Method for analyzing measurement uncertainty of involute hole array type beam quality measurement system

Abstract

The application discloses a measurement uncertainty analysis method of a involute hole array type light beam quality measurement system, comprising the following steps: constructing an ideal sampling model of a light beam measurement system; establishing an error model; based on the ideal sampling model and the error model, constructing an error-containing sampling operator, which is used for simulating the process of sampling the known ideal light beam under the influence of error sources and obtaining a simulated sampling signal, and obtaining the simulated sampling signal; reconstructing an image of the generated simulated sampling signal by using the ideal sampling model, obtaining a reconstructed light beam distribution, and obtaining an evaluation result by comparing the reconstructed light beam distribution with the ideal light beam distribution; and based on the evaluation result, setting an acceptable threshold or range for the evaluation index, and determining the engineering feasible tolerance range of each error source. The method disclosed by the application determines the engineering feasible tolerance of each error, and the tolerance data can be directly converted into hardware design index requirements.

Description

Technical Field

[0001] This invention relates to a method for analyzing the measurement uncertainty of an involute aperture array beam quality measurement system, belonging to the field of optical technology. Background Technology

[0002] High-power lasers have wide applications in inertial confinement fusion, laser processing, and directed energy systems. Beam quality is a key indicator for evaluating the performance of high-power laser systems, directly affecting energy transmission efficiency and effectiveness. Therefore, accurately measuring the spatial distribution, beam size, and energy characteristics of the beam is of great significance.

[0003] Traditional beam quality measurement methods mainly include CCD direct imaging, pinhole scanning, and Shack-Hartmann wavefront sensors. CCD direct imaging is the most commonly used method, but it faces significant challenges in high-power scenarios: to protect the CCD from damage, the laser needs to be significantly attenuated (typically exceeding 40 dB), and attenuating optics are prone to introducing thermal distortion and nonlinear effects at high power densities, affecting measurement accuracy. Pinhole scanning acquires the beam distribution through point-by-point scanning, offering high spatial resolution, but its slow scanning speed makes it unsuitable for dynamic measurements and online monitoring. Shack-Hartmann wavefront sensors are primarily used for wavefront measurements, are equally sensitive to high-power lasers, and are relatively expensive.

[0004] To address the specific needs of high-power laser beam measurement, a beam measurement method based on rotating aperture sampling has been researched and applied. This method uses an array of small apertures arranged in an involute pattern to achieve spatial sampling through rotational scanning, converting two-dimensional spatial information into a one-dimensional temporal signal, and then reconstructing the beam distribution through calculation. Compared with traditional methods, this method has the following advantages: (1) It uses a single detector instead of a CCD array, avoiding direct irradiation of the sensor by high-power laser; (2) The aperture itself has a high power tolerance, making it suitable for high-power scenarios; (3) The system structure is simple and the cost is low.

[0005] However, the measurement accuracy of involute aperture beam quality measuring instruments is affected by a variety of error sources: Mechanically, there is vibration (especially vibration in the direction of beam propagation) and speed fluctuation during high-speed rotation; In manufacturing, the dimensional accuracy of the pinholes is limited by the machining process. How these errors affect the final measurement results and the allowable range of various errors are crucial for system design and quality control.

[0006] The lack of systematic error modeling and tolerance analysis in existing technologies leads to a lack of quantitative and scientific guidance in system design and manufacturing.

[0007] Therefore, it is necessary to conduct uncertainty analysis on the involute aperture beam quality measuring instrument to solve the above problems. Summary of the Invention

[0008] To overcome the above problems, in-depth research was conducted, and a measurement uncertainty analysis method for an involute aperture array beam quality measurement system was proposed. The method is characterized by the following steps: S1. Construct an ideal sampling model for the beam measurement system to describe the relationship between each sampling event and the discretized image vector of the beam under error-free conditions; S2. Establish an error model to simulate the non-ideal sampling process caused by error sources; S3. Based on the ideal sampling model and the error model, an error sampling operator is constructed to simulate the process of sampling a known ideal beam and obtaining a simulated sampling signal under the influence of an error source. S4. Using the ideal sampling model, the generated simulated sampling signal is reconstructed to obtain the reconstructed beam distribution. By comparing the reconstructed beam distribution with the ideal beam distribution, the evaluation result is obtained. S5. Based on the evaluation results, determine the engineering feasible tolerance range for each error source by setting acceptable thresholds or ranges for the evaluation indicators.

[0009] In a preferred embodiment, in S1, the sampling process of the involute aperture array measurement system is modeled as a linear mapping, and the sampling aperture passes through the beam region sequentially during the rotation process. Each sampling event records the integral value of the light intensity within the area covered by the aperture.

