Side pump module light beam detection system and detection method thereof

Abstract

The invention provides a side pump module light beam detection system in a high-energy picosecond laser amplification process and a detection method thereof. According to the side pump module light beam detection system and the detection method thereof, quantitative evaluation is provided through the relevance between fluorescence distribution and light spot gain, the blank of side pump module light beam quality detection and analysis is filled up, the detection efficiency is greatly improved, the comprehensive performance of the detected side pump module is evaluated more comprehensively and deeply, and the detection accuracy is improved. The crystal structure design and pumping process parameters are optimized, and unprecedented and multi-dimensional high-precision data support is provided.

Description

Technical Field

[0001] This invention belongs to the field of laser technology, specifically relating to a side-pump module beam detection system and its detection method in the high-energy picosecond laser amplification process. Background Technology

[0002] In high-energy picosecond laser amplification, the laser beam quality is a crucial parameter, directly impacting the potential damage to optical components and the effectiveness of subsequent laser applications. To ensure good output beam quality, studying the evolution of the laser spot during high-energy amplification is essential. The first step is to investigate the influence of the gain medium on beam quality or spot distribution. Existing high-energy picosecond laser amplifiers often employ side-pumped modules as the gain medium.

[0003] In existing technologies, beam quality testing of side-pumped modules mainly relies on empirical indicators or local parameters (such as spot uniformity and power gain factor), lacking quantitative analysis of the correlation between gain distribution and fluorescence distribution. Existing methods struggle to accurately assess the actual performance differences of side-pumped modules with different process designs during laser amplification, leading to a high risk of optical component damage and limited laser application effectiveness.

[0004] Meanwhile, traditional methods for evaluating the beam quality of side-pumped modules mainly rely on empirical indicators (such as observation of beam uniformity and measurement of power gain) or local parameter analysis, lacking a systematic quantification of the intrinsic correlation between fluorescence distribution and beam gain. This results in an inability to accurately assess the actual performance differences of side-pumped modules with different process designs in high-energy picosecond laser amplification. This evaluation blind spot not only increases the risk of damage to optical components due to uneven gain distribution but also limits the stability of laser output quality and application effectiveness (such as insufficient precision machining accuracy and fluctuations in the efficiency of medical laser treatment).

[0005] Therefore, there is an urgent need to develop a better beam detection system and method for the side-pump module in the high-energy picosecond laser amplification process. Summary of the Invention

[0006] The purpose of this invention is to overcome the deficiencies in the prior art and provide a side-pump module beam detection system and its detection method in the high-energy picosecond laser amplification process.

[0007] Before describing the content of this invention, the following terms are defined as follows:

[0008] The term "Nd:YAG" refers to neodymium-doped yttrium aluminum garnet.

[0009] The term "CCD" refers to a charge-coupled device, a semiconductor device that converts optical images into digital signals.

[0010] The term "CMOS" refers to Complementary Metal-Oxide Semiconductor.

[0011] The term "PTA" refers to peak intensity / average intensity, also known as the ratio of peak value to average value.

[0012] In the description of this invention, it should be understood that the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0013] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0014] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0015] To achieve the above objectives, a first aspect of the present invention provides a side-pump module beam detection system, the side-pump module beam detection system comprising:

[0016] An imaging mechanism used to acquire beam spatial information of the pump module under test;

[0017] A spot measurement mechanism for detecting the intensity of light spots with and without gain;

[0018] A power measurement mechanism for detecting gain ratio; and

[0019] A wavefront measurement mechanism used to monitor the transmission thermal distortion of the pump module under test.

[0020] According to the side-pump module beam detection system of the first aspect of the present invention, the beam spot measurement mechanism is based on the formula G(r) = F X (r) Fit to determine the minimum X value, where G is the intensity curve of the beam after it actually gains gain, F is the intensity curve of the beam before it gains gain, and r is the beam radius.

[0021] Preferably, X ≤ 5; more preferably, X ≤ 2; even more preferably, X ≤ 0.5; most preferably, X ≤ 0.25.

