A Square Flat-Top Beam Shaping Method Based on Circular Resolved Phase

Abstract

This invention belongs to the field of laser beam shaping and relates to a method for shaping a square flat-top beam based on a circular resolving phase. By determining the parameters of the incident beam and the target square flat-top beam, this invention obtains a circular resolving phase that achieves a circular flat-top beam with a diameter equal to the side length of the square. This circular resolving phase is used as the initial value for iteratively optimizing the diffraction phase distribution of the square flat-top beam. Based on the parameters of the incident beam and the square flat-top beam, the circular resolving phase is iteratively optimized to obtain the final optimized diffraction phase distribution. This optimized diffraction phase distribution is input into a spatial light modulator, which generates a square flat-top beam on the focal plane of its rear lens. This invention can simultaneously achieve a square flat-top beam with high energy utilization, high top uniformity, and no speckle, meeting the requirements of high-quality laser processing.

Description

Technical Field

[0001] This invention belongs to the field of laser beam shaping and relates to a method for shaping a square flat-top beam based on a circular analytical phase. Background Technology

[0002] Ultrafast laser processing technology has been widely used in ultra-precision machining processes such as drilling, scribing, and engraving. The lasers used are mostly high-power pulsed lasers such as femtosecond, picosecond, and nanosecond lasers, with an output laser spot distribution close to a Gaussian pattern. Figure 2 Left image. Due to the high power and complex spot pattern of the laser, the energy distribution of the laser beam is uneven, with strong energy in the center and weak energy at the edges, resulting in an irregular shape and numerous speckles. This uneven energy distribution leads to unevenness on the surface of the workpiece, making it difficult to machine deep holes with steep sidewalls, and the excessively high energy in some areas can easily burn the workpiece. Therefore, spatial beam shaping of the laser beam to generate a flat-top beam with concentrated and uniform energy distribution has become a necessary prerequisite for high-precision and high-quality machining. In addition, when machining complex shapes, beam scanning is often required, making precise beam overlap particularly important. However, common circular flat-top beams suffer from reduced top uniformity during overlap due to their curved edge characteristics. In contrast, square flat-top beams offer an effective solution to overcome these difficulties, such as... Figure 2 The image on the right.

[0003] Currently, there are two main methods for generating square flat-top beams. One is a shaping method based on geometric optics, which uses lenses and optical elements to adjust the beam shape to generate a square flat-top beam. The other is a shaping method based on diffraction optics, which calculates the diffraction phase distribution required for shaping using analytical methods or phase retrieval algorithms. The calculated phase distribution is then recorded on a diffraction optical element or input into a spatial light modulator. When an incident beam with a Gaussian spot energy spatial distribution illuminates this element, a square flat-top beam corresponding to the diffraction phase distribution is generated on the focal plane of the lens behind it. Spatial light modulators are widely used due to their flexibility.

[0004] However, in existing technologies, shaping methods based on geometric optics principles require combinations of various lenses and optical elements, resulting in complex structures, large sizes, and heavy weight. In diffraction optics shaping methods, the flat-top beam obtained by calculating the phase distribution analytically suffers from high energy at the beam edge and very low energy utilization. Figure 3 The left image shows the diffraction phase distribution calculated analytically, and the right image shows the corresponding square flat-top beam output. Relatively speaking, the traditional phase retrieval algorithm has a faster convergence speed and higher energy utilization of the calculated flat-top beam, but its top uniformity is not high and the output beam has many speckles, such as... Figure 4The left image shows the diffraction phase distribution calculated by the traditional phase retrieval algorithm, and the right image shows the corresponding output square flat-top beam. Therefore, none of the above methods can simultaneously meet the requirements of high energy utilization, high top uniformity, and no speckle for flat-top beams. Summary of the Invention

[0005] The technical solution adopted by this invention to solve the technical problem is: a method for shaping a square flat-top beam based on a circular analytical phase, comprising the following steps:

[0006] Step S1: Determine the parameters of the incident beam, which include the wavelength of the incident beam and the spatial distribution of the beam's energy.

[0007] Step S2: Determine the parameters of the square flat-top beam, which include the wavelength of the square flat-top beam and the spatial distribution of the beam's energy.

[0008] Step S3: Determine the circular resolving phase based on the parameters of the incident beam and the square flat-top beam, and use the circular resolving phase as the initial value of the diffraction phase distribution. The diffraction phase distribution is the diffraction phase distribution of shaping the incident beam into a square flat-top beam.