[0010] In a preferred embodiment, the ideal sampling model is expressed as:

[0011] in, Represents all sampled events. For the sampling matrix, The sampling matrix represents the discretized image vector of the beam to be measured, and the elements of the sampling matrix are the overlap areas between the sampling aperture and each pixel of the image during the sampling event.

[0012] In a preferred embodiment, in S2, the error sources include Z-axis vibration error, rotational speed error, and opening size error, wherein the Z-axis vibration error is the Gaussian random vibration generated in the Z-axis direction during the high-speed rotation of the rotating disk; The rotational speed error is the deviation between the actual rotational speed and the nominal rotational speed of the rotating disk; The aperture size error is the deviation between the actual size and the nominal size of each sampling aperture in the involute aperture array.

[0013] In a preferred embodiment, the Z-axis vibration error model is used to represent the error introduced by the actual size change of the sampling beam due to vibration, while the system still reconstructs it according to the ideal focal plane. Z-axis vibration causes the sampling plane to deviate from the focal plane of the beam, resulting in defocusing and beam broadening on the sampling plane. The broadening factor is expressed as:

[0014] in, This represents the mean of multiple independent vibration samples generated by the Monte Carlo method. This is the effective depth of focus for the system.

[0015] In a preferred embodiment, the rotational speed error model is used to represent the error caused by restoring the spatial misalignment resulting from treating the actual sampling position as the theoretical sampling position. In the speed error model, the angle error is represented as:

[0016] in, For the first The cumulative angle error at each sampling time. This represents the angular position of the sampling point within the current rotation. This represents the relative deviation of the rotational speed.

[0017] In a preferred embodiment, the aperture size error model is a normal distribution model, more preferably a truncated normal distribution model, the third The actual diameter of each hole for:

[0018] in Nominal diameter Let the aperture deviation be a random variable. Indicates a normal distribution. The variance of the normal distribution.

[0019] In a preferred embodiment, in step S3, the parameters in the error model are substituted into the ideal sampling model to generate an error-containing sampling matrix that reflects the actual physical process. The matrix is ​​used to determine the known ideal beam distribution. Sampling is performed to obtain an analog sampling signal. , is represented as: .

[0020] In a preferred embodiment, in S4, the reconstruction is based on the sampling vector. Restore the original image The inverse problem, the image reconstruction includes the following steps: S41. Back projection initial reconstruction: The sampled data is mapped back to the image space by transposing the sampling matrix, and the coverage is normalized to obtain the initial reconstruction result. S42. Total Variation Regularization: The initial reconstruction result is solved by minimizing the objective function to obtain the reconstructed beam distribution.

[0021] The beneficial effects of this invention include: (1) It can comprehensively and systematically analyze the independent effects of multiple error sources on beam reconstruction quality; (2) The engineering feasible tolerances for various errors were determined. These tolerance data can be directly converted into hardware design index requirements, providing accurate and quantifiable design basis for engineering practice. Attached Figure Description

[0022] Figure 1 A schematic flowchart of a measurement uncertainty analysis method for an involute aperture array beam quality measurement system according to a preferred embodiment of the present invention is shown. Figure 2 This shows a schematic diagram of the ideal beam spot when the error source is Z-axis vibration error in Example 1; Figure 3 This diagram shows a beam spot reconstructed using the adaptive TV regularization method when the error source is Z-axis vibration error in Example 1. Figure 4 The amplitude is shown when the error source in Example 1 is Z-axis vibration error. A schematic diagram illustrating the effects of vibration. Figure 5 The diagram shows the size error of the reconstructed spot and the distribution curves of the structural similarity (SSIM) under different amplitudes when the error source is Z-axis vibration error in Example 1. Figure 6 This illustrates the error source in Example 1 when the error is the opening size error. Schematic diagram of the reconstructed light spot under positive error; Figure 7 The maximum value of the opening error in Example 1 is shown when the error source is the opening size error. The corresponding curves for SSIM and PSNR within the range; Figure 8 The cross-sectional light intensity curve in the X direction is shown when the error source is the opening size error in Example 1. Figure 9 The image shows the cross-sectional light intensity curve in the Y direction when the error source is the opening size error in Example 1. Figure 10The diagram shows the reconstructed beam spot results when the error source is rotational speed error, and the ideal beam spot and rotational speed errors are 0.1%, 0.5%, 1%, 2%, and 5%, respectively. Figure 11 The curves showing the relationship between SSIM and PSNR and the speed error are illustrated in Example 1 when the error source is the speed error. Figure 12 The curves showing the errors of the long axis and short axis of the reconstructed beam spot compared to the ideal beam spot and the rotational speed error when the error source is rotational speed error in Example 1 are shown. Figure 13 The curves of energy retention rate and speed error are shown when the error source is speed error in Example 1; Figure 14 The image quality under different signal-to-noise ratio conditions is shown in Example 1; Figure 15 The shaft measurement error under different signal-to-noise ratio conditions is shown in Example 1. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more apparent.

