Method for eliminating rotation influence of polarization grating

Abstract

The invention relates to a method for eliminating the influence of polarization grating rotation. The method comprises the following steps: firstly, providing a rotation model based on a liquid crystal polarization grating and analyzing a two-dimensional error caused by the rotation of a single grating; mat lab is adopted for simulation, the 10-degree liquid crystal polarization grating is analyzed, and an error value caused in the two-dimensional direction is obtained; secondly, adopting two liquid crystal grating groups through experiments, rotating 10-degree gratings to obtain error data, and comparing the error data with a simulation result to verify the simulation reliability; secondly, carrying out grating rotation error analysis on the two liquid crystal polarization gratings, and respectively fitting an error correction experimental formula and a theoretical formula in a two-dimensional direction; finally, the fitted correction formula is substituted into a system control program, errors caused by grating rotation are corrected, and the light beam pointing precision is improved. The method provided by the invention provides technical support for subsequent application in laser radars, laser weapons and laser communication.

Description

Technical Field

[0001] The invention relates to the technical field of medical drainage instruments, and in particular to a method for eliminating the influence of polarization grating rotation. Background Art

[0002] Liquid crystal optical phased array technology can be widely used in free space optical communication, infrared countermeasures, laser pointers, laser radar, optical switches, etc. due to its advantages of no mechanical movement, small size, light weight, and easy conformality. In order to achieve large-angle deflection of the light beam, most liquid crystal optical phased arrays adopt a two-level beam deflection strategy, that is, a combination of high-precision small-angle scanning devices and large-angle beam rough scanning devices to achieve large-angle continuous scanning of the laser beam. Among them, the combination of liquid crystal spatial light modulators and liquid crystal polarization gratings has been widely studied due to its advantages of high scanning accuracy, large angle, and easy implementation. In terms of large-angle scanning of light beams, the earliest large-angle beam scanning system based on liquid crystal polarization gratings was studied by Jihwan Kim and other researchers in 2008. The liquid crystal polarization grating was used to successively achieve quasi-continuous deflection of light beams with field angles of ±15°, ±26°, ±40°, ±52°, etc. In 2016, Steven et al. developed a new liquid crystal polarization grating device, which used a multi-layer liquid crystal polarization grating cascade to achieve two-dimensional light beam discrete scanning with an angular resolution of 3.2° and a scanning field of view of 64°×64°.

[0003] In terms of high-precision beam pointing, Paul F.McManamon et al. first proposed the use of variable period grating method for beam deflection in 2009, and analyzed the factors affecting the beam pointing accuracy of liquid crystal phased array. In 2014, Qiao Tianyuan et al. analyzed the influence of voltage quantization, different wavefront incidents, and different deflection angles on the pointing accuracy of liquid crystal spatial light modulators. The optimized beam pointing accuracy can reach 0.04mrad. In 2015, Wang Xiangru proposed the sub-aperture coherence method and improved the scanning accuracy to address the problem of low pointing accuracy of the variable period grating method caused by pixelation factors. In 2017, Wang Xiangru analyzed the influence of manufacturing process errors, voltage quantization errors, liquid crystal material properties, etc. of liquid crystal optical phased arrays on scanning accuracy. In 2021, Wang Chengmiao proposed the radial sub-aperture coherence method, which further improved the pointing accuracy and stability of liquid crystal phased arrays in practical applications. In 2019, Li Songzhen established a beam deflection system based on a cascade of liquid crystal spatial light modulators and liquid crystal polarization gratings, which achieved high-precision two-dimensional beam deflection at a wavelength of 730nm, with a pointing accuracy of 30μrad. In 2022, Fan Jiaxin et al. analyzed the influence of factors such as voltage quantization, electrode duty cycle, and voltage frequency, and used a particle swarm optimization algorithm to achieve high-precision pointing of liquid crystal phased arrays. In the same year, Wang C et al. established a liquid crystal optical phased array beam scanning system, which used the Gerchberg–Saxton algorithm to achieve incident plane wave segmentation, so that the system pointing accuracy reached 16μrad. A small amount of work has preliminarily studied the influence of some parameters of the liquid crystal phased array on the beam deflection accuracy. In recent years, some work has successively studied the influence of oblique incidence of the beam on the beam pointing of the liquid crystal polarization grating, but has not yet considered the influence of the liquid crystal polarization grating on the beam pointing accuracy when it rotates, nor has it established a formula for introducing correction beam pointing accuracy. Pointing accuracy is the core indicator of the liquid crystal phased array. Understanding the changing law of the beam deflection accuracy of the liquid crystal phased array is of great significance for the optimal design of the liquid crystal phased array and the realization of high-precision beam deflection.

