of the present invention.

[0063] Figure 5 A schematic diagram of the change in target magnitude of different light sources with distance provided by an embodiment of the present invention.

[0064] Figure 6 This is a schematic diagram of how the observed irradiance ratio of different light sources varies with distance, provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0065] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0066] An embodiment of the present invention provides a method for calculating the apparent magnitude of a target in optical observation in Earth-Moon space, comprising:

[0067] Step 1: Integrate the solar irradiance in the visible light band to obtain the irradiance of the solar visible light reaching the earth; the irradiance of the solar visible light reaching the earth is used as the irradiance of the solar direct light reaching the target;

[0068] Step 2: Simplify the earth into a diffuse reflecting Lambertian sphere with a completely diffuse reflecting surface, and obtain the irradiance of the light reflected from the earth reaching the target through the Lambertian body reflection law;

[0069] Step 3: Integrate the irradiance of the moon's reflected light reaching the target in the visible light band to obtain the irradiance of the moonlight reaching the target;

[0070] Step 4: Use a Lambertian sphere with both specular and diffuse reflection to simulate target characteristics, and construct a target magnitude model based on the relationship between irradiance and magnitude.

[0071] Step 5: Based on the target apparent magnitude model, the first irradiance of the target when sunlight is the light source is obtained by the irradiance of direct sunlight reaching the target, the second irradiance of the target when earth reflected light is the light source is obtained by the irradiance of earth reflected light reaching the target, and the third irradiance of the target when moonlight is the light source is obtained by the irradiance of moonlight reaching the target;

[0072] Step six, summing the first target irradiance, the second target irradiance, and the third target irradiance to obtain the irradiance of the target reflected light received by the sensor. Based on the target apparent magnitude model, the apparent magnitude of the target in the Earth-Moon space optical observation is obtained from the irradiance of the target reflected light received by the sensor.

[0073] Since the Earth's orbit around the Sun is not a strict circle, the distance from the Sun to the Earth changes throughout the year, causing the solar irradiance to change continuously as the Earth orbits. The irradiance from the Sun to the Earth is between 1320 and 1412 W / m 2 To simplify the calculation, the irradiance projected by the sun on a unit area 1 AU away from the sun and perpendicular to the direction of the sun's rays per unit time is taken as the solar constant, and the approximate average value is .

[0074] The present invention considers the situation of visible light detection, and needs to integrate the solar irradiance in the visible light band (0.4~0.7 μm) and take the average distance between the sun and the earth as , the radius of the sun , approximating sunlight as parallel blackbody radiation. By integration, the irradiance of the sun's visible light to the earth is:

[0075] ;

[0076] The average distance from the Earth to the Moon is , which is much smaller than the average distance between the sun and the earth, so the irradiance of the sun’s visible light to the earth can be approximated as the irradiance of the sun’s direct light reaching the target. As the irradiance constant of the visible light of the sun in the Earth-Moon space, that is, the irradiance of the direct sunlight reaching the target, it is recorded as Therefore, in step 1, the calculation method for the irradiance of direct sunlight reaching the target is:

[0077] ;

[0078] Where, is the irradiance of direct sunlight reaching the target, is the irradiance of the sun’s visible light reaching the Earth, is the radius of the sun, is the average distance between the Earth and the Sun, is Planck's constant, is the speed of light in vacuum, is the wavelength of light, is a natural constant, is the Boltzmann constant, is the absolute temperature of the solar blackbody.

[0079] Sunlight directly hitting the Earth's surface is reflected into space, forming earthshine. Compared to the sunlight irradiance received by a target, earthshine is much smaller. Simplifying the Earth into a diffuse Lambertian sphere with a completely diffuse reflective surface, the reflectivity of visible light can be taken as 0.4. The irradiance of earthshine is then:

[0080] ;

[0081] in, is the irradiance of the earth's reflected light reaching the target, is the radius of the Earth, is the distance between the Earth and the target, is the reflectivity, is the ground phase function, is the angle between the sun, the earth and the target. For the earth simplified as a diffuse Lambertian sphere, the phase function is:

[0082] ;but,

[0083] In step 2, the irradiance of the earth's reflected light reaching the target is calculated as follows:

[0084] ;

[0085] Where, is the irradiance of the earth's reflected light reaching the target, is the angle between the sun, the earth and the target, is the radius of the Earth, is the distance between the Earth and the target, is the Earth's reflectivity.

