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The construction of small-size retroreflectory system with submillimeter target error for low-orbit satellites, including Lomonosov spacecraft, is suggested. The factors, which influence on the energy and precision characteristics of small-size retroreflectory system, are determined.
Теги: corner-cube-reflectors small-size retroreflectory system малогабаритная ретрорефлекторная система уголковые отражатели
The panels of corner-cube-reflector (AR), or so-called retroreflectory systems (RS), are installed in all modern navigation and geodesic spacecrafts (SC) [1–7]. The intended purpose of such systems consists in the reflection of the beam of laser rangefinder back to the detector of optical and laser station for precision measurement of the distance to SC.
Small-size RS "Pyramid" developed in JSC "Scientific and Manufacturing Corporation "Systems of Precision Instrument Engineering" represents the pyramid-shaped construction of four CR with the common vertex (Fig. 1). Its weight is only 60 g and overall dimensions do not exceed 40 mm.
In order to reach the required energy and precision characteristics it is necessary for the construction parameters of RS to provide the optimal directivity diagram of reflected radiation, which is typically characterized by equivalent scattering area of cross-section (CS). The phenomenon of velocity aberration results in the fact that the optimal direction of detection of reflected laser beam does not concur with the axis of directivity diagram and it depends on the satellite velocity, in other words on the height of its orbit. The average value of velocity aberration [1, 2, 4] for low-orbit satellites is about 8". It means that particularly at such angle from the axis of directivity diagram CS must be maximal, and it is required to expand the directivity diagram somehow, for example, to reduce the size of CR. However, at the same time the aperture decreases, and detected energy of laser radiation is reduced in general.
At zenithal area of SC overflying the angle of incidence on all four CR is approximately equal to 54°. During the movement of satellite from horizon to zenith, CR aperture decreases and it has oval shape. As a result, CS is maximal at zenith viewing angle θzen = 63° (see Fig. 2, tilt angle β = 27°) and minimal in case of satellite location in zenith area θzen = 0...10°. Maximal values of CS are reached when the radiation is incident only on one CR.
Minimums I correspond to the case when the radiation is incident on two CR during the satellite overflying along the trajectory located in the plane α (α – plane formed by the point of location of quantum-optical station and normal vector directed along the tangent to the surface of earth ellipsoid). Minimums II correspond to the satellite location on traverse, and at the same time the angular deflection of axis of laser beam reflected from RS is maximal due to the phenomenon of velocity aberration.
At the same time, the distance to satellite is minimal in zenith area and maximal (by more than three times) in case of satellite location on horizon. Since the number of photons reflected from satellite and received by ground quantum-optical station is inversely proportional to the fourth degree of distance to satellite, the reduction of CR aperture in zenith area is compensated by the distance decrease.
The influence of two factors results in the fact that the number of photons recorded by optical and laser station is maximal at zenith viewing angle of satellite θzen = 40°. As opposed to other analogous retroreflectory systems [7], the quantity of photons reflected from RS "Pyramid" and recorded by photodetector does not significantly vary during the satellite overflying along celestial sphere.
In case of increase of CR quantity, CS and probability of radiation reflection from two and more CR grow. If the distance from laser transmitter to individual CR in RS differs, the extension of response signal causing so-called target error occurs. For RS "Pyramid" the target error is very low at the expense of CR small size and connection of their vertexes. Maximal value of error occurs when the radiation is incident on several CR at once upon their unsymmetrical arrangement from the axis of laser beam, and in such case the optical path in these CR does not concur. Error minimum corresponds to the case of laser beam incidence on two identically oriented CR or to the case of reflection of laser radiation only from one CR. In general, the estimated value of target error does not exceed 0.5 mm when measuring the distance to SC.
Two small-size retroreflectory systems "Pyramid" designed at JSC "SMC "SPIE" were located onboard the SC "Lomonosov" within the framework of space experiment in laser location jointly with the Research Institute of Nuclear Physics of Moscow State University, Corporation VNIIEM and FSUE TsNIImash with the participation of FSUE "VNIIFTRI" (Fig. 3). The satellite was launched in sun synchronous orbit with the height of 500 km in April 2016 with the scientific equipment of Moscow State University in order to study the phenomena in the upper layers and Earth’s atmosphere.
Each RS representing the pyramid of four corner-cube-reflectors (see Fig. 1) is capable to reflect the laser pulses from the whole lower hemisphere. One RS is glued to the satellite frame and the other one is glued to the extension rod at the distance of about 2 m from the first RS.
Carried out laser measurements of distance allowed observing two signal tracks with the distance between them of only 0.5–2 m depending on the satellite orientation relative to laser station at the moment of observation. In this case so-called single-photon mode was used; at this mode the distance with the error of several centimeters is determined by counting the single signal photons coming from RS. Single-photon mode can be reached at the expense of increase of probing laser beam divergence to 20–30 seconds of arc.