[0025] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0026] According to the present invention, a method for analyzing the measurement uncertainty of an involute aperture array-type beam quality measurement system is provided, such as... Figure 1 As shown, it includes the following steps: S1. Construct an ideal sampling model for the beam measurement system to describe the relationship between each sampling event and the discretized image vector of the beam under error-free conditions; S2. Establish an error model to simulate the non-ideal sampling process caused by error sources; S3. Based on the ideal sampling model and the error model, an error sampling operator is constructed to simulate the process of sampling a known ideal beam and obtaining a simulated sampling signal under the influence of an error source. S4. Using the ideal sampling model, the generated simulated sampling signal is reconstructed to obtain the reconstructed beam distribution. By comparing the reconstructed beam distribution with the ideal beam distribution, the evaluation result is obtained. S5. Based on the evaluation results, determine the engineering feasible tolerance range for each error source by setting acceptable thresholds or ranges for the evaluation indicators.

[0027] The working principle of the involute aperture array beam quality analyzer is as follows: a laser beam is irradiated onto a high-speed rotating chopper disk, such as... Figure 2 As shown, the chopper disk has sampling apertures arranged in an involute pattern. When a beam passes through a sampling aperture, part of the light passes through the aperture to reach the detector and is recorded as a timing signal. By combining the known aperture positions and rotation angles, the timing signal can be mapped to a spatial position, and then the two-dimensional distribution of the beam can be recovered through a reconstruction algorithm.

[0028] In a preferred embodiment, in S2 to S5, only one error source is evaluated each time to determine the engineering feasible tolerance range of the error source.

[0029] In another preferred embodiment, in S2 to S5, multiple error sources are simultaneously provided, and the multiple error sources are evaluated simultaneously to determine the engineering feasible tolerance range of different error sources when multiple error sources exist simultaneously.

[0030] In S1, the sampling process of the involute aperture array measurement system can be modeled as a linear mapping. The sampling aperture passes through the beam region sequentially during the rotation process, and the integral value of the light intensity within the area covered by the aperture is recorded for each sampling event.

[0031] The ideal sampling model is expressed as:

[0032] in, Represents all sampled events. For the sampling matrix, This represents the discretized image vector of the beam to be measured.

[0033] According to the present invention, the discretized image vector of the beam under test is: Pixel, element in the sampling matrix Indicates the first The sampling event in the sampling event The contribution weight of each pixel to the sampled value.

[0034] In this invention, the beam to be measured is an elliptical beam.

[0035] According to the present invention, the sampling matrix H The sampling method is constructed based on the geometric overlap between the sampling aperture and the pixel grid. For each sampling event, the overlap area between the current sampling aperture and each pixel is calculated as a sampling matrix based on the center coordinates and radius of the current sampling aperture. That is, the elements of the sampling matrix are the overlap areas between the sampling aperture and each pixel of the image in the sampling event.

[0036] Preferably, since the precise overlap calculation between circular holes and square pixels is quite complex, this invention employs a sub-pixel subdivision method for numerical approximation, and further... Each row is normalized so that the sampled value represents a weighted average of the light intensity within the aperture coverage area.

[0037] In S2, the error sources include Z-axis vibration error, rotational speed error, and opening size error. The Z-axis vibration error is the Gaussian random vibration generated in the Z-axis direction during the high-speed rotation of the rotating disk due to factors such as installation eccentricity, motor vibration, and bearing clearance. The Z-axis direction refers to the optical axis direction. The rotational speed error is the deviation between the actual rotational speed and the nominal rotational speed of the rotating disk; The aperture size error is the deviation between the actual size and the nominal size of each sampling aperture in the involute aperture array.

[0038] Furthermore, Z-axis vibration causes the sampling surface to deviate from the focal plane of the beam, and the beam becomes defocused and broadened on the sampling surface. According to the present invention, the Z-axis vibration error model is used to represent the error introduced by the actual size change of the sampling beam caused by vibration, while the system still reconstructs it according to the ideal focal plane.

[0039] Preferably, in the Z-axis vibration error model, the radius of the ideal focal plane beam is set as:

[0040] in, This represents the beam radius at the defocus distance z. The waist radius is Rayleigh length, To measure the wavelength of the light beam.

