Multi-element pose error distribution method for light path collimation

Abstract

The invention belongs to the technical field of error analysis in optical installation and adjustment tests, and provides a multi-element pose error distribution method for light path collimation in order to analyze results of a Monte Carlo method and perform error distribution by using the results, element pose error analysis based on the Monte Carlo method, Markov chain establishment, and multi-element pose error distribution based on the Monte Carlo method. Error analysis results are used as guidance, element weight factors are used as driving, and an anti-local optimal algorithm is used for assistance, so that efficient redistribution of element pose errors is realized, the quality of an integrally designed light path is improved, researchers can be assisted in distinguishing error-sensitive light path elements, and better light path performance is realized under limited cost.

Description

Technical Field

[0001] The invention belongs to the technical field of error analysis in optical assembly and adjustment testing. Background Art

[0002] Geometric and manufacturing errors in optical components are unavoidable, so optical system design requires error analysis to ensure that the actual position of components is strictly controlled within the error range dictated by system performance. Furthermore, integrated assembly design requires constraints on the positions of individual optical components, and the errors of individual components often couple to each other. The results of error analysis specify the manufacturing errors of mechanical parts and determine whether adjustments and alignment are necessary, directly impacting solution costs and crucial for subsequent design optimization.

[0003] Nowadays, the MC (Monte Carlo) method is widely used in the error analysis modules of various optical design software. This method randomly generates a large number of samples that conform to the error distribution, simulates the probabilistic behavior of the manufacturing / assembly process for each of the n groups of samples, obtains n groups of data, and extracts relevant parameters such as the mean and standard deviation of the n groups of data, and then calculates their impact on the final assembly or performance. Although the MC method has been widely used in the field of error analysis, the error prediction of optical components by simulating the probabilistic behavior of the manufacturing / assembly process does not fully fit the actual situation, and it is impossible to achieve error distribution to achieve the effect of improving the performance of the optical path. On the other hand, the development and progress of technology has promoted the proposal and improvement of many optical component adjustment methods. Therefore, it is necessary to use the MC method to supplement and support related research. Summary of the Invention

[0004] In order to make the optical element error analysis more in line with the actual situation, the present invention proposes a multi-element posture error allocation method for optical path collimation by analyzing the MC results and using them to perform error allocation.

[0005] Multi-element pose error allocation method for optical path alignment, such as Figure 1 As shown, it specifically includes the following steps:

[0006] Build a mathematical model and obtain initial conditions:

[0007] This includes setting the ideal positions and model parameters of m optical elements to obtain the ideal light trajectory;

[0008] The model parameters include the emission condition that meets the collimation standard, the preset target success rate P0, and the initial error range [Δθmin, Δθmax];

[0009] Set the pose error Δθi = Δθave, i = 1, 2, 3…m, where Δθave is used to describe the looseness of the error condition. Use the MC method to obtain n sets of data. By summarizing the n sets of data, extract the success rate of uniform error distribution as the initial maximum success rate Pmax.

[0010] Build a Markov chain and compare the success rate:

[0011] The pose errors Δθi assigned to each optical element form the error distribution array {Δθi}, Δθave is the average value of each element in {Δθi}, and Δθave is maintained unchanged, so that each element in {Δθi} produces random direction and random size changes, recorded as Δθ'i, and substituted into Δθ'i to the MC algorithm to obtain the success rate Pj = nj / n, indicating that there are nj groups of n groups of data that meet the set emission conditions; the goal of the optimization algorithm is to increase the success rate to the preset target success rate under the most relaxed error conditions to ensure the collimation of the optical path; compare P j and Pmax. If Pj>Pmax, it proves that the modification has optimized the error distribution. Accept the update and make Δθi=Δθ'i. Otherwise, reject the update and keep Δθi unchanged. At the same time, record Pmax=Max(P1,P2…Pj) as the success rate of the corresponding error distribution. Continue to randomly modify the error distribution based on Δθi and obtain j simulation results. By comparing Pj and Pmax, determine whether the system performance is successfully optimized, and then decide whether to update the error and the maximum success rate. Repeat the above process until the success rate is fully improved and converges.

