Abstract
In this paper, the scan mirror assembly for the space experiment Aerosol-UA scanning polarimeter (ScanPol) is described. The aim of the Ukrainian space mission Aerosol-UA is to create a database of the optical characteristics of aerosol and cloud particles in the Earth’s atmosphere over a long period of time. The optical characteristics of aerosol and cloud particles are derived from multiangular measurements. Multiangular scanning in ScanPol is provided by scan mirror assembly, which contains a reactive torque compensator electric motor and two scan mirrors, mounted on the shaft of the motor. The control system of the scan mirror assembly enables continuous scanning with a constant speed of the space under investigation. This control system tolerates movements of the orbiting satellite and preserves invariability of its spatial position. The polarimeter ScanPol is designed to acquire spatial, temporal, and spectral-polarimetric measurements simultaneously to minimize instrumental effects and “false” polarizations due to scene movement. Instrumental polarization, introduced by the mirrors of scan assembly, is minimized through the polarization compensated two-mirror scheme which contains two mirrors with orthogonal planes of incidence. In this paper, the polarimetric model of the polarization compensated two scan mirrors is considered. Theoretical calculations are given that substantiate the maximum allowable error of the relative angular position of the mirrors is 15 arcmin (0.25°), and the method of adjustment and control of the angular position of the mirrors is proposed. The polarization properties of mirrors are modelled in the spectral range of 370–1680 nm for bulk oxide-free aluminum. It is obtained that the maximum instrumental polarization of the unadjusted mirror system should be observed at 865 nm, and thus, the polarization characteristics of the scanning system at a given wavelength could be considered as representative for ScanPol in general. The key steps for assembling the unit are illustrated.
Highlights
Two-Mirror System4.1. Requirements for the Mirror Alignment. Both mirrors of TSM (Figure 1) change the polarization of incident light. To minimize the instrumental light polarization of the TSM as a whole, a polarization compensated two-mirror scheme (Figure 4) is used. Note the instrumental polarization of an optical system is the polarization of light at the output of the optical system for an unpolarized input. e polarization compensation in scheme (Figure 4) is provided under the condition of the complete identity of optical characteristics of mirrors M1 and M2, when plane-parallel rays fall on mirrors M1 and M2 at the same angles and when the angle between the planes of incidence of rays at mirrors is 90°. When the aforementioned conditions are not met, the polarization compensation is violated too, and uncompensated instrumental polarization will be mixed into the polarization of the input scene. Nonparallelism of rays will also violate the polarization compensation of the mirror pair (Figure 4) [9]. For the evaluation of the influence of the accuracy of mirror alignment in the scheme of Figure 4 on the level of instrumental polarization of TSM, the Mueller matrix method was used. In the Mueller method, the polarization of the beam is represented by the Stokes vector S. e optical system is represented by the Mueller M matrix. A view of the Stokes vector S in the general form is given in the following equation: Angular speed (rad/s) Torque coefficient (Nm/A) Moment of inertia (kg·m2) Active winding resistance (Phm) Electromagnetic winding time constant (s) Moment of resistance (N m) Electromechanical time constant (s) Power consumption in operating mode (Watt) , where I, Q, U, and V are Stokes parameters; I is also the total intensity of the light; p is the degree of polarization of the light; and θ and ε are the azimuth and angle of ellipticity of the light polarization ellipse, respectively. Remote sensing often deals with partially or completely linearly polarized light. e angle of ellipticity of the partially or completely linearly polarized light is zero (ε 0°), and the fourth Stokes parameter is zero (V 0) as well. us the Stokes vector takes the following form: cos(2θ) sin(2θ) U arctgQ, where the parameter p means the degree of linear polarization (DoLP) and θ is the azimuth of linear polarization (AoLP). e Mueller matrix M connects the light polarizations at the input and output of the optical system as where Sin and Sout are the Stokes vectors of the input and output light and M is the Mueller matrix of the optical system. To describe the polarization characteristics of the TSM (Figures 