A method and system for optimizing the mixing of amplitude and phase of projected light field

Abstract

The present invention belongs to the technical field related to projection light field control, and discloses a method and system for hybrid optimization of the amplitude and phase of a projection light field, wherein the method includes: calculating the actual generated projection light field based on the input light field; substituting the parameters of the target projection light field and the parameters of the actual generated projection light field into an objective function model to determine whether a preset threshold is met; the objective function model includes an amplitude objective function and a phase objective function, which are used to evaluate the accuracy of the amplitude and phase of the actual generated projection light field; if the preset threshold of the objective function model is not met, the input amplitude and input phase of the input light field are optimized and updated using a gradient method until the preset threshold of the objective function model is met or the number of optimizations reaches a preset number. The present invention achieves complex amplitude control of the light field with higher degrees of freedom by hybrid optimization of the amplitude and phase of the light field, while simultaneously controlling the amplitude and phase distribution of the generated light field.

Description

Technical Field

[0001] The present invention belongs to the technical field related to projection light field control, and more specifically, relates to a method and system for hybrid optimization of projection light field amplitude and phase. Background Art

[0002] With technological advancements, the requirements for optical systems are becoming increasingly stringent, particularly in fields such as microelectronics, biomedical imaging, and precision measurement. This poses unprecedented challenges to the precision and complexity of optical components. For example, photolithography, a key technology in micro- and nano-manufacturing, involves using light to transfer patterns onto a photosensitive material called a photoresist. Photolithography is widely used in semiconductor manufacturing, microelectronics, micromechanical systems (MEMS), biochips, optical components, and nanotechnology. Masked photolithography is a key component of photolithography, in which a pattern on a mask is projected onto an image plane using a projection system. However, when the light field characteristics approach the diffraction limit of the projection system, severe distortion occurs. This phenomenon, known as the optical proximity effect, refers to the deviation between the actual image and the ideal image due to diffraction and interference of light waves during optical imaging. The proximity effect can lead to image distortion, reduced resolution, and decreased contrast. Therefore, during projection imaging, the light field must be optimized to ensure consistency between the generated light field and the designed light field. Furthermore, structured light fields have found widespread applications in deep subwavelength object sensing and patterned wafer defect detection. During these inspection processes, the parameters used to generate the structured light field have a significant impact on the test results, determining, to a certain extent, the reliability and detection limit of the test results. Therefore, it is crucial to generate an actual structured light field that is consistent with the designed structured light field.

[0003] Existing optical proximity correction optimization focuses on controlling the amplitude of the generated light field. This approach describes light field optimization as a discrete mathematical problem, inversely determining the mask pattern based on the desired photoresist pattern. Existing light field optimization methods focus on optimizing amplitude, which can distort other light field parameters and affect light field accuracy. Summary of the Invention

[0004] In response to the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method and system for hybrid optimization of the amplitude and phase of the projected light field, which solves the problem that the existing light field optimization method focuses on optimizing and controlling the amplitude, and there is a problem that other parameters of the light field will be distorted, thereby affecting the accuracy of the light field. The purpose is to achieve higher-degree-of-freedom complex amplitude control of the light field by hybrid optimization of the light field amplitude and phase, while controlling the amplitude and phase distribution of the generated light field.

[0005] To achieve the above object, according to one aspect of the present invention, a method for hybrid optimization of the amplitude and phase of a projected light field is provided, comprising:

[0006] The projection light field is actually generated based on the input light field calculation;

[0007] Substituting the parameters of the target projected light field and the parameters of the actually generated projected light field into an objective function model, and determining whether the calculated value of any function in the objective function model meets the corresponding preset threshold requirements; wherein the objective function model includes an amplitude objective function and a phase objective function, which are used to evaluate the accuracy of the amplitude and phase of the actually generated projected light field;

[0008] If the amplitude objective function and / or the phase objective function do not meet the corresponding preset threshold requirements, the gradient method is used to optimize and update the input amplitude and input phase of the input light field until both the amplitude objective function and the phase objective function meet the corresponding preset threshold requirements or the number of optimizations reaches a preset number.