[0012] The final result output includes the loosest error condition that can meet the collimation requirements and the error sensitivity of each optical component;

[0013] The loosest error condition that can meet the collimation requirements is described by Δθave; the specific error distribution after optimization is described by Δθi. The posture error Δθi allocated to some optical elements in {Δθi} decreases, indicating that the optical element is sensitive to errors and the posture of the key optical element should be restricted. Correspondingly, the posture error Δθi allocated to some optical elements increases, indicating that the posture of the optical element has little effect on the collimation of the optical path, thereby achieving the error share being "distributed" to the key optical elements.

[0014] Furthermore, during the success rate comparison process, an optimization module is added. When Pj > Pmax, an update is accepted. When Pj ≤ Pmax, a random value is taken from the range (0, 1). If the random value is less than exp[-A + B(Pj - Pmax)], the update is accepted; otherwise, the update is rejected. Parameters A and B > 0 are used to control the strength of the measure: the larger A is, the weaker the measure; the larger B is, the stronger the measure.

[0015] Furthermore, an optimization module 2 is added when accepting error allocation updates. Whenever an error allocation update is received, the optical elements with large allocation changes during the update process are recorded and weight factors are accumulated for them. Feedback is given to the optimization algorithm to encourage the update of the optical elements. After several simulations, the weight factors are cleared and re-accumulated to avoid excessive accumulation of some optical elements that affects the convergence speed.

[0016] Furthermore, an optimization module three is added to realize the feedback adjustment error in the error distribution method. When the algorithm optimizes the error distribution and the success rate Pj increases and is greater than P0, it means that the current error condition Δθave still has room for relaxation. In this case, Δθave is increased and re-substituted into the algorithm. If the success rate Pj is still less than P0 after convergence under algorithm optimization, it means that the current error condition Δθave is too loose to meet the collimation requirements. In this case, Δθave is reduced and re-substituted into the algorithm, and the critical value of Δθave is finally output.

[0017] Technical effects:

[0018] The present invention starts from the uniform distribution of multi-component errors, adopts the MC method to analyze the component posture errors, simulates the impact of errors on the optical path, evaluates the collimation, and builds a Markov chain guided by the collimation. Under the restriction that the overall error level remains unchanged, the redistribution of the posture errors of multiple components is achieved, and the most relaxed error conditions are obtained under the premise of ensuring the collimation of the optical path, and an optimized error distribution scheme and error-sensitive elements are given. In the actual integrated assembly and adjustment application, it is often costly to design an adjustment structure for each optical element. However, the present invention reflects the error-sensitive elements in the optical path, selects key elements to design corresponding adjustment structures, and thus improves the overall performance of the optical path under limited manufacturing and assembly costs. At the same time, the optimization module one and the optimization module two are added to introduce anti-local optimal and weight factor methods. Guided by the error analysis results and driven by the component weight factors, the MC analysis results are fed back to the algorithm to force program optimization. At the same time, the optimization module three relaxes / tightens the error conditions and repeats the algorithm based on the feedback of the optimization results to further optimize the error distribution.

[0019] The present invention focuses more on the error analysis of optical elements in actual situations, helps to achieve better optical path performance under limited manufacturing and assembly costs, and provides a powerful supplement to the error allocation work performed by error analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a flowchart of the overall process of the present invention.

[0021] Figure 2 A three-dimensional diagram showing the convergence of the success rate for optimization module 1.

[0022] Figure 3 This is a diagram of the specific laser light path layout of an embodiment of the present invention.

[0023] Figure 4 This is a flowchart of the overall process of an embodiment of the present invention.

[0024] Figure 5 It is the Gaussian distribution diagram of the actual error under the pose error Δθi.

[0025] Figure 6 To increase the success rate Pj comparison chart of extraction before and after optimization modules one and two, Figure 6 (a) is the picture without adding effect. Figure 6 (b) is the added effect diagram.

[0026] Figure 7 Schematic diagram showing the gradual improvement in success rate as the algorithm optimizes system performance.

