Diffractive optical element design method based on automatic differentiation and free-form surface technology

Abstract

The invention discloses a diffractive optical element design method based on automatic differentiation and a free-form surface technology, and belongs to the field of optical design. The implementation method comprises the following steps: expressing phase distribution corresponding to a diffractive optical element as superposition of multiple layers of local free-form surfaces; calculating the intensity distribution of the input light field which is modulated by the diffractive optical element and then propagated to a target plane through a scalar diffraction theory; and in combination with automatic differential and multi-scale optimization strategies, phase distribution is optimized by adopting a gradient descent method. The phase distribution of the diffractive optical element is represented by a continuous and smooth free-form surface, so that the phase surface is always continuous and smooth in the optimization process, the curvature distribution of the curved surface is further restrained in the optimization process, and the processing difficulty of the diffractive optical element is reduced; in the optimization process, random phases and phase singular points are avoided, and speckle noise is suppressed; the superposition representation phase distribution of multiple layers of local free-form surfaces is adopted, and a multi-scale optimization strategy is matched, so that the dependence on an initial phase can be eliminated, and the convergence of iteration is ensured.

Description

Technical Field

[0001] The invention belongs to the field of optical design, and in particular relates to a diffraction optical element design method based on automatic differentiation and free-form surfaces. Background Art

[0002] Laser beam shaping is a key link in laser processing technology. By precisely controlling the spatial distribution characteristics of the laser beam, it can effectively improve the accuracy and speed of advanced laser processing technologies such as laser additive manufacturing, laser welding, and wafer laser annealing, providing strong support for high-quality and high-efficiency production in the modern manufacturing industry. Diffractive optical elements (DOEs), as a key tool for laser beam shaping, have demonstrated tremendous technical strength.

[0003] However, traditional DOE design methods for beam shaping, such as iterative Fourier transform method (including Gerchberg-Saxton algorithm and its improved algorithm) and simulated annealing algorithm, have certain limitations. Iterative Fourier transform algorithm is prone to fall into local optimal solution, and its effect is highly dependent on the choice of initial phase; while simulated annealing algorithm can find a better global optimal solution, but its calculation process is time-consuming and inefficient. More importantly, the phase distribution obtained by these traditional algorithm designs is often disordered, which not only increases the difficulty of DOE processing, but also the phase singularities in the random phase will cause speckle noise, which significantly affects the beam shaping performance on the target surface.

[0004] In order to overcome these challenges, a composite design method combining geometric optics and iterative Fourier transform algorithm has emerged, such as the literature [Feng ZX, Froese BD, Liang R G. Composite method for precise freeform optical beam shaping. Applied Optics, 2015, 54 (31): 9364-9369]. This method first solves the free-form surface for beam shaping under the framework of geometric optics approximation, and then uses the free-form surface as the initial solution of the diffractive optical element to iterate the Fourier transform algorithm. In this way, this method can design a phase distribution that is smoother and has a better shaping effect than the GS algorithm. However, although this method has made some progress, its algorithm complexity is still high, and the obtained surface is in a quasi-regular form, which still needs to be further optimized.

[0005] In recent years, deep learning has shown its strong application potential in many fields, and automatic differentiation technology, as a key technology, can solve the gradient of the loss function to the variable by itself. This makes the gradient descent algorithm combined with automatic differentiation technology show the advantages of high efficiency, flexibility and accuracy in solving complex problems. Therefore, it is expected that by introducing this advanced technology, the problems that are difficult to overcome in traditional DOE design methods can be solved, and the further development and application of DOE technology can be promoted. Summary of the invention

[0006] The purpose of the present invention is to provide a diffractive optical element design method based on automatic differentiation and free-form surface technology, which realizes the design of diffractive optical elements based on automatic differentiation and free-form surface technology, can perform rapid optimization without relying on initial values, and at the same time ensure that the optimized DOE phase distribution is continuous and smooth, and can achieve the purpose of low processing difficulty and high optical performance.

[0007] The purpose of the present invention is achieved through the following technical solutions.

