Laser gyroscope plane self-reproduction light path resolving method considering manufacturing error

Abstract

The invention belongs to the technical field of inertial navigation, and discloses a laser gyroscope plane self-reproduction light path resolving method considering manufacturing errors. According to the method, based on the transformation principle of paraxial light beams in matrix optics, the beam waist position of Gaussian light beams in the laser gyroscope is analyzed, and accurate calculation of the self-reappearing light path of the laser gyroscope under the influence of multiple errors is achieved by combining the transformation characteristic of geometric light beams in a two-dimensional light path and the characteristic of the self-reappearing light path. The invention provides a laser gyroscope plane self-reproduction light path resolving method with high accuracy, aiming at the problem of overlarge calculation error, especially multi-source error, caused by neglecting of a high-order error term and ambiguity of a cavity length change reference position in an existing laser gyroscope light path deviation matrix equation. By adopting the method provided by the invention, the position error of the self-reappearing light beam is obviously reduced, the calculation error is reduced by more than two orders of magnitude, and powerful technical support and guidance are provided for prototype design and engineering manufacturing of the high-precision laser gyroscope.

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] Laser gyro is a precision gyro developed based on the Sagnac effect. It has the advantages of short startup time, high precision, large dynamic range, small size, light weight and low power consumption. It is widely used in navigation, positioning, orientation and attitude control systems of various high-precision motion carriers. At the same time, the autonomy, concealment and information completeness of modern strapdown inertial navigation systems with laser gyro as the main component are more in line with modern military applications, making laser gyro technology a member of the basic supporting technologies of modern weapon systems. As a high-precision sensor, even small errors need to be taken into comprehensive consideration. The cavity changes introduced by the manufacturing and adjustment process of the laser gyro will inevitably lead to the translation and distortion of the reflector, thereby causing the position of the self-reproducing optical path in the resonant cavity to change. The change in the position of the light beam may cause the change in the fundamental mode loss, resulting in the disappearance of the fundamental mode or the oscillation of other higher-order modes. In addition, the change in the position of the light spot on each lens will lead to the change in the total scattering amount, thereby changing the locking threshold of the gyro. The cavity change may also affect the zero drift of the Langmuir flow. All these will bring about errors that are difficult to ignore for the gyroscope. Therefore, it is extremely important to study the self-reproducing optical path of the laser gyroscope.

[0003] In existing reports, the research on the change of the optical path in the laser gyroscope mainly focuses on the transformation matrix of the Gaussian beam in the cavity. At present, the method of calculating the self-reproducing optical path through the three-dimensional operation matrix of the Gaussian beam in the cavity has made certain breakthroughs, expanding the geometric dimension of the research to three-dimensional space, but it does not consider multiple high-order error terms caused by the error coupling introduced by the manufacturing and assembly process, and does not clarify the reference position of the cavity length change. There are non-negligible errors, which may lead to excessive laser loss or even laser disappearance, and the gyroscope cannot work properly.

[0004] In actual engineering, when the laser gyroscope is in operation, the errors that have a greater impact on the change of the self-reproducing optical path are concentrated in the plane of the gyroscope optical path, and the errors in the direction perpendicular to the gyroscope plane have a relatively small impact on the change of the self-reproducing optical path and can be ignored. Therefore, a two-dimensional plane self-reproducing optical path solution method can be used to study the change of the gyroscope's self-reproducing optical path, 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 proposes a high-accuracy plane self-reproducing optical path solution method considering the aforementioned multiple errors. The calculation error of the gyroscope's self-reproducing optical path position and angle is significantly reduced, the output performance and accuracy of the laser gyroscope are improved, and strong support is provided for the construction of the forward design and development capabilities of high-precision laser gyroscopes. Summary of the invention

[0005] In view of the above problems, the present invention discloses a method for solving the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors. The method is aimed at the application of laser gyroscopes in high-precision navigation, positioning and attitude control systems. By accurately solving 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 accuracy of the laser gyroscope and provide more reliable technical support for modern weapon systems and high-precision motion carrier navigation. More specifically, 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, and the self-reproducing optical path of the laser gyroscope under the influence of multiple errors is solved based on the transformation characteristics of the geometric light beam in the two-dimensional optical path and the characteristics of the self-reproducing optical path, and the feasibility and effectiveness of the 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 a self-reproducing optical path to achieve accurate solution of the self-reproducing optical path of a 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 considering assembly manufacturing errors is established;