[0086] In step 3, the method for constructing the lunar magnitude phase function is:

[0087] ;

[0088] Where, is the lunar magnitude, ; is the first fitting coefficient of the phase angle, is the second fitting coefficient of the phase angle. Sunlight directly hitting the lunar surface is reflected into space to form moonlight. By referring to the fitting coefficient of the lunar phase function, the irradiance of the lunar reflected light received by the target at different angles to the moon can be obtained. First, the lunar phase angle (the angle between the sun, moon, and earth) obtained by observation at the top of the earth's atmosphere is , interpolate to get the lunar magnitude corresponding to the phase angle and wavelength ;in 、 As shown in Table 1:

[0089] Table 1

[0090]

[0091] Ignoring the difference in distance from the Sun to the Earth and from the Sun to the Moon, the irradiance of the moon's reflected light reaching the top of the Earth's atmosphere is:

[0092] ;

[0093] in, is the radius of the moon, is the distance from the moon to the earth, is the radius of the Earth. is the lunar reflectivity, which is taken as 0.116. For targets in the cislunar space, the irradiance of the lunar reflected light reaching the top of the Earth’s atmosphere is taken as Replaced by the distance from the moon to the target , the lunar phase angle is replaced by the angle between the sun, moon and target , the irradiance of the moon's reflected light reaching the target is:

[0094] ;

[0095] Where, is the irradiance of the moon's reflected light reaching the target, The wavelength is The irradiance of sunlight reaching the moon. is the moon phase function, is the moon magnitude phase function in Replace with obtained; among them, is the angle between the sun, moon and target, is the lunar phase angle observed at the top of the Earth's atmosphere.

[0096] By integrating the irradiance of the moon's reflected light reaching the target from 0.4μm to 0.7μm in the visible light band, we can obtain the function of the lunar irradiance received by the target as the angle between the target, the moon, and the sun changes, that is, the irradiance of the moonlight reaching the target:

[0097] ;

[0098] Where, is the irradiance of moonlight reaching the target, is the lunar reflectivity, is the radius of the moon, is the distance from the moon to the target.

[0099] The target irradiance received by the sensor needs to be determined by the angles between the sun, the earth, the moon, the target, and the sensor. The relationship between them is as follows: Figure 1 shown. Figure 1 In the equation, S is the mass center of the sun, M is the mass center of the moon, E is the mass center of the earth, T is the target, and O is the observer. For the convenience of subsequent calculations, let ∠STO = , ∠ETO= , ∠MTO= , ∠SMT= , ∠SET= .

[0100] The optical properties of the target, i.e., space debris, are affected by factors such as the material and relative position of the debris. To simplify the calculation, a Lambertian sphere with both specular reflection and diffuse reflection is used here to simulate the target characteristics, so that the reflectivity of the target is the same in all directions.

[0101] In step 4, the target apparent magnitude model is:

[0102] ;

[0103] Where, is the target apparent magnitude, is the apparent magnitude of the Sun, is the irradiance of the target reflected light reaching the sensor, is the irradiance of direct sunlight reaching the target.

[0104] In addition, in the prior art, when only sunlight is considered as the light source, the second apparent magnitude model obtained is:

[0105] ;

[0106] Where, The target magnitude calculated for the target second magnitude model, is the apparent magnitude of the Sun, is the average reflectivity, is the cross-sectional area of ​​the Lambertian sphere, is the target observation distance, is the proportional coefficient of target diffuse reflection and specular reflection, is the diffuse reflection phase angle function, is the mirror reflection phase angle function; where

[0107] ;

[0108] ;

[0109] The irradiance of the target reflected light reaching the sensor in the target apparent magnitude model constructed by the present invention The irradiance contributions of sunlight, earth reflection and moonlight are taken into account at the same time. Compared with the second apparent magnitude model in the prior art that only considers the irradiance contribution of sunlight, the calculation results of the target apparent magnitude model constructed using the present invention are more accurate.