[0041] Z-axis vibration causes changes in the equivalent beam size during sampling, resulting in errors in the beam size in the reconstruction results.

[0042] In the Z-axis vibration error model, the defocus widening amplitude, i.e. the sampling error caused by vibration, is represented by the widening factor:

[0043] in, This represents the mean of multiple independent vibration samples generated by the Monte Carlo method. This is the effective depth of focus for the system.

[0044] Furthermore, in the Monte Carlo method, the Z-axis vibration is set to a Gaussian distribution model, more preferably with a mean of zero and a standard deviation of [missing value]. / 3 Gaussian distribution model, This represents the vibration amplitude.

[0045] Rotational speed error causes the actual angular position of the sampling point to deviate from the ideal value. According to the present invention, the rotational speed error model is used to represent the error caused by restoring the spatial misalignment resulting from treating the actual sampling position as the theoretical sampling position.

[0046] According to the present invention, the rotational speed error model takes into account the photoelectric pair synchronization mechanism: each revolution is marked by a photoelectric pulse, the angle error accumulates linearly within the revolution, and is reset to zero at the end of each revolution.

[0047] Furthermore, the angle error in the speed error model is expressed as:

[0048] in, For the first The cumulative angle error at each sampling time. This represents the angular position of the sampling point within the current rotation. This represents the relative deviation of the rotational speed.

[0049] Furthermore, the spatial displacement caused by the rotational speed error in the rotational speed error model is expressed as:

[0050]

[0051] in, Indicates spatial displacement. This represents the radius of the sampling point from the axis of rotation. This indicates the angle error caused by the rotational speed error. This indicates the rotational speed error.

[0052] Preferably, the aperture size error model is a truncated normal distribution model, the first... The actual diameter of each hole for:

[0053] in Nominal diameter Let the aperture deviation be a random variable. Indicates a normal distribution. The variance is the variance of the normal distribution.

[0054] In S3, the parameters in the error model are substituted into the ideal sampling model to generate an error sampling matrix that reflects the actual physical process. The matrix is ​​used to determine the known ideal beam distribution. Sampling is performed to obtain an analog sampling signal. , is represented as:

[0055] According to the present invention, this process simulates the situation in actual measurement where the sampled data deviates from the ideal value due to the presence of errors.

[0056] Preferably, in order to accurately reflect the effect of aperture size on the intensity of the sampled signal, row normalization is disabled in this step, so that the sampled value directly represents the integral of the transmitted light power.

[0057] In S4, the reconstruction is based on the sampled vectors. Restore the original image The inverse problem, the image reconstruction includes the following steps: S41. Back projection initial reconstruction: The sampled data is mapped back to the image space by transposing the sampling matrix, and the coverage is normalized to obtain the initial reconstruction result. S42. Total Variation Regularization: The initial reconstruction result is solved by minimizing the objective function to obtain the reconstructed beam distribution.

[0058] In S41, the initial reconstruction result is represented as follows:

[0059] in, This represents the transpose of the sampling matrix. Indicates analog sampled signal, Indicates the first The initial reconstruction result corresponding to each pixel.

[0060] In S42, the minimization objective function is expressed as:

[0061]

[0062] in, For regularization parameters, TV( ) is the isotropic total variation norm.

[0063] Preferably, .

[0064] The objective function employs TV regularization, which effectively suppresses reconstruction artifacts and noise while preserving the edge features of the light spot.

[0065] Preferably, a non-negativity constraint is also provided. ≥ 0, to ensure the physical rationality of light intensity distribution.

[0066] According to the present invention, the Split-Bregman iterative algorithm is used for solving the problem. Preferably, the maximum number of iterations is 200, and the convergence criterion is that the relative change in the objective function between two consecutive iterations is less than 10. -5 .

[0067] Preferably, the intensity distribution of the initial reconstruction result is used as a weight map, and the central region of the light spot is weighted... Reduced, preferably reduced to 0.2 To preserve peak detail and maintain the remaining area constant.

[0068] Preferably, the central region of the light spot refers to a region where the intensity is greater than a threshold, such as a region where the intensity is greater than 50% of the peak value.

[0069] A spatial adaptive strategy is adopted to reduce the regularization intensity in the center region of the light spot to preserve peak details, and to enhance the regularization in the edge region to suppress sampling fringes.

[0070] According to the present invention, the evaluation result characterizes the impact of error sources on the measurement result. The evaluation uses indicators including structural similarity index and peak signal-to-noise ratio. The structural similarity index is expressed as:

[0071] in, The image vector is discretized from the ideal beam. To reconstruct the discretized image vector of the beam, , Images , The local mean, , For image , Local standard deviation, For mutual covariance, , To prevent the stability constant from having a denominator of zero.