[0022] According to the side-pump module beam detection system of the first aspect of the present invention, the imaging mechanism includes:

[0023] A convex lens group for image transmission; and

[0024] A cage-like structure for fixing the convex lens spacing and the imaging surface of the convex lens group.

[0025] According to the side pump module beam detection system of the first aspect of the present invention, the convex lens group includes at least two convex lenses, and the at least two convex lenses include a first lens and a second lens;

[0026] Preferably, the convex lens group includes two convex lenses, and / or

[0027] Preferably, the distance from the imaging surface of the detected module to the first lens is equal to the focal length of the first lens, the spacing between the lens groups is equal to the sum of the focal lengths of the first lens and the second lens, and the distance from the spot measurement mechanism, the power measurement mechanism, and the wavefront measurement mechanism to the second lens is equal to the focal length of the second lens.

[0028] According to the side-pump module beam detection system of the first aspect of the present invention, the beam spot measurement mechanism includes a filter and a beam analyzer;

[0029] Preferably, the filter is coated with a film that transmits the laser wavelength of the pump module under test, so as to reflect the pump light wavelength in the pump module under test; and / or

[0030] Preferably, the beam analyzer is a CCD-based beam analyzer and / or a CMOS-based beam analyzer.

[0031] According to the side-pump module beam detection system of the first aspect of the present invention, the beam analyzer includes a beam analysis function module for obtaining beam spot distribution data. The beam spot distribution data includes at least the signal intensity at each pixel location of the image captured by the beam analyzer.

[0032] According to the side-pump module beam detection system of the first aspect of the present invention, the power measurement mechanism includes a power measurement filter and an optical power meter;

[0033] Preferably, the power measurement filter uses a coating that transmits the laser wavelength of the pump module under test, in order to reflect the pump light wavelength in the pump module under test; and / or

[0034] Preferably, the optical power meter is used to measure the power of the laser transmitted through the pump module on the test side.

[0035] According to the side pump module beam detection system of the first aspect of the present invention, the wavefront measurement mechanism includes a wavefront measurement filter and a wavefront analyzer;

[0036] Preferably, the wavefront measurement filter is coated with a film that transmits the laser wavelength of the pump module under test, so as to reflect the pump light wavelength in the pump module under test; and / or

[0037] Preferably, the wavefront analyzer is used to measure the wavefront of the laser transmitted through the pump module under test.

[0038] A second aspect of the present invention provides a method for detecting a beam from a side pump module, the method comprising using the side pump module beam detection system described in the first aspect of the present invention.

[0039] According to the detection method of the second aspect of the present invention, the detection method comprises:

[0040] The seed light passes through the side-pump module under test and then enters the side-pump module beam detection system described in the first aspect of the present invention. The exit face of the side-pump module under test is the imaging surface of the side-pump module beam detection system. The relative delay between the side-pump module under test and the seed light is adjusted to change whether the seed light gains gain. The light then passes through the imaging mechanism to the spot measurement mechanism, where the intensity of the gain-free and gain-gain spots is compared and analyzed.

[0041] Preferably, according to the detection method described above, the operation of the light spot measuring mechanism further includes: finding the center position of the light spot based on the centroid of the data intensity distribution, taking this position as the center, dividing each data point by a maximum value for normalization, and then taking the average of the light intensity distribution at each angle along the radial direction.

[0042] Specifically, according to a preferred embodiment of the present invention, the present invention provides a side-pump module beam detection system and method. By measuring the correlation between fluorescence distribution and beam gain, a detection parameter X is proposed to quantitatively evaluate the gain uniformity of the side-pump module under test. Specifically, this includes: acquiring fluorescence distribution data using a 4f imaging system, comparing the beam intensity with and without gain, and using the formula G(r) = F... X(r) The optimal X value is determined by fitting. The smaller the X value, the higher the beam quality of the module. Where G is the intensity curve of the actual gain obtained by the beam, F is the fluorescence distribution intensity curve, and r is the spot radius. This invention overcomes the shortcomings of traditional evaluation methods and provides a reliable basis for the optimized design of high-energy picosecond laser amplifiers.