[0110] In step 5, the calculation method of the target first irradiance is:

[0111] ;

[0112] The calculation method of the target second irradiance is:

[0113] ;

[0114] The calculation method of the target third irradiance is:

[0115] ;

[0116] Where, is the first irradiance of the target, is the target second irradiance, is the target third irradiance; is the average reflectivity, is the cross-sectional area of ​​the Lambertian sphere, is the target observation distance, is the proportional coefficient of target diffuse reflection and specular reflection;

[0117] is the first diffuse reflection phase angle function, in Replace with obtained; is the first mirror reflection phase angle function, in Replace with obtained; is the solar phase angle formed by the sensor and the target relative to the sun;

[0118] is the second diffuse reflection phase angle function, in Replace with obtained; is the second mirror reflection phase angle function, in Replace with obtained; is the earth phase angle formed by the sensor and the target relative to the earth;

[0119] is the third diffuse reflection phase angle function, in Replace with obtained; is the third mirror reflection phase angle function, in Replace with obtained; is the lunar phase angle of the sensor and target relative to the moon.

[0120] Taking into account sunlight, earth reflection, and moonlight, the calculation method for the irradiance of the target reflected light received by the sensor in step 6 is:

[0121] ;

[0122] Where, is the irradiance of the target reflected light received by the sensor, is the distance between the target and the sensor.

[0123] Take the solar magnitude as In step 6, the calculation method for the apparent magnitude of the optical observation target in the Earth-Moon space is:

[0124] ;

[0125] Where, is the apparent magnitude of the target in optical observation in Earth-Moon space, is the radius of the Lambertian sphere, is the phase function, that is, the angle function formed by the sun, the earth and the target.

[0126] The following is a verification example to verify the effect of the method disclosed in the present invention.

[0127] Example 1: The impact of reflected light on the target

[0128] The irradiance of earthshine and moonlight is much less than that of sunlight and is often ignored in simulation calculations. However, during a solar eclipse or when the angle of sunlight is unfavorable for observation, earthshine and moonlight can be used to observe the target. Because the irradiance and apparent magnitude of a target are affected by multiple variables, such as the relative positions of the Sun, Moon, Earth, target, and detector, three fixed scenarios are assumed to determine the impact of earthshine on the target's irradiance and apparent magnitude.

[0129] like Figure 2 、 Figure 3 and Figure 4 As shown, S is the mass center of the sun, M is the mass center of the moon, E is the mass center of the earth, T is the target, and O is the observer. Assume that the target is located on the line connecting the earth and the moon, and the radius The cross-sectional area of ​​a Lambertian sphere is 1m. , average reflectivity The distance between the moon and the target is 0.175. Set as , the distance between the earth and the target Set as ,and , the distance between the sun and the target Set as Keeping the distance between the earth and the sun constant, the distance between the probe and the target Assume that the sun-moon-target angle ∠SMT ( )、Moon-target-probe angle ∠MTO( ), Sun-Earth-target angle ∠SET ( ), Earth-target-detector angle ∠ETO ( ), sun-target-detector angle ∠STO ( ) are all 20° to ensure the same observation angle.

[0130] Calculate the first irradiance of the target observed with the sun as the light source and the target's first apparent magnitude for:

[0131] ;

[0132] ;

[0133] Calculate the second irradiance of the target observed with the earth as the light source and the target's second magnitude for:

[0134] ;

[0135] ;

[0136] ;

[0137] Calculate the third irradiance of the target observed with the moon as the light source and the target's third magnitude for:

[0138] ;

[0139] ;

[0140] ;

[0141] In summary, the irradiance of the target reflected light observed with the sun, earth and moon as light sources is calculated and the apparent magnitude of optical observation targets in cislunar space for:

[0142] ;

[0143] ;

[0144] in, 、 and Follow Changes such as Figure 5 As shown, and Respectively The ratio value of 、 , follow Changes such as Figure 6 shown.

[0145] Figure 5 and Figure 6 In the figure, the x-axis is the distance between the moon and the target. , the range is 10000km~250000km, Figure 5 In the figure, the y-axis is the apparent magnitude of the detected target. Figure 6 In the y-axis, the ratio of target irradiance is given. Figure 5 It can be found that under the hypothetical scenario conditions, the target is within about 17500km from the moon. Less than 18, about 162,500 km away from the moon, less than 18; and Figure 6 The ratio value in shows that under the same observation angle, and Much smaller than This means that when observations can be made using sunlight, the effects of moonlight and earth reflection can be ignored. However, when observations cannot be made using sunlight, there is an opportunity to use moonlight and earth reflection to achieve observations.

[0146] The beneficial effects of the present invention are:

[0147] 1. To simplify the calculation, the present invention integrates the solar irradiance within the visible light band to obtain the irradiance of the sun's visible light reaching the Earth. Since the average distance from the Earth to the Moon is much smaller than the average distance between the Sun and the Earth, the present invention uses the irradiance of the sun's visible light reaching the Earth as the irradiance of the sun's direct light reaching the target.