[0072] The structural similarity index is an image quality index that comprehensively considers brightness, contrast, and structural information. It is sensitive to structural changes in an image, and the larger the value, the more similar it is to the original image.

[0073] The peak signal-to-noise ratio is expressed as:

[0074]

[0075] in, Indicates peak signal-to-noise ratio. As an intermediate variable, The maximum pixel value of the image. Discretize the image pixel values ​​for an ideal light beam. To reconstruct the discretized image pixel values ​​of the beam.

[0076] Preferably, the evaluation index also includes spot size error, which is the percentage of size error in the major and minor axes of the beam spot, reflecting the impact of the error on the measurement of the beam's geometric characteristics.

[0077] Preferably, the evaluation index further includes the energy retention rate, which is the ratio of the total energy of the reconstructed beam to the total energy of the ideal beam, reflecting the impact of error on the accuracy of energy measurement.

[0078] In S5, the hardware engineering feasibility tolerance range of the involute aperture array beam quality measurement system is determined by setting acceptable thresholds or ranges for the evaluation metrics.

[0079] The acceptable thresholds or ranges for specific evaluation indicators can be set by those skilled in the art according to actual needs.

[0080] Preferably, the engineering feasible tolerance range of the Z-axis vibration error is determined based on the evaluation index spot size error. More preferably, the acceptable threshold or range of the evaluation index is determined with reference to the following engineering practice: spot size error is less than 5%.

[0081] Preferably, the engineering feasible tolerance range of the rotational speed error is determined based on the evaluation index SSIM and peak signal-to-noise ratio. More preferably, the acceptable threshold or range of the evaluation index is determined with reference to the following engineering practices: SSIM > 0.9, peak signal-to-noise ratio PSNR ≥ 30 dB, corresponding to a reconstruction mean square error not exceeding 3.2% of the signal peak value.

[0082] Preferably, the engineering feasible tolerance range for the opening size error is determined based on the evaluation index Structural Similarity Index (SSIM) and Peak Signal-to-Noise Ratio (PSNR); more preferably, the acceptable threshold or range of the evaluation index is determined with reference to the following engineering practice: SSIM ≥ 0.8.

[0083] Preferably, the method further includes performing noise robustness analysis on the system: Gaussian white noise with different signal-to-noise ratios is superimposed on the sampled signal, and steps S4 and S5 are repeated to evaluate the system's performance under different noise levels and determine the system's tolerance requirements for signal-to-noise ratio.

[0084] Preferably, the engineering feasible tolerance range of the signal-to-noise ratio is determined based on the evaluation index SSIM and the peak signal-to-noise ratio; more preferably, the acceptable threshold or range of the evaluation index is determined with reference to the following engineering practice: SSIM > 0.85.

[0085] Example Example 1 An experiment was conducted to determine the engineering feasibility tolerance range of an involute aperture array beam quality measurement system, including the following steps: S1. Construct an ideal sampling model for the beam measurement system to describe the relationship between each sampling event and the discretized image vector of the beam under error-free conditions; S2. Establish an error model to simulate the non-ideal sampling process caused by error sources; S3. Based on the ideal sampling model and the error model, an error sampling operator is constructed to simulate the process of sampling a known ideal beam and obtaining a simulated sampling signal under the influence of an error source. S4. Using the ideal sampling model, the generated simulated sampling signal is reconstructed to obtain the reconstructed beam distribution. By comparing the reconstructed beam distribution with the ideal beam distribution, the evaluation result is obtained. S5. Based on the evaluation results, determine the engineering feasible tolerance range for each error source by setting acceptable thresholds or ranges for the evaluation indicators.

[0086] In S1, the sampling process of the involute aperture array measurement system is modeled as a linear mapping. The sampling aperture passes through the beam region sequentially during the rotation process, and the integral value of the light intensity within the area covered by the aperture is recorded for each sampling event.

[0087] The ideal sampling model is expressed as:

[0088] In S2, the error sources include Z-axis vibration error, rotational speed error, and opening size error. In the Z-axis vibration error model, the radius of the ideal focal plane beam is set as:

[0089] In the Z-axis vibration error model, the defocus widening amplitude, i.e. the sampling error caused by vibration, is represented by the widening factor:

[0090] in, It is 340 μm.