1 and 4), it is necessary to define its Mueller matrix. e Mueller matrix of an ideal metal mirror is well known (see, for example, [10]): MMrs,p ⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦, where rs,p |rs,p|exp(φs,p) are the complex reflection coefficients for the projection of the electric components of the incident beam on the plane of incidence (p) and on its orthogonal plane (s) (Figure 4). Note that matrix (5) is written in Eigen Geometry, where the z-axis is directed along the direction of light propagation and the x- and y-axes are parallel to the projections Es and Ep electric component of the light, respectively. is coordinate system is the Eigen Geometry because the light with linear polarizations along the x- or y-axis of this coordinate system does not change its polarization when reflected by the mirror. When rotating the coordinate system of the incident light around the z-axis by an angle α, matrix (5) will turn to ⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦. In the normal position, the planes of incidence of the rays on the mirrors M1 and M2 (Figure 4) are rotated relative to each other by an angle of 90°, so for the mirror M2 –α 90°. According to the Muller matrix method, taking into account equations (5)–(7), the polarization characteristics of TSM can be described by a matrix product of the form: MTSM MM2rs,p,90° · MM1rs,p, 0°, where MTSM is the general Muller matrix for two scan mirrors, MM1(r0s,°p,) is the Muller matrix of the mirror M1, and MM2(rs,p,90°)is the matrix of the mirror M2, rotated by 90° with respect to the first one, which is calculated using (5). Assuming that the polarization characteristics rs,p of the first and the second mirrors of the configuration (Figure 4) are identical, from (8) it could be obtained that MTSM is an identity diagonal matrix with some scale factor. In other words, a pair of mirrors (Figure 4) in this case will be polarization-neutral (i.e., polarization compensated). e misalignments of the system mirrors will affect the polarization compensation. For the sake of simplicity, let fix the mirror M1 and assume that the light falls on it at the angle i 45°. e displacement of the second mirror relative to the exact position comes down to the rotations relative to two axes: “Axis 1” and “Axis 2” (Figure 5). is simplification is obviously acceptable because the degree of neutrality of the mirror system (Figure 4) will depend on the difference between the angles of the light incidence on the mirrors M1 and M2 and on the angle α between their planes of incidence. e tilts of the mirror M2 around axis 1 (Figure 5) correspond to the change of the angle α by the value of β relative to exact position α 90°. e tilts of the mirror M2 around axis 2 (Figure 5) correspond to the change of the incidence angle by the value of c relative to exact position i 45°. e dependence of the mirror system matrix on the tilts of the mirror M2 can be determined using (8) as where rs′,p are the new complex reflection coefficients of the mirror M2 with some tilt c around axis 2 (Figure 5). e coefficients of reflection rs,p are related to the angle of incidence and the complex refractive index of the mirror material N(λ) n(λ) − j · k(λ) through Fresnel and Snell’s equations: rs where λ is the light wavelength, j is the imaginary unit, N0 1 is the refractive index of air, and φ is the angle of refraction. As it was assumed above, the light incidence angle for the mirror M1 is i 45°. Since for the mirror M2 this angle is changed to i 45° ± c, according to (10) and (11), the reflection coefficients rs′,p are not equal to rs,p for M1. In the scan mirror assembly (SMA), aluminum mirrors are used. To calculate rs′,p in (10) and (11), it is necessary to substitute the refractive index N(λ) for aluminum. It is well known that the accurate polarization properties of aluminum mirrors are difficult to model. In fact, the refractive index of aluminum mirror strongly depends on (1) the coating process features [11], (2) the presence of a film of alumina (Al2O3) on the mirror, and (3) the presence of dust on the surface [10]. erefore, the information on the dispersion dependences of aluminum films differs in different references (see, for example, [11,12,13,14,15]). Our paper uses data from [16] based on [11]. Table 2 and Figure 6 show the real n(λ) and imaginary k(λ) part of the complex refractive index N(λ) of the model aluminum mirror for the wavelengths used in scanning polarimeter (ScanPol). Using the data from Table 2 and equations (4) and (9)–(11) and considering the tilts of the mirror M2 around axes 1 and 2 in the ranges of angles β, c ∈[−1°, 1°] relative to exact positions α 