[0027] Figure 8 Schematic diagram of the non-uniform distribution of errors of various optical elements after optimization in the embodiment. DETAILED DESCRIPTION

[0028] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by ordinary technicians in this field without making creative work by adopting the embodiments of the present invention are within the scope of protection of the present invention.

[0029] Furthermore, adding an optimization module 1 during the success rate comparison process can prevent local optimal strategies, enhance the repeatability of the optimization program, and improve the reliability of the final results. When Pj>Pmax, the update is accepted. When Pj≤Pmax, it is not simply rejected, but accepted with a smaller probability. Take a random value in the range of (0,1], and accept the update when the random value is less than exp[-A+B(Pj-Pmax)], otherwise reject the update. The parameters A and B>0 are used to control the intensity of the measures: the larger A is, the weaker the intensity of the measures; the larger B is, the stronger the intensity of the measures. The optimization module 1 can accept updates with a smaller probability when the system performance degrades, that is, introduce anti-local optimal measures. Considering that the greater the difference between Pj and Pmax, the smaller the probability of accepting the update, and it eventually converges to zero, the function adopts the e exponential form.

[0030] For the pose error Δθi, the success rate Pmax = F(Δθi) can be considered as a function of the error, which is regarded as a multi-dimensional potential field, such as Figure 2As shown, a three-dimensional diagram of success rate convergence is shown. The axes r1, r2, r3... are represented by Δθ1, Δθ2, Δθ3..., respectively. The process of increasing the success rate until convergence is considered to be finding a path that tends to the maximum value in the Δθi space, where (Δθ1, Δθ2, Δθ3) constitutes a three-dimensional function space. While keeping the average error constant, points are taken on the plane. The darker the color on the plane, the worse the collimation, and the lighter the color, the better the collimation. The optimization module introduces random "jumps" in the process of finding a path that increases the success rate, which forces the final result to fall on the maximum value rather than the maximum value to avoid local optimality.

[0031] Furthermore, when receiving error allocation updates, an optimization module 2 is added, introducing weighting factors to improve optimization efficiency and accelerate convergence. Each time an error allocation update is received, the algorithm records any optical elements with significant allocation changes during the update process and accumulates weighting factors for these elements. This feedback is fed back into the optimization algorithm to encourage updates to these optical elements. After several simulations, the weighting factors are cleared and re-accumulated to prevent excessive accumulation of errors in some optical elements, which can affect convergence. In the initial stages, this optimization module accelerates the allocation of errors to key optical elements; during the convergence phase, it encourages sufficient variation in Δθi to find the optimal solution.

[0032] In this embodiment, the optimization module 2 adopts the remainder function mod(j, C), where j represents the jth simulation, C is a fixed integer, and the weight factor is reset once every C accumulations; when mod(j, C) = 0, j is an integer multiple of C, and the weight factor is reset; mod(j, C) ≠ 0, the weight factor is accumulated.

[0033] Furthermore, an optimization module three is added to realize the feedback adjustment error in the error distribution method. When the algorithm optimizes the error distribution so that the success rate Pj increases and is greater than the preset target success rate, it means that the current error condition Δθave still has room for relaxation. Increase Δθave and re-substitute it into the algorithm. If the success rate Pj under algorithm optimization is still less than the preset target success rate until convergence, it means that the current error condition Δθave is too loose to meet the collimation requirements. Reduce Δθave and re-substitute it into the algorithm, and finally output the critical value of Δθave. In the above process, Δθmin and Δθmax are kept unchanged. The critical value of Δθave output by the optimization module three is the most relaxed error condition that can meet the success rate requirements. If the average value of {Δθi} is less than the critical value, no matter how the error is distributed, the required success rate cannot be achieved.

[0034] The following provides a specific laser optical path and then uses the overall error distribution process of the embodiment of the present invention. The optical path diagram is as follows: Figure 3 As shown, it consists of a laser 1, a beam splitter prism 2, a first plane mirror 3, a second plane mirror 4 and a beam splitter prism 5 for combining light. The overall process is as follows Figure 4 shown.