[0008] The design method of diffractive optical element based on automatic differentiation and free-form surface technology includes the following steps:

[0009] Step 1: Characterize the phase distribution φ(x,y) of the diffractive optical element using a locally controllable multi-layer superposition free-form surface:

[0010]

[0011] The above formula is formed by superposition of k layers of basis functions, where (x, y) represents the coordinates of the sampling point on the diffractive optical element, n p and m p are the number of basis functions in the pth layer along the x and y directions, n p and m p As the number of layers increases, is a basis function in the p-th layer, is the shape parameter of the basis function, is the weight parameter of the basis function, all and Denoted as variable v.

[0012] Step 2: Let k = 1, and change n p 、m p , and Assign initial values, where and It can be obtained by phase fitting;

[0013] Step 3: Use scalar diffraction theory to calculate the illumination distribution I2(x',y') of the incident light field after phase modulation by the diffractive optical element and propagation to the target surface:

[0014]

[0015] Where (x', y') represents the coordinates of the sampling point on the target plane, P z represents the diffraction propagation operator, z is the propagation distance, and u0(x,y) is the complex amplitude distribution of the incident light field;

[0016] Step 4: Based on the simulated illumination distribution I2(x',y') on the target surface and the required illumination distribution I target (x',y') constructs the loss function Loss(I2,I target ), used to express the degree of difference between the simulated illuminance distribution and the required illuminance distribution;

[0017] Step 5: Use automatic differentiation technology to automatically solve the gradient grad(v) of the loss function Loss to the variable v:

[0018]

[0019] And the variable v is updated by using a differential-based optimizer, and the corresponding phase distribution data is updated;

[0020] Step 6, iteratively executing steps 3 to 5 until the number of iterations reaches a preset threshold, thereby obtaining optimized phase distribution data;

[0021] Step 7: Determine whether the difference between the illuminance distribution I2(x',y') corresponding to the optimized phase surface at this time and the target illuminance distribution is acceptable. If it is acceptable, the design is terminated. If it is not acceptable, a layer of basis function expression is added on the basis of the existing phase distribution, that is, the current k=k0 is set to k=k0+1, and the parameters of the new layer of basis function are set, σ np,i,j and w np,i,j It can be obtained through the phase distribution data obtained in step 6;

[0022] Step 8: Iterate steps 3 to 7 to obtain the phase distribution data of the final design, and calculate the surface data of the corresponding diffractive optical element, that is, realize the design of the diffractive optical element based on automatic differentiation and free-form surface technology.

[0023] In the step 1, f i,j (x,y;σ np,i,j ) The specific form of the basis function is Gaussian radial basis function or B-spline function.

[0024] Preferably, in step 2, n p | p＝1 =5, m p | p＝1 =5.

[0025] The scalar diffraction theory in step three includes an angular spectrum calculation method, a Rayleigh-Sommerfeld convolution calculation method, a Fresnel diffraction calculation method and a Fraunhofer diffraction calculation method.

[0026] The loss function in step 4 includes root mean square deviation and relative root mean square deviation.

[0027] The differential-based optimizer in step five includes a stochastic gradient descent algorithm, an Adam algorithm, a momentum gradient descent algorithm, and an adaptive gradient descent algorithm.

[0028] The diffractive optical element has a continuous surface, wherein one side of the surface is preset as a plane, a spherical surface or a free-form surface, and the data of the other side of the surface is calculated based on the form of the incident surface and the calculated continuous phase distribution.

[0029] The diffractive optical element has a micro-relief surface, wherein one side of the surface can be preset as a plane, a spherical surface or a free-form surface, and the data of the other side of the surface is calculated after phase folding according to the incident surface form and the calculated phase distribution.

[0030] The materials of the diffractive optical element include fused quartz, BK7 glass, zinc selenide and polymethyl methacrylate.

[0031] The loss function also includes a curvature constraint of the phase function. The curvature constraint is introduced into the loss function in the form of a penalty function to achieve control of the curvature, thereby improving machinability.

