CN116429252A - A Comprehensive Parameter Evaluation Method for Laser Beam Quality - Google Patents

Abstract

The invention relates to a comprehensive parameter evaluation method of laser beam quality, which belongs to the field of laser beam characteristic measurement. This method eliminates the influence of airflow disturbance by averaging multiple measurements; considering the size of the multi-mode laser light source, the point spread function is used to convolve with the light source to calculate the far-field spot image of the multi-mode laser, which solves the problem of multi-mode laser measurement errors Problem: When reducing or expanding the beam, use the wavefront after deducting the background W _bg to calculate the far-field spot image to reduce the error of the far-field spot; use the Shack-Hartmann wavefront detector to measure the wavefront, PV and RMS and other parameters, it overcomes the problem that the existing Shack-Hartmann wavefront detector measures the laser beam quality factor ^M2 , which has a large measurement error and can only be measured qualitatively, and achieves accurate measurement of the beam quality factor of single-mode or multi-mode lasers , laser wavefront, PV and RMS and other parameters to realize the measurement of comprehensive parameters of laser beam quality.

Description

A Comprehensive Parameter Evaluation Method for Laser Beam Quality

technical field

The invention relates to a comprehensive parameter evaluation method of laser beam quality, which belongs to the field of laser beam characteristic measurement.

Background technique

In 1917, Einstein proposed the theory of "stimulated emission", which provided an important theoretical basis for the generation of laser light. In 1960, the American physicist Maiman invented the ruby laser, which issued the first practically applicable laser. With the continuous advancement of science and technology, the application of lasers in military, industrial, medical and other fields is becoming more and more common. With the rapid development of laser technology and applications, it is more and more important to detect the quality of laser beams. The International Organization for Standardization defines the parameters used to evaluate the quality of beams—the laser beam quality factor M ² as the beam waist radius of the actual beam (beam propagation The place where the beam radius is the smallest in the direction is called the beam waist) and the product of its far-field divergence angle and the corresponding product of the ideal Gaussian mode beam. Therefore, in order to evaluate the beam quality, it is necessary to obtain the beam waist radius of the actual beam and its far-field Field divergence angle, both of these parameters belong to the focusing spot size parameter.

The existing methods for measuring the focus spot size include array detection method and mechanical scanning method. Among them, the mechanical scanning method includes the slit scanning method, the moving knife-edge method and the iris method. In foreign countries, the mechanical scanning technology has been relatively mature, and many foreign companies have developed special beam quality measuring instruments. For example, Zhao Juncheng and others adopted a roller slit measurement method [Zhao Juncheng, Yin Wanhong, Liu Jianping, et al. Research on the quality measurement method of laser beams with orthogonal slit scanning [J]. Applied Optics, 2020, 41( 04):704-710] is a mechanical scanning technology, which directly uses the roller to scan the slit to scan the measured laser beam and then calculate the beam quality. And array detection technology (see [Sheldakova YV, Cherezova TY, Kudryashov A V. M2 sensor for the adaptive optical system [C]. Seventh International Conference on Laser and Laser-Information Technologies. International Society for Optics and Photonics, 2002, 4644: 392- 399]) is a relatively promising beam detection technology derived from photodetectors such as CCD cameras. The laser light intensity distribution can be directly measured through the CCD, and the light intensity value of each point can be obtained by using the camera pixel value. The spot size of the laser can be calculated according to the distribution range of the light intensity value on the CCD camera, that is, the spot size can be obtained from the light intensity attenuation values at different positions. According to the properties of laser transmission, the laser transmission characteristic curve can be fitted by using the measurement data of spot size at different positions, and then the beam quality parameters such as laser far-field divergence angle and beam quality factor can be obtained. Since the use of CCD does not need to change the internal structure of the laser beam, so It will not affect the quality of the laser beam, so the array detection method is also the most commonly used method to measure the quality of the beam. However, whether it is the mechanical scanning method or the array detection method, the multi-point method is used to measure the beam quality. This method cannot measure the beam quality in real time, and often introduces certain measurement errors, and the final calculated M ² will also be caused by the accumulation of errors. There are larger errors.