[0091] In the speed error model, the angle error is represented as:

[0092] In the speed error model, the spatial displacement caused by the speed error is represented as follows:

[0093]

[0094] The aperture size error model is a truncated normal distribution model, the first... The actual diameter of each hole for:

[0095] In S3, the parameters in the error model are substituted into the ideal sampling model to generate an error sampling matrix that reflects the actual physical process. The matrix is ​​used to determine the known ideal beam distribution. Sampling is performed to obtain an analog sampling signal. , is represented as:

[0096] In S4, the reconstruction is based on the sampled vectors. Restore the original image The inverse problem, the image reconstruction includes the following steps: S41. Back projection initial reconstruction: The sampled data is mapped back to the image space by transposing the sampling matrix, and the coverage is normalized to obtain the initial reconstruction result. S42. Total Variation Regularization: The initial reconstruction result is solved by minimizing the objective function to obtain the reconstructed beam distribution.

[0097] In S41, the initial reconstruction result is represented as follows:

[0098] In S42, the minimization objective function is expressed as:

[0099]

[0100] in, The intensity distribution of the initial reconstruction result is used as a weight map, and the intensity in the central region of the light spot (the region where the intensity is greater than 50% of the peak value) is weighted. Reduced to 0.2 To preserve peak detail and maintain the remaining area constant The Split-Bregman iterative algorithm is used to solve the problem. A maximum of 200 iterations is preferred, and the convergence criterion is that the relative change in the objective function between two consecutive iterations is less than 10. -5 .

[0101] The evaluation metrics include structural similarity index, peak signal-to-noise ratio, spot size error, and energy retention rate.

[0102] In S5, the engineering feasible tolerance range for Z-axis vibration error is determined based on the evaluation index of spot size error, and the spot size error is less than 5%; The engineering feasible tolerance range for rotational speed error is determined based on the evaluation indicators SSIM (Structure Similarity Index) and PSNR (Peak Signal-to-Noise Ratio). If the SSIM is greater than 0.9 and the PSNR is greater than 30 dB, the corresponding mean square error of reconstruction shall not exceed 3.2% of the peak signal value. The engineering feasible tolerance range for opening size error is determined based on the evaluation indicators SSIM (Structural Similarity Index) and peak signal-to-noise ratio (PSNR), with SSIM ≥ 0.8. The method also includes performing noise robustness analysis on the system: Gaussian white noise with different signal-to-noise ratios is superimposed on the sampled signal, and steps S4 and S5 are repeated to evaluate the system performance under different noise levels and determine the system's signal-to-noise ratio tolerance requirements. The engineering feasible tolerance range of the signal-to-noise ratio is determined based on the evaluation index Structural Similarity Index (SSIM) and Peak Signal-to-Noise Ratio (PSNR). The acceptable threshold or range of the evaluation index is determined with reference to the following engineering practice: SSIM > 0.85.

[0103] An elliptical Gaussian beam was used as the test target in the experiment, with a major axis diameter of... minor axis diameter Major-minor axis ratio .

[0104] Figures 2-5 The beam reconstruction results are shown when the error source is Z-axis vibration error. Figure 2 For an ideal beam spot, Figure 3 The beam spot is reconstructed using the adaptive TV regularization method. Figure 4 It is the amplitude A schematic diagram illustrating the effects of vibration. Figure 5 These are the size error of the reconstructed light spot and the distribution curves of the structural similarity (SSIM) under different amplitudes.

[0105] from Figures 2-5 As can be seen, with the increase of Z-axis vibration amplitude, the reconstructed spot exhibits a significant trend of size increase, which is consistent with the defocusing characteristics of Gaussian beams. When the vibration amplitude reaches... The spot size error reached The vibration amplitude reached Dimensional error reaches The range of SSIM variation is relatively small; when the amplitude reaches... Even when the SSIM parameter is above 0.85, it can still maintain a value above 0.85. This is because the essential characteristic of the SSIM parameter is structural similarity, and vibrations within a small range will only cause the light spot to scale up or down without changing its shape. Therefore, the SSIM is not sensitive to Z-axis vibration. In engineering design, the diameter error should be used as the core evaluation index for this type of error.

[0106] Furthermore, Z-axis vibration primarily causes overall spot widening through defocusing, affecting dimensional measurement accuracy without altering the spot's structural shape. A 100 μm vibration results in a diameter error of approximately 4.8%. Based on acceptable thresholds or ranges, Z-axis vibration should be controlled within 100 μm.