[0009] Step S4: Based on the parameters of the incident beam and the square flat-top beam, substitute the initial value of the diffraction phase distribution into the phase recovery algorithm for iterative optimization to obtain the optimized diffraction phase distribution;

[0010] Step S5: Input the optimized diffraction phase distribution into the spatial light modulator to generate a square flat-top beam with high energy utilization, high top uniformity, and no speckle.

[0011] Preferably, in step S3, the circular resolving phase is the resolving phase distribution of shaping the incident beam into a circular flat-top beam derived from theory, wherein the diameter of the circular flat-top beam is equal to the side length of the square flat-top beam; the circular resolving phase is used as the initial value for realizing the diffraction phase distribution of the square flat-top beam.

[0012] Preferably, in step S3, the incident beam is a circular incident beam with a Gaussian spot energy spatial distribution; the square flat-top beam is a beam with a square cross-section and a flat-top spot energy spatial distribution.

[0013] More preferably, the amplitude distribution formula of the incident beam is u in The incident beam has a waist radius of w1, and the amplitude distribution formula for the square flat-top beam is u. t The side length of the square flat-top beam is d, which is also the diameter of the circular flat-top beam.

[0014] First, the circular analytical phase is derived. Based on the mapping relationship between the focal plane coordinates and the spatial light modulator coordinates: r2(r1), where r1 is the coordinate position on the spatial light modulator and r2 is the coordinate position on the focal plane, the phase distribution expression on the spatial light modulator can be expressed as:

[0015]

[0016] Where λ is the wavelength of the incident beam, and f is the focal length of the lens following the spatial light modulator. Assume the output circular flat-top beam has uniform intensity within its radius. When a Gaussian beam with a beam waist radius of w1 is incident on the spatial light modulator, according to the law of conservation of energy, we can obtain:

[0017]

[0018] Next, due to the size limitations of the spatial light modulator and the focal plane, the mapping relationship between the r2 coordinate on the spatial light modulator and the r1 coordinate on the focal plane can be expressed according to the energy distribution ratio of the input beam and the target beam as follows:

[0019]

[0020] By combining the mapping relationship and the phase distribution expression, the circular analytical phase can be obtained:

[0021]

[0022] Secondly, by directly inputting the circular resolving phase into the spatial light modulator, a circular flat-top beam with a diameter of d can be generated. In this invention, the circular resolving phase is used as the initial value for the diffraction phase distribution to generate a square flat-top beam.

[0023] Preferably, in step S4, the amplitude distribution formula u of the incident beam is determined based on the parameters of the incident beam. in The amplitude distribution formula u of the square flat-top beam is determined based on the parameters of the beam. t The initial value of the diffraction phase distribution, the amplitude distribution formula of the incident beam, and the amplitude distribution formula of the square flat-top beam are substituted into the phase retrieval algorithm for iterative optimization to obtain the final optimized diffraction phase distribution.

[0024] More preferably, in the iterative optimization of the phase recovery algorithm, the top uniformity and energy utilization rate are calculated in each loop. The top uniformity γ = 1 - δ, where δ is the top non-uniformity, and the energy utilization rate is represented by ρ.

[0025] More preferably, the top non-uniformity and energy utilization rate are specifically defined as follows:

[0026]

[0027]

[0028]

[0029] Where W represents the flat-top beam region on the focal plane; I(x2,y2) represents the light intensity distribution of all regions on the entire focal plane, including the flat-top beam region and the non-flat-top regions at its edges; n is the total number of samples of discrete points in the flat-top beam region; This represents the average light intensity in the flat-top beam region.

[0030] More preferably, the top nonuniformity δ represents the unevenness of the top light intensity distribution in the flat-top region of the output beam. The smaller the value of the top nonuniformity δ, that is, the larger the top uniformity γ = 1 - δ, the more uniform the light intensity distribution in the flat-top beam region.

[0031] More preferably, the energy utilization rate ρ is the ratio of the sum of the light intensity at all points in the flat-top beam region to the sum of the light intensity of the output beam. The energy utilization rate ρ represents the proportion of the flat-top beam in the entire output beam. The higher the value of the energy utilization rate ρ, the greater the proportion of the flat-top beam in the output beam.