[0004] Liquid crystal is an anisotropic material. Liquid crystal molecules produce anisotropy with the director as the axis. Liquid crystal is mainly composed of electrodes and liquid crystal boxes. A single electrode and the liquid crystal box together form a phase-controlled unit. When different voltages are applied to the liquid crystal electrodes, the liquid crystal molecules in the liquid crystal box will deflect the director under the action of the external electric field. Liquid crystal polarization grating is based on this characteristic of liquid crystal. By controlling the orientation of liquid crystal molecules, a periodic orientation distribution is formed, thereby modulating the incident circularly polarized light. The director of the liquid crystal molecule changes by 180° in one period, which is the period of the liquid crystal polarization grating. Liquid crystal polarization gratings are divided into active and passive types. Active liquid crystal polarization gratings have three states: no deflection, +1 level deflection and -1 level deflection, which correspond to the application of voltage, no voltage, right-handed and left-handed circularly polarized light incidence. Passive liquid crystal polarization gratings, that is, passive liquid crystal polarization gratings, have two states: +1 level deflection and -1 level deflection. When the incident light is right-handed circularly polarized light, all light passing through the liquid crystal polarization grating is diffracted to the +1 order. If the incident light is left-handed circularly polarized light, all light is diffracted to the -1 order. The polarization state of light incident on the liquid crystal polarization grating can be controlled by a liquid crystal half-wave plate, which is controlled by applying a voltage to produce a half-wave or 0 phase delay, thereby achieving control of the left-handed or right-handed polarization state. Therefore, liquid crystal polarization gratings and liquid crystal half-wave plates are usually used in pairs to achieve light beam deflection control.

[0005] Liquid crystal polarization grating is used as a beam deflection device. In liquid crystal optical phased array lidar, the deflection angle of the liquid crystal polarization grating determines the scanning angle of the system. In addition, since the preparation of the liquid crystal polarization grating itself is difficult, the prepared polarization grating will have a certain angle relative to the horizontal direction. That is, the rotation of the liquid crystal polarization grating will eventually affect the beam deflection angle, greatly reducing the pointing accuracy of the system and directly affecting the accuracy of the target detection position.

[0006] In view of the influence of the rotation of the liquid crystal polarization grating on the pointing accuracy of the laser beam, the present invention provides a method for eliminating the influence of the rotation of the polarization grating and provides a correction method to achieve high-precision scanning of the beam. Summary of the invention

[0007] The purpose of the present invention is to overcome the problems existing in the prior art, provide a method for eliminating the influence of polarization grating rotation, realize accurate calculation of grating rotation error in liquid crystal polarization grating cascade system, and provide technical support for high-precision pointing of laser beam scanning system.

[0008] In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

[0009] A method for eliminating the influence of polarization grating rotation, the method comprising the following steps:

[0010] Step S1: establishing a grating rotation model based on the grating diffraction equation;

[0011] Step S2: introducing the grating rotation angle to obtain the error relationship between the grating rotation and the outgoing light beam pointing accuracy;

[0012] Step S3: using a grating rotation experiment to simulate and analyze different grating rotation situations, and verifying the correctness and accuracy of the error relationship between the grating rotation and the output light beam pointing accuracy by comparing with the simulation results;

[0013] Step S4: Substitute the established error relationship between the grating rotation and the output light beam pointing accuracy into the control algorithm to correct the influence of the grating rotation.

[0014] Furthermore, in step S1, multiple polarization gratings are cascaded, and each outgoing light passing through a grating is obliquely incident on the next grating, and the actual outgoing angle passing through each grating is calculated by the grating diffraction equation. The grating diffraction equation is:

[0015] d*(sinθ1±sinθ0)=k*λ (1);

[0016] In formula (1), d is the grating period, θ0 is the incident angle, θ1 is the diffraction angle, k is the diffraction order, and λ is the wavelength of the light beam. When θ1 and θ0 are on the same side of the normal, it is the sum of the two; when θ1 and θ0 are on different sides of the normal, it is the difference between the two.

[0017] According to formula (1), the influence of a certain polarization grating on the beam pointing accuracy at different rotation angles is analyzed. According to the grating diffraction equation transformation, the exit angle of the beam passing through the current polarization grating is:

[0018]

[0019] In formula (2), is the exit angle of the current polarization grating of the light beam, d n is the period of the current polarization grating, λ is the laser wavelength, where when the incident angle θ0 is 0, that is, the light beam is vertically incident on the first liquid crystal polarization grating;

[0020] The light spot rotates on the camera target surface in a circle with R as radius, and L is the distance from the grating to the camera lens. We can get:

[0021]

[0022] The error caused by grating rotation is the difference between the pixel offset when the grating is not rotated and the pixel offset when the grating is rotated, that is, the error calculation formula in two directions can be obtained:

[0023] Δl || =Rl ||(4)

[0024] Δl ⊥ =Rl ⊥ (5);

[0025] In formulas (4) and (5), l || is the pixel offset caused by the grating rotation parallel to the beam deflection direction, l ⊥ is the pixel offset caused by the grating rotation perpendicular to the beam deflection direction, Δl || is the pixel offset caused by the rotation of the grating relative to the ideal state of the grating in the direction parallel to the beam deflection, Δl ⊥ It is the pixel offset caused by the grating rotation relative to the ideal grating state in the direction perpendicular to the beam deflection direction.

