Trajectory optimization method of double-wedge scanning mirror for ambient gas imaging measurement

Abstract

The present invention relates to the field of dual-wedge imaging technology, specifically a trajectory optimization method for a dual-wedge scanning mirror used for ambient gas imaging measurement. The method first calculates the relationship between the spot scanning trajectory radius and the rotation angle difference between the two wedge mirrors of the scanning mirror. The radius is then divided equally, and the required value for different trajectory radii is inversely solved using the Newton iteration method. The calculated angle difference is then fitted to a time-dependent function. When the rotational speeds of the two wedge mirrors satisfy this function, the trajectory distribution of the scanning spot is made more uniform, resulting in a spiral scanning trajectory with a uniform radius distribution. Furthermore, the rotational speeds of the two wedge mirrors can be controlled to adjust the density of the trajectory distribution according to actual scanning requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of double-wedge imaging, and in particular to a trajectory optimization method of a double-wedge scanning mirror for ambient gas imaging measurement. Background Art

[0002] Traditional gas measurement telemetry based on laser absorption spectroscopy uses a fixed beam, relying on pan-tilt-tilt rotation to achieve point-to-point gas measurement. This method can only measure gas concentration at a specific point, but cannot directly determine the gas concentration distribution across an area or array, nor can it account for the movement of gas clouds. To achieve area measurement, a dual-wedge scanning mirror system is used.

[0003] The dual-wedge scanning mirror used in the dual-wedge scanning mirror system consists of a pair of wedge mirrors on the same rotating axis, and spiral scanning is achieved by rotating the two wedge mirrors. However, during use, the two wedge mirrors usually rotate at a constant speed, which results in an uneven distribution of the spiral scanning track. Areas where the spiral scanning track is densely distributed will cause repeated detection by the dual-wedge scanning mirror system, reducing detection efficiency; areas where the spiral scanning track is sparsely distributed will cause the dual-wedge scanning mirror system to miss detections. This shows that the planning of the spiral scanning track of the dual-wedge scanning mirror system at this stage needs to be improved. Summary of the Invention

[0004] In order to avoid and overcome the technical problems existing in the prior art, the present invention provides a trajectory optimization method for a double-wedge scanning mirror for ambient gas imaging measurement. The present invention can effectively improve the distribution uniformity of the spiral scanning path.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The trajectory optimization method of a double-wedge scanning mirror for ambient gas imaging measurement includes the following optimization steps:

[0007] G1, construct the relationship function between the radius R of the spiral scanning trajectory of the light spot and the rotation angle difference Δθ of the two wedge mirrors;

[0008] G2. Obtain the radius R of each arithmetic arrangement and simultaneously obtain the angle difference Δθ corresponding to each radius R;

[0009] G3. Fit the obtained angle differences Δθ into a function of time And find the function The derivative of

[0010] G4. Obtain the rotational speed ω1(t) of wedge mirror 1 at time t and the rotational speed ω2(t) of wedge mirror 2 at time t, and calculate the real-time rotational speed difference Δω(t) between wedge mirror 1 and wedge mirror 2, Δω(t)=ω1(t)-ω2(t);

[0011] G5, function The derivative of is taken as the reference value, and the real-time speed difference Δω(t) is made equal to the reference value at the corresponding moment, and a spiral scanning trajectory with uniform radius can be obtained.

[0012] As a further solution of the present invention: the specific process of step G1 is as follows:

[0013] G11. Arrange wedge mirror 1 and wedge mirror 2 of the same specifications coaxially along the rotation axis, with the horizontal mirror surface of wedge mirror 1 and the horizontal mirror surface of wedge mirror 2 facing each other, and the distance between the two horizontal mirror surfaces along the rotation axis is set to S;

[0014] G12. Direct a laser beam of a set wavelength along the rotation axis, passing through wedge mirrors 1 and 2 in sequence, and then irradiating the background wall. The background wall and the rotation axis are perpendicular to each other. With the intersection of the rotation axis and the background wall as the origin, establish a plane coordinate system O-XY. The positive direction of the Y axis is vertically upward, and the positive direction of the X axis is horizontally to the right. The coordinates of the light spot in the plane coordinate system O-XY are expressed as (x, y).