[0035] Step 1: Build a mathematical model and introduce the ideal pose and model parameters of the optical elements. The criterion for successful output is that the included angle between the two laser beams after combining light is less than a certain fixed angle. The success rate of the optical path collimation meeting the standard under a certain error distribution is extracted through this criterion. The upper and lower limits of the error distribution are Δθmin and Δθmax, representing the highest and lowest errors under the current technical cost conditions. Set the variables of the optimization algorithm. The allocated error is represented by Δθi, where i = 1 to 5, corresponding to the element numbers. The initial values of Δθi are all taken as Δθave, and the weight factors Wi for driving the error distribution are all initially taken as 1. Obtain the success rate Pj of the j-th simulation according to the successful output criterion. The maximum success rate in the optimization process is expressed as Pmax, and the initial value is set to 0. When Pj ≥ P0 = 80%, the current error distribution meets the collimation condition.

[0036] Step 2: Substitute Δθi into the MC algorithm for error analysis. The normal vector of the element surface may randomly rotate along the x, y, and z axes. The rotation angle is randomly taken within [-Δθi, Δθi] to mimic the probability behavior of errors during the manufacturing process. The distribution probability follows a Gaussian distribution, as Figure 5 shown, where the Gaussian distribution parameter σ = Δθi / 2. The non-ideal pose of the element will cause the output situation to deteriorate. Determine whether this set of data meets the standard according to the successful output criterion. Conduct and record n sets of data. When n is large enough, the simulation is sufficient to describe the collimation quality of the optical path under the error distribution Δθi. Refine the success rate P1 = n1 / n, where n1 is the number of data sets that meet the standard in n sets of simulations. Update Pmax = P1 to complete the first simulation.

[0037] Set the single change range dθ of the error distribution, randomly take values within [-dθ, dθ] and accumulate them to Δθi (i = 1 to 5) to achieve changes in random directions and magnitudes, substitute them into the MC algorithm for the second simulation, and extract the success rate P2.

[0038] Step 3: Compare Pj with P0 and determine whether Pj tends to converge. If Pj ≥ P0, it means that the current error condition Δθave can meet the success rate requirement after optimization. Appropriately increase Δθave according to the dichotomy method to relax the pose error condition. If Pj < P0 and Pj tends to converge, it represents that the current error condition is too loose and it is still difficult to meet the requirement after optimization. Appropriately decrease Δθave according to the dichotomy method to tighten the error condition. If the change amount of Δθave is less than the minimum resolution of the error design, output the current Δθi and Δθave as the optimized error distribution and error condition. Otherwise, update the uniformly distributed Δθi = Δθave, truncate the current optimization loop, and re-perform the optimization algorithm. If Pj < P0 and Pj does not converge, it represents that there is still room for optimizing the error distribution. Do not update Δθi and continue to execute the optimization algorithm.

[0039] After step 3, if Δθi is updated, jump to step 2 and repeat the loop; if Δθi is not updated, proceed to step 4.

[0040] Step 4: Compare Pj and Pmax.

[0041] If Pj>Pmax, accept the error allocation update. If Pj≤Pmax, randomly select rand in the range [0,1] and compare it with exp(-A+B(Pj-Pmax)). If rand is less than the parameter, accept the error allocation, otherwise reject and retain the original allocation. Where A and B are constants greater than zero. Obviously, exp[-A+B(Pj-Pmax)] decreases monotonically with Pj and is always less than 1. Introduce the e index to prevent local optimality. For example Figure 2 As shown, the limit case where Δθ2 is maximum and Δθ1 and Δθ3 approach zero has the overall maximum success rate; the local maximum success rate is achieved when Δθ3 is maximum and Δθ1Δθ2 approach zero. The anti-local optimal measure represented by a can help the algorithm avoid local optimality to a certain extent.

[0042] Step 5: Use the remainder function mod to determine whether the number of simulations j is a multiple of the positive integer C.

[0043] If j does not divide C, weight factors are accumulated based on the change in error distribution. If the change in Δθi for a component during the previous update was significant and the update was accepted, Wi is accumulated positively to increase it. Conversely, if the component error change was small, Wi is reduced to decrease it. If j does divide C, Wi is set to 1, which resets the weight factors after every C simulations to prevent excessive accumulation that slows optimization.

[0044] Step 6: Change the error distribution according to the weight factor.