[0148] 2. During remote sensing observations of the Earth, the Earth itself exhibits different reflectivities due to different surface covers. However, in the present invention, the target is very far away from the Earth, and the impact of different surface covers on the reflectivity is very limited. Simplifying the Earth into a diffusely reflecting Lambertian sphere with a completely diffusely reflecting surface can effectively simulate the Earth's reflected light at a longer distance scale. The irradiance of the Earth's reflected light reaching the target can be quickly obtained through the Lambertian body reflection law.

[0149] 3. After sunlight directly hits the surface of the moon, it is reflected into space to form moonlight. By referring to the fitting coefficient of the lunar phase function, the irradiance of the moon's reflected light reaching the target is integrated in the visible light band to obtain a more accurate irradiance of the moonlight reaching the target.

[0150] 4. Space debris is an object that has both specular reflection and diffuse reflection properties. Therefore, the present invention uses a Lambertian sphere that has both specular reflection and diffuse reflection to better simulate the characteristics of space debris, thereby constructing a target apparent magnitude model based on the relationship between irradiance and apparent magnitude.

[0151] 5. The irradiance of the target reflected light reaching the sensor in the target apparent magnitude model constructed by the present invention takes into account the irradiance contributions of sunlight, earth reflected light, and moonlight. Compared with the second apparent magnitude model in the prior art that only considers the irradiance contribution of sunlight, the calculation results of the target apparent magnitude model constructed by the present invention are more accurate.

[0152] 6. The present invention takes into account the conditions of sunlight, moonlight, and earth reflection light, and also includes the moon and the earth in the scope of light source calculation, that is, the irradiance of sunlight, moonlight, and earth reflection light is calculated at the same time. Based on the target apparent magnitude model, the irradiance of direct sunlight reaching the target is used to obtain the first irradiance of the target when sunlight is the light source, the irradiance of earth reflection light reaching the target is used to obtain the second irradiance of the target when earth reflection light is the light source, and the irradiance of moonlight reaching the target is used to obtain the third irradiance of the target when moonlight is the light source; since the irradiances of sunlight, moonlight, and earth reflection light are calculated separately, the contribution rates of moonlight and earth reflection light to the target brightness can be evaluated. This optimization scheme effectively determines the impact of moonlight and earth reflection light on space-based optical observations in the Earth-Moon space.

[0153] 7. The irradiance of the target's first, second, and third irradiances are summed to obtain the irradiance of the target's reflected light received by the sensor. Based on the target apparent magnitude model, the apparent magnitude of the target observed in the Earth-Moon space obtained from the irradiance of the target's reflected light received by the sensor is a more accurate calculation result of the target's apparent magnitude. This solves the problem of being unable to accurately obtain the target's apparent magnitude without considering the influence of moonlight and earth reflection light, and the problem of being unable to calculate the target's apparent magnitude in the absence of sunlight, thereby improving the accuracy of the brightness estimation of the target observed in the Earth-Moon space.

[0154] 8. When the sun is blocked or other unfavorable observation conditions are present, the feasibility of using moonlight and earth reflection to observe the target can be determined by the calculation results of the present invention.

[0155] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for calculating the apparent magnitude of an optical observation target in Earth-Moon space, characterized in that: include: Step 1: Integrate the solar irradiance in the visible light band to obtain the irradiance of the solar visible light reaching the earth; The irradiance of the sun's visible light reaching the earth is taken as the irradiance of the sun's direct light reaching the target; Step 2: Simplify the earth into a diffuse reflecting Lambertian sphere with a completely diffuse reflecting surface, and obtain the irradiance of the light reflected from the earth reaching the target through the Lambertian body reflection law; Step 3: Integrate the irradiance of the moon's reflected light reaching the target in the visible light band to obtain the irradiance of the moonlight reaching the target; Step 4: Use a Lambertian sphere with both specular and diffuse reflection to simulate target characteristics, and construct a target magnitude model based on the relationship between irradiance and magnitude. Step 5: Based on the target apparent magnitude model, the first irradiance of the target when sunlight is the light source is obtained by the irradiance of direct sunlight reaching the target, the second irradiance of the target when earth reflected light is the light source is obtained by the irradiance of earth reflected light reaching the target, and the third irradiance of the target when moonlight is the light source is obtained by the irradiance of moonlight reaching the target; Step six, summing the first target irradiance, the second target irradiance, and the third target irradiance to obtain the irradiance of the target reflected light received by the sensor. Based on the target apparent magnitude model, the apparent magnitude of the target in the Earth-Moon space optical observation is obtained from the irradiance of the target reflected light received by the sensor.