Many scholars at home and abroad have begun to study how to measure the beam quality in real time. They found that the complex amplitude can be reconstructed using the wavefront phase, and then the beam diffraction and transmission formula can be used to calculate the far-field divergence angle and beam waist width to measure the beam quality. For example, based on the slope measurement recovery Shack-Hartmann wavefront measurement technique of phase[Sheldakova JV, Kudryashov AV, Zavalova V Y. Beam quality measurements with Shack-Hartmann wavefront sensor and M2-sensor: comparison of two methods[C].Laser Resonators and Beam ControlIX,2007 ,6452:645207]. But the value it measures is inaccurate, it can only be measured qualitatively, and it can only be measured for single-mode lasers, and the measurement results for multi-mode lasers are wrong, which limits its practical application. The main reason is that in the actual optical path test process, the lens, airflow and other influences in the optical path will introduce distortion. Even if the optical path distortion can be reduced by very precise optical path adjustment, it cannot be completely eliminated; the distortion caused by indoor airflow disturbance cannot be passed. When these distortions are involved in the calculation of the far-field spot, it will affect the size of the spot and cause errors in the calculation of ^M2 . Therefore, the conventional Shack-Hartmann wavefront measurement technology can only The qualitative measurement of the laser beam quality factor M ² cannot be widely used.

In view of the previous problems, the Shack-Hartmann wavefront sensor is used instead of the traditional receiver CCD to evaluate the beam quality, and a reasonable method is used to overcome the influence of unfavorable factors and reduce measurement errors. The Shack-Hartmann wavefront sensor The device is easy to operate and can effectively shorten the beam evaluation time. When using the new algorithm to measure the laser beam, we can simultaneously obtain key parameters such as the wavefront distribution of the laser beam, the PV and RMS values of the wavefront, the light intensity distribution, the peak light intensity, and the laser beam quality factor ^M2 . It is of great significance and wide application value to laser research.

Contents of the invention

In order to solve the existing Shaker-Hartman wavefront measurement technology can only qualitatively measure the laser beam quality factor M ² problem, the invention provides a kind of comprehensive parameter evaluation method of laser beam quality, said method is based on Shaker-Hartman The wavefront detector SHWFS is realized, and the Shaker Hartimann wavefront detector is composed of a microlens array and a photodetector, and all microlenses in the microlens array have the same diameter and focal length; the method includes:

Step 1, using parallel light as a light source, using the photodetector to measure the background distortion W _bg of the optical path;

Step 2, using the laser to be measured as the light source, using the photodetector to collect the light lattice pattern of the laser beam multiple times to obtain the distorted wavefront, and taking the average value of the distorted wavefront obtained from multiple measurements, and using the averaged distortion Wavefront, calculate peak-to-valley PV and root mean square RMS;

Step 3, when the laser source to be tested is a single-mode laser, calculate the far-field spot image by using the distorted wavefront after deducting the background _Wbg , and obtain the actual image of the far-field spot; when the laser source to be tested is a multi-mode laser, consider The zoom ratio of the optical path and the size of the light source are used to convolve the point spread function calculated from the distorted wavefront after deducting the background W _bg with the image after the light source has been scaled to obtain the actual far-field spot image;

Step 4: Calculate the far-field spot size of the laser to be tested and the ideal far-field spot size according to the far-field spot image, and use their ratio to calculate the laser beam quality factor M ² parameter.

Optionally, the step 1 includes:

Using parallel light as a light source, using the photodetector to obtain a corresponding light lattice pattern, the light point in each sub-aperture in the light lattice pattern is used as the position of the reference light point, and the light points in all sub-apertures are relative to the center of the aperture. The shift in position is called the background distortion W _bg of the optical path.

Optionally, in the step 2, the photodetector is used to collect the light lattice pattern of the laser beam multiple times to obtain the distorted wavefront, including:

Using the laser to be measured as a light source, using the photodetector to collect the light lattice pattern of the laser beam multiple times;

Measuring the offset of the light spot in each sub-aperture in the light dot matrix pattern relative to the position of the reference light spot;

的测量来重构畸变波前，得到整个畸变波前W：Calculate the wavefront slope in each subaperture based on the offset of the spot relative to the reference spot position within each subaperture and based on the local slope of the distorted wavefront

The measurement of the distortion wavefront is reconstructed, and the entire distortion wavefront W is obtained:

Among them, (G _ix ,G _iy ) is the wavefront slope value along the x direction and along the y direction measured by the i-th sub-lens measured by SHWFS; Z _i represents the i-th Zernike mode, and the value of i ranges from 1 to n, n is the number of lenses included in the microlens array; [a ₁ ... a _n ] ^T represents the coefficient of the Zernike polynomial;