[0032] The beneficial effects of this invention are:

[0033] This invention determines the parameters of the incident beam and the target square flat-top beam to obtain the circular resolving phase of the circular flat-top beam with a diameter equal to the side length of the square. This circular resolving phase is used as the initial value of the diffraction phase distribution to achieve the square flat-top beam. Based on the parameters of the incident beam and the square flat-top beam, the circular resolving phase is iteratively optimized to obtain the final optimized diffraction phase distribution. This optimized diffraction phase distribution is input into a spatial light modulator, which can generate a square flat-top beam on the focal plane of its rear lens. Attached Figure Description

[0034] Figure 1 This is a flowchart of a square flat-top beam shaping method based on circular analytical phase according to the present invention;

[0035] Figure 2 This is an intensity distribution diagram of the incident beam and the square flat-top beam of the present invention;

[0036] Figure 3 It shows the diffraction phase distribution calculated by the existing analytical method and the corresponding intensity distribution of the square flat-top beam.

[0037] Figure 4It shows the diffraction phase distribution calculated by existing traditional phase retrieval algorithms and the corresponding intensity distribution of the square flat-top beam.

[0038] Figure 5 This is the final optimized diffraction phase distribution diagram obtained by the present invention;

[0039] Figure 6 This is the intensity distribution map of the square flat-top beam generated by the present invention; Detailed Implementation

[0040] The relevant technologies of this invention will now be described in detail and completely with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0041] refer to Figures 1-6 This invention provides a method for shaping a square flat-top beam based on a circular analytical phase. The diffraction phase distribution is calculated by optimizing the circular analytical phase, and then input into a spatial light modulator to shape the incident beam with a Gaussian spot energy spatial distribution into a square flat-top beam with a flat-top spot energy spatial distribution.

[0042] This invention provides a method for shaping a square flat-top beam based on a circular analytical phase, comprising:

[0043] S1. Determine the parameters of the incident beam, including the wavelength and the spatial distribution of the beam's energy. S2. Determine the parameters of the square flat-top beam, including the wavelength and the spatial distribution of the beam's energy. S3. Determine the circular resolving phase based on the parameters of the incident beam and the square flat-top beam, using this circular resolving phase as the initial value for the diffraction phase distribution. S4. Substitute the circular resolving phase as the initial value into a phase retrieval algorithm based on the parameters of the incident beam and the square flat-top beam for iterative optimization to obtain the optimized diffraction phase distribution. S5. Inputting the optimized diffraction phase distribution into a spatial light modulator can achieve a square flat-top beam with high energy utilization, high top uniformity, and no speckle.

[0044] Determining a circular resolving phase based on the parameters of the incident beam and the square flat-top beam, and using the circular resolving phase as the initial value for the diffraction phase distribution, includes: determining the circular resolving phase, wherein the circular resolving phase is the resolving phase distribution derived theoretically for shaping the incident beam into a circular flat-top beam, and the diameter of the circular flat-top beam is equal to the side length of the square flat-top beam; and using the circular resolving phase as the initial value for realizing the diffraction phase distribution of the square flat-top beam.

[0045] The incident beam is a circular incident beam with a Gaussian spot energy spatial distribution; the square flat-top beam is a beam with a square cross-section and a flat-top spot energy spatial distribution.

[0046] The formula for the amplitude distribution of the incident beam is u in The incident beam has a waist radius of w1; the amplitude distribution formula for a square flat-top beam is u. t The side length of the square flat-top beam is d, which is also the diameter of the circular flat-top beam. There is a mapping relationship between the focal plane coordinates r2 and the spatial light modulator coordinates r1: r2(r1). The phase distribution formula on the spatial light modulator can be expressed as: Where λ is the wavelength of the incident beam, and f is the focal length of the lens following the spatial light modulator. Assuming the output circular flat-top beam has uniform intensity within its radius, when a Gaussian beam with a beam waist radius of w1 is incident on the spatial light modulator, according to the law of conservation of energy, we can obtain: Next, due to the size limitations of the spatial light modulator and the focal plane, the mapping relationship between the coordinates r2 on the spatial light modulator and the coordinates r1 on the focal plane can be expressed according to the energy distribution ratio of the input beam and the target beam as follows:

[0047]

[0048] By combining the mapping relationship and the phase distribution expression, the circular analytical phase can be obtained:

[0049]

[0050] By directly inputting this circular resolving phase into a spatial light modulator, a circular flat-top beam with a diameter of d can be generated. In this invention, however, the circular resolving phase is used as the initial value for the diffraction phase distribution to generate a square flat-top beam.