2. The method for calculating the apparent magnitude of an optically observed target in Earth-Moon space according to claim 1, wherein: In step 1, the calculation method for the irradiance of direct sunlight reaching the target is: ； Where, is the irradiance of direct sunlight reaching the target, is the irradiance of the sun’s visible light reaching the Earth, is the radius of the sun, is the average distance between the Earth and the Sun, is Planck's constant, is the speed of light in vacuum, is the wavelength of light, is a natural constant, is the Boltzmann constant, is the absolute temperature of the solar blackbody.

3. The method for calculating the apparent magnitude of an optically observed target in Earth-Moon space according to claim 2, wherein: In step 2, the irradiance of the earth's reflected light reaching the target is calculated as follows: ； Where, is the irradiance of the earth's reflected light reaching the target, is the angle between the sun, the earth and the target, is the radius of the Earth, is the distance between the Earth and the target, is the Earth's reflectivity.

4. The method for calculating the apparent magnitude of an optically observed target in Earth-Moon space according to claim 3, wherein: In step 3, the irradiance of moonlight reaching the target is calculated as: ； Where, is the irradiance of moonlight reaching the target, is the lunar reflectivity, is the radius of the moon, is the distance from the moon to the target, is the moon phase function, is the moon magnitude phase function in Replace with obtained; among them, is the angle between the sun, moon and target, is the lunar phase angle observed at the top of the Earth's atmosphere.

5. The method for calculating the apparent magnitude of an optically observed target in Earth-Moon space according to claim 4, wherein: In step 3, the irradiance of the moon's reflected light reaching the target is calculated as follows: ； Where, is the irradiance of the moon's reflected light reaching the target, The wavelength is The irradiance of sunlight reaching the moon.

6. A method for calculating the apparent magnitude of an optically observed target in Earth-Moon space according to claim 4 or 5, characterized in that: In step 3, the method for constructing the lunar magnitude phase function is: ； Where, is the lunar magnitude, ; is the first fitting coefficient of the phase angle, is the second fitting coefficient of the phase angle.

7. The method for calculating the apparent magnitude of an optically observed target in Earth-Moon space according to claim 6, wherein: In step 4, the target apparent magnitude model is: ； Where, is the target apparent magnitude, is the apparent magnitude of the Sun, is the irradiance of the target reflected light reaching the sensor, is the irradiance of direct sunlight reaching the target.

8. The method for calculating the apparent magnitude of an optically observed target in Earth-Moon space according to claim 7, wherein: In step 5, the calculation method of the target first irradiance is: ； The calculation method of the target second irradiance is: ； The calculation method of the target third irradiance is: ； Where, is the first irradiance of the target, is the second irradiance of the target, is the target third irradiance; is the average reflectivity, is the cross-sectional area of ​​the Lambertian sphere, is the target observation distance, is the proportional coefficient of target diffuse reflection and specular reflection; is the first diffuse reflection phase angle function, is the first specular reflection phase angle function, is the solar phase angle formed by the sensor and the target relative to the sun; is the second diffuse reflection phase angle function, is the second mirror reflection phase angle function, is the earth phase angle formed by the sensor and the target relative to the earth; is the third diffuse reflection phase angle function, is the third mirror reflection phase angle function, is the lunar phase angle of the sensor and target relative to the moon.

9. The method for calculating the apparent magnitude of an optically observed target in Earth-Moon space according to claim 8, wherein: In step 6, the calculation method of the irradiance of the target reflected light received by the sensor is: ； Where, is the irradiance of the target reflected light received by the sensor, is the distance between the target and the sensor.

10. The method for calculating the apparent magnitude of an optically observed target in Earth-Moon space according to claim 9, wherein: In step 6, the calculation method for the apparent magnitude of the optical observation target in the Earth-Moon space is: ； Where, is the apparent magnitude of the target in optical observation in Earth-Moon space, is the radius of the Lambertian sphere, is the phase function, that is, the angle function formed by the sun, the earth and the target.

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