90° and i 45°, the boundary estimates were obtained for the degree pinst max|p0 − p′|100% (Figure 7) and the azimuth of the instrumental polarization θinst max|θ0 − θ′| (Figure 8), where p0 and θ0 are, respectively, the degree and azimuth of the linear polarization of the light at the input of the TSM and p′ and θ′ are, respectively, the degree and azimuth of the linear polarization of the light at the output of the TSM. e pinst does not depend on p0, but it is increased with an increase in β and c (see Figure 8). e θinst dependence with β and c is increased as the value of p0 decreases from 1 to 0 (see Figures 8 and 9). Figure 8 shows the θinst estimates at p0 0.2. Figures 7–9 show the significant dependence of the TSM instrumental polarization on the light wavelength. It is seen the value of instrumental polarization is the greatest for the spectral range λ 865 nm. us, in setting accuracy requirements for the alignment of the mirror system, we relied on the spectral component λ 865 nm. e declared maximum error in determining the degree of linear polarization of light by ScanPol in all spectral ranges is Δp ≤ 0.15%. e declared maximum error in determining the azimuth of the linear polarization is Δθ ≤ 0.2° at p0 ≥ 0.2 [17] since here Δθ has a weak dependence on p0. As it was expected for p0 > 0.2 the dependence of Δθ on p0 will grow significantly, thereby under this condition there is no sense to determine θ separately due to the significant error. e expectation has been confirmed at least for the spectral component λ 865 nm (Figure 9). Given the other sources of systematic errors in ScanPol to achieve the declared error limits Δp and Δθ, the instrumental polarization of the TSM should not exceed pinst 0.1°. From the dependences in Figures 7–9 for the spectral component λ 865 nm, it can be seen that (12) will be met if the errors of the mirror setup (Figure 5) do not exceed 0.25° (15 arcmin) pinst (%) (b) Figure 8: Continued. 0.00 λ = 865 nm (a) λ = 410 nm (b) λ = 1378 nm Figure 9: Continued. 0.00 λ = 1620 nm Figure 9: Dependence of the boundary value of the azimuth θinst of the instrumental polarization of the TSM on the mirror M2 tilt around axes 1 and 2 (as shown in Figure 5) at degrees of linear polarization p0 < 0.2. c ≤ 15 arc min , At higher values of errors in the position of TSM mirrors or if the increase in the accuracy of determining the angle of linear polarization of the input light is needed, it is necessary to calibrate the TSM according to the method described in [17]. 4.2. e Procedure for Adjustment. To achieve an accuracy of 15 arcmin for the mirror installation in TSM, an appropriate method and optical bench were developed. Two certified standards of angles were used on the bench: a glass cube with surfaces of 90° named a control optical element (COE) and a pentaprism guaranteeing to return the light beam at 90°. e angle tolerances of the glass cube and the pentaprism are 2 arcmin. e adjustment of the TSM includes the following steps: Step 1 (illustrated in Figure 10): preassemble the TSM with the ability to rotate around its own axis. We use the axis that is a structural element of the electric motor and that is fixed during adjustment in the auxiliary mounting assembly. In input window 1, a framed COE is installed, which provides its tilt along the three axes. Step 2 (illustrated in Figure 11): the pentaprism is placed in front of the TSM. It deflects laser beam 1 by 90° on screen 2. At this point, mark P2 is made. e distance between labels P1 and P2 is determined in the projection on the X-axis. Step 3 (illustrated in Figure 12): laser 2 is placed into the alignment system that directs the beam to the COE and Mirror 1 Mirror 2 the position of the reflected beam from the COE is fixed using label P3. Label P3 is selected arbitrarily. When we rotate the TSM by angle 90°, the second laser beam, reflected from the next face of the COE, will create a label P4. If label P4 coincides with label P3, it means that we have rotated the TSM by 90° ± 2 arcmin. Step 4 (illustrated in Figure 13): mirror 1 is removed, and the TSM is rotated at angle 90°. e correct position of the unit is controlled such that label P4 coincides with label P3 obtained in step 3. e distance between labels P2 and P5 in the projection on the X-axis is determined. If the segment P2–P5 is equal to the segment P1–P2, defined in step 2, mirror 2 is installed in the TSM at an angle of 90°. Otherwise, mirror 2 must be adjusted. Step 5 (illustrated in Figure 14): place mirror 1 and rotate the TSM at an angle of 90°. e angle of rotation is controlled using a beam from laser 2, which is reflected from the surface of the COE and must coincide with label P4 on screen 2. We fix the position by label P6 of the beam from laser 1 on screen 2 (Figure 14), which passed through the TSM. At the exact angle of mirror 2 relative to mirror 1, equal to 90°, the spots from laser 1 must be placed on a single line along the Y-axis, which passes through label P5, and must be at a distance of the base between mirror 1 and 2 centers from the specified label. If this condition is not satisfied, we adjust mirror 2. e distance between the TSM and screen 2 is 5 meters. e label position error on the screen and their alignment is ≤3 mm, which gives an error of the viewing angle