[0051] Based on the parameters of the incident beam and the square flat-top beam, the initial value of the diffraction phase distribution is substituted into the phase retrieval algorithm for iterative optimization to obtain the optimized diffraction phase distribution. This includes: determining the amplitude distribution formula u of the incident beam based on the parameters of the incident beam. inThe amplitude distribution formula u of the square flat-top beam is determined based on the parameters of the square flat-top beam. t The initial value of the diffraction phase distribution, the amplitude distribution formula of the incident beam, and the amplitude distribution formula of the square flat-top beam are substituted into the phase retrieval algorithm for iterative optimization to obtain the final optimized diffraction phase distribution. In each iteration, the top uniformity and energy utilization rate are calculated. The top uniformity γ = 1 - δ, where δ is the top non-uniformity, and the energy utilization rate is represented by ρ.

[0052] The specific definitions are as follows:

[0053]

[0054]

[0055]

[0056] Where W represents the flat-top beam region on the focal plane; I(x2,y2) represents the light intensity distribution of all regions on the entire focal plane, including the flat-top beam region and the non-flat-top regions at its edges; n is the total number of samples of discrete points in the flat-top beam region; The average light intensity of the flat-top beam region is represented by γ. Top uniformity δ represents the unevenness of the light intensity distribution at the top of the flat-top region of the output beam. The smaller the value, the larger the top uniformity γ, indicating a more uniform light intensity distribution in the flat-top beam region. Energy efficiency ρ is the ratio of the sum of the light intensities at all points in the flat-top beam region to the sum of the light intensities of the output beam. It represents the proportion of energy from the flat-top beam in the entire output beam; a higher energy efficiency value indicates a greater proportion of energy from the flat-top beam in the output beam.

[0057] The final optimized diffraction phase distribution is input into the spatial light modulator, and a square flat-top beam with a side length of d is generated at the focal plane of the lens thereafter. This square flat-top beam has high energy efficiency, high top uniformity and no speckle.

[0058] This invention provides a method for shaping a square flat-top beam based on a circular resolving phase. By using the parameters of the incident beam and the square flat-top beam, a circular resolving phase is determined. This circular resolving phase is used as the initial value of the diffraction phase distribution for generating the square flat-top beam. This initial value of the diffraction phase distribution is then cyclically optimized in a phase retrieval algorithm to obtain the final optimized diffraction phase distribution. The final optimized diffraction phase distribution is then input into a spatial light modulator. When the incident beam illuminates this spatial light modulator loaded with the final optimized diffraction phase distribution, a square flat-top beam with high energy utilization, high top uniformity, and no speckle is generated on the focal plane of the lens.

[0059] Figure 1 A flowchart of a square flat-top beam shaping method based on circular analytical phase provided by an embodiment of the present invention is given, the method comprising the following steps 1-5:

[0060] Step S1: Determine the parameters of the incident beam, which include the wavelength of the incident beam and the spatial distribution of the beam's energy.

[0061] Step S2: Determine the parameters of the square flat-top beam, which include the wavelength of the square flat-top beam and the spatial distribution of the beam's energy.

[0062] The incident beam is a circular incident beam with a Gaussian spot energy spatial distribution; the square flat-top beam is a beam with a square cross-section and a flat-top spot energy spatial distribution.

[0063] That is, in the embodiments of the present invention, a circular incident beam with Gaussian spot energy distribution can be shaped into a square flat-top beam with flat-top spot energy spatial distribution.

[0064] Step S3: Determine the circular resolving phase based on the parameters of the incident beam and the square flat-top beam, and use the circular resolving phase as the initial value of the diffraction phase distribution. The diffraction phase distribution is the diffraction phase distribution of the incident beam shaped into a square flat-top beam.

[0065] Step S4: Based on the parameters of the incident beam and the parameters of the square flat-top beam, substitute the initial value of this diffraction phase distribution into the phase recovery algorithm for iterative optimization to obtain the optimized diffraction phase distribution.

[0066] Step S5: Inputting the optimized diffraction phase distribution into the spatial light modulator can achieve a square flat-top beam with high energy utilization, high top uniformity, and no speckle on the focal plane of the lens behind it.

[0067] In this embodiment of the invention, a circular resolving phase for achieving a circular flat-top beam is derived based on the parameters of the incident beam and the target square flat-top beam. This circular resolving phase is used as the initial value for the diffraction phase distribution of the square flat-top beam. The amplitude distribution formulas for the incident beam and the square flat-top beam are then determined. These initial values, the amplitude distribution formulas for the incident beam and the square flat-top beam are then substituted into a phase retrieval algorithm for iterative optimization, resulting in the final optimized diffraction phase distribution. This optimized diffraction phase distribution can shape the square flat-top beam. Inputting this optimized diffraction phase distribution into a spatial light modulator generates a square flat-top beam on the focal plane of its rear lens. This method overcomes the problems of poor beam uniformity and speckle in traditional phase retrieval algorithms that use randomly generated phases as initial values ​​for diffraction phase distribution during iterative optimization. It yields a square flat-top beam with good top uniformity, high energy utilization, no speckle, and easy overlap.