[0026] Furthermore, in step S2, the influence of grating rotation on the pointing accuracy of light beams with different incident angles under the premise of considering grating diffraction is derived through equations (3) and (4), equations (3) and (5):

[0027]

[0028] In formula (6) and formula (7), θ R is the equivalent grating rotation angle, which represents the equivalent angle of rotation of all polarization gratings in the system.

[0029] Furthermore, in step S3, simulation software is used to analyze the effect of the rotation of a single grating on the pointing accuracy, and the errors caused in two directions can be obtained by equations (6) and (7); the grating rotation experiment is set as follows: the light emitted by the laser is collimated by a collimating lens, and then becomes linearly polarized light after passing through a polarizer, and the linearly polarized light becomes circularly polarized light after passing through a 1 / 4 wave plate, and then is incident on a liquid crystal half-wave plate and a liquid crystal polarization grating, and finally the laser spot is intercepted on a CCD camera; then the liquid crystal polarization grating is rotated at multiple angles by a rotating platform, with counterclockwise rotation as a "+" angle and clockwise rotation as a "-" angle, and the position of the spot at different rotation angles is intercepted by a CCD camera, and the spots at different positions are recorded respectively.

[0030] Furthermore, in step S3, the centroid of the spot of the liquid crystal polarization grating at different rotation angles is calculated using the following formula:

[0031]

[0032] In formula (8) and formula (9), (x i，j ,y i，j ) are the coordinates of the pixel point (i, j), I i，jis the light intensity at the pixel point (i, j). According to the obtained centroid coordinates, the offset relative to the coordinates when the liquid crystal polarization grating is not rotated is calculated, and then the actual offset angle of the light spot is calculated by the following formula:

[0033] tanθ=Δl*D / f (10)

[0034] In formula (10), θ is the actual offset angle of the light spot, Δl is the distance the light spot is offset from the center, D is the pixel size, and f is the focal length of the focusing lens.

[0035] Furthermore, in step S4, two errors in the light beam deflection direction and the error perpendicular to the light beam deflection direction are corrected to improve the light beam pointing accuracy.

[0036] Further, in step S4, if the deflection of the target angle θ is achieved, the actual deflection angle will be θ' ​​due to the influence of the grating rotation. On the target surface of the CCD camera, it will be observed that the "+" and "-" angle spots are not in the same deflection direction, and the "+" angle spot is offset in the direction of the beam deflection, and the "-" angle spot is offset in the direction opposite to the beam deflection direction. The grating rotation angle θ can be obtained by obtaining the offset of the beam perpendicular to the beam deflection direction when the beam is deflected at the "+" and "-" angles. R , through θ R The error Δθ of the grating rotation in the beam deflection direction is obtained || and the error Δθ perpendicular to the beam deflection direction ⊥ , subtract the error from the “+” angle and add the error to the “-” angle at the original spot position to complete the spot pointing accuracy correction.

[0037] Furthermore, in step S4, the grating rotation angle θ is calculated by the following formula: R :

[0038]

[0039] In formula (11), It is the offset of the light spot between the “+” and “-” angles perpendicular to the beam deflection direction;

[0040] Substituting Δl in equation (4) and equation (5) || and Δl ⊥ Substituting into formula (10) we can get:

[0041]

[0042] In equations (12) and (13), Δθ || is the error value caused by the grating rotation in the direction parallel to the beam deflection, Δθ ⊥ This is the error value caused by the grating rotation in the direction perpendicular to the beam deflection direction.

[0043] Furthermore, in step S4, for the relationship between the beam pointing accuracy error and the grating rotation angle, after obtaining the error values ​​caused by the grating in the two deflection directions of the beam at different rotation angles, a relationship curve between the grating rotation angle and the error in the two deflection directions of the beam is fitted to form the following formula:

[0044]

[0045] Similarly, by using equations (12) and (13), we can substitute different θ in the grating rotation experiment: R The error values ​​of the corresponding two deflection directions are obtained by The error curve is fitted to a fixed value of 0.1783 rad, forming the following formula:

[0046]

[0047] Δθ ⊥理论 =0.17928*θ R (17)

[0048] Compare the experimental and theoretical fitting formula coefficients of formula (14) and formula (15), formula (16) and formula (17), and compare the coincidence of the fitting curves of the two to verify the correctness of the theoretical formula. In the error correction process, the obtained Δθ || and Δθ ⊥ Substituting the actual angle for correction can achieve beam deflection at the target angle.

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

[0050] The present invention aims at the influence of the rotation of the liquid crystal polarization grating on the pointing accuracy of the laser beam and provides a correction method to achieve high-precision scanning of the beam. Firstly, a rotation model is given based on the liquid crystal polarization grating and the two-dimensional error caused by the rotation of a single grating is analyzed; Matlab is used for simulation, and the 10° liquid crystal polarization grating is analyzed to obtain the error value caused in the two-dimensional direction; then, two liquid crystal grating groups are used in an experiment to rotate the grating by 10° to obtain error data and compare it with the simulation result to verify the reliability of the simulation; then, the error of grating rotation is analyzed for the two liquid crystal polarization gratings, and the experimental formula and theoretical formula of error correction in the two-dimensional direction are fitted respectively; finally, the fitted correction formula is substituted into the system control program to correct the error caused by the grating rotation, so that the beam pointing accuracy is improved; technical support is provided for subsequent applications in laser radar, laser weapons and laser communications. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 The liquid crystal polarization grating rotation model of the present invention;

[0052] Figure 2 It is a schematic diagram of the camera target surface of the present invention.