The scan mirror assembly for the space experiment Aerosol-UA scanning polarimeter (ScanPol) is described. e aim of the Ukrainian space mission Aerosol-UA is to create a database of the optical characteristics of aerosol and cloud particles in the Earth’s atmosphere over a long period of time. e optical characteristics of aerosol and cloud particles are derived from multiangular measurements
The polarimetric model of the polarization compensated two scan mirrors is considered. eoretical calculations are given that substantiate the maximum allowable error of the relative angular position of the mirrors is 15 arcmin (0.25°), and the method of adjustment and control of the angular position of the mirrors is proposed. e polarization properties of mirrors are modelled in the spectral range of 370–1680 nm for bulk oxide-free aluminum
Summary
4.1. Requirements for the Mirror Alignment. Both mirrors of TSM (Figure 1) change the polarization of incident light. To minimize the instrumental light polarization of the TSM as a whole, a polarization compensated two-mirror scheme (Figure 4) is used. Note the instrumental polarization of an optical system is the polarization of light at the output of the optical system for an unpolarized input. e polarization compensation in scheme (Figure 4) is provided under the condition of the complete identity of optical characteristics of mirrors M1 and M2, when plane-parallel rays fall on mirrors M1 and M2 at the same angles and when the angle between the planes of incidence of rays at mirrors is 90°. When the aforementioned conditions are not met, the polarization compensation is violated too, and uncompensated instrumental polarization will be mixed into the polarization of the input scene. Nonparallelism of rays will also violate the polarization compensation of the mirror pair (Figure 4) [9]. For the evaluation of the influence of the accuracy of mirror alignment in the scheme of Figure 4 on the level of instrumental polarization of TSM, the Mueller matrix method was used. In the Mueller method, the polarization of the beam is represented by the Stokes vector S. e optical system is represented by the Mueller M matrix. A view of the Stokes vector S in the general form is given in the following equation: Angular speed (rad/s) Torque coefficient (Nm/A) Moment of inertia (kg·m2) Active winding resistance (Phm) Electromagnetic winding time constant (s) Moment of resistance (N m) Electromechanical time constant (s) Power consumption in operating mode (Watt) , where I, Q, U, and V are Stokes parameters; I is also the total intensity of the light; p is the degree of polarization of the light; and θ and ε are the azimuth and angle of ellipticity of the light polarization ellipse, respectively. Remote sensing often deals with partially or completely linearly polarized light. e angle of ellipticity of the partially or completely linearly polarized light is zero (ε 0°), and the fourth Stokes parameter is zero (V 0) as well. us the Stokes vector takes the following form: cos(2θ) sin(2θ) U arctgQ, where the parameter p means the degree of linear polarization (DoLP) and θ is the azimuth of linear polarization (AoLP). e Mueller matrix M connects the light polarizations at the input and output of the optical system as where Sin and Sout are the Stokes vectors of the input and output light and M is the Mueller matrix of the optical system. To describe the polarization characteristics of the TSM (Figures 1 and 4), it is necessary to define its Mueller matrix. e Mueller matrix of an ideal metal mirror is well known (see, for example, [10]): MMrs,p ⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦, where rs,p |rs,p|exp(φs,p) are the complex reflection coefficients for the projection of the electric components of the incident beam on the plane of incidence (p) and on its orthogonal plane (s) (Figure 4). Note that matrix (5) is written in Eigen Geometry, where the z-axis is directed along the direction of light propagation and the x- and y-axes are parallel to the projections Es and Ep electric component of