Express formula (1) in matrix form:

G＝F·A (2)

Among them, G is the wavefront slope vector measured by SHWFS, F is the wavefront reconstruction matrix with a dimension of 2m×n, and A is the coefficient vector of the Zernike polynomial;

According to the measured slope G, the least squares solution of the Zernike coefficient vector A of the wavefront to be measured is:

A＝(F ^T F) ^-1 G (3)

After the coefficient A is obtained, it can be substituted into formula (4) to obtain the phase information of the entire distorted wavefront W;

Thus, the distribution of the wavefront W to be measured is obtained. W is a matrix composed of N×N grid points, wherein the effective data are the data in the area of the inner truncated circle, and there are M pieces in total.

Optionally, it is assumed that the light lattice pattern of the laser beam is collected M times in step 2, and the interval between each collection is fixed; the calculation formulas of peak-to-valley PV and root mean square RMS in step 2 are as follows:

PV＝W _max -W _min (5)

Among them, W _max represents the maximum value among the M effective data in the wavefront W obtained by a single measurement, W _min represents the minimum value among the M valid data in the wavefront W obtained by a single measurement; W _j represents the The measured wavefront.

Optionally, in step 3, when the laser light source to be measured is a single-mode laser, the diameter of the actual far-field spot image is directly calculated according to the distorted wavefront W:

I(x,y)表示激光光束的幅度；W(x,y)表示激光光束的相位；x表示x方向上的坐标，y表示y方向上的坐标；λ是激光波长，exp表示自然常数e为底的指数函数；i表示复数的基本单位。in,

I(x,y) represents the amplitude of the laser beam; W(x,y) represents the phase of the laser beam; x represents the coordinate in the x direction, y represents the coordinate in the y direction; λ is the laser wavelength, exp represents the natural constant e Base exponential function; i represents the basic unit of complex numbers.

Optionally, in step 3, when the laser light source to be measured is a multimode laser, calculate its point spread function PSF:

Then the actual spot is the convolution of the ideal image O of the light source and the point spread function PSF:

I=O*PSF (9).

Optionally, the formula for calculating the parameters of the laser beam quality factor M in step ⁴ is as follows:

d_f是焦点为f的透镜焦平面上的光束直径，因此，where _d0 is the beam diameter in the near field and the divergence angle

_df is the beam diameter at the focal plane of the lens with focal point f, so,

Among them, d(I _{far field} ) represents the far-field spot size of the laser to be measured; d _gauss represents the ideal far-field spot size.

Optionally, if the diameter of the laser to be measured does not match the aperture of the Shack-Hartmann wavefront detector, a lens group is used to reduce or expand the beam.

Optionally, the microlens array includes at least 20*20 microlenses.

The beneficial effects of the present invention are:

Eliminate the influence of airflow disturbance by averaging multiple measurements; consider the size of the multi-mode laser light source, use the point spread function to convolve with the light source to calculate the far-field spot image of the multi-mode laser, and solve the problem of multi-mode laser measurement errors; When shrinking or expanding the beam, use the wavefront after deducting the background W _bg to calculate the far-field spot image, reduce the error of the far-field spot; use the Shack-Hartmann wavefront detector to measure parameters such as wavefront, PV and RMS , overcomes the problem that the existing Shaker-Hartmann wavefront detector measures the laser beam quality factor M ² with large measurement errors and can only be measured qualitatively, and achieves accurate measurement of the beam quality factor of single-mode or multi-mode lasers, laser Wavefront, PV, RMS and other parameters to realize the measurement of comprehensive parameters of laser beam quality.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings that need to be used in the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those skilled in the art, other drawings can also be obtained based on these drawings without creative effort.

Figure 1 is a schematic diagram of the principle of the measurement optical path when beam shrinkage or beam expansion is required; 1 is a laser, 2 and 3 are lenses, and 4 is a Shack-Hartmann wavefront detector.

Figure 2 is a schematic diagram of the principle of the direct measurement optical path. 1 is a laser, and 4 is a Shack-Hartmann wavefront detector.

Fig. 3 is the experimental light path diagram; The laser device of 633nm is arranged, the attenuation plate that is used for attenuating light intensity, and reflective mirror is used for the folding axis of light path, and the first lens and the second lens form a beam expander to expand the diameter of laser beam; Finally use The Shack-Hartmann wavefront detector measures the laser beam.