[0053] Figure 3 The parallel light beam deflection direction error relationship diagram of the present invention, wherein a: grating rotation "-" angle, b: grating rotation "+" angle;

[0054] Figure 4 It is a relationship diagram of the vertical beam deflection direction error of the present invention, wherein a: grating rotation "-" angle, b: grating rotation "+" angle;

[0055] Figure 5 ; is a diagram showing the relationship between the deflection angle and error of the liquid crystal polarization grating of the present invention, wherein a: is parallel to the deflection direction of the light beam, and b: is perpendicular to the deflection direction of the light beam;

[0056] Figure 6 This is a graph showing the relationship between the beam deflection angle and the error when the 10° grating of the present invention rotates 1°, wherein a is parallel to the beam deflection direction, and b is perpendicular to the beam deflection direction;

[0057] Figure 7 The light spot position diagram of the grating of the present invention at different rotation angles;

[0058] Figure 8 The light spot simulation and error position comparison diagram of the 10° polarization grating of the present invention at different rotation angles, where a is parallel to the beam deflection direction, and b is perpendicular to the beam deflection direction;

[0059] Fig. 9 This is a diagram of the light spot deflection angle when the 10° polarization grating of the present invention rotates 1°;

[0060] Fig.10 This is a comparison diagram of the deflection angle errors of the two liquid crystal polarization grating groups of the present invention, where a is parallel to the light beam deflection direction, and b is perpendicular to the light beam deflection direction;

[0061] Fig.11 is an error correction flow chart of the entire light beam scanning system of the present invention;

[0062] Fig.12 is a graph showing the relationship between the grating rotation angle and the error parallel to the light beam deflection direction of the present invention;

[0063] Fig.13 is a graph showing the relationship between the grating rotation angle of the present invention and the error perpendicular to the light beam deflection direction;

[0064] Fig.14 A diagram of a beam deflection system of the present invention;

[0065] Fig.15This is a comparison diagram of the light spot position before and after correction of the present invention, wherein a: the light spot position diagram before correction, b: the light spot position diagram after correction;

[0066] Fig.16 This is a comparison diagram of the light spot position before and after correction of the present invention. DETAILED DESCRIPTION

[0067] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0068] A method for eliminating the influence of polarization grating rotation, the method comprising the following steps:

[0069] Step S1: establishing a grating rotation model based on the grating diffraction equation;

[0070] Step S2: introducing the grating rotation angle to obtain the error relationship between the grating rotation and the outgoing light beam pointing accuracy;

[0071] Step S3: using a grating rotation experiment to simulate and analyze different grating rotation situations, and verifying the correctness and accuracy of the error relationship between the grating rotation and the output light beam pointing accuracy by comparing with the simulation results;

[0072] Step S4: Substitute the established error relationship between the grating rotation and the output light beam pointing accuracy into the control algorithm to correct the influence of the grating rotation.

[0073] In step S1, multiple polarization gratings are cascaded, and the outgoing light passing through each grating is obliquely incident on the next grating, such as Figure 1 As shown, when the liquid crystal polarization grating is not rotated, the light beam passes through the liquid crystal polarization grating to achieve angle deflection, which is the position of the dotted light spot; when the grating rotates along the x-axis direction by θ r When the light beam is directed to the x-axis and y-axis, an angle component will be formed, resulting in the light spot being at the solid circle position, which affects the beam pointing accuracy. The actual exit angle passing through each grating is calculated using the grating diffraction equation. The grating diffraction equation is:

[0074] d*(sinθ1±sinθ0)=k*λ (1);

[0075] In formula (1), d is the grating period, θ0 is the incident angle, θ1 is the diffraction angle, k is the diffraction order, and λ is the wavelength of the light beam. When θ1 and θ0 are on the same side of the normal, it is the sum of the two; when θ1 and θ0 are on different sides of the normal, it is the difference between the two.

[0076] According to formula (1), the influence of a certain polarization grating on the beam pointing accuracy at different rotation angles is analyzed. According to the grating diffraction equation transformation, the exit angle of the beam passing through the current polarization grating is:

[0077]

[0078] In formula (2), is the exit angle of the current polarization grating of the light beam, d n is the period of the current polarization grating, λ is the laser wavelength, where when the incident angle θ0 is 0, that is, the light beam is vertically incident on the first liquid crystal polarization grating;

[0079] like Figure 2 As shown, through the camera target surface schematic diagram in the figure, the light spot rotates on the camera target surface to form a circle with R as the radius, and L is the distance from the grating to the camera lens, we can get:

[0080]

[0081] The error caused by grating rotation is the difference between the pixel offset when the grating is not rotated and the pixel offset when the grating is rotated, that is, the error calculation formula in two directions can be obtained:

[0082] Δl || =Rl || (4)

[0083] Δl ⊥ =Rl ⊥ (5);

[0084] In formulas (4) and (5), l || is the pixel offset caused by the grating rotation parallel to the beam deflection direction, Δl ⊥ is the pixel offset caused by the grating rotation perpendicular to the beam deflection direction, Δl || is the pixel offset caused by the rotation of the grating relative to the ideal state of the grating in the direction parallel to the beam deflection, Δl ⊥ It is the pixel offset caused by the grating rotation relative to the ideal grating state in the direction perpendicular to the beam deflection direction.