[0043] According to the preferred embodiments described above, the side-pump module beam detection system and method of the present invention provides a detection parameter X based on the nonlinear relationship between fluorescence distribution and beam gain, expressed by the mathematical formula G(r)=F X (r) By fitting fluorescence distribution data with gain distribution curves, a quantitative and standardized evaluation of the gain uniformity of the pump module under test is achieved for the first time. Here, G represents the intensity curve of the actual gain obtained by the beam, F represents the fluorescence distribution intensity curve, and r represents the spot radius. This parameter X not only objectively reflects the manufacturing quality of different modules but also provides manufacturers with direct guidance for optimizing crystal structure design and adjusting pump parameters. This systematically reduces the risk of beam distortion during laser amplification, improving the reliability and application efficiency of high-energy laser systems.

[0044] According to another preferred embodiment of the present invention, a highly integrated and fully functional comprehensive performance testing system for side pump modules is constructed. This system integrates image transmission, spot analysis, power monitoring, and wavefront detection, and is approximately 60 centimeters long, enabling simultaneous and accurate measurement of multiple key performance parameters of the side pump module under test.

[0045] According to another preferred embodiment of the present invention, the core components of the detection system include an imaging mechanism lens group, a first convex lens (2), an imaging mechanism lens group, a second convex lens (3), a first 45° sampling mirror (wedge) (5), a beam analyzer (4), a second 45° sampling mirror (wedge) (6), a wavefront analyzer (7), and an optical power meter (8), arranged sequentially along the optical path, as shown in the figure. Figure 6 As shown. To ensure the mechanical stability and optical path collimation accuracy of the system, the entire device uses four high-strength small steel pipes as the core frame, which run through and firmly fix two sets of plano-convex lenses (2, 3), two power beam splitters (5, 6), and the receiving head of the optical power meter (8), forming a rigid overall optical platform, as shown by the dotted line in the figure. In front of the first convex lens (2), a positioning steel pipe of about 15 cm in length is specially extended, and its end is precision-machined so that it can be closely fitted to the output end face of the pump module (1) under test. The present invention cleverly establishes the end face of the pump module under test as the object plane reference of the system, which not only simplifies the assembly and adjustment process, but also ensures the repeatability accuracy of imaging and detection from a structural point of view.

[0046] According to another preferred embodiment of the present invention, during operation, the light beam output from the pump module under test first enters a 4f image transfer system composed of two plano-convex lenses, each with a focal length of 150mm. This structure ensures that the light field distribution on the object plane (the end face of the pump module under test) is transmitted to the image plane without distortion. Subsequently, the light beam reaches the first 45° sampling mirror (5). This beam splitter splits the incident light according to a preset fixed beam splitting ratio: a small portion of the energy is precisely reflected to the beam analyzer (4) above. This reflected light path is also constrained and fixed by four small steel pipes to ensure that the beam spot shape is not destroyed during transmission. The beam analyzer (4) then captures and analyzes the two-dimensional intensity distribution of this beam spot, providing raw data for evaluating the beam spot uniformity and calculating the gain uniformity parameter X. Most of the beam energy transmitted through the first sampling mirror (5) continues to be transmitted backward to the second 45° sampling mirror (6). Here, another portion of the energy is reflected to the wavefront analyzer (7) below. This reflected light path also uses the same steel pipe fixing structure to ensure pointing stability. The wavefront analyzer (7) is responsible for accurately measuring the wavefront phase information of the beam, thereby directly and quantitatively evaluating various aberrations (such as spherical aberration, coma, etc.) introduced by the pump module under test, providing a key basis for judging the optical processing quality and pump thermal effect of the module. Finally, the remaining beam energy that penetrates the second sampling mirror (6) is directly guided to the optical power meter (8) at the end.

[0047] Since the beam splitting ratio of all sampling mirrors used in the detection system has been precisely calibrated and is a known fixed value, the actual output power of the pump module under test can be inverted and displayed in real time and accurately by embedding the corresponding ratio conversion program in the display unit of the optical power meter, thereby realizing reliable measurement of the gain multiple.