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

[0011] The step 1 is: analyzing 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] In order to obtain high speed measurement performance, all resonant cavities need to use various reflectors to ensure that the wave mode runs self-consistently in the ring resonant cavity, maintain the laser gain medium in the cavity to form a stable light field, and the generated laser should be able to form a closed loop through the center of each capillary and aperture, and the closed-loop optical path in the laser resonant cavity should be in the center of each capillary and aperture in the cavity. Small planar cavity laser gyroscopes are generally divided into triangular cavities and square cavities. In the square cavity, its reflectors are composed of two spherical mirrors and two plane mirrors. The following analysis will take the laser gyroscope with adjacent spherical mirrors as an example.

[0013] First, according to the symmetry of the forward and reverse beams in the laser gyroscope, the waist position 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. The propagation matrix of the optical path is analyzed with an ideal two-dimensional cross-sectional diagram of the gyroscope:

[0014]

[0015] Right now:

[0016]

[0017] In formula (15), L is the side length of the square gyroscope, and R is the radius of curvature 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 operate 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, the light beam is emitted from a point on the positive y semi-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 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 the spherical reflector 1 is:

[0021]

[0022] in:

[0023]

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

[0025]

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

[0027]

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

[0029]

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

[0031]

[0032] The beam equation after the third reflection is converted into the form of 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, after four reflections, the light beam will return to the vicinity of the initial point and intersect the y-axis at (0, -k r4 x4+y4), and the slope is k r4 .

[0041] The step three is: calculating 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 verifying the feasibility and effectiveness of the 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 the light beam runs 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 being implemented digitally. This method is very suitable for implementing the calculation of the self-reproducing optical path of an engineered laser gyroscope.

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

[0049] Figure 1 It is a flow chart of a specific implementation scheme 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 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 in conjunction with the accompanying drawings and simulation data of specific embodiments.

[0055] First of all, it should be noted that Figure 1 is a flow chart of the specific implementation plan of this embodiment, which shows the complete process from analyzing the shape of the laser gyroscope resonant cavity and the arrangement of the reflectors, to determining the waist position of the Gaussian beam, to establishing a two-dimensional Gaussian beam operation model that takes manufacturing errors into account, and finally solving the initial deviation based on the self-reproducing optical path characteristics. Figure 2 is a schematic diagram of the optical path model in this embodiment, which clearly depicts the optical path layout of the laser gyro, including the positional relationship between the spherical mirror and the plane mirror, and the propagation path of the light beam in the resonant cavity. The intersection of the light beam and the reflector is also marked in the figure to facilitate understanding of the reflection and transmission process of the light beam in the cavity. Figure 3It 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 errors and cavity length errors of the four reflectors, and 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 error obtained after the three beams are simulated in this embodiment. This figure compares the existing algorithm, the patent algorithm, and the ideal situation where the light spot position deviation intersects with the initial surface after the beam travels one circle. The line graph can intuitively show the significant effect of the patent algorithm in reducing the position error. Figure 5 This is a line graph of the angular error obtained after the three beam simulations in this embodiment. This graph compares the angular deviation of the beam from the initial surface after one cycle under different algorithms. Similarly, through the display of the line graph, it can be clearly seen that the algorithm of this embodiment has the advantage of reducing the angular error.

[0056] A method for calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors. The method is aimed at the application of laser gyroscopes in high-precision navigation, positioning and attitude control systems. The method accurately calculates the self-reproducing optical path under the influence of multiple errors introduced during the manufacturing and assembly process, and aims to improve the output performance and accuracy of the laser gyroscope, and provide more reliable technical support for modern weapon systems, high-precision motion carrier navigation, etc. The method is based on the transformation principle of paraxial beams in matrix optics, analyzes the 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 and the characteristics of the self-reproducing optical path to achieve accurate calculation of 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 resonant cavity shape and reflector arrangement of the laser gyro, 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, it can be seen that the 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. The propagation matrix of the optical path is analyzed with an ideal two-dimensional cross-sectional diagram of the gyroscope:

[0061]

[0062] Right now:

[0063]

[0064] Due to M11 =M 22 , and M 11 M 22 -M 12 M 21 =1. From the stability criterion of the ring resonator, we know that 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 take the waist position between the two plane mirrors as the starting point of the light beam for further analysis.