[0085] In step S2, the influence of grating rotation on the pointing accuracy of light beams with different incident angles under the premise of considering grating diffraction is derived through equations (3) and (4), equations (3) and (5):

[0086]

[0087] In formula (6) and formula (7), θ R is the equivalent grating rotation angle, which represents the equivalent angle of rotation of all polarization gratings in the system.

[0088] In step S3, the influence of the rotation of the single grating on the pointing accuracy is analyzed by using MATLAB simulation software, and the errors caused in two directions can be obtained by equations (6) and (7); Figure 3 and Figure 4As shown in the figure, it can be seen that the larger the grating rotation angle is, the larger the pointing error caused in the light spot deflection direction is. At the same time, when the grating rotates clockwise and the light spot deflection angle is deflected to the "+" angle range, the error caused in the light spot deflection direction is positive, and the error caused perpendicular to the light spot deflection direction is negative. When the light spot deflection angle is deflected to the "-" angle range, the directions of the errors caused in the two directions are opposite. Figure 4 a. Figure 5 As shown in a, when the grating rotates counterclockwise and the light spot deflection angle is deflected to the "+" angle range, the errors caused are all positive, and when the light spot deflection angle is deflected to the "-" angle range, the errors caused are all negative, such as Figure 4 b. Figure 5 b; in addition, the influence of the grating rotation in the direction perpendicular to the deflection direction of the light spot is greater than that in the deflection direction of the light spot; the beam scanning system uses the liquid crystal polarization grating in Table 1 to achieve large-angle, high-precision two-dimensional scanning of the light beam:

[0089] Table 1 Liquid crystal polarization grating group of the system

[0090] Serial number 1 2 3 4 5 6 7 Diffraction angle (deg) 0.1575 0.315 0.63 1.26 2.52 5.04 10.08 Grating period (μm) 387.06 193.53 96.77 48.38 24.2 12.11 6.08

[0091] ,pass Figure 5 From the relationship diagram between the simulated liquid crystal polarization grating period and the spot deflection direction error, it can be seen that the larger the deflection angle of the liquid crystal polarization grating, the greater the error in the beam pointing accuracy; when the liquid crystal polarization grating deflection angle is between 0.15° and 10.08°, the grating rotation pointing accuracy is: parallel to the beam deflection direction, the maximum error is 0.025%; perpendicular to the beam deflection direction, the maximum error is 3%; when the grating deflection angle is less than 0.5°, the grating rotation pointing error in both directions is close to 0 and can be ignored; by analyzing the error caused by the beam with different deflection angles when the grating rotates 1° at 10°, as shown in the figure: Figure 6As shown, it can be seen that the grating rotation will cause the direction of the light beam to be inconsistent when it is deflected to the "+" angle and the "-" angle, which will eventually cause the light spot to jump significantly during the scanning process from the "-" angle to the "+" angle; when the light beam deflection angle is at the "+" angle, the errors caused in both directions are positive; when the light beam deflection angle is at the "-" angle, the errors caused in both directions are negative; and as the light beam deflection angle increases, the grating rotation will have a greater impact on the light beam pointing accuracy. The corresponding grating rotation experiment is set up as follows: the light emitted by the laser is collimated by a collimating lens, then passes through a polarizer to become linearly polarized light, the linearly polarized light passes through a 1 / 4 wave plate to become circularly polarized light, and then is incident on a liquid crystal half-wave plate and a liquid crystal polarization grating, the liquid crystal polarization grating can be a 1° polarization grating and a 10° polarization grating, and finally the laser spot is intercepted on a CCD camera; then the liquid crystal polarization grating is rotated at multiple angles by a rotating platform, with counterclockwise rotation as a "+" angle and clockwise rotation as a "-" angle, and the position of the spot at different rotation angles is intercepted by a CCD camera, and the spots at different positions are recorded respectively. In this embodiment, a total of 12 rotations are performed, and the spots at different positions are recorded respectively; Figure 7 As shown in the figure, from top to bottom are +1, 0, and -1 light spots respectively. It can be seen that when the 10° grating is not rotated, the three light spots are located in a vertical line; when the grating rotation angle is a negative angle, the -1 level is at the left oblique position of the +1 light spot; when the grating rotation angle is a negative angle, the -1 level is at the right oblique position of the +1 light spot.