[0048] Compared with existing technologies, the side pump module beam detection system and its detection method of the present invention may have, but are not limited to, the following beneficial effects:

[0049] 1) The side-pump module beam detection system and its detection method of the present invention, in particular, proposes a quantitative evaluation by means of the correlation between fluorescence distribution and beam gain, which fills the gap in beam quality detection and analysis of side-pump modules and has significant value in helping manufacturers optimize the design of side-pump modules and reduce system maintenance costs.

[0050] 2) The side-pump module beam detection system and method of this invention overcome the limitations of traditional detection devices with their single function. On a compact optical platform, it achieves comprehensive and parallel detection of the side-pump module under test, including gain uniformity (quantified by X-value), gain factor (measured by power), near-field spot intensity distribution (measured by a beam analyzer), and output wavefront quality (measured by a wavefront analyzer). This not only greatly improves detection efficiency but, more importantly, provides unprecedented, multi-dimensional, high-precision data support for a comprehensive and in-depth evaluation of the overall performance of the side-pump module under test, and for optimizing its crystal structure design and pumping process parameters. Attached Figure Description

[0051] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings, wherein:

[0052] Figure 1 This is a schematic diagram of the core test optical path (4f imaging system) of the side pump module beam detection system exemplified in Example 1;

[0053] Figure 2 This is a data processing flowchart of the side pump module beam detection system as exemplified in Example 1;

[0054] Figure 3-5 The image shows a comparison of the fit between the beam gain and fluorescence distribution of different side-pump modules in the beam detection system of Example 1 (including the optimization effect of the X value).

[0055] Figure 6 This is a complete test optical path diagram of the side pump module beam detection system exemplified in Example 1.

[0056] above Figure 3-6 The process of measuring fluorescence distribution, analyzing gain, and determining X-value using the side-pump module beam detection system of Example 1 is clearly demonstrated, along with the complete optical path, which forms the core basis of this invention.

[0057] Explanation of reference numerals in the attached figures:

[0058] 1. Nd:YAG side pump module; 2. First convex lens of imaging mechanism lens group; 3. Second convex lens of imaging mechanism lens group; 4. CCD-based beam analyzer; 5. 45-degree sampling mirror (wedge); 6. 45-degree sampling mirror (wedge); 7. Wavefront analyzer; 8. Optical power meter. Detailed Implementation

[0059] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. However, it should be understood that these embodiments are only used for more detailed and specific description, and should not be construed as limiting the present invention in any way.

[0060] This section provides a general description of the materials and testing methods used in the experiments of this invention. While many of the materials and methods of operation used to achieve the objectives of this invention are well known in the art, the invention is still described in as much detail as possible herein. It will be apparent to those skilled in the art that, unless otherwise stated in the context, the materials and methods of operation used in this invention are well known in the art.

[0061] Example 1

[0062] This embodiment is an exemplary description of the side pump module beam detection system and its detection method of the present invention.

[0063] like Figure 1 As shown, the side pump module beam detection system of this embodiment includes: an Nd:YAG side pump module 1, a convex lens 2 with a focal length of 300mm, a convex lens 3 with a focal length of 300mm, and a CCD-based beam analyzer 4 (hereinafter referred to as CCD).

[0064] The beam detection system of the side pump module in this embodiment is based on Figure 1 The optical path shown was tested. The seed light, from left to right, first passes through the Nd:YAG side-pump module 1. The adjustable delay controls whether the seed light gains gain. After passing through the Nd:YAG crystal rod, the light, with the right end face of the side-pump module as the object plane, is transmitted via two 300mm focal length convex lenses (2 and 3) for 4f image transmission to the CCD-based beam analyzer 4 (containing a CCD camera). Then, using the fluorescence distribution data acquired by the CCD camera, the beam distribution of the ungained spot (module delay adjustment) and the gained spot (module delay alignment) are recorded respectively. The beam analysis software embedded in the CCD camera is used to export the beam distribution data. This file includes the signal intensity at each pixel location. Through data processing, the beam distribution can be reconstructed. Then, the software continues to extract data from the txt file. The software finds the center position of the beam based on the centroid of the data intensity distribution. Using this position as the center, each data point is divided by a maximum value for normalization. Then, the radial distribution of light intensity at each angle is averaged. This yields the normalized average value of the light spot distribution at each radius for all angles in polar coordinates, i.e., the light spot distribution on the average radius. Furthermore, by symmetrically superimposing the obtained radius light spot distribution onto the other side, the averaged light spot distribution on the diameter can be obtained.