[0068] Example:

[0069] This embodiment is a square flat-top beam example. The incident beam is a circular beam with a Gaussian spot energy spatial distribution, with a wavelength λ of 1030 nm and a beam waist radius w1 of 2.1 mm. The target square flat-top beam is a square flat-top beam with a flat-top spot energy spatial distribution, with a wavelength λ of 1030 nm and a side length d of 1.0 mm. The focal length f of the lens is 250 mm. The amplitude distribution of the circular beam with the Gaussian spot energy spatial distribution satisfies:

[0070]

[0071] Here, A represents the incident light amplitude, which can be normalized and set to A = 1; w1 represents the beam waist radius of the incident Gaussian beam, x1 represents the abscissa of the spatial light modulator, and y1 represents the ordinate of the spatial light modulator. The amplitude distribution of a square flat-top beam with a flat-top spot energy spatial distribution satisfies:

[0072]

[0073] Here, B is the amplitude of the flat-top beam, which can be normalized and set to B=1; d represents the side length of the square flat-top beam with energy distribution of the flat-top beam; x2 represents the abscissa of the focal plane of the lens, and y2 represents the ordinate of the focal plane of the lens. Figure 2 This is a cross-sectional view showing the incident Gaussian beam and the target square flat-top beam in an embodiment of the present invention.

[0074] Next, the circular analytical phase is derived. There is a certain mapping relationship between the focal plane coordinates and the spatial light modulator coordinates: r2(r1), where r1 is the coordinate position on the spatial light modulator. r2 is the coordinate position on the focal plane. The phase distribution expression on a spatial light modulator can be expressed as:

[0075]

[0076] First, assume that the output circular flat-top beam has uniform intensity within its radius. When a Gaussian beam with a beam waist radius of w1 is incident on a spatial light modulator, according to the law of energy conservation, we can obtain:

[0077]

[0078] Next, due to the size limitations of the spatial light modulator and the focal plane, the mapping relationship between the r2 coordinate on the spatial light modulator and the r1 coordinate on the focal plane can be expressed according to the energy distribution ratio of the input beam and the target beam as follows:

[0079]

[0080] By combining the mapping relationship and the phase distribution expression, the circular analytical phase can be obtained:

[0081]

[0082] By directly inputting this circular resolving phase into a spatial light modulator, a circular flat-top beam with a diameter of d can be generated. In this invention, this circular resolving phase is used as the initial value for the diffraction phase distribution to generate a square flat-top beam.

[0083] The initial value of the diffraction phase distribution is:

[0084]

[0085] The amplitude distribution formula of the incident beam is as follows:

[0086]

[0087] The amplitude distribution formula for the square flat-top beam is as follows:

[0088]

[0089] The phase retrieval algorithm, such as the Gerchberg-Saxton algorithm, is used to iteratively calculate the top homogeneity γ and energy efficiency ρ. The calculation stops when the top homogeneity γ and energy efficiency ρ meet the target requirements or the number of iterations reaches its maximum value, yielding the final optimized diffraction phase distribution, such as... Figure 5 .

[0090] The final optimized diffraction phase distribution is input into the spatial light modulator, and a square flat-top beam with side length d is generated at the focal plane of the subsequent lens, as shown below. Figure 6 Its top uniformity γ is as high as 0.923, while its energy utilization ρ also reaches 0.945. This square flat-top beam has high energy utilization, high top uniformity, and no speckle.

[0091] The shaping effect of the square flat-top beam shaping method based on circular analytical phase in this embodiment is compared with that of the phase recovery algorithm with random initial phase. Figure 3 As shown in the right figure, the square flat-top beam shaped by the phase retrieval algorithm with random initial phase has an energy utilization rate of 0.898, but its top uniformity is only 0.742.

[0092] In summary, this invention, by determining the parameters of the incident beam and the target square flat-top beam, derives the circular resolving phase for achieving a circular flat-top beam with a diameter equal to the side length of the square. This circular resolving phase is used as the initial value for the diffraction phase distribution of the square flat-top beam. Based on the parameters of the incident beam and the square flat-top beam, the circular resolving phase is iteratively optimized to obtain the final optimized diffraction phase distribution. This optimized diffraction phase distribution is then input into a spatial light modulator, generating a square flat-top beam on the focal plane of its rear lens. This invention can simultaneously achieve a square flat-top beam with high energy utilization, high top uniformity, and no speckle, meeting the requirements of high-quality laser processing. Therefore, this invention has broad application prospects.