[0092] In step S3, the centroid of the spot of the liquid crystal polarization grating at different rotation angles is calculated using the following formula:

[0093]

[0094] In formula (8) and formula (9), (x i，j ,y i，j ) are the coordinates of the pixel point (i, j), I i，j is the light intensity at the pixel point (i, j). According to the obtained centroid coordinates, the offset relative to the coordinates when the liquid crystal polarization grating is not rotated is calculated, and then the actual offset angle of the light spot is calculated by the following formula:

[0095] tanθ=Δl*D / f (10),

[0096] In formula (10), θ is the actual deflection angle of the light spot, Δl is the distance of the light spot relative to the center, D is the pixel size, and f is the focal length of the focusing lens. In this embodiment, the pixel size is 3.2 μm, and the focal length of the lens is 28 mm. Using formula (10), the actual deflection angle of the light spot can be obtained, and the error value at each rotation angle can be calculated. The experimental value and the theoretical value are compared through the polar coordinate diagram, as shown in FIG. Figure 8As shown in the figure, it can be seen that in both directions, the light spot simulation of the 10° polarization grating with different rotation angles is close to the error position; next, the control program is used to realize the light beam scanning of the two liquid crystal polarization gratings, with scanning angles of 11°, 9°, -9°, and -11°, and the light spot position is recorded on the CCD camera, as shown in Fig. 9 As shown; consistent with the above method for calculating the angle offset under 10° polarization grating rotation, the angle offset of the spot at the "+" and "-" angles perpendicular to the beam deflection direction is obtained, as shown in Table 2:

[0097]

[0098] ; Compare the calculated angle offset with Fig.10 By comparing the simulation results, it can be seen that when the 10° grating is rotated 1° and the light spot is at the positions of ±9 and ±11°, the offset in the direction perpendicular to the beam deflection is about 0.17°, while the simulation result is 0.17°, and the offset in the direction parallel to the beam deflection is about 0.0013°, while the simulation result is 0.0013°, which verifies the accuracy of the experiment.

[0099] In step S4, the influence of polarization grating rotation on the beam pointing accuracy is reduced mainly by correcting two errors, one in the beam deflection direction and the other in a direction perpendicular to the beam deflection direction, so as to improve the beam pointing accuracy.

[0100] In step S4, if the deflection of the target angle θ is achieved, the actual deflection angle will be θ′ due to the influence of the grating rotation. On the target surface of the CCD camera, it will be observed that the “+” and “-” angle light spots are not in the same deflection direction, and the “+” angle light spot is offset in the direction of the beam deflection, and the “-” angle light spot is offset in the direction opposite to the beam deflection direction. The grating rotation angle θ can be obtained by obtaining the offset of the beam perpendicular to the beam deflection direction when the beam is deflected at the “+” and “-” angles. R , through θ R The error Δθ of the grating rotation in the beam deflection direction is obtained || and the error Δθ perpendicular to the beam deflection direction ⊥ The spot pointing accuracy correction is completed by subtracting the error from the “+” angle and adding the error to the “-” angle of the original spot position; the accuracy of the correction method can be verified by calculating the error between the actual deflection angle of the system spot before and after correction and the target deflection angle.

[0101] In step S4, the grating rotation angle θ is calculated by the following formula: R :

[0102]

[0103] In formula (11), It is the offset of the light spot between the “+” and “-” angles perpendicular to the beam deflection direction;

[0104] Substituting Δl in equation (4) and equation (5) || and θl ⊥ Substituting into formula (10) we can get:

[0105]

[0106] In equations (12) and (13), Δθ || is the error value caused by the grating rotation in the direction parallel to the beam deflection, Δθ ⊥ is the error value caused by the grating rotation in the direction perpendicular to the beam deflection direction; in this embodiment, Fig.11 As shown in the error correction block diagram, for the two-dimensional target angle θ to be achieved ||1 and θ ⊥1 , due to the rotation of the grating, the actual deflection angle is θ ||2 and θ ⊥2 , in order to obtain So we know the grating rotation angle θ R ; Subsequent correction process for beam pointing accuracy: If θ R Greater than 0, the “+” angle is in the direction of the light spot deflection minus Δθ || , perpendicular to the deflection direction of the light spot minus Δθ ⊥ ; “-” angle is in the direction of light spot deflection plus Δθ || , plus Δθ perpendicular to the deflection direction of the light spot ⊥ ; if θ R Less than 0, the “+” angle is in the direction of the light spot deflection minus Δθ || , plus Δθ perpendicular to the deflection direction of the light spot ⊥ ; “-” angle is in the direction of light spot deflection plus Δθ || , perpendicular to the deflection direction of the light spot minus Δθ ⊥ In this way, the pointing accuracy of the beam scanning system can be improved by analyzing and calculating the errors in the two scanning directions of the light beam and correcting these errors in the beam deflection angle.