the light, respectively. is coordinate system is the Eigen Geometry because the light with linear polarizations along the x- or y-axis of this coordinate system does not change its polarization when reflected by the mirror. When rotating the coordinate system of the incident light around the z-axis by an angle α, matrix (5) will turn to ⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦. In the normal position, the planes of incidence of the rays on the mirrors M1 and M2 (Figure 4) are rotated relative to each other by an angle of 90°, so for the mirror M2 –α 90°. According to the Muller matrix method, taking into account equations (5)–(7), the polarization characteristics of TSM can be described by a matrix product of the form: MTSM MM2rs,p,90° · MM1rs,p, 0°, where MTSM is the general Muller matrix for two scan mirrors, MM1(r0s,°p,) is the Muller matrix of the mirror M1, and MM2(rs,p,90°)is the matrix of the mirror M2, rotated by 90° with respect to the first one, which is calculated using (5). Assuming that the polarization characteristics rs,p of the first and the second mirrors of the configuration (Figure 4) are identical, from (8) it could be obtained that MTSM is an identity diagonal matrix with some scale factor. In other words, a pair of mirrors (Figure 4) in this case will be polarization-neutral (i.e., polarization compensated). e misalignments of the system mirrors will affect the polarization compensation. For the sake of simplicity, let fix the mirror M1 and assume that the light falls on it at the angle i 45°. e displacement of the second mirror relative to the exact position comes down to the rotations relative to two axes: “Axis 1” and “Axis 2” (Figure 5). is simplification is obviously acceptable because the degree of neutrality of the mirror system (Figure 4) will depend on the difference between the angles of the light incidence on the mirrors M1 and M2 and on the angle α between their planes of incidence. e tilts of the mirror M2 around axis 1 (Figure 5) correspond to the change of the angle α by the value of β relative to exact position α 90°. e tilts of the mirror M2 around axis 2 (Figure 5) correspond to the change of the incidence angle by the value of c relative to exact position i 45°. e dependence of the mirror system matrix on the tilts of the mirror M2 can be determined using (8) as where rs′,p are the new complex reflection coefficients of the mirror M2 with some tilt c around axis 2 (Figure 5). e coefficients of reflection rs,p are related to the angle of incidence and the complex refractive index of the mirror material N(λ) n(λ) − j · k(λ) through Fresnel and Snell’s equations: rs where λ is the light wavelength, j is the imaginary unit, N0 1 is the refractive index of air, and φ is the angle of refraction. As it was assumed above, the light incidence angle for the mirror M1 is i 45°. Since for the mirror M2 this angle is changed to i 45° ± c, according to (10) and (11), the reflection coefficients rs′,p are not equal to rs,p for M1. In the SMA, aluminum mirrors are used. To calculate rs′,p in (10) and (11), it is necessary to substitute the refractive index N(λ) for aluminum. It is well known that the accurate polarization properties of aluminum mirrors are difficult to model. In fact, the refractive index of aluminum mirror strongly depends on (1) the coating process features [11], (2) the presence of a film of alumina (Al2O3) on the mirror, and (3) the presence of dust on the surface [10]. erefore, the information on the dispersion dependences of aluminum films differs in different references (see, for example, [11,12,13,14,15]). Our paper uses data from [16] based on [11]. Table 2 and Figure 6 show the real n(λ) and imaginary k(λ) part of the complex refractive index N(λ) of the model aluminum mirror for the wavelengths used in ScanPol. Using the data from Table 2 and equations (4) and (9)–(11) and considering the tilts of the mirror M2 around axes 1 and 2 in the ranges of angles β, c ∈[−1°, 1°] relative to exact positions α 90° and i 45°, the boundary estimates were obtained for the degree pinst max|p0 − p′|100% (Figure 7) and the azimuth of the instrumental polarization θinst max|θ0 − θ′| (Figure 8), where p0 and θ0 are, respectively, the degree and azimuth of the linear polarization of the light at the input of the TSM and p′ and θ′ are, respectively, the degree and azimuth of the linear polarization of the light at the output of the TSM. e pinst does not depend on p0, but it is increased with an increase in β and c (see Figure 8). e θinst dependence with β and c is increased as the value of p0 decreases from 1 to 0 (see Figures 8 and 9). Figure 8 shows the θinst estimates at p0 