Fig. 4 is a simulation diagram of the reference spot and the distorted spot of the Shack-Hartmann wavefront detector, wherein (a) is a dot matrix diagram formed by a plane wave; (b) is a dot matrix diagram of a distorted wavefront aberration.

Fig. 5 is a schematic diagram of the calculation principle of the wavefront slope.

In Fig. 6, (a) is the simulation diagram of the point spread function corresponding to the distorted wavefront, (b) is the simulation diagram of the distorted wavefront, and (c) is the light dot matrix diagram.

In Fig. 7, (a) is a simulation diagram of a point spread function of a plane wave, and (b) is a simulation diagram of a pupil function.

Detailed ways

In order to make the purpose, technical solution and advantages of the present invention clearer, the following will further describe in detail the embodiments of the present invention in conjunction with the accompanying drawings.

Embodiment one:

This embodiment provides a comprehensive parameter evaluation method for laser beam quality, the main steps are as follows:

1) When the diameter of the laser beam does not match the aperture of the Shack-Hartmann wavefront detector, two lenses are needed to shrink or expand the beam, as shown in Figure 1, 1 is the laser, 2 and 3 are lenses, 4 is the Shack-Hartmann wavefront detector. The focal points of the lens 2 and the lens 3 coincide, the laser 1 is located on the object plane of the lens 2 , and the Shack-Hartmann wavefront detector 4 is located on the image plane of the lens 3 . When the diameter of the laser beam matches the aperture of the Shack-Hartmann wavefront detector, it can be directly measured, as shown in Figure 2, 1 is the laser, and 4 is the Shack-Hartmann wavefront detector.

2) For the optical path in Figure 1, the parallel light output of the zygo interferometer can be used as the light source instead of 1 light source. At this time, the distortion measured by the Shack-Hartmann wavefront detector is to calibrate the distortion of the optical path, as Background distortion W _bg of the light path.

3) Use the Shack-Hartmann wavefront detector to collect light lattice images to obtain the distorted wavefront, repeat the wavefront measurement at intervals of 1 second, and measure the wavefront at least 10 times, and average the measured wavefront to eliminate indoor airflow disturbance The influence of; use the average distortion wavefront to calculate the peak-to-valley PV and root mean square RMS;

4) When the laser source to be tested is a single-mode laser, the far-field spot image is calculated by using the distorted wavefront after deducting the background _Wbg to obtain the actual far-field spot image; when the laser source to be tested is a multi-mode laser, it is necessary to consider For the scaling ratio of the optical path and the size of the light source, the point spread function calculated by using the distorted wavefront after deducting the background W _bg is convolved with the image scaled by the light source to obtain the actual far-field spot image;

5) Calculate the far-field spot size of the laser to be measured and the ideal far-field spot size according to the far-field spot image, and use their ratio to calculate the laser beam quality factor ^M parameter;

Embodiment two:

The present embodiment provides a kind of comprehensive parameter evaluation method of laser beam quality, and described method is used for simultaneously measuring parameters such as laser beam wavefront distribution, wavefront PV and RMS value, light intensity distribution, light intensity peak value, M ^factor , In this embodiment, the diameter of the laser beam does not match the aperture of the Shack-Hartmann wavefront detector as an example. The optical path system shown in Figure 3 is built. The optical path system includes: lasers, attenuators, mirrors, and A lens, a second lens, and a Shaker Hartimann wavefront detector SHWFS; the Shaker Hartimann wavefront detector is composed of a microlens array and a photodetector CCD positioned at the focal point of the lens, and the microlens array includes at least 20* 20 microlenses, and all microlenses have the same diameter and focal length. The laser beam emitted by the laser passes through the attenuation sheet, changes the direction of the beam through the mirror, passes through the first lens and the second lens in turn, and then reaches the Shaker-Hartimann wavefront detector. The wavefront incident on the SHWFS is divided into approximately The plane wave is then imaged on the CCD on the back focal plane, and forms a corresponding light lattice pattern.

Measuring a wavefront based on the light lattice pattern, comprising:

Since the microlens array divides the entire wavefront into multiple sub-apertures, first measure the offset of the light spot in each sub-aperture in the light lattice pattern relative to the reference light spot position, please refer to Figure 4; the reference light spot position can be used The parallel light output of the zygo interferometer is obtained as a light source instead of a laser.