[0107] In step S4, the relationship between the beam pointing accuracy error and the grating rotation angle is obtained by Figure 7 After obtaining the error values ​​caused by different grating rotation angles in the two deflection directions of the light beam, the relationship curve between the grating rotation angle and the error in the two deflection directions of the light beam is fitted to form the following formula:

[0108]

[0109] Δθ ⊥实验 =0.17734*θ R (16);

[0110] Similarly, by using equations (12) and (13), we can substitute the equations of the grating rotation experiment into Figure 7 Different θ R The error values ​​of the corresponding two deflection directions are obtained by The fixed value is 0.1783rad, and the distance L from the 10° grating to the camera lens is measured to be 27.8mm. The error curve is fitted to form the following formula:

[0111]

[0112] Δθ ⊥理论 =0.17928*θ R (17)

[0113] Compare the experimental and theoretical fitting formula coefficients of formula (14) and formula (15), formula (16) and formula (17), and compare Fig.12 and Fig.13 It can be seen that the two fitting curves basically coincide, verifying the correctness of the theoretical formula. In the error correction process, the obtained Δθ || and Δθ ⊥ Substituting the actual angle for correction can achieve beam deflection at the target angle.

[0114] Finally, the beam pointing accuracy correction experiment can be performed

[0115] The beam pointing accuracy of the two liquid crystal polarization gratings is corrected, such as Fig.14 As shown, using the beam deflection system, the light emitted by the 1064nm laser is collimated by the collimation system to form a 6.5mm diameter beam; the beam passes through the polarizer and is reflected by the non-polarizing beam splitter prism to the reflective liquid crystal spatial light modulator; then it is reflected again by the 1 / 4 wave plate and finally enters the liquid crystal polarization grating group, which is deflected and projected onto the camera. The control software of the laser beam scanning system is used to perform a horizontal beam scanning experiment, and the scanning results are recorded on the camera target surface.

[0116] In the experiment, the light beam scanned four angles, namely -11°, -9°, 9°, and 11°, and the scanning direction was from left to right along the horizontal axis. Fig.15 a gives the positions of the four scanning spots. It can be seen that before correction, the spot is rotated in the counterclockwise direction by the grating, which causes the system to scan in the same direction and the spot cannot be on the same vertical line. Next, substitute equations (15) and (17) into the control program of the beam scanning system, and the spot position is Fig.15 b. For analysis Fig.15The beam pointing error in the image is calculated by the centroid of the spot image collected by the CCD camera to obtain the offset of the spot on the camera target surface. The specific results are shown in Table 3:

[0117] Table 3 Comparison of experimental and simulation data

[0118] Deflection Angle Before calibration After correction error 11° 10.8241° 10.9995° .0.0005° 9° 8.8057° 9.0003° 0.0003° -9° -8.8145° -8.9999° 0.0001° -11° -10.8068° -10.9993° 0.0007° ,from Fig.16 It can be seen that the actual deflection angle after correction is very close to the theoretical value, and the error magnitude reaches 10μrad, achieving high-precision angle deflection.

[0119] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for eliminating the influence of polarization grating rotation, characterized in that: The method comprises the following steps: Step S1: establishing a grating rotation model based on the grating diffraction equation; Step S2: introducing the grating rotation angle to obtain the error relationship between the grating rotation and the outgoing light beam pointing accuracy; Step S3: using a grating rotation experiment to simulate and analyze different grating rotation situations, and verifying the correctness and accuracy of the error relationship between the grating rotation and the output light beam pointing accuracy by comparing with the simulation results; Step S4: Substitute the established error relationship between the grating rotation and the output light beam pointing accuracy into the control algorithm to correct the influence of the grating rotation.

2. The method for eliminating the influence of polarization grating rotation according to claim 1, characterized in that: In step S1, multiple polarization gratings are cascaded, and the outgoing light passing through each grating is obliquely incident on the next grating. The actual outgoing angle passing through each grating is calculated by the grating diffraction equation. The grating diffraction equation is: d*(sinθ1±+sinθ0)=k*λ (1); In formula (1), d is the grating period, θ0 is the incident angle, θ1 is the diffraction angle, k is the diffraction order, and λ is the wavelength of the light beam. When θ1 and θ0 are on the same side of the normal, it is the sum of the two; when θ1 and θ0 are on different sides of the normal, it is the difference between the two. According to formula (1), the influence of a certain polarization grating on the beam pointing accuracy at different rotation angles is analyzed. According to the grating diffraction equation transformation, the exit angle of the beam passing through the current polarization grating is: In formula (2), is the exit angle of the current polarization grating of the light beam, d n is the period of the current polarization grating, λ is the laser wavelength, where when the incident angle θ0 is 0, that is, the light beam is vertically incident on the first liquid crystal polarization grating; The light spot rotates on the camera target surface in a circle with R as radius, and L is the distance from the grating to the camera lens. We can get: The error caused by grating rotation is the difference between the pixel offset when the grating is not rotated and the pixel offset when the grating is rotated, that is, the error calculation formula in two directions can be obtained: Δl || =R-l || (4) Δl ⊥ =R-l ⊥ (5); In formulas (4) and (5), l || is the pixel offset caused by the grating rotation parallel to the beam deflection direction, l ⊥ is the pixel offset caused by the grating rotation perpendicular to the beam deflection direction, Δl || is the pixel offset caused by the rotation of the grating relative to the ideal state of the grating in the direction parallel to the beam deflection, Δl ⊥ It is the pixel offset caused by the grating rotation relative to the ideal grating state in the direction perpendicular to the beam deflection direction.