[0093] It should be emphasized that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A method for shaping a square flat-top beam based on circular analytical phase, characterized in that, Includes the following steps: Step S1: Determine the parameters of the incident beam, which include the wavelength of the incident beam and the spatial distribution of the beam's energy. Step S2: Determine the parameters of the square flat-top beam, which include the wavelength of the square flat-top beam and the spatial distribution of the beam's energy. Step S3: Determine the circular resolving phase based on the parameters of the incident beam and the square flat-top beam, and use the circular resolving phase as the initial value of the diffraction phase distribution. The diffraction phase distribution is the diffraction phase distribution of shaping the incident beam into a square flat-top beam. Step S4: Based on the parameters of the incident beam and the square flat-top beam, substitute the initial value of the diffraction phase distribution into the phase recovery algorithm for iterative optimization to obtain the optimized diffraction phase distribution; Step S5: Input the optimized diffraction phase distribution into the spatial light modulator to generate a square flat-top beam with high energy utilization, high top uniformity and no speckle. In step S3, the circular analytical phase is the derived analytical phase distribution for shaping the incident beam into a circular flat-top beam, wherein the diameter of the circular flat-top beam is equal to the side length of the square flat-top beam; the circular analytical phase is used as the initial value for realizing the diffraction phase distribution of the square flat-top beam. In step S3, the incident beam is a circular incident beam with a Gaussian spot energy spatial distribution, and the square flat-top beam is a beam with a square cross-section and a flat-top spot energy spatial distribution.

2. The method for shaping a square flat-top beam based on a circular analytical phase according to claim 1, characterized in that, The amplitude distribution formula of the incident beam is: The beam waist radius of the incident beam is The formula for the amplitude distribution of a square flat-top beam is: The side length of the square flat-top beam is d, which is also the diameter of the circular flat-top beam. The circular analytical phase formula is: in, λ is the wavelength of the incident beam; f is the focal length of the lens after the spatial light modulator. The coordinates are the position on the spatial light modulator; By directly inputting the circular resolving phase into the spatial light modulator, a circular flat-top beam with a diameter of d can be generated; the circular resolving phase will be used as the initial value of the diffraction phase distribution for generating a square flat-top beam.

3. The method for shaping a square flat-top beam based on a circular analytical phase according to claim 1, characterized in that, In step S4, the amplitude distribution formula of the incident beam is determined based on the parameters of the incident beam. The amplitude distribution formula of the square flat-top beam is determined based on its parameters. The initial value of the diffraction phase distribution, the amplitude distribution formula of the incident beam, and the amplitude distribution formula of the square flat-top beam are substituted into the phase retrieval algorithm for iterative optimization to obtain the final optimized diffraction phase distribution.

4. The method for shaping a square flat-top beam based on a circular analytical phase according to claim 3, characterized in that, In the iterative optimization of the phase retrieval algorithm, the top uniformity and energy utilization rate are calculated cyclically, where the top uniformity... , It refers to top non-uniformity, energy utilization efficiency. To express.

5. The method for shaping a square flat-top beam based on a circular analytical phase according to claim 4, characterized in that, The specific definitions of top non-uniformity and energy utilization rate are as follows: Where W represents the flat-top beam region on the focal plane. This represents the light intensity distribution across all regions of the entire focal plane, including the flat-top beam region and the non-flat-top regions at its edges; n is the total number of discrete points sampled in the flat-top beam region. This represents the average light intensity in the flat-top beam region.

6. The method for shaping a square flat-top beam based on a circular analytical phase according to claim 5, characterized in that, The top non-uniformity refers to the unevenness of the top of the flat-top region of the output beam. The smaller the value, the lower the top uniformity. The larger the value, the more uniform the light intensity distribution in the flat-top beam region.

7. The method for shaping a square flat-top beam based on a circular analytical phase according to claim 5, characterized in that, The energy utilization rate It is the ratio of the sum of the light intensity at all points in the flat-top beam region to the sum of the light intensity of the output beam, representing energy utilization efficiency. This represents the proportion of the flat-top beam in the entire output beam; the higher the energy utilization rate, the greater the proportion of the flat-top beam in the output beam.

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