[0032] Beneficial effects:

[0033] 1. The diffractive optical element design method based on automatic differentiation and free-form surface technology disclosed in the present invention represents the phase distribution of the diffractive optical element with a free-form surface, thereby ensuring that the designed phase surface is always continuous and smooth, significantly reducing the processing difficulty and reducing the influence of high-order diffraction orders and stray light on the shaping effect;

[0034] 2. The diffractive optical element design method based on automatic differentiation and free-form surface technology disclosed in the present invention avoids the appearance of random phase and phase singularity in the design process, thereby effectively suppressing speckle noise and improving the shaping accuracy of the diffractive optical element;

[0035] 3. The diffractive optical element design method based on automatic differentiation and free-form surface technology disclosed in the present invention uses a gradient descent algorithm based on automatic differentiation to optimize the phase distribution of the diffractive optical element. It is simple and easy to implement, and can achieve rapid optimization with the help of GPU computing power, greatly improving the design efficiency.

[0036] 4. The diffractive optical element design method based on automatic differentiation and free-form surface technology disclosed in the present invention adopts multi-order superposition free-form surfaces to characterize the phase distribution, and is matched with a multi-scale optimization strategy. It can get rid of the dependence on the initial phase while ensuring the convergence of the iteration, reducing the design difficulty, and can design a diffractive optical element that generates arbitrarily complex illumination distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A flow chart of a diffractive optical element design method based on automatic differentiation and free-form surface technology disclosed in the present invention;

[0038] Figure 2 The step of calculating the diffracted light field in Embodiment 1 of the present invention;

[0039] Figure 3 (a) is a schematic diagram of a diffraction scene in Example 1 of the present invention;

[0040] Figure 3 (b) is the target illumination pattern of Example 1 of the present invention;

[0041] Figure 3 (c) is a DOE phase distribution designed based on the traditional iterative Fourier transform algorithm (IFTA) for the purpose of Example 1;

[0042] Figure 3 (d) is the simulated illumination distribution corresponding to the design result based on the traditional iterative Fourier transform algorithm (IFTA) for the target of Example 1;

[0043] Figure 3 (e) is a continuous DOE phase distribution designed by the method of the present invention for the purpose of Example 1;

[0044] Figure 3 (f) is the result after phase folding using the DOE phase distribution designed by the method of the present invention for the purpose of Example 1;

[0045] Figure 3 (g) is the target surface simulated illumination distribution corresponding to the design result of the method of the present invention for the target of Example 1;

[0046] Figure 4 (a) is a schematic diagram of a diffraction scene in Example 2 of the present invention;

[0047] Figure 4 (b) is the target spot pattern of Example 2 of the present invention;

[0048] Figure 4 (c) DOE phase distribution designed for Example 2 of the present invention;

[0049] Figure 4(d) is the simulated illumination distribution on the target surface of Example 2 of the present invention;

[0050] Figure 5 (a) is a schematic diagram of a diffraction scene in Example 3 of the present invention;

[0051] Figure 5 (b) is the target spot pattern of Example 3 of the present invention;

[0052] Figure 5 (c) DOE phase distribution designed for Example 3 of the present invention;

[0053] Figure 5 (d) is the simulated illumination distribution on the target surface of Example 3 of the present invention;

[0054] Figure 6 (a) is a schematic diagram of a diffraction scene in Example 4 of the present invention;

[0055] Figure 6 (b) is the illumination distribution of the input light beam in Example 4 of the present invention;

[0056] Figure 6 (c) is the target light spot on the focal plane in Example 4 of the present invention;

[0057] Figure 6 (d) is a three-dimensional schematic diagram of the CPP phase designed for Example 4 of the present invention;

[0058] Figure 6 (e) is a two-dimensional schematic diagram of the CPP phase designed for Example 4 of the present invention;

[0059] Figure 6 (f) is the simulated illumination distribution on the focal plane in Example 4 of the present invention;

[0060] Figure 7 (a) is the target spot pattern of Example 5 of the present invention;

[0061] Figure 7 (b) A 3D model of a continuous diffractive optical element designed for Example 5 of the present invention;

[0062] Figure 7 (c) is the simulated illumination distribution on the target surface in Example 5 of the present invention;

[0063] Figure 7 (d) is the diffractive optical element processed in Example 5 of the present invention;

[0064] Figure 7 (e) Figure 7 (d) The actual spot distribution of the diffractive optical element shown. DETAILED DESCRIPTION

[0065] The specific implementation of the present invention is further described below in conjunction with the drawings and examples.