[0107] Figures 6-9 The effect of the aperture size error of the involute hole on the reconstruction results is shown. Figure 6 yes A schematic diagram of the reconstructed light spot under positive error (larger aperture). Figure 7 The maximum hole opening error is ±5. The curves corresponding to SSIM and PSNR within the range show that, as can be analyzed from the graphs, within ±4... Within this range, the impact on PSNR is relatively small, maintaining a minimum peak signal-to-noise ratio of 35dB. However, it has a significant impact on SSIM, especially when the aperture error reaches ±2.5. When the beam quality drops below 0.8, it is no longer within the range of excellent beam quality. This is because the inconsistent aperture size leads to different beam energy collected by different apertures. During restoration, the beam will be distorted due to the different collected energy, deviating from the original shape. Figure 8 and Figure 9 These are the cross-sectional light intensity curves in the X direction (vertical scanning direction) and the Y direction (scanning direction), respectively. Since the X direction corresponds to different apertures, their sizes may vary, resulting in a large deviation and more fluctuations in the restored curve. The Y direction corresponds to one aperture, and under positive error conditions, the energy collected by this aperture is fixed to be larger than the ideal light spot, causing the restored light spot to still maintain a Gaussian shape on this curve, although the overall energy is higher.

[0108] Figures 10-13 The beam reconstruction results are shown when the error source is the aperture size error. Figure 10 (a) (f) shows the reconstructed beam spot results with ideal beam spot and rotation speed errors of 0.1%, 0.5%, 1%, 2%, and 5%, respectively; Figure 11 The curves showing the relationship between SSIM, PSNR, and speed error are presented. Figure 12 The curves showing the errors in the major and minor axes of the reconstructed beam spot compared to the ideal beam spot, and the rotational speed error, are presented. Figure 13 The curves showing energy retention rate and rotational speed error are presented.

[0109] from Figures 10-13 As can be seen, the shape of the restored light spot is highly sensitive to rotation speed errors. Figure 10 (c) Even a mere 0.5% error is enough to cause the shape to deviate significantly from the ideal beam spot. Figure 11The PSNR can reach nearly the acceptable lower limit (30 dB) at 0.4%, but the SSIM decreases slightly. When the rotational speed error reaches 3.25%, the SSIM is close to the excellent boundary value (0.8). This is due to the definition of the SSIM itself. Therefore, when measuring this model, the SSIM is not a very suitable parameter. As the rotational speed error increases, both the SSIM and PSNR show a monotonic decreasing trend overall, and there are individual errors that cause fluctuations in the curve. This is because the rotational speed error causes the misalignment of the light spot, and in some directions, it happens to be more similar to the ideal light beam spot, resulting in the obtained results. This effect can also be reflected in Figure 12 The errors of the major axis and minor axis of the restored light spot also increase overall as the rotational speed error increases, but there is still a fluctuating trend. For example, Figure 10 In (d), due to the large rotational speed error, the light spot is distorted, making the light spot more like the ideal light beam spot rotated by a certain angle. This will make both the major axis and minor axis closer to the ideal light beam spot, resulting in a false appearance of reduced error. Therefore, the actual size error should focus on before the first peak of 0.35%. After that, it is the false error reduction caused by larger errors. In Figure 13 It can be seen that as the rotational speed error increases, the energy is basically stable ( > 90%) below 1.5%, and drops sharply. It has dropped to 61% at 2%. This shows that when it exceeds 1.5%, there will be an effect similar to Figure 10 (e), causing the target restored light spot to deviate from the measurement area. Therefore, the rotational speed error should be controlled within 0.4%. At this time, SSIM ≥ ⅔, PSNR ≥ 30 dB, and the errors of the major axis and minor axis ≤ , meeting the application requirements.

[0110] Figure 14 shows the image quality under different signal-to-noise ratios (SNR), Figure 15 shows the axis measurement error under different signal-to-noise ratios.

[0111] From Figure 14-15 it can be seen that: (1) High signal-to-noise ratio region (SNR > 40 dB): SSIM > 0.99, PSNR > 64 dB, and the errors of the major and minor axes are both < 10%. The system performance is close to the ideal state. This corresponds to the situation where the detector noise is very low.

[0112] (2) Medium signal-to-noise ratio region (25 dB < SNR < 40 dB): The SSIM is between , and the PSNR is between 45 - 64 dB. Good reconstruction quality can still be obtained. This is the working range of most practical applications.

[0113] (3) Low signal-to-noise ratio region (SNR<20 dB): The reconstruction quality is significantly reduced, the SSIM drops below 0.71, and the major and minor axis errors increase significantly. Noise severely interferes with the effective extraction of the signal.

[0114] Therefore, the signal-to-noise ratio of the measurement system should be set to >25 dB.

[0115] The engineering feasibility tolerance range of the involute aperture array beam quality measurement system can be obtained by combining the results, as shown in Table 1.

[0116] Table 1

[0117] In the description of this invention, it should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0118] The present invention has been described above with reference to preferred embodiments; however, these embodiments are merely exemplary and illustrative. Various substitutions and modifications can be made to the present invention based on these embodiments, all of which fall within the scope of protection of the present invention.