[0065] By processing the raw data files of the measured fluorescence distribution and gain spot distribution using the above method, the normalized intensity distribution across the average spot diameter can be obtained. Then, by dividing the gain spot by the non-gain spot, the numerical diameter gain distribution data is obtained. Finally, the corresponding curve is plotted. The formula G(r) = F... XThe gain distribution curve G(r) is compared with the fluorescence distribution curve F(r). Finally, an exponential term X is added to the fluorescence distribution curve intensity to fit the gain distribution along the diameter. The optimal X value is used to detect and evaluate the beam quality of the module. Here, G is the intensity curve of the beam after it actually gains gain, F is the intensity curve of the beam before it gains gain, and r is the spot radius.

[0066] Furthermore, the error under fitting to a specific parameter X can be evaluated to describe the accuracy of the parameter X value. In this embodiment, the inventors calculate the fitting error between the gain distribution data and the fluorescence distribution data, that is, they process the data (n data points) at multiple points using the following error formula, where σ 2 If the result is less than 0.001, then the fitting results of the two curves are considered to be in line with expectations.

[0067] The preferred error formula used in this embodiment is:

[0068]

[0069] Among them, y i The normalized fluorescence intensity value after adding the exponent X, y' i This represents the normalized gain intensity value, where the subscript i represents different radius coordinates;

[0070] σ 2 The variance is the average of the squared errors between the fluorescence intensity and gain intensity at different radii after adding an exponent X.

[0071] i represents the coordinates of the data point representing the radius in the measurement data. This represents the upper bound of the number of data points, where i starts from 1 and continues up to n.

[0072] The beam detection system for the side pump module in this embodiment was tested with side pump modules of different sizes to illustrate the versatility of the beam detection system of the present invention. The specific testing conditions and results are as follows:

[0073] 7mm diameter test side pump module 1:

[0074] Conditions: Pump current 80A, voltage 50.4V, duty cycle 12.5%;

[0075] Results: The fluorescence distribution PTA along the x-axis was 1.39, and along the y-axis it was 1.38. After fitting, X = 2, indicating that the square of the fluorescence distribution matches the gain distribution. Figure 3 ).

[0076] 5mm diameter test side pump module:

[0077] Conditions: Pump current 80A, voltage 84.1V, duty cycle 12.5%;

[0078] Results: The fluorescence distribution PTA on the x-axis was 1.18, and on the y-axis it was 1.21. After fitting, X = 0.5, and the square root of the fluorescence distribution matched the gain distribution. Figure 4 ).

[0079] 7mm diameter test side pump module 2:

[0080] Conditions: Pump current 125A, voltage 87.8V, duty cycle 12.5%;

[0081] Results: The fluorescence distribution PTA along the x-axis was 1.25, the PTA along the y-axis was 1.25, and the fitted value X = 0.25. The fourth root of the fluorescence distribution matched the gain distribution. Figure 5 ).

[0082] While the effects of some embodiments have been shown above, those skilled in the art should understand that, based on the concept of the present invention, other embodiments not specifically shown or other technical solutions of the present invention not shown in the embodiments can also achieve the same technical effects as those claimed in the summary section:

[0083] 1. Quantitative evaluation: For the first time, the correlation between fluorescence distribution and spot gain is quantified by X value, which solves the limitations of traditional empirical evaluation.

[0084] 2. Optimize laser performance: By screening high-quality side pump modules through X-value selection, the risk of damage to optical components can be reduced and the laser amplification efficiency can be improved.

[0085] 3. Process Guidance: Providing data support for test manufacturers to optimize crystal design and pump parameters, for example, X=2 in 7mm test module 1, X=0.5 in 5mm test module 2, and X=0.25 in 7mm test module 2. Figure 3-5 ).