[0066] Example 1

[0067] The diffractive optical element design method based on automatic differentiation and free-form surface technology disclosed in this embodiment is used to design a DOE that produces a Gaussian portrait illumination distribution. The input light field is a Gaussian beam with a waist radius of 2 mm and a wavelength of 632.8 nm. The side length of the DOE is 4 mm, and the discretized sampling grid of the DOE is 400×400. The target surface is located 150 mm behind the DOE, the side length of the target illumination distribution is 8 mm, and the discretized sampling grid of the target illumination distribution is 800×800.

[0068] like Figure 1 As shown, the design method of the diffractive optical element based on automatic differentiation and free-form surface technology disclosed in this embodiment has the following specific implementation steps:

[0069] Step 1: Select the B-spline function as the basis function. The specific form of the phase distribution is:

[0070]

[0071] Where: u and v range from [0,1], N i,3 (u) and N j,3 (v) is the cubic B-spline basis function, are the control point coordinate parameters. In this example, the basis function parameters are only and The effect is equivalent to and All Let it be variable v;

[0072] Step 2: Give k and n p 、m p , Assign initial values, where k = 1, n1 = 5, m1 = 5, P 5,i,j The elements in the matrix are set to random numbers between 0 and 2π;

[0073] Step 3: Use scalar diffraction theory to calculate the illumination distribution I2(x',y') of the incident light field after it passes through the diffractive optical element and propagates to the target surface:

[0074] I2(x',y')=|P z [u0(x,y)e jφ(x,y) ]| 2 (5)

[0075] Where (x', y') represents the sampling point on the target plane, P zrepresents the diffraction propagation operator, z is the propagation distance, and u0(x, y) is the amplitude distribution of the incident light field. The scalar diffraction theory adopted in this embodiment is the angular spectrum theory, and formula (2) is written as:

[0076]

[0077] In the formula, and Represents Fourier transform and inverse Fourier transform, respectively, x and f y represents the spatial frequency, H(f x ,f y ) is the transfer function.

[0078] The specific calculation steps are as follows:

[0079] Step 3.1: Determine whether the sampling frequency of the transfer function in the angular spectrum theory satisfies the sampling theorem, that is, whether it satisfies the following inequality:

[0080]

[0081] Where Δf is the sampling interval of the spectrum plane, φ is the phase distribution, and f is the spatial frequency.

[0082] Step 3.2: In Example 1, inequality (7) holds true, and the angular spectrum method based on fast Fourier transform is used to calculate the diffraction light field. Since the discretized grids of the input light field and the output light field are 400×400 and 800×800, it is necessary to fill the input light field with zeros so that the calculation window for the diffraction calculation is 1200×1200. Perform a two-dimensional Fourier transform on the zero-filled input light field, multiply it with the transfer function, and then perform a two-dimensional inverse Fourier transform. The central rectangular area of ​​800×800 is taken as the light field distribution on the target surface at this time. The entire diffraction calculation process is as follows. Figure 2 As shown;

[0083] Step 4: According to the illumination distribution I2(x',y') on the target surface and the required illumination distribution I target (x',y') constructs the loss function:

[0084]

[0085] Where I2(i,j) is the value of I2(x',y') in the i-th row and j-th column. target (i,j) is I target The value of row i and column j of (x',y'), I2(x',y') and I target (x', y') are both m×n matrices;

[0086] Step 5: Use the automatic differentiation technology in deep learning to automatically solve the gradient grad(v) of the loss function Loss to the variable v:

[0087]

[0088] Use Adam optimizer to update variable v;

[0089] Step 6: Repeat steps 3 to 5 until the number of iterations reaches 500, and the phase surface φ is obtained. k＝1 ;

[0090] Step 7: Add a layer of basis function based on the phase surface in step 6. After adjustment, k = 2, n2 = m2 = 20, and the newly added parameter P 20,i,j The value of the surface φ at this time k＝1 The specific fitting method is:

[0091] ① For the curved surface φ k＝1 Uniform sampling is performed to obtain a 20×20 uniform matrix as P 20,i,j The initial value of

[0092] ②Construct loss function:

[0093]

[0094] ③ Use automatic differentiation technology to automatically solve the variable P 20,i,j About loss function fit The gradient of the loss function is optimized using the Adam optimizer fit and update the variable P 20,i,j After 500 rounds of optimization, the fitting is completed and the final P is obtained. 20,i,j . Repeat steps 3 to 6;

[0095] Step 8: Add a layer of basis function on the basis of the phase surface, k = 3, n3 = m3 = 40, and the newly added parameter P 40,i,j The value of the surface shape φ k＝2 The fitting is obtained. Repeat steps 3 to 6;

[0096] Step 9: Add a layer of basis function on the basis of the phase surface. After adjustment, k=4, n4=m4=80, and the newly added parameter P 80,i,j The value of the surface shape φ k＝3 The fitting is obtained. Repeat steps 3 to 6;

[0097] Step 10: Add a layer of basis function on the basis of the phase surface. After adjustment, k = 5, n4 = m4 = 160, and the newly added parameter P 160,i,j The value of the surface shape φ k＝4 The fitting is obtained. Repeat steps 3 to 6;

[0098] Step 11: Obtain the designed diffractive optical element phase distribution, perform phase folding on the continuous phase distribution, and the folded phase φ wrap =mod 2πM [φ], where M is an integer greater than 1, and in this embodiment, M=1. The incident surface of the diffractive optical element is set as a plane, and the height function h(x, y) of the exit surface can be calculated by the following formula:

[0099]

[0100] In the formula, n is the refractive index and λ is the wavelength. The material of the diffractive optical element is set to polymethyl methacrylate. The input light field is regulated by the designed diffractive optical element to generate a near specific illumination distribution I on the target surface. target Illuminance distribution at (x',y') I2(x',y').

[0101] The diffraction scene schematic diagram of embodiment 1 of the present invention is as follows Figure 3 As shown in (a), Figure 3 (b) is the normalized target spot pattern of Example 1 of the present invention. Figure 3 (c) shows the phase distribution of the DOE designed based on the traditional iterative Fourier transform algorithm, which is characterized by random disorder, which causes inconvenience in the processing process. Figure 3 (d) is a simulated illumination distribution obtained after the iterative Fourier transform algorithm (IFTA) is used for the purpose of Example 1. Due to the random disorder of the phase distribution, there is a lot of speckle noise in the simulated illumination distribution. Figure 3 (e) The DOE phase distribution designed by the method of the present invention for the purpose of Example 1 is smooth and continuous overall; Figure 3 (f) Figure 3 (e) is the result after phase folding of the phase distribution shown in Figure 1. The final simulated illumination distribution is shown in Figure 2. Figure 3 As shown in (g), the speckle noise is well suppressed and is very close to the target result;

[0102] Example 2

[0103] The diffractive optical element design method described in this embodiment can be used to design a DOE that generates a cubic illumination distribution, as shown in the schematic diagram. Figure 4 As shown in (a), the target image is Figure 4(b) The design parameters are similar to those in Example 1, except that the propagation distance is changed from 180 mm to 400 mm. The design method and steps are basically the same as those in Example 1, except that the diffraction propagation operator needs to use the bandwidth-extended angular spectrum method based on fast Fourier transform [Zhang WH, Zhang H, Jin G F. Band-extended angular spectrum method for accurate diffraction calculation in a wide propagation range. Optics Letters, 2020, 45(6): 1543-1546] to calculate the diffraction light field to avoid spectral aliasing errors.

[0104] Figure 4 (c) is the final designed DOE phase distribution of Example 2, which is smooth and continuous overall; Figure 4 (d) shows the illumination distribution of the Gaussian beam on the target surface after being regulated by the designed DOE, which is very close to the target illumination distribution.