的测量来重构畸变波前；Calculate the wavefront slope in the subaperture according to the offset of the light spot in each subaperture relative to the reference spot position (see Figure 5), and based on the local slope of the distorted wavefront

measurements to reconstruct the distorted wavefront;

In formula (1), (G _ix ,G _iy ) is the wavefront slope value along the x-direction and y-direction measured by the i-th sub-lens measured by SHWFS; Z _i represents the i-th Zernike mode, i ranges from 1 to The value of n.

Express formula (1) in matrix form:

G＝F·A (2)

Among them, G is the wavefront slope vector measured by SHWFS, F is the wavefront reconstruction matrix with a dimension of 2m×n, and A is the coefficient vector of the Zernike polynomial. Therefore, according to the measured slope G, the least squares solution of the Zernike coefficient vector A of the wavefront to be measured is:

A＝(F ^T F) ^-1 G (3)

After the coefficient A is obtained, it can be substituted into formula (4) to obtain the phase information of the entire distorted wavefront W.

Thus, the distribution of the wavefront to be measured is obtained.

On this basis, the PV value of the wave front is obtained by subtracting the minimum value from the maximum value of the wave front W, and its root mean square RMS is calculated according to the wave front W:

PV＝W _max -W _min (5)

When the number of microlenses in SHWFS is large enough, for example, more than 20x20 microlenses, the light intensity collected by the CCD of SHWFS also reflects the light intensity distribution in the direction of vertical beam propagation.

After obtaining the phase W(x,y) and amplitude I(x,y) of the laser beam, the ^M2 beam parameters can be calculated.

In the existing literature, the calculation of the far-field spot diameter is to directly calculate the light intensity distribution based on the distorted wavefront W, but this is actually a point spread function. Therefore, this method is feasible for a point light source, but for a certain size For the light source, there will be a large error. Therefore, for a target with a certain size, the application uses the Fourier transform algorithm to calculate the point spread function, and then uses the point spread function to convolve the target to obtain the actual image of the laser spot.

For point lights:

in,

For a light source with a certain size, first calculate its point spread function PSF:

in,

Then the actual spot is the convolution of the ideal image O of the light source and the point spread function PSF:

I=O*PSF (9)

The laser beam quality factor M ² is calculated from the relation given in the international standard ISO/DIS 11146:

where _d0 is the beam diameter in the near field, θ is the divergence angle, and λ is the laser wavelength.

定义，其中d_f是焦点为f的透镜焦平面上的光束直径。公式(10)也可以近似表示为：The divergence angle θ is given by the equation

Definition, where _df is the beam diameter at the focal plane of the lens with focal point f. Formula (10) can also be approximated as:

So far, we can calculate the wavefront W according to formulas (1)～(4), calculate PV and RMS according to (5) and (6), and calculate the far field of a point light source or a light source with a certain size according to (7)～(9) light intensity distribution. Finally, the laser beam quality factor M ² is calculated according to (10) or (11).

In the present embodiment, the laser is a single-mode laser, the laser wavelength λ=633nm, the focal point f=25nm of the first lens, the focal point f=100nm of the second lens, and the microlens array of the Shaker-Hartimann wavefront detector includes 29*29 a microlens.

Based on the optical path built above, the point spread function corresponding to the obtained distorted wavefront is shown in (a) in Figure 6, (b) in Figure 6 is the distorted wavefront, and (c) in Figure 6 is the light lattice; (a) in Fig. 7 is the point spread function of the plane wave, and (b) in Fig. 7 is the pupil function. The calculation result M ² is 10.48. It can be seen that the scheme of the present application can quantitatively measure the laser beam quality factor M ² .

Part of the steps in the embodiments of the present invention can be realized by software, and the corresponding software program can be stored in a readable storage medium, such as an optical disk or a hard disk.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within range.

Claims (9)