3. The method for eliminating the influence of polarization grating rotation according to claim 2, characterized in that: In step S2, the influence of grating rotation on the pointing accuracy of light beams with different incident angles under the premise of considering grating diffraction is derived through equations (3) and (4), equations (3) and (5): In formula (6) and formula (7), θ R is the equivalent grating rotation angle, which represents the equivalent angle of rotation of all polarization gratings in the system.

4. The method for eliminating the influence of polarization grating rotation according to claim 3, characterized in that: In step S3, simulation software is used to analyze the influence of the rotation of a single grating on the pointing accuracy, and the errors caused in two directions can be obtained through equations (6) and (7); the grating rotation experiment is set as follows: the light emitted by the laser is collimated by a collimating lens, and then becomes linearly polarized light after passing through a polarizer, and the linearly polarized light becomes circularly polarized light after passing through a 1 / 4 wave plate, and then is incident on a liquid crystal half-wave plate and a liquid crystal polarization grating, and finally the laser spot is intercepted on a CCD camera; then the liquid crystal polarization grating is rotated at multiple angles by a rotating platform, with counterclockwise rotation as a "+" angle and clockwise rotation as a "-" angle, and the position of the spot at different rotation angles is intercepted by a CCD camera, and the spots at different positions are recorded respectively.

5. The method for eliminating the influence of polarization grating rotation according to claim 4, characterized in that: In step S3, the centroid of the spot of the liquid crystal polarization grating at different rotation angles is calculated using the following formula: In formula (8) and formula (9), (x i，j ,y i，j ) are the coordinates of the pixel point (i, j), I i，j is the light intensity at the pixel point (i, j). According to the obtained centroid coordinates, the offset relative to the coordinates when the liquid crystal polarization grating is not rotated is calculated, and then the actual offset angle of the light spot is calculated by the following formula: tanθ=Δl*D / f (10), In formula (10), θ is the actual offset angle of the light spot, Δl is the distance the light spot is offset from the center, D is the pixel size, and f is the focal length of the focusing lens.

6. The method for eliminating the influence of polarization grating rotation according to claim 5, characterized in that: In the step S4, two errors, one in the direction of light beam deflection and the other in the direction perpendicular to the light beam deflection, are corrected to improve the light beam pointing accuracy.

7. The method for eliminating the influence of polarization grating rotation according to claim 6, characterized in that: In step S4, if the deflection of the target angle θ is achieved, the actual deflection angle will be θ′ due to the influence of the grating rotation. On the CCD camera target surface, it will be observed that the "+" and "-" angle spots are not in the same deflection direction, and the "+" angle spot is offset in the direction of the beam deflection, and the "-" angle spot is offset in the direction opposite to the beam deflection direction. The grating rotation angle θ can be obtained by obtaining the offset of the beam perpendicular to the beam deflection direction when the beam is deflected at the "+" and "-" angles. R , through θ R The error Δθ of the grating rotation in the beam deflection direction is obtained || and the error Δθ perpendicular to the beam deflection direction ⊥ , subtract the error from the "+" angle and add the error to the "-" angle at the original spot position to complete the spot pointing accuracy correction.

8. The method for eliminating the influence of polarization grating rotation according to claim 7, characterized in that: In step S4, the grating rotation angle θ is calculated by the following formula: R : In formula (11), It is the offset of the light spot between the "+" and "-" angles perpendicular to the beam deflection direction; Substituting Δl in equation (4) and equation (5) || and Δl ⊥ Substituting into formula (10) we can get: In equations (12) and (13), Δθ || is the error value caused by the grating rotation in the direction parallel to the beam deflection, Δθ ⊥ It is the error value caused by the grating rotation in the direction perpendicular to the beam deflection direction.

9. The method for eliminating the influence of polarization grating rotation according to claim 8, characterized in that: In step S4, for the relationship between the beam pointing accuracy error and the grating rotation angle, after obtaining the error values ​​caused by the grating in the two deflection directions of the beam at different rotation angles, a relationship curve between the grating rotation angle and the error in the two deflection directions of the beam is fitted to form the following formula: Dth ⊥实验 =0.17737*θ R (16); Similarly, by using equations (12) and (13), we can substitute different θ in the grating rotation experiment: R The error values ​​of the corresponding two deflection directions are obtained by The error curve is fitted to a fixed value of 0.1783 rad, forming the following formula: Dth ⊥理论 =0.17928*θ R (17), Compare the experimental and theoretical fitting formula coefficients of formula (14) and formula (15), formula (16) and formula (17), and compare the coincidence of the fitting curves of the two to verify the correctness of the theoretical formula. In the error correction process, the obtained Δθ || and Δθ ⊥ Substituting the actual angle for correction can achieve beam deflection at the target angle.

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