[0045] Δθi is randomly assigned values within the range [Δθi - Wi × dθ, Δθi + Wi × dθ]. Obviously, the weights of components that have significantly changed over the first C simulations have a value Wi greater than 1, while those with less change have a value Wi less than 1. The larger the weight factor, the more dramatic the component error change. The weight factor helps identify key error-sensitive components in the early stages of the simulation, accelerating the change in their error range. Later in the simulation, some Δθi may reach upper and lower limits and become unable to change further. The weight factor helps the algorithm allocate resources to other components, avoiding wasted computing power.

[0046] Step 7: Substitute the updated error back into the MC algorithm, jump to step 2 and repeat the cycle. The optimization stops when the success rate reaches P0 or converges.

[0047] like Figure 6 As shown in Figure 3, the process of extracting Pj tending to converge to the maximum value is shown. The red, black, and blue curves represent three repeated optimizations under the same initial conditions and algorithm parameters. Figure 6 In (a), under the initial uniform error distribution, the success rate of the firing is generally less than 70%. When the optimization algorithm of the present invention is applied, the success rate is improved by at least 3%, indicating that the non-uniform error distribution obtained by the optimization algorithm performs better.

[0048] However, the introduction of the MC method makes the algorithm random and prone to falling into the local optimal trap. The error distribution cannot be fully optimized and the performance is not fully improved. It can be seen that Figure 6 (a) The optimization results of the red, black, and blue curves are different each time. Therefore, it is necessary to pay attention to the repeatability of the algorithm and expect that multiple optimizations can consistently produce good results. Figure 6 (b) After adding optimization modules 1 and 2, the red, black, and blue curves all achieve good optimization results, prompting Pj to generally converge to a high success rate, which in turn helps adjust Δθave and provides a reliable basis for finding relaxed error conditions. This embodiment includes a total of five components in the optical path. As the number of components increases, local optimality issues become more prominent, and the optimization algorithm requires more computing power. Therefore, introducing anti-local optimality + weighting factors can effectively improve algorithm performance and efficiency.

[0049] The optimization module 3 implements the algorithm feedback adjustment error condition corresponding to step 3, in which the binary method adjusts Δθave and repeatedly optimizes the algorithm until it approaches the critical value. The success rate evolution under different Δθave is as follows Figure 7 As shown, at this time, Δθmin and Δθmax are set to 0.6' and 3', and Δθave starts to iterate from the initial value 1.200'. In order to ensure the clarity of the curve, only part of Δθave is selected to draw the graph. The process of Δθave approaching the critical value is shown in Figure 7 In the illustration, the critical value of Δθave is near 1.48'. When Δθave>1.48', the error condition is loose, and the Pj curve fails to increase to more than 80% until convergence, such as the green curve Δθave=1.482. When Δθave<1.48', the error condition is strict, and the curve rises rapidly to Pj=80%, such as the red curve Δθave=1.428.

[0050] Figure 8 The results of the optimization algorithm are shown, with an initial uniform error distribution of Δθave = 1.20' and an optimized error distribution of Δθave = 1.47'. The improvement in Δθave relaxes the overall error conditions. The final error analysis shows that Δθ3 is the smallest, indicating that reflector 3 is most sensitive to error, followed by laser 1, beam splitter 2, and second plane mirror 4. Beam splitter 5, the beam combining component, is the least sensitive to error.

[0051] In summary, the optimization algorithm in this embodiment follows this process: Given a given error condition, a Markov Chain Monte Carlo method with an anti-local optimum and weighting factor module is used to allocate the error. If the component position has a minor impact on the optical path alignment, the error is allocated to other components. Based on whether the optimization can increase Pj to above 80%, the error level is adjusted and the optimization algorithm is repeated until the required overall optical path performance is achieved under the most relaxed error conditions.

[0052] The contents not described in detail in this specification belong to the existing technology known to those skilled in the art. At the same time, for those skilled in the art, according to the concept of the present invention, there may be changes in the specific implementation methods and application scope. In summary, the contents of this specification should not be understood as limiting the present invention.