[0105] Example 3

[0106] The diffractive optical element design method described in this embodiment can be used to design a DOE for cube illumination distribution in a large-angle diffraction scene, as shown in the schematic diagram. Figure 5 As shown in (a), the target image is Figure 5 (b). The input light field is a Gaussian beam with a waist radius of 0.5 mm and a wavelength of 632.8 nm. The side length of the DOE is 0.5 mm, and the discretized sampling grid of the DOE is 500×500. The target surface is located 100 mm behind the DOE, the side length of the target illumination distribution is 60.3 mm, and the discretized sampling grid of the target illumination distribution is 500×500. The design method is basically the same as that of Example 1, except that due to the different diffraction scenes, the diffraction propagation operator in formula (1) adopts the Rayleigh-Sommerfeld diffraction integral calculation method.

[0107] Figure 5 (c) is the final designed DOE phase distribution of Example 3, which is smooth and continuous overall; Figure 5 (d) shows the illumination distribution of the Gaussian beam on the target surface after being regulated by the designed DOE, which is very close to the target illumination distribution.

[0108] Example 4

[0109] The diffractive optical element design method described in this embodiment can be used to design a special diffractive optical element, namely a continuous phase plate (CPP). The input light field distribution u0(x, y) is a 12th-order super-Gaussian beam:

[0110]

[0111] In the formula, R is 155mm. The wavelength of the laser is 351nm. The side length of the CPP is 336mm, and the discretized sampling grid of the DOE is 1024×1024. After the input light field is phase modulated by the CPP, it is focused by a lens with a focal length of 2232mm. The focal plane is the target plane, as shown in the schematic diagram. Figure 6 As shown in (a), the input illumination distribution is Figure 6 As shown in (b), the target illumination distribution on the focal plane is Figure 6 As shown in (c), the side length of the target illumination distribution is 2.385 mm, and the discretized sampling grid of the target illumination distribution is 1024×1024. The design method of Example 4 is basically the same as that of Example 1, except that the diffraction propagation operator in equation (1) in Example 4 is a Fraunhofer diffraction calculation method based on Fourier transform.

[0112] Figure 6 (d) and (e) are the three-dimensional and two-dimensional graphs of the CPP phase distribution of the final design of Example 4, respectively, which are smooth and continuous as a whole; Figure 6 (f) shows the illumination distribution generated on the focal plane after the laser is modulated by CPP, which is very close to the target spot.

[0113] Example 5

[0114] The diffractive optical element design method described in this embodiment can be used to design a continuous thin lens to shape the laser beam. The input illumination distribution is obtained by actually measuring the illumination distribution of the laser beam and fitting it:

[0115]

[0116] The laser wavelength is 632.8nm. The side length of the lens is 10.08mm, and the discretized sampling grid is 4200×4200. After the input light field passes through the thin lens, a specific pattern with a side length of 52.73mm is generated at a distance of 200mm. The target spot pattern is as follows Figure 7 (a) is shown. The Fresnel diffraction method based on single-step Fourier transform is used to calculate the diffracted light field distribution. A 5×5 initial B-spline surface is used, and a multi-surface superposition optimization strategy is adopted after preliminary optimization. The number of control points of the B-spline surface with the highest scale is 640×640. The final designed diffractive optical element with a continuous surface is shown in Figure 7 As shown in (b), the simulated illumination distribution on the target surface is as follows: Figure 7 (c) shows that Figure 7 The target spot shown in (a) is very close. The free-form surface lens processed by diamond turning is as follows Figure 7 As shown in (d), the corresponding actual test spot is Figure 7 (e) as shown.

[0117] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be deemed to be included in the protection scope of the present invention.