Notwithstanding the small size, every RS provided the sufficient level of response signal. According to our evaluation (the comparative measurements by satellites "Stella" and "Lageos’ were performed), CS was up to 100 000 m 2.
The results of space experiment allow recommending the retroreflectory system "Pyramid" for the installation in low-orbit spacecrafts in order to determine their orientation and monitor additionally the deployment of SC components in space.
Small-size RS "Pyramid" developed in JSC "Scientific and Manufacturing Corporation "Systems of Precision Instrument Engineering" represents the pyramid-shaped construction of four CR with the common vertex (Fig. 1). Its weight is only 60 g and overall dimensions do not exceed 40 mm.
In order to reach the required energy and precision characteristics it is necessary for the construction parameters of RS to provide the optimal directivity diagram of reflected radiation, which is typically characterized by equivalent scattering area of cross-section (CS). The phenomenon of velocity aberration results in the fact that the optimal direction of detection of reflected laser beam does not concur with the axis of directivity diagram and it depends on the satellite velocity, in other words on the height of its orbit. The average value of velocity aberration [1, 2, 4] for low-orbit satellites is about 8". It means that particularly at such angle from the axis of directivity diagram CS must be maximal, and it is required to expand the directivity diagram somehow, for example, to reduce the size of CR. However, at the same time the aperture decreases, and detected energy of laser radiation is reduced in general.
At zenithal area of SC overflying the angle of incidence on all four CR is approximately equal to 54°. During the movement of satellite from horizon to zenith, CR aperture decreases and it has oval shape. As a result, CS is maximal at zenith viewing angle θzen = 63° (see Fig. 2, tilt angle β = 27°) and minimal in case of satellite location in zenith area θzen = 0...10°. Maximal values of CS are reached when the radiation is incident only on one CR.
Minimums I correspond to the case when the radiation is incident on two CR during the satellite overflying along the trajectory located in the plane α (α – plane formed by the point of location of quantum-optical station and normal vector directed along the tangent to the surface of earth ellipsoid). Minimums II correspond to the satellite location on traverse, and at the same time the angular deflection of axis of laser beam reflected from RS is maximal due to the phenomenon of velocity aberration.
At the same time, the distance to satellite is minimal in zenith area and maximal (by more than three times) in case of satellite location on horizon. Since the number of photons reflected from satellite and received by ground quantum-optical station is inversely proportional to the fourth degree of distance to satellite, the reduction of CR aperture in zenith area is compensated by the distance decrease.
The influence of two factors results in the fact that the number of photons recorded by optical and laser station is maximal at zenith viewing angle of satellite θzen = 40°. As opposed to other analogous retroreflectory systems [7], the quantity of photons reflected from RS "Pyramid" and recorded by photodetector does not significantly vary during the satellite overflying along celestial sphere.
In case of increase of CR quantity, CS and probability of radiation reflection from two and more CR grow. If the distance from laser transmitter to individual CR in RS differs, the extension of response signal causing so-called target error occurs. For RS "Pyramid" the target error is very low at the expense of CR small size and connection of their vertexes. Maximal value of error occurs when the radiation is incident on several CR at once upon their unsymmetrical arrangement from the axis of laser beam, and in such case the optical path in these CR does not concur. Error minimum corresponds to the case of laser beam incidence on two identically oriented CR or to the case of reflection of laser radiation only from one CR. In general, the estimated value of target error does not exceed 0.5 mm when measuring the distance to SC.
Two small-size retroreflectory systems "Pyramid" designed at JSC "SMC "SPIE" were located onboard the SC "Lomonosov" within the framework of space experiment in laser location jointly with the Research Institute of Nuclear Physics of Moscow State University, Corporation VNIIEM and FSUE TsNIImash with the participation of FSUE "VNIIFTRI" (Fig. 3). The satellite was launched in sun synchronous orbit with the height of 500 km in April 2016 with the scientific equipment of Moscow State University in order to study the phenomena in the upper layers and Earth’s atmosphere.
Each RS representing the pyramid of four corner-cube-reflectors (see Fig. 1) is capable to reflect the laser pulses from the whole lower hemisphere. One RS is glued to the satellite frame and the other one is glued to the extension rod at the distance of about 2 m from the first RS.
Carried out laser measurements of distance allowed observing two signal tracks with the distance between them of only 0.5–2 m depending on the satellite orientation relative to laser station at the moment of observation. In this case so-called single-photon mode was used; at this mode the distance with the error of several centimeters is determined by counting the single signal photons coming from RS. Single-photon mode can be reached at the expense of increase of probing laser beam divergence to 20–30 seconds of arc.
Notwithstanding the small size, every RS provided the sufficient level of response signal. According to our evaluation (the comparative measurements by satellites "Stella" and "Lageos’ were performed), CS was up to 100 000 m 2.
The results of space experiment allow recommending the retroreflectory system "Pyramid" for the installation in low-orbit spacecrafts in order to determine their orientation and monitor additionally the deployment of SC components in space.
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