Claims

1. A method for analyzing the measurement uncertainty of an involute aperture array-type beam quality measurement system, characterized in that, Includes the following steps: S1. Construct an ideal sampling model for the beam measurement system to describe the relationship between each sampling event and the discretized image vector of the beam under error-free conditions; S2. Establish an error model to simulate the non-ideal sampling process caused by error sources; S3. Based on the ideal sampling model and the error model, an error sampling operator is constructed to simulate the process of sampling a known ideal beam and obtaining a simulated sampling signal under the influence of an error source. S4. Using the ideal sampling model, the generated simulated sampling signal is reconstructed to obtain the reconstructed beam distribution. By comparing the reconstructed beam distribution with the ideal beam distribution, the evaluation result is obtained. S5. Based on the evaluation results, determine the engineering feasible tolerance range for each error source by setting acceptable thresholds or ranges for the evaluation indicators.

2. The method for analyzing the measurement uncertainty of the involute aperture array beam quality measurement system according to claim 1, characterized in that, In S1, the sampling process of the involute aperture array measurement system is modeled as a linear mapping. The sampling aperture passes through the beam region sequentially during the rotation process, and the integral value of the light intensity within the area covered by the aperture is recorded for each sampling event.

3. The method for analyzing the measurement uncertainty of the involute aperture array beam quality measurement system according to claim 2, characterized in that, The ideal sampling model is expressed as: in, Represents all sampled events. For the sampling matrix, The sampling matrix represents the discretized image vector of the beam to be measured, and the elements of the sampling matrix are the overlap areas between the sampling aperture and each pixel of the image during the sampling event.

4. The method for analyzing the measurement uncertainty of the involute aperture array beam quality measurement system according to claim 1, characterized in that, In S2, the error sources include Z-axis vibration error, rotational speed error, and opening size error. The Z-axis vibration error is the Gaussian random vibration generated in the Z-axis direction during the high-speed rotation of the rotating disk. The rotational speed error is the deviation between the actual rotational speed and the nominal rotational speed of the rotating disk; The aperture size error is the deviation between the actual size and the nominal size of each sampling aperture in the involute aperture array.

5. The method for analyzing the measurement uncertainty of the involute aperture array beam quality measurement system according to claim 1, characterized in that, The Z-axis vibration error model is used to represent the error introduced when the actual size of the sampling beam changes due to vibration, but the system still reconstructs it according to the ideal focal plane. Z-axis vibration causes the sampling plane to deviate from the focal plane of the beam, resulting in defocusing and beam broadening on the sampling plane. The broadening factor is expressed as: in, This represents the mean of multiple independent vibration samples generated by the Monte Carlo method. This is the effective depth of focus for the system.

6. The method for analyzing the measurement uncertainty of the involute aperture array beam quality measurement system according to claim 1, characterized in that, The rotational speed error model is used to represent the error caused by restoring the spatial misalignment resulting from treating the actual sampling position as the theoretical sampling position. In the speed error model, the angle error is represented as: in, For the first The cumulative angle error at each sampling time. This represents the angular position of the sampling point within the current rotation. This represents the relative deviation of the rotational speed.

7. The method for analyzing the measurement uncertainty of the involute aperture array beam quality measurement system according to claim 1, characterized in that, The aperture size error model is a normal distribution model, and the first... The actual diameter of each hole for: in Nominal diameter Let the aperture deviation be a random variable. Indicates a normal distribution. The variance is the normal distribution.

8. The method for analyzing the measurement uncertainty of the involute aperture array beam quality measurement system according to claim 1, characterized in that, In S3, the parameters in the error model are substituted into the ideal sampling model to generate an error sampling matrix that reflects the actual physical process. The matrix is ​​used to determine the known ideal beam distribution. Sampling is performed to obtain an analog sampling signal. , is represented as: 。 9. The method for analyzing the measurement uncertainty of the involute aperture array beam quality measurement system according to claim 1, characterized in that, In S4, the reconstruction is based on the sampled vectors. Restore the original image The inverse problem, the image reconstruction includes the following steps: S41. Back projection initial reconstruction: The sampled data is mapped back to the image space by transposing the sampling matrix, and the coverage is normalized to obtain the initial reconstruction result. S42. Total Variation Regularization: The initial reconstruction result is solved by minimizing the objective function to obtain the reconstructed beam distribution.

10. The method for analyzing the measurement uncertainty of the involute aperture array beam quality measurement system according to claim 9, characterized in that, In S42, the minimization objective function is expressed as: in, For regularization parameters, TV( ) is the isotropic total variation norm.

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