Claims

1. A multi-element pose error allocation method for optical path alignment, characterized in that: The specific steps include: Build a mathematical model and obtain initial conditions: This includes setting the ideal positions and model parameters of m optical elements to obtain the ideal light trajectory; The model parameters include the emission condition that meets the collimation standard, the preset target success rate P0, and the initial error range [Δθmin, Δθmax]; Set the pose error Δθi = Δθave, i = 1, 2, 3…m, where Δθave is used to describe the looseness of the error condition. Use the MC method to obtain n sets of data. By summarizing the n sets of data, extract the success rate of uniform error distribution as the initial maximum success rate Pmax. Build a Markov chain and compare the success rate: The pose errors Δθi assigned to each optical element form the error distribution array {Δθi}, where Δθave is the average value of each element in {Δθi}. Maintaining Δθave unchanged, each element in {Δθi} undergoes random changes in direction and size, recorded as Δθ'i. Substituting Δθ'i into the MC algorithm yields a success rate Pj = nj / n, indicating that nj groups of data out of n groups meet the set emission conditions. The goal of the optimization algorithm is to increase the success rate to the preset target success rate under the most relaxed error conditions to ensure the collimation of the optical path; compare Pj with Pmax. If Pj>Pmax, it proves that the modification has optimized the error distribution and accepts the update, making Δθi=Δθ'i; otherwise, reject the update and keep Δθi unchanged; at the same time, record Pmax=Max(P1,P2…Pj) as the success rate of the corresponding error distribution; continue to randomly modify the error distribution based on Δθi and obtain j simulation results. By comparing Pj and Pmax, it is determined whether the system performance is successfully optimized, and then decide whether to update the error and maximum success rate. Repeat the above process until the success rate is fully improved and converges; The final result output includes the loosest error condition that can meet the collimation requirements and the error sensitivity of each optical component; The loosest error condition that can meet the collimation requirements is described by Δθave; the specific error distribution after optimization is described by Δθi. The posture error Δθi allocated to some optical elements in {Δθi} decreases, indicating that the optical element is sensitive to error and the posture of the key optical element should be restricted. Correspondingly, the posture error Δθi allocated to some optical elements increases, indicating that the posture of the optical element has little effect on the collimation of the optical path, thereby achieving the error share being "distributed" to the key optical elements.

2. The multi-element pose error allocation method for optical path alignment according to claim 1, characterized in that: In the process of comparing success rates, an optimization module 1 is added. When Pj>Pmax, the update is accepted. When Pj≤Pmax, a random value is taken in the range of (0,1]. When the random value is less than exp[-A+B(Pj-Pmax)], the update is accepted; otherwise, the update is rejected. The parameters A and B>0 are used to control the intensity of the measures: the larger A is, the weaker the measures are; the larger B is, the stronger the measures are.

3. The multi-element pose error allocation method for optical path alignment according to claim 2, characterized in that: When receiving error allocation updates, an optimization module 2 is added. Whenever an error allocation update is received, the optical elements with large allocation changes during the update process are recorded and their weight factors are accumulated. This feedback is fed back to the optimization algorithm to encourage updates to these optical elements. After several simulations, the weight factors are cleared and re-accumulated to avoid excessive accumulation of some optical elements that affects the convergence speed.

4. The multi-element pose error allocation method for optical path alignment according to claim 3, characterized in that: The optimization module 2 adopts the remainder function mod(j,C), where j represents the jth simulation, C is a fixed integer, and the weight factor is reset once every C accumulations; when mod(j,C)=0, j is an integer multiple of C, the weight factor is reset; mod(j,C)≠0, the weight factor is accumulated.

5. The multi-element pose error allocation method for optical path alignment according to claim 1, characterized in that: Adding optimization module three can realize the feedback adjustment error in the error distribution method. When the algorithm optimizes the error distribution and the success rate Pj increases and is greater than P0, it means that the current error condition Δθave still has room for relaxation. Increase Δθave and re-substitute it into the algorithm. If the success rate Pj is still less than P0 after convergence under algorithm optimization, it means that the current error condition Δθave is too loose to meet the collimation requirements. Reduce Δθave and re-substitute it into the algorithm, and finally output the critical value of Δθave.

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