Claims

1. A diffractive optical element design method based on automatic differentiation and free-form surface technology, characterized by: The following steps are included: Step 1: Characterize the phase distribution φ(x,y) of the diffractive optical element using a locally controllable multi-layer superposition free-form surface: The above formula is formed by superposition of k layers of basis functions, where (x, y) represents the coordinates of the sampling point on the diffractive optical element, n p and m p are the number of basis functions in the pth layer along the x and y directions, n p and m p As the number of layers increases, is a basis function in the p-th layer, is the shape parameter of the basis function, is the weight parameter of the basis function, all and Let it be variable v; Step 2: Let k = 1, and change n p 、m p , and Assign initial values, where and Obtained through phase fitting; Step 3: Use scalar diffraction theory to calculate the light intensity distribution I2(x',y') of the incident light field after phase modulation by the diffractive optical element and propagation to the target surface: I2(x',y')=|P z [u0(x,y)e jφ(x,y) ]| 2 (2) Where (x', y') represents the coordinates of the sampling point on the target plane, P z represents the diffraction propagation operator, z is the propagation distance, and u0(x,y) is the complex amplitude distribution of the incident light field; Step 4: Based on the simulated light intensity distribution I2(x',y') on the target surface and the required light intensity distribution I target (x',y') constructs the loss function Loss(I2,I target ), used to express the degree of difference between the simulated light intensity distribution and the required light intensity distribution; Step 5: Use automatic differentiation technology to automatically solve the gradient grad(v) of the loss function Loss to the variable v: And the variable v is updated by using a differential-based optimizer, and the corresponding phase distribution data is updated; Step 6, iteratively executing steps 3 to 5 until the number of iterations reaches a preset threshold, thereby obtaining optimized phase distribution data; Step 7: Determine whether the difference between the light intensity distribution I2(x',y') corresponding to the optimized phase surface at this time and the target light intensity distribution is acceptable. If it is acceptable, the design is terminated. If it is not acceptable, a layer of basis function expression is added on the basis of the existing phase distribution, that is, the current k=k0 is set to k=k0+1, and the parameters of the new layer of basis function are set. and It can be obtained through the phase distribution data obtained in step 6; Step 8: Iterate steps 3 to 7 to obtain the phase distribution data of the final design and calculate the surface data of the corresponding diffractive optical element.

2. The method for designing a diffractive optical element based on automatic differentiation and free-form surface technology according to claim 1, characterized in that: In the step 1, f i,j (x,y;σ np,i,j ) The specific form of the basis function is Gaussian radial basis function or B-spline function.

3. The design method of a diffractive optical element based on automatic differentiation and free-form surface technology according to claim 1, characterized in that: In the step 2, n p | p＝1 =5, m p | p＝1 =5.

4. The design method of a diffractive optical element based on automatic differentiation and free-form surface technology according to claim 1, characterized in that: The scalar diffraction theory in step three includes an angular spectrum calculation method, a Rayleigh-Sommerfeld convolution calculation method, a Fresnel diffraction calculation method and a Fraunhofer diffraction calculation method.

5. The design method of a diffractive optical element based on automatic differentiation and free-form surface technology according to claim 1, characterized in that: The loss function in step 4 includes root mean square deviation and relative root mean square deviation.

6. The design method of a diffractive optical element based on automatic differentiation and free-form surface technology according to claim 1, characterized in that: The differential-based optimizer in step five includes a stochastic gradient descent algorithm, an Adam algorithm, a momentum gradient descent algorithm, and an adaptive gradient descent algorithm.

7. The design method of a diffractive optical element based on automatic differentiation and free-form surface technology according to claim 1, characterized in that: The diffractive optical element has a continuous surface, wherein one side of the surface is preset as a plane, a spherical surface or a free-form surface, and the data of the other side of the surface is calculated based on the form of the incident surface and the calculated continuous phase distribution.

8. The design method of a diffractive optical element based on automatic differentiation and free-form surface technology according to claim 1, characterized in that: The diffractive optical element has a micro-relief surface, wherein one side of the surface can be preset as a plane, a spherical surface or a free-form surface, and the data of the other side of the surface is calculated after phase folding according to the incident surface form and the calculated phase distribution.

9. The design method of a diffractive optical element based on automatic differentiation and free-form surface technology according to claim 1, characterized in that: The materials of the diffractive optical element include fused quartz, BK7 glass, zinc selenide and polymethyl methacrylate.

10. The diffractive optical element design method based on automatic differentiation and free-form surface technology according to claim 5, characterized in that: The loss function also includes a curvature constraint of the phase function, and the curvature constraint is introduced into the loss function in the form of a penalty function to achieve control of the curvature.

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