[0009] According to the projection light field amplitude and phase hybrid optimization method provided by the present invention, it is assumed that the target projection light field is a complex amplitude field, and the parameters of the target projection light field include a target amplitude pattern and a target phase pattern;

[0010] The parameters of the actually generated projection light field include an actual amplitude pattern and an actual phase pattern.

[0011] According to the projection light field amplitude and phase hybrid optimization method provided by the present invention, the amplitude objective function includes an amplitude difference function, and the amplitude difference function is used to represent the error between the actual amplitude pattern and the target amplitude pattern;

[0012] The phase target function includes a phase difference function, and the phase difference function is used to represent the error between the actual phase pattern and the target phase pattern.

[0013] According to the projection light field amplitude and phase hybrid optimization method provided by the present invention, the amplitude objective function further includes an amplitude upper limit function, and the amplitude upper limit function is used to limit the upper limit of the actual amplitude pattern;

[0014] The phase target function further includes a phase upper limit function, which is used to limit the upper limit of the actual phase pattern.

[0015] According to the projection light field amplitude and phase hybrid optimization method provided by the present invention, the actual generation of the projection light field by calculating the input light field specifically includes:

[0016] The vector imaging model is used to calculate the complex amplitude of the projected light field actually generated after the input light field propagates to the image plane;

[0017] Based on the complex amplitude of the actually generated projection light field, an actual amplitude pattern and an actual phase pattern of the actually generated projection light field are extracted.

[0018] According to the projection light field amplitude and phase hybrid optimization method provided by the present invention, the complex amplitude of the projection light field actually generated is obtained by the following formula:

[0019]

[0020] Where H represents the kernel function of the vector imaging model; Represents the convolution operation; E image Represents the complex amplitude of the actual generated projection light field; M i represents the input light field, the subscript i represents the iteration factor; m and n represent the number of grids; T g-g is the coordinate mapping relationship between the input field and the generated field; W is the window function of the projection system; NA represents the numerical aperture of the imaging lens; α, β, γ are the frequency domain coordinates on the lens plane, and the subscripts en and ex represent the entrance and exit pupils, respectively.

[0021] According to the projection light field amplitude and phase hybrid optimization method provided by the present invention, the actual amplitude pattern includes the amplitude profile of the actually generated projection light field and the profile exceeding the amplitude upper limit in the actually generated projection light field;

[0022] The actual phase pattern includes the phase profile of the actually generated projected light field and the profile exceeding the phase upper limit in the actually generated projected light field; it is specifically obtained by the following formula:

[0023]

[0024] Among them, Z A With Z P Represents the amplitude profile and phase profile of the actual generated projection light field; Z′ A and Z′ P Indicates the contours exceeding the upper limit of amplitude and phase in the actual generated projected light field; E image Represents the complex amplitude of the actual generated projection light field; a A 、a P , a′ A and a′ P Expressed as steepness factor; b A 、b P , b′ A and b′ P Expressed as a threshold, usually b A Smaller than the target amplitude value, b P Smaller than the target phase value, b′ A Larger than the target amplitude value, b′ P Larger than the target phase value; angle represents the calculated phase angle of the complex number.

[0025] According to the projection light field amplitude and phase hybrid optimization method provided by the present invention, the gradient method is used to optimize and update the input amplitude and input phase of the input light field, specifically comprising: calculating and obtaining the gradient of the amplitude objective function and the gradient of the phase objective function, and optimizing and updating the input amplitude and input phase of the input light field according to the gradient of the amplitude objective function and the gradient of the phase objective function;

[0026] The gradient of the amplitude objective function includes the gradient of the amplitude difference function and the gradient of the amplitude upper limit function;

[0027] The gradient of the phase objective function includes the gradient of the phase difference function and the gradient of the phase upper limit function.

[0028] According to the projection light field amplitude and phase hybrid optimization method provided by the present invention, the