1. a comprehensive parameter evaluation method of laser beam quality, it is characterized in that, described method realizes based on Shaker Hartimann wavefront detector SHWFS, described Shaker Hartimann wavefront detector is made up of microlens array and photodetector Constitute, all microlenses in the microlens array have identical diameter and focal length; Described method comprises: Step 1, using parallel light as a light source, using the photodetector to measure the background distortion W _bg of the optical path; Step 2, using the laser to be measured as the light source, using the photodetector to collect the light lattice pattern of the laser beam multiple times to obtain the distorted wavefront, and taking the average value of the distorted wavefront obtained from multiple measurements, and using the averaged distortion Wavefront, calculate peak-to-valley PV and root mean square RMS; Step 3, when the laser source to be tested is a single-mode laser, calculate the far-field spot image by using the distorted wavefront after deducting the background _Wbg , and obtain the actual image of the far-field spot; when the laser source to be tested is a multi-mode laser, consider The zoom ratio of the optical path and the size of the light source are used to convolve the point spread function calculated from the distorted wavefront after deducting the background W _bg with the image after the light source has been scaled to obtain the actual far-field spot image; Step 4: Calculate the far-field spot size of the laser to be tested and the ideal far-field spot size according to the far-field spot image, and use their ratio to calculate the laser beam quality factor M ² parameter. 2. The method according to claim 1, wherein said step 1 comprises: Using parallel light as a light source, using the photodetector to obtain a corresponding light lattice pattern, the light point in each sub-aperture in the light lattice pattern is used as the position of the reference light point, and the light points in all sub-apertures are relative to the center of the aperture. The shift in position is called the background distortion W _bg of the optical path. 3. The method according to claim 2, wherein, in the step 2, the photodetector is used to collect the light lattice pattern of the laser beam multiple times to obtain a distorted wavefront, including: Using the laser to be measured as a light source, using the photodetector to collect the light lattice pattern of the laser beam multiple times; Measuring the offset of the light spot in each sub-aperture in the light dot matrix pattern relative to the position of the reference light spot; Calculate the wavefront slope in each subaperture based on the offset of the spot relative to the reference spot position within each subaperture and based on the local slope of the distorted wavefront

The measurement of the distortion wavefront is reconstructed, and the entire distortion wavefront W is obtained:

Among them, (G _ix ,G _iy ) is the wavefront slope value along the x direction and along the y direction measured by the i-th sub-lens measured by SHWFS; Z _i represents the i-th Zernike mode, and the value of i ranges from 1 to n, n is the number of lenses included in the microlens array; [a ₁ ... a _n ] ^T represents the coefficient of the Zernike polynomial; Express formula (1) in matrix form: G＝F·A (2) Among them, G is the wavefront slope vector measured by SHWFS, F is the wavefront reconstruction matrix with a dimension of 2m×n, and A is the coefficient vector of the Zernike polynomial; According to the measured slope G, the least squares solution of the Zernike coefficient vector A of the wavefront to be measured is: A＝(F ^T F) ^-1 G (3) After the coefficient A is obtained, it can be substituted into formula (4) to obtain the phase information of the entire distorted wavefront W;

Thus, the distribution of the wavefront W to be measured is obtained. W is a matrix composed of N×N grid points, wherein the effective data are the data in the area of the inner truncated circle, and there are M pieces in total. 4. method according to claim 3, it is characterized in that, assuming that step 2 collects the light lattice pattern of M times laser beam altogether, each collection interval is fixed time; In described step 2, peak-to-valley value PV and root mean square The RMS calculation formula is as follows: PV＝W _max -W _min (5)

Among them, W _max represents the maximum value among the M effective data in the wavefront W obtained by a single measurement, W _min represents the minimum value among the M valid data in the wavefront W obtained by a single measurement; W _j represents the The measured wavefront. 5. The method according to claim 4, wherein in step 3, when the laser light source to be measured is a single-mode laser, the diameter of the actual far-field spot image is directly calculated according to the distortion wavefront W distributed:

in,

I(x,y) represents the amplitude of the laser beam; W(x,y) represents the phase of the laser beam; x represents the coordinate in the x direction, y represents the coordinate in the y direction; λ is the laser wavelength, exp represents the natural constant e Base exponential function; i represents the basic unit of complex numbers. 6. The method according to claim 5, wherein, in the step 3, when the laser light source to be measured is a multimode laser, calculate its point spread function PSF:

Then the actual spot is the convolution of the ideal image O of the light source and the point spread function PSF: I=O*PSF (9). 7. method according to claim 6, is characterized in that, described step 4 laser beam quality factor M ² parameter computing formulas are as follows:

where _d0 is the beam diameter in the near field and the divergence angle

_df is the beam diameter at the focal plane of the lens with focal point f, so,

Among them, d(I _farfield ) represents the far-field spot size of the laser to be measured; d _gauss represents the ideal far-field spot size. 8. The method according to claim 1, wherein if the diameter of the laser to be measured does not match the aperture of the Shack-Hartmann wavefront detector, a lens group is used to reduce or expand the beam . 9. The method according to claim 1, wherein the microlens array comprises at least 20*20 microlenses.

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