[0086] Although the invention has been described to a certain extent, it is obvious that appropriate changes can be made to various conditions without departing from the spirit and scope of the invention. Those skilled in the art should understand that the invention is not limited to the described embodiments, but falls within the scope of the claims, including equivalent substitutions for each element.

Claims

1. A beam detection system for a side-pump module, characterized in that, The side pump module beam detection system includes: An imaging mechanism used to acquire beam spatial information of the pump module under test; A spot measurement mechanism for detecting the intensity of light spots with and without gain; A power measurement mechanism for detecting gain ratio; and A wavefront measurement mechanism used to monitor the transmission thermal distortion of the pump module under test.

2. The side pump module beam detection system according to claim 1, characterized in that, The light spot measurement mechanism uses the formula G(r) = F X (r) Fit to determine the minimum X value, where G is the intensity curve of the beam after it actually gains gain, F is the intensity curve of the beam before it gains gain, and r is the beam radius. Preferably, X ≤ 5; more preferably, X ≤ 2; even more preferably, X ≤ 0.5; most preferably, X ≤ 0.

25.

3. The side pump module beam detection system according to claim 1 or 2, characterized in that, The imaging mechanism includes: A convex lens group for image transmission; and A cage-like structure for fixing the convex lens spacing and the imaging surface of the convex lens group.

4. The side pump module beam detection system according to claim 3, characterized in that, The convex lens group includes at least two convex lenses, and the at least two convex lenses include a first lens and a second lens; Preferably, the convex lens group includes two convex lenses, and / or Preferably, the distance from the imaging surface of the detected module to the first lens is equal to the focal length of the first lens, the spacing between the lens groups is equal to the sum of the focal lengths of the first lens and the second lens, and the distance from the spot measurement mechanism, the power measurement mechanism, and the wavefront measurement mechanism to the second lens is equal to the focal length of the second lens.

5. The side pump module beam detection system according to any one of claims 1 to 4, characterized in that, The spot measurement mechanism includes a filter and a beam analyzer; Preferably, the filter is coated with a film that transmits the laser wavelength of the pump module under test, so as to reflect the pump light wavelength in the pump module under test; and / or Preferably, the beam analyzer is a CCD-based beam analyzer and / or a CMOS-based beam analyzer.

6. The side pump module beam detection system according to any one of claims 1 to 5, characterized in that, The beam analyzer includes a beam analysis function module for obtaining beam spot distribution data. The beam spot distribution data includes at least the signal intensity at each pixel location in the image captured by the beam analyzer.

7. The side pump module beam detection system according to any one of claims 1 to 6, characterized in that, The power measurement mechanism includes a power measurement filter and an optical power meter; Preferably, the power measurement filter uses a coating that transmits the laser wavelength of the pump module under test, in order to reflect the pump light wavelength in the pump module under test; and / or Preferably, the optical power meter is used to measure the power of the laser transmitted through the pump module on the tested side.

8. The side pump module beam detection system according to any one of claims 1 to 7, characterized in that, The wavefront measurement mechanism includes a wavefront measurement filter and a wavefront analyzer; Preferably, the wavefront measurement filter is coated with a film that transmits the laser wavelength of the pump module under test, so as to reflect the pump light wavelength in the pump module under test; and / or Preferably, the wavefront analyzer is used to measure the wavefront of the laser transmitted through the pump module under test.

9. A method for detecting the beam of a side pump module, characterized in that, The detection method includes using: the side pump module beam detection system according to any one of claims 1-8; Preferably, the detection method includes: allowing seed light to pass through the side-pump module under test and then enter the side-pump module beam detection system according to any one of claims 1-8, wherein the exit face of the side-pump module under test is the imaging surface of the side-pump module beam detection system; adjusting the relative delay between the side-pump module under test and the seed light to change whether the seed light gains gain; and comparing and analyzing the intensity of the gain-free and gain-gain beams by reaching the beam spot measurement mechanism through the imaging mechanism.

10. The detection method according to claim 9, characterized in that, The operation of the light spot measurement mechanism also includes: finding the center position of the light spot according to the centroid of the data intensity distribution, taking this position as the center, dividing each data point by a maximum value for normalization, and then taking the average of the light intensity distribution at each angle along the radial direction.

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