[0065] Step 2: Establish a three-dimensional Gaussian beam operation model taking 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 operation 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 shown in the figure. Figure 2 As shown. The equations for mirrors 1-4 are:

[0067]

[0068] The beam from It is emitted in the approximate positive direction of x. The side length of the ideal optical path is l, the radius of curvature 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 the 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 the light beam runs 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 fact, 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 the self-consistent operation of the wave mode in the ring resonant cavity and maintain the formation of a stable light field of the laser gain medium in the cavity. 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 and the initial point and the angle difference with the departure time 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 existing algorithm results and the results of this algorithm are input into the simulation model to calculate the distance deviation between the light spot that intersects the initial surface after the light beam travels one circle and the initial point, as well as the beam angle deviation, and 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 patent algorithm, as well as the calculation results under ideal conditions. From the results, it can be seen that the position deviation of the existing algorithm is relatively large, which is 9.65um. The distance error of this algorithm is 0.0888um, which is 2 orders of magnitude lower than the error of the result 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 with the algorithm error of this embodiment, the error is reduced by 3 orders of magnitude. The above calculation results show that the accuracy of the self-reproducing beam position and angle deviation obtained by the method of the present invention is significantly improved compared with the existing algorithm, and the calculation error is reduced by more than 2 orders of magnitude, which proves the feasibility and effectiveness of the laser gyroscope planar self-reproducing optical path solution method considering the manufacturing error 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 protection scope of the present invention; any technical solutions formed by equivalent transformation or equivalent replacement shall fall within the protection scope of the present invention; some parts not elaborated in detail in the present invention belong to the known technologies of those skilled in the art.

Claims

1. A method for accurately calculating the self-reproducing optical path of a laser gyroscope plane taking into account manufacturing errors, characterized in that: The method is based on the transformation principle of paraxial beams in matrix optics, analyzes the 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 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.

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: 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 considering assembly manufacturing errors is established; Step 3: According to the characteristics of the self-reproducing optical path, the initial deviation, that is, the offset of the beam waist position and the initial angle offset, is calculated.

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

4. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 2 or 3, characterized in that: In the above step one, based on the symmetry of the forward and reverse beams of light in the laser gyroscope, it can be known that the 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. The propagation matrix of the optical path is analyzed with an ideal two-dimensional cross-sectional diagram of the gyroscope: Right now: In formula (2), L is the side length of the square gyroscope, and R is the radius of curvature 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.

5. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 2, 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.

6. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 5, 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.

7. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 2, 5 or 6, characterized in that: In the step 2, the gyro optical path plane is regarded as the xoy plane, the two spherical reflectors are in the first and second quadrants respectively, the light beam is emitted from a point on the positive y semi-axis along the approximate 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 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 the spherical reflector 1 is: in: The beam equation after the first reflection is converted into the form of x=ky+n, where k is: The intersection point of the light beam and plane reflector 2 is: The beam equation after the second reflection is converted into the form of y=kx+n, where k is: The intersection point of the light beam and the plane reflector 3 is: The beam equation after the third reflection is converted into the form of 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 (12) in At this time, after four reflections, the light beam will return to the vicinity of the initial point and intersect the y-axis at (0, -k r4 x4+y4), and the slope is k r4 .

8. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 2, 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.

9. The method for accurately calculating the planar self-reproducing optical path of a laser gyroscope taking into account manufacturing errors according to claim 2 or 8, characterized in that: The initial deviation solution process is implemented by computing software, and the solution result is input into the optical computing simulation software for verification; specifically, the initial deviation obtained by 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 the light beam runs 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 the light beam runs one circle in the cavity can be observed and calculated through simulation to verify the feasibility and effectiveness of this method.

10. 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, and resonant cavities composed of different numbers and types of reflectors.

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