0.2. Figures 7–9 show the significant dependence of the TSM instrumental polarization on the light wavelength. It is seen the value of instrumental polarization is the greatest for the spectral range λ 865 nm. us, in setting accuracy requirements for the alignment of the mirror system, we relied on the spectral component λ 865 nm. e declared maximum error in determining the degree of linear polarization of light by ScanPol in all spectral ranges is Δp ≤ 0.15%. e declared maximum error in determining the azimuth of the linear polarization is Δθ ≤ 0.2° at p0 ≥ 0.2 [17] since here Δθ has a weak dependence on p0. As it was expected for p0 > 0.2 the dependence of Δθ on p0 will grow significantly, thereby under this condition there is no sense to determine θ separately due to the significant error. e expectation has been confirmed at least for the spectral component λ 865 nm (Figure 9). Given the other sources of systematic errors in ScanPol to achieve the declared error limits Δp and Δθ, the instrumental polarization of the TSM should not exceed pinst 0.1°. From the dependences in Figures 7–9 for the spectral component λ 865 nm, it can be seen that (12) will be met if the errors of the mirror setup (Figure 5) do not exceed 0.25° (15 arcmin) pinst (%) (b) Figure 8: Continued. 0.00 λ = 865 nm (a) λ = 410 nm (b) λ = 1378 nm Figure 9: Continued. 0.00 λ = 1620 nm Figure 9: Dependence of the boundary value of the azimuth θinst of the instrumental polarization of the TSM on the mirror M2 tilt around axes 1 and 2 (as shown in Figure 5) at degrees of linear polarization p0 < 0.2. c ≤ 15 arc min , At higher values of errors in the position of TSM mirrors or if the increase in the accuracy of determining the angle of linear polarization of the input light is needed, it is necessary to calibrate the TSM according to the method described in [17]. 4.2. e Procedure for Adjustment. To achieve an accuracy of 15 arcmin for the mirror installation in TSM, an appropriate method and optical bench were developed. Two certified standards of angles were used on the bench: a glass cube with surfaces of 90° named a control optical element (COE) and a pentaprism guaranteeing to return the light beam at 90°. e angle tolerances of the glass cube and the pentaprism are 2 arcmin. e adjustment of the TSM includes the following steps: Step 1 (illustrated in Figure 10): preassemble the TSM with the ability to rotate around its own axis. We use the axis that is a structural element of the electric motor and that is fixed during adjustment in the auxiliary mounting assembly. In input window 1, a framed COE is installed, which provides its tilt along the three axes. Step 2 (illustrated in Figure 11): the pentaprism is placed in front of the TSM. It deflects laser beam 1 by 90° on screen 2. At this point, mark P2 is made. e distance between labels P1 and P2 is determined in the projection on the X-axis. Step 3 (illustrated in Figure 12): laser 2 is placed into the alignment system that directs the beam to the COE and Mirror 1 Mirror 2 the position of the reflected beam from the COE is fixed using label P3. Label P3 is selected arbitrarily. When we rotate the TSM by angle 90°, the second laser beam, reflected from the next face of the COE, will create a label P4. If label P4 coincides with label P3, it means that we have rotated the TSM by 90° ± 2 arcmin. Step 4 (illustrated in Figure 13): mirror 1 is removed, and the TSM is rotated at angle 90°. e correct position of the unit is controlled such that label P4 coincides with label P3 obtained in step 3. e distance between labels P2 and P5 in the projection on the X-axis is determined. If the segment P2–P5 is equal to the segment P1–P2, defined in step 2, mirror 2 is installed in the TSM at an angle of 90°. Otherwise, mirror 2 must be adjusted. Step 5 (illustrated in Figure 14): place mirror 1 and rotate the TSM at an angle of 90°. e angle of rotation is controlled using a beam from laser 2, which is reflected from the surface of the COE and must coincide with label P4 on screen 2. We fix the position by label P6 of the beam from laser 1 on screen 2 (Figure 14), which passed through the TSM. At the exact angle of mirror 2 relative to mirror 1, equal to 90°, the spots from laser 1 must be placed on a single line along the Y-axis, which passes through label P5, and must be at a distance of the base between mirror 1 and 2 centers from the specified label. If this condition is not satisfied, we adjust mirror 2. e distance between the TSM and screen 2 is 5 meters. e label position error on the screen and their alignment is ≤3 mm, which gives an error of the viewing angle
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