[0015] Wedge mirror 1 and wedge mirror 2 rotate in the same direction, and the rotation angle is the angle between them and the positive direction of the Y axis; the rotation angular velocity of wedge mirror 1 is ω1(t), and the rotation angle of wedge mirror 1 is θ1(t); the rotation angular velocity of wedge mirror 2 is ω2(t), and the rotation angle of wedge mirror 2 is θ2(t);

[0016] G13, the incident angle of the laser into the wedge mirror is α i Then the laser is refracted in the wedge mirror with an angle of α p The refraction angle of the refracted laser light when it is emitted from the inside of the wedge mirror 1 into the air is α; the distance between the incident point and the exit point of the laser light on the wedge mirror 1 along the rotation axis is T, and T is the thickness of the center point of the wedge mirror 1;

[0017] When the laser is incident on the air by the wedge mirror 2, the angle between the emitted light and the rotation axis is 2α, and the distance between the exit point and the background wall is Z. The distance between the incident point and the exit point of the laser on the wedge mirror 2 along the rotation axis is T+T';

[0018] G14. According to the principle of light propagation, the coordinates (x, y) of the light spot can be expressed as follows:

[0019]

[0020] A=Z*tanα+((2T+T′)*tan(α i -α p )+S*tanα);

[0021] B=Z*tanα;

[0022] Among them, A and B are parameters;

[0023] G15. The calculation formula for the radius R of the spiral scanning trajectory with the origin of the plane coordinate system O-XY as the center can be obtained from the coordinates (x, y) of the light spot as follows:

[0024]

[0025] Where Δθ(t) represents the function of Δθ changing with time t.

[0026] As a further solution of the present invention: the specific steps of step G2 are as follows:

[0027] G21. Divide the value range of the radius R into several equal parts, and sort the radii R obtained after the equal divisions in sequence to form the corresponding arithmetic progression M.

[0028] G22. Based on the calculation formula for radius R, use Newton's iteration method to solve the angle difference Δθ corresponding to each radius R in the arithmetic sequence M.

[0029] As a further solution of the present invention: function The construction process is as follows:

[0030] G31. Express each radius R in the arithmetic progression M as a linear function with time as the independent variable, that is, R = kt, where k represents the slope;

[0031] G32, take the linear function corresponding to each radius R as the independent variable and the corresponding angle difference as the dependent variable, and perform linear regression fitting to obtain the function

[0032] As a further solution of the present invention: after obtaining the function that changes with time Afterwards, To take the derivative, use the function The derivative of is used as a reference value, and the real-time rotational speed difference between wedge mirror 1 and wedge mirror 2 is calculated at the same time, and the real-time rotational speed difference is made equal to the reference value at the same moment, so that a spiral scanning trajectory with uniform radius distribution can be obtained.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] The present invention first calculates the relationship between the radius of the light spot scanning trajectory and the rotation angle difference between the two wedge mirrors of the scanning mirror. The radius is then divided equally, and the required value for different trajectory radii is inversely solved using the Newton iteration method. The calculated angle difference is then fitted to a time-dependent function. When the rotation speeds of the two wedge mirrors satisfy this function, the trajectory distribution of the scanning light spot is more uniform, resulting in a spiral scanning trajectory with a uniform radius distribution. Furthermore, the rotation speeds of the two wedge mirrors can be controlled to adjust the density of the trajectory distribution according to actual scanning requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is the main flow chart of the present invention.

[0036] Figure 2 Schematic diagram of the structure of the double wedge scanning mirror in the present invention.

[0037] Figure 3 This is a diagram of a spiral scanning trajectory with uniformly varying radius in the present invention. DETAILED DESCRIPTION

[0038] The following will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0039] like Figure 1 and Figure 2 As shown, the double-wedge scanning mirror used is composed of a pair of wedge mirrors on the same rotation axis. When light passes through wedge mirror one, it is refracted and deflected by an angle. When it passes through wedge mirror two, it is refracted and deflected by an angle again. Similar to the right-hand screw rule, the thumb points in the positive direction of the z-axis, and the other four fingers are bent in the direction of the positive rotation angle of the wedge mirror. When the two wedge mirrors rotate in the same direction and there is a certain difference in the rotation speed, a spiral scanning trajectory will appear. By changing the rotation speed and direction of the two wedge mirrors, different spiral scanning trajectories can be obtained.

[0040] like Figure 2 As shown in the figure, the two wedge mirrors have the same specifications, θ1 and θ2 represent the rotation angles of the two wedge mirrors around the z axis, and Figure 2 The initial rotation angles of the two wedge mirrors shown in the figure are both 0. The thickness at the center of the wedge mirror is T, and the deflection angle is α. The distance between the two wedge mirrors is S. The distance between the wedge mirror and the diffuse reflection plane (the background wall) is Z. Because the two wedge mirrors use the same specifications, r1 and r2 both satisfy: r1 = r2 = Z * tan(α). Figure 2 The situation shown in the figure corresponds to the situation when the radius of the light spot scanning track is the largest. In general, the position of the light spot on the diffuse reflection plane can be expressed by the following formula:

[0041]

[0042] Among them, r d It is a variable. When the parameters of the wedge mirror are selected, the change of the beam deflection angle is mainly determined by θ1 and θ2 of wedge mirror 1 and wedge mirror 2 relative to the z-axis.

[0043] r d =(2T+T′)*tan(α i -α p )+S*tanα;

[0044] Among them, only T' is a variable, but its variation is extremely small, so its effect on r can be ignored. d The influence of r d is a constant. When the parameters of the wedge scanning mirror are fixed, r1, r2, r d All of them can be regarded as constants, so A=r1+r d , B=r2, then the position information of the light spot on the background wall is as follows:

[0045]

[0046] The calculation formula for the radius R of the spiral scanning trajectory with the origin of the plane coordinate system O-XY as the center can be obtained from the coordinates (x, y) of the light spot as follows:

[0047]

[0048] To ensure a uniform change in the spiral scanning trajectory, the radius R of the spiral scanning trajectory must change uniformly over time t, so that the radius R has a linear relationship with time t, that is, R = kt, where k is the slope. Δθ is a controllable variable, and the functional relationship between Δθ and time t, Δθ(t), must be determined. The calculated Δθ(t) ensures that the radius R satisfies R = kt.

[0049] Given the above expression of radius R with respect to Δθ, we can directly find Δθ(R) by transposing the terms. Substituting R=kt, we can get Then by simple substitution we can get This satisfies the aforementioned requirements. However, the inverse trigonometric function exists here, and as time t increases, it will exceed the domain of definition, which is inconvenient for subsequent rotation control. Therefore, to solve it, we propose an iterative inverse solution combined with polynomial fitting.

[0050] To find Δθ(R), divide the radius R into equal parts, either large or small, and construct an arithmetic progression M consisting of arithmetic elements. Use Newton's iterative method to solve the elements in M for the Δθ corresponding to different radii R. These solved Δθ can also form an array N.

[0051] Now let's take an example of the inverse solution principle: for example, the maximum radius of the scanning trajectory is 100, and the scanning radius of the light spot can vary from 1 to 100. The purpose is to make the scanning trajectory of the light spot change evenly from small to large or from large to small. Here, the radius of the scanning trajectory is equalized, and it is hoped that the radius changes uniformly from 1 to 100 with an interval of 1, so that the numbers 1, 2, 3...100 form an arithmetic progression M. Then we need to find the angle difference Δθ corresponding to different radii. When the radius R = 1, the corresponding angle difference is Δθ1 when the radius is inversely solved. When the radius R = 2, the corresponding angle difference is Δθ2 when the radius is inversely solved. Similarly, when the radius R = 100, the corresponding angle difference is Δθ when the radius is inversely solved. 100 ; These Δθ1, Δθ2...Δθ 100 It can form an array N. When the expression of R(Δθ) is known, the value of Δθ can be inversely calculated from the radius R, so the Newton iteration method is used for inverse solution. The obtained Δθ1, Δθ2...Δθ 100 The element and the corresponding radius value R can be fitted with a polynomial to obtain the expression of Δθ(R).

[0052] After Newton's iteration method, Δθ can be inversely solved when the radius R is known. Calculate the corresponding Δθ for each arithmetic element in the previous array M. These Δθ1, Δθ2...Δθ 100 An array N is formed, and then the function expression of Δθ(R) is fitted by polynomial fitting. Since when R=kt, a scanning trajectory with a radius that changes uniformly with time can be obtained, so the expression of Δθ(kt) can be directly obtained by substituting it. Where k is a constant, the corresponding expression can be obtained by simple substitution.

[0053] Since the rotation angle difference of the wedge mirror is Δθ=θ1-θ2, that is, Δθ(t)=θ1(t)-θ2(t), taking the derivative of both sides, we get .make The derivative of When the scanning spot trajectory of the dual-wedge scanning mirror system is equal, the scanning spot trajectory of the dual-wedge scanning mirror system can show a uniform variation pattern. This scanning mirror system will be subsequently applied in similar detection scenarios such as gas leaks and air mass positioning laser detection. It can reduce some repetitive detection outside the test area, ensure the uniformity of the spot scanning throughout the test area, and improve detection efficiency.

[0054] The two dimensional parameters of the double wedge mirror are consistent. The material used for the wedge mirror is K9, and the refractive index of the wedge mirror is 1.5168. The wedge angle β is 3°53′. The thickest part of the wedge mirror is 2.36mm, the thinnest part is 1.5mm, and the diameter of the wedge mirror is 12.7mm. T = 0.5*(2.36+1.5) = 1.93mm. The incident angle α i The wedge angle β is 3°53′, which is 3.8833° when converted into degrees. According to the law of refraction, the refraction angle α can be obtained. p The angle is 2.5591°. After another refraction, the angle of light emitted from the wedge mirror is α = 2.0069°. The distance S between the two lenses is 10mm, and the distance Z between the wedge mirror and the diffuse reflection plane is 5000mm. r1 = r2 ≈ 175mm. In this embodiment, the fluctuation value of T' does not exceed 0.05mm, which is basically negligible compared to the 2T value of 2*1.93mm. Therefore, this small fluctuation of T' can be basically ignored, so it is approximately considered that r d Also a constant value, r d = 0.4396mm. Therefore, A = 175.4396mm and B = 175mm. When the initial positions of both wedge mirrors are 0, with wedge mirror one rotating at 5° / s and wedge mirror two rotating at 4.5° / s, and time t, then the rotation angle θ1 of wedge mirror one is 5*t, and the rotation angle θ2 of wedge mirror two is 4.5*t. Therefore, the above scanning trajectory radius R can be expressed as a function of time t:

[0055]

[0056] Then solve the corresponding arithmetic sequence M and array N according to the above formula, and then use Newton's iteration method to solve the inverse problem, and then use the Newton iteration method to solve the arithmetic sequence M and array N according to the above formula. Adjust the rotation speed of the two wedge mirrors to obtain Figure 3 The spiral scanning trajectory shown has a uniformly changing radius.

[0057] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A trajectory optimization method for a double-wedge scanning mirror for ambient gas imaging measurement, characterized in that: The optimization steps include: G1, construct the relationship function between the radius R of the spiral scanning trajectory of the light spot and the rotation angle difference Δθ of the two wedge mirrors; G2, obtain the radius R of each arithmetic arrangement, and use the relationship function in step G1 to calculate the angle difference Δθ corresponding to each radius R; G3. Fit the obtained angle differences Δθ into a function of time And find the function The derivative of G4. Obtain the rotational speed ω1(t) of wedge mirror 1 at time t and the rotational speed ω2(t) of wedge mirror 2 at time t, and calculate the real-time rotational speed difference Δω(t) between wedge mirror 1 and wedge mirror 2, Δω(t)=ω1(t)-ω2(t); G5, function The derivative of is taken as the reference value, and the real-time speed difference Δω(t) is made equal to the reference value at the corresponding moment, and a spiral scanning trajectory with uniform radius can be obtained.

2. The trajectory optimization method of a double-wedge scanning mirror for ambient gas imaging measurement according to claim 1, characterized in that: The specific process of step G1 is as follows: G11. Arrange wedge mirror 1 and wedge mirror 2 of the same specifications coaxially along the rotation axis, with the horizontal mirror surface of wedge mirror 1 and the horizontal mirror surface of wedge mirror 2 facing each other, and the distance between the two horizontal mirror surfaces along the rotation axis is set to S; G12. Pass a laser of a set wavelength through wedge mirrors 1 and 2 along the rotation axis, and then illuminate the background wall. The background wall and the rotation axis are perpendicular to each other. With the intersection of the rotation axis and the background wall as the coordinate origin, establish a plane coordinate system O-XY. The positive direction of the Y axis is vertically upward, and the positive direction of the X axis is horizontally to the right. The coordinates of the light spot in the plane coordinate system O-XY are expressed as (x, y). Wedge mirror 1 and wedge mirror 2 rotate in the same direction, and the rotation angle is the angle between them and the positive direction of the Y axis; the rotation angular velocity of wedge mirror 1 is ω1(t), and the rotation angle of wedge mirror 1 is θ1(t); the rotation angular velocity of wedge mirror 2 is ω2(t), and the rotation angle of wedge mirror 2 is θ2(t); G13, the incident angle of the laser into the wedge mirror is α i Then the laser is refracted in the wedge mirror with an angle of α p The refraction angle of the refracted laser light when it is emitted from the inside of the wedge mirror 1 into the air is α; the distance between the incident point and the exit point of the laser light on the wedge mirror 1 along the rotation axis is T, and T is the thickness of the center point of the wedge mirror 1; When the laser is incident on the air by the wedge mirror 2, the angle between the emitted light and the rotation axis is 2α, and the distance between the exit point and the background wall is Z. The distance between the incident point and the exit point of the laser on the wedge mirror 2 along the rotation axis is T+T'; G14. According to the principle of light propagation, the coordinates (x, y) of the light spot can be expressed as follows: A=Z*tanα+((2T+T′)tan(α i -α p )+S*tanα); B=Z*tanα; Among them, A and B are parameters; G15. The calculation formula for the radius R of the spiral scanning trajectory with the origin of the plane coordinate system O-XY as the center can be obtained from the coordinates (x, y) of the light spot as follows: Where Δθ(t) represents the function of Δθ changing with time t.

3. The trajectory optimization method of a double-wedge scanning mirror for ambient gas imaging measurement according to claim 2, characterized in that: The specific steps of step G2 are as follows: G21. Divide the value range of the radius R into several equal parts, and sort the radii R obtained after the equal divisions in order to form the corresponding arithmetic progression M. G22. Based on the calculation formula for radius R, use Newton's iteration method to solve the angle difference Δθ corresponding to each radius R in the arithmetic sequence M.

4. The trajectory optimization method of a double-wedge scanning mirror for ambient gas imaging measurement according to claim 3, characterized in that: function The construction process is as follows: G31. Express each radius R in the arithmetic progression M as a linear function with time as the independent variable, that is, R = kt, where k represents the slope; G32, take the linear function corresponding to each radius R as the independent variable and the corresponding angle difference as the dependent variable, and perform linear regression fitting to obtain the function 5. The trajectory optimization method of a double-wedge scanning mirror for ambient gas imaging measurement according to claim 4, characterized in that: In the function that changes with time Afterwards, To take the derivative, use the function The derivative of is used as a reference value, and the real-time rotational speed difference between wedge mirror 1 and wedge mirror 2 is calculated at the same time, and the real-time rotational speed difference is made equal to the reference value at the same moment, so that a spiral scanning trajectory with uniform radius distribution can be obtained.

Images