A method for calculating the planar self-reproducing optical path of a laser gyroscope considering manufacturing errors

Abstract

The invention belongs to the field of inertial navigation technology and discloses a method for solving the planar self-reproducing optical path of a laser gyroscope taking manufacturing errors into consideration. The method is based on the transformation principle of paraxial light beams in matrix optics, analyzes the beam waist position of a Gaussian light beam in a laser gyroscope, and combines the transformation characteristics of a geometric light beam in a two-dimensional light path and the characteristics of the self-reproducing light path to achieve accurate solution of the self-reproducing light path of the laser gyroscope under the influence of multiple errors. The invention addresses the problem of excessive calculation errors, especially multi-source errors, existing in the optical path deviation matrix equation of the existing laser gyroscope due to neglect of high-order error terms and unclear reference position of cavity length variation. A method for solving the planar self-reproducing light path of a laser gyroscope with high accuracy is proposed. The method proposed by the invention significantly reduces the position error of the self-reproducing light beam, and the calculation error is reduced by more than two orders of magnitude, providing strong technical support and guidance for the prototype design and engineering manufacturing of high-precision laser gyroscopes.

Description

Technical Field

[0001] The invention belongs to the technical field of inertial navigation and discloses a method for calculating a laser gyroscope plane self-reproducing optical path taking manufacturing errors into consideration. Background Art

[0002] The laser gyro (LGG) is a precision gyroscope developed based on the Sagnac effect. It boasts advantages such as fast startup time, high precision, wide dynamic range, compact size, light weight, and low power consumption. It is widely used in navigation, positioning, orientation, and attitude control systems for various high-precision moving vehicles. Furthermore, the autonomy, stealth, and information integrity of modern strapdown inertial navigation systems, which utilize LGGs as their primary components, make them highly suitable for modern military applications, making LGG technology a fundamental supporting technology for modern weapon systems. As a high-precision sensor, even minute errors must be comprehensively considered. Cavity variations introduced during the manufacturing and assembly of LGGs inevitably cause translation and distortion of the reflector mirrors, leading to changes in the position of the self-reproducing optical path within the resonant cavity. These changes in beam position can cause variations in fundamental mode loss, leading to the extinction of the fundamental mode or the initiation of other higher-order modes. Furthermore, changes in the position of the light spot on each mirror lead to changes in the total scattering, which in turn alters the gyro's locking threshold. Cavity variations can also affect the nulling of the Langmuir flow. All of these will bring about errors that are difficult to ignore in the gyroscope. Therefore, it is extremely important to study the self-reproducing optical path of the laser gyroscope.

[0003] Existing reports on the optical path variations within laser gyros have primarily focused on the transformation matrix of the Gaussian beam within the cavity. While some breakthroughs have been made in calculating the self-reproducing optical path using the three-dimensional matrix of the Gaussian beam within the cavity, extending the geometric dimension of the research to three dimensions, these methods fail to account for multiple higher-order error terms caused by coupling errors introduced during the manufacturing and assembly processes, and the reference position for cavity length variation is not clearly defined. This leads to non-negligible errors, which can lead to excessive laser loss or even laser extinction, rendering the gyro inoperable.

[0004] In actual engineering, when the laser gyroscope is in operation, the errors that have a greater impact on the self-reproducing optical path changes are concentrated in the gyroscope optical path plane, and the errors in the direction perpendicular to the gyroscope plane have a relatively small impact on the self-reproducing optical path changes and can be ignored. Therefore, a two-dimensional plane self-reproducing optical path solution method can be used to study the self-reproducing optical path changes of the gyroscope, and the solution of the two-dimensional plane optical path is relatively simple. To this end, this patent starts from the two-dimensional plane optical path and considers the aforementioned multiple errors to propose a highly accurate plane self-reproducing optical path solution method. This significantly reduces the calculation error of the gyroscope's self-reproducing optical path position and angle, improves the laser gyroscope's output performance and accuracy, and provides strong support for the construction of high-precision laser gyroscope forward design and development capabilities. Summary of the Invention

[0005] In response to the above-mentioned problems, the present invention discloses a method for calculating the planar self-reproducing optical path of a laser gyroscope, taking into account manufacturing errors. This method, targeted at the application of laser gyros in high-precision navigation, positioning, and attitude control systems, accurately calculates the self-reproducing optical path under the influence of multiple errors introduced during the manufacturing and assembly process, aiming to improve the output performance and precision of the laser gyroscope and provide more reliable technical support for modern weapon systems and high-precision motion carrier navigation. More specifically, based on the transformation principle of paraxial beams in matrix optics, the waist position of the Gaussian beam in the laser gyroscope is analyzed. Based on the transformation characteristics of the geometric beam in the two-dimensional optical path and the characteristics of the self-reproducing optical path, the self-reproducing optical path of the laser gyroscope under the influence of multiple errors is calculated, and the feasibility and effectiveness of this method are verified through simulation.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a method for accurately solving the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors. The method is based on the transformation principle of paraxial light beams in matrix optics, analyzes the waist position of a Gaussian light beam in a laser gyroscope, and combines the transformation characteristics of a geometric light beam in a two-dimensional optical path and the characteristics of the self-reproducing optical path to achieve accurate solution of the self-reproducing optical path of the laser gyroscope under the influence of multiple errors.

[0007] The method comprises the following steps:

[0008] Step 1: Analyze and determine the waist position of the Gaussian beam in the laser gyro based on the resonant cavity shape and reflector arrangement.

[0009] Step 2: Based on the beam waist position, a two-dimensional Gaussian beam operation model is established that takes into account assembly and manufacturing errors;

[0010] Step 3: According to the characteristics of the self-reproducing optical path, the initial deviation is calculated, that is, the offset of the beam waist position and the initial angle offset.

[0011] The first step is to analyze the waist position of the Gaussian beam in the cavity based on the resonant cavity shape and the arrangement of the reflectors of the laser gyroscope.

[0012] To achieve high speed measurement performance, all resonant cavities require mirrors to ensure self-consistent operation of the wave modes within the ring resonator, maintaining a stable optical field within the laser gain medium. The generated laser light should be able to form a closed loop through the center of each capillary segment and aperture, and the closed-loop optical path within the laser resonant cavity should be located at the exact center of each capillary segment and aperture within the cavity. Small planar cavity laser gyros are generally divided into triangular cavities and square cavities. In the square cavity, the mirrors are composed of two spherical mirrors and two plane mirrors. The following analysis will take a laser gyro with adjacent spherical mirrors as an example.

[0013] First, based on the symmetry of the forward and reverse beams in the laser gyroscope, the beam waist of the Gaussian beam will be located at the symmetrical center of the optical path, that is, the center of the two spherical mirrors or the two plane mirrors. Analyzing the ideal two-dimensional cross-section of the gyroscope, the propagation matrix of the optical path is:

[0014]

[0015] Right now:

[0016]

[0017] In formula (15), L is the side length of the square gyroscope, and R is the curvature radius of the spherical mirror. According to the stability criterion of the Gaussian beam in the ring resonator, the center of the two spherical mirrors or the two plane mirrors is the location of the Gaussian beam waist, which can be regarded as the starting point of the beam when studying the full cycle of the beam.

[0018] The second step is to establish a two-dimensional Gaussian beam operation model taking into account assembly and manufacturing errors based on the Gaussian beam waist position.

[0019] In the laser gyro optical path, since the change of the vertical gyro plane direction has a relatively small impact on the optical path, compared to establishing a three-dimensional optical path analysis model, the two-dimensional model is simpler to calculate and has a certain degree of accuracy. The gyro optical path plane is regarded as the xoy plane, the two mirrors are in the first and second quadrants respectively, and the light beam is emitted from a point on the positive y semi-axis along the approximately positive x direction. The ideal optical path side length is l, the curvature radius of the spherical mirror is R, and the position error and angular error of each mirror are Δx respectively. n , Δy n , Δθ n , the initial deviation of the beam is d, θ, k = tanθ, then the beam has the following equation during the interaction with the reflector:

[0020] The intersection point of the light beam and spherical reflector 1 is:

[0021]

[0022] in:

[0023]

[0024] The beam equation after the first reflection is converted to the form x=ky+n, where k is:

[0025]

[0026] The intersection point of the light beam and plane mirror 2 is:

[0027]

[0028] The beam equation after the second reflection is converted to the form y = kx + n, where k is:

[0029]

[0030] The intersection point of the light beam and the plane mirror 3 is:

[0031]

[0032] The beam equation after the third reflection is converted to the form x=ky+n, where k is:

[0033]

[0034] The intersection point of the light beam and the spherical reflector 4 is:

[0035]

[0036] in:

[0037]

[0038] The beam equation after the third reflection is converted into the form of y=kx+n:

[0039] y=k r4 (x-x4)+y4 (25)

[0040] in At this time, the light beam will return to the vicinity of the initial point after four reflections and intersect the y-axis at (0, -k r4 x4+y4), and the slope is k r4 .

[0041] The third step is to calculate the initial deviation, that is, the offset of the beam waist position and the initial angle offset, according to the characteristics of the self-reproducing optical path, and verify the feasibility and effectiveness of this method through simulation.

[0042] If the beam satisfies the self-reproduction condition, then:

[0043]

[0044] By inputting the calculation process into the calculation software, the initial deviation d and θ of the light beam can be obtained by solving the equation in formula (26). The above deviation terms are input into the optical calculation simulation software. The position and angle deviation of the light beam relative to the starting point after running one circle in the cavity can be observed and calculated through simulation to verify the feasibility and effectiveness of this method.

[0045] The beneficial effects of the present invention and the prior art are:

[0046] (1) The present invention provides a method for solving the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors. According to the transformation principle of paraxial light beams in matrix optics, the waist position of the Gaussian light beam in the laser gyroscope is analyzed. Based on the transformation characteristics of the geometric light beam in the two-dimensional optical path and the characteristics of the self-reproducing light path, the self-reproducing light path of the laser gyroscope under the influence of manufacturing errors is solved.

[0047] (2) The present invention provides a method for solving the planar self-reproducing optical path of a laser gyroscope taking manufacturing errors into consideration. The final calculation equation has the advantage of digital implementation. This method is very suitable for the implementation of engineering laser gyroscope self-reproducing optical path calculation.

[0048] (3) The present invention provides a method for calculating the self-reproducing optical path of a laser gyroscope plane taking into account manufacturing errors, which can be extended and applied to the design of laser gyroscopes of other shapes and has universal applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of a specific embodiment of the present invention.

[0050] Figure 2 It is a schematic diagram of the optical path model in the present invention.

[0051] Figure 3 It is a light path simulation model diagram in the present invention.

[0052] Figure 4 It is a line graph of position errors obtained after simulation of the three light beams in the present invention.

[0053] Figure 5 It is a line graph of the angular errors obtained after simulating the three light beams in the present invention. DETAILED DESCRIPTION

[0054] In order to more clearly understand the purpose, technical solutions and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and simulation data of specific embodiments.

[0055] First of all, it should be noted that Figure 1 This is a flowchart of the specific implementation plan of this embodiment. The figure shows the complete process from analyzing the shape of the laser gyro resonator and the arrangement of the reflectors, to determining the waist position of the Gaussian beam, to establishing a two-dimensional Gaussian beam operation model considering manufacturing errors, and finally solving the initial deviation based on the self-reproducing optical path characteristics. Figure 2 This is a schematic diagram of the optical path model used in this embodiment. This diagram clearly depicts the laser gyro's optical path layout, including the positional relationship between the spherical and plane mirrors, as well as the beam's propagation path within the resonant cavity. The intersection of the beam and the reflector is also marked, facilitating understanding of the beam's reflection and transmission within the cavity. Figure 3This is a diagram of the optical path simulation model in this embodiment, which shows a laser gyroscope self-reproducing optical path test model built using simulation software. The model includes the angular error and cavity length error of the four reflectors, which is used to verify the accuracy and effectiveness of the solution method proposed in the present invention. Figure 4 This is a line graph of the position errors obtained after simulating the three beams in this embodiment. This graph compares the deviation in the position of the beam spot after one complete beam travel, the algorithm in this patent, and an ideal situation. The line graph clearly demonstrates the significant effect of this patented algorithm in reducing position errors. Figure 5 This is a line graph of the angular errors obtained after simulating the three beams in this embodiment. This graph compares the angular deviations from the initial plane after a beam completes one cycle using different algorithms. Again, the line graph clearly demonstrates the advantages of this embodiment's algorithm in reducing angular errors.

[0056] A method for calculating the planar self-reproducing optical path of a laser gyroscope, taking into account manufacturing errors, is disclosed. This method, targeted at applications of laser gyroscopes in high-precision navigation, positioning, and attitude control systems, accurately calculates the self-reproducing optical path under the influence of multiple errors introduced during the manufacturing and assembly process. The method aims to improve the output performance and precision of the laser gyroscope, providing more reliable technical support for modern weapon systems and high-precision motion carrier navigation. Based on the transformation principle of paraxial beams in matrix optics, the method analyzes the beam waist position of a Gaussian beam in a laser gyroscope. The method combines the transformation characteristics of geometric beams in a two-dimensional optical path with the characteristics of the self-reproducing optical path to accurately calculate the self-reproducing optical path of the laser gyroscope under the influence of multiple errors.

[0057] The method comprises the following steps:

[0058] Step 1: Based on the laser gyro's resonant cavity shape and reflector arrangement, analyze the waist position of the Gaussian beam in the cavity.

[0059] Small planar cavity laser gyroscopes are generally divided into triangular cavities and square cavities. In the square cavity, its reflector is composed of two spherical mirrors and two plane mirrors. The following analysis will take the square cavity laser gyroscope with adjacent spherical mirrors as an example.

[0060] First, based on the symmetry of the forward and reverse beams in the laser gyroscope, the beam waist of the Gaussian beam is located at the symmetric center point of the optical path, that is, the center of the two spherical mirrors or the two plane mirrors. Analyzing with an ideal two-dimensional cross-section of the gyroscope, the propagation matrix of the optical path is:

[0061]

[0062] Right now:

[0063]

[0064] Because M11 =M 22 , and M 11 M 22 -M 12 M 21 =1. According to the stability criterion of the ring resonator, a light beam with its waist at the center of two spherical mirrors or two plane mirrors can exist stably in the resonator. The next step will be to further analyze the beam waist position between the two plane mirrors as the starting point of the light beam.

[0065] Step 2: Establish a three-dimensional Gaussian beam operation model that takes into account errors based on the Gaussian beam waist position.

[0066] In step 1, the waist position of the Gaussian beam is determined. When studying the full cycle of the beam, it can be regarded as the starting point of the beam. From this, the beam and the reflector can be converted into straight lines and curves on the xoy plane, and then the optical path operation model of the laser gyroscope can be established. The specific schematic diagram is as follows: Figure 2 As shown. The equations for mirrors 1-4 are:

[0067]

[0068] The beam from Emitted along the approximate positive direction of x, the ideal optical path length is l, the curvature radius of the spherical mirror is R, and the position error and angular error of each reflector are Δx respectively n , Δy n , Δθ n , the initial deviation of the beam is d, θ, k = tanθ, then the intersection points of the beam with the reflector during operation are:

[0069]

[0070]

[0071] in:

[0072]

[0073]

[0074] Step 3: Calculate the initial deviation, i.e., the offset of the beam waist position and the initial angle offset, based on the characteristics of the self-reproducing optical path, and verify the feasibility and effectiveness of this method through simulation.

[0075] After four reflections, the light beam returns to the vicinity of the initial point and then intersects the y-axis at (0, -k r4 x4+y4), and its slope is kr4. If the beam satisfies the self-reproduction condition, then:

[0076]

[0077] By inputting the calculation process into the calculation software, the initial deviation d and θ of the light beam can be obtained by solving the equation in formula (40). The above deviation terms are input into the optical calculation simulation software. The position and angle deviation of the light beam relative to the starting point after running one circle in the cavity can be observed and calculated through simulation to verify the feasibility and accuracy of this method.

[0078] The optical part of the laser gyroscope is mainly composed of a glass cavity, two spherical mirrors and two plane mirrors. During the optical design, the optical axis will pass through the center point or the middle axis of each geometric part. However, in reality, due to various errors, the light beam cannot run along the ideal optical axis, and the largest error introduced is the processing and adjustment error, which mainly includes the translation and distortion of the four mirrors. All resonant cavities need to use various mirrors to ensure that the wave mode runs self-consistently in the ring resonant cavity and maintain the laser gain medium in the cavity to form a stable light field. The generated laser should be able to form a closed loop through the center of each capillary and aperture, that is, when the light beam travels one circle, the position deviation of the light spot that intersects with the initial surface from the initial point and the angle difference from the departure should be 0. Use simulation software to build a self-reproducing optical path test model of the laser gyroscope that includes the angular error of the four mirrors and the cavity length error. The simulation model is as follows: Figure 4 As shown, the results of the existing algorithm and the results of this algorithm are input into the simulation model to calculate the distance deviation between the light spot where the light beam intersects the initial surface after traveling one circle and the initial point, as well as the beam angle deviation. At the same time, they are compared with the ideal situation. The results are shown in Tables 1 and 2.

[0079] Table 1 Calculation results of spot position deviation

[0080]

[0081] Table 2 Calculation results of spot angle deviation

[0082]

[0083] Tables 1 and 2 show the calculation results of the spot position deviation and angle deviation obtained by simulating the existing algorithm and the patented algorithm, as well as the calculation results under ideal conditions. The results show that the position deviation of the existing algorithm is large, 9.65 μm. The distance error of the proposed algorithm is 0.0888 μm, which is 2 orders of magnitude lower than the error of the existing calculation method. Analysis of the spot angle deviation results shows that the error of the existing algorithm is 3.16×10 -5 rad, the error of the algorithm in this embodiment is 7.74×10 - 8rad, compared to the algorithm error of this embodiment, which is reduced by 3 orders of magnitude. The above calculation results show that the accuracy of the self-reproducing beam position and angular deviation obtained by the method of the present invention is significantly improved compared to the existing algorithm, and the calculation error is reduced by more than 2 orders of magnitude. This proves the feasibility and effectiveness of the method for solving the planar self-reproducing optical path of the laser gyroscope considering manufacturing errors proposed in this embodiment, and provides strong technical support for the prototype design and engineering manufacturing of high-precision laser gyroscopes.

[0084] The above are only specific steps of the present invention and do not constitute any limitation to the scope of protection of the present invention; any technical solutions formed by equivalent transformation or equivalent replacement fall within the scope of protection of the present invention; the parts not elaborated in detail in the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors, characterized by: The method is based on the transformation principle of paraxial beams in matrix optics, analyzes the beam waist position of the Gaussian beam in the laser gyroscope, and combines the transformation characteristics of the geometric beam in the two-dimensional optical path with the characteristics of the self-reproducing optical path to achieve an accurate solution for the self-reproducing optical path of the laser gyroscope under the influence of multiple errors. The method comprises the following steps: Step 1: Analyze and determine the waist position of the Gaussian beam in the laser gyro based on the resonant cavity shape and reflector arrangement. Step 2: Based on the beam waist position, a two-dimensional Gaussian beam operation model is established that takes into account assembly and manufacturing errors; Step 3: Calculate the initial deviation, i.e. the offset of the beam waist position and the initial angle offset, based on the characteristics of the self-reproducing optical path; In the second step, the gyro optical path plane is regarded as the xoy plane, the two spherical reflectors are respectively in the first and second quadrants, the light beam is emitted from a point on the positive y axis along the approximate positive x direction, the ideal optical path side length is l, the spherical mirror curvature radius is R, and the position error and angular error of each reflector are Δx respectively. n , Δy n , Δθ n , the initial deviation of the beam is d, θ, k = tanθ, then the beam has the following equation during the interaction with the reflector: The intersection point of the light beam and spherical reflector 1 is: in: The beam equation after the first reflection is converted to the form x=ky+n, where k is: The intersection point of the light beam and plane mirror 2 is: The beam equation after the second reflection is converted to the form y = kx + n, where k is: The intersection point of the light beam and the plane mirror 3 is: The beam equation after the third reflection is converted to the form x=ky+n, where k is: The intersection point of the light beam and the spherical reflector 4 is: in: The beam equation after the third reflection is converted into the form of y=kx+n: y=k r4 (x-x4)+y4 (10) in At this time, the light beam will return to the vicinity of the initial point after four reflections and intersect the y-axis at (0, -k r4 x4+y4), and the slope is k r4 .

2. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 1, characterized in that: In the step 1, by analyzing the symmetry of the forward and reverse beams in the laser gyro, it is determined that the waist position of the Gaussian beam is at the symmetric center point of the optical path, that is, the center of the two spherical mirrors or the two plane mirrors.

3. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 1 or 2, characterized in that: In the first step, based on the symmetry of the forward and reverse beams in the laser gyroscope, the beam waist of the Gaussian beam will be at the symmetric center point of the optical path, that is, the center of the two spherical mirrors or the two plane mirrors. Analyzing the ideal two-dimensional cross-section of the gyroscope, the propagation matrix of the optical path is: Right now: In formula (12), L is the side length of the square gyroscope, and R is the curvature radius of the spherical mirror. According to the stability criterion of the Gaussian beam in the ring resonator, the center of the two spherical mirrors or the two plane mirrors is the location of the Gaussian beam waist, which can be regarded as the starting point of the beam when studying the full cycle of the beam.

4. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 1, characterized in that: In step 2, the two-dimensional Gaussian beam operation model takes into account the position error and angular error of the reflector, as well as the initial deviation of the beam, and establishes the beam operation equation through the interaction process between the beam and the reflector.

5. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 4, characterized in that: The light beam operation equation includes the intersection position of the light beam and each reflector and the light beam equation after each reflection.

6. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 1, characterized in that: In step three, by solving the beam motion equation, the initial deviation of the beam is obtained, including the offset of the beam waist position and the initial angle offset, to meet the self-reproduction condition.

7. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 1, characterized in that: The initial deviation is solved by computing software, and the solution result is input into optical computing simulation software for verification. Specifically, the initial deviation obtained by the solution is input into the optical computing simulation software, and the position and angle deviation of the light beam relative to the starting point after running one circle in the cavity is observed and calculated. If the beam satisfies the self-reproduction condition, then: By inputting the calculation process into the calculation software, the initial deviation d and θ of the light beam can be obtained by solving the equation in formula (13). The above deviation terms are input into the optical calculation simulation software. The position and angle deviation of the light beam relative to the starting point after running one circle in the cavity can be observed and calculated through simulation to verify the feasibility and effectiveness of this method.

8. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 1 or 2, characterized in that: The method is applicable to laser gyro designs of different shapes, including triangular and square cavities, as well as resonant cavities composed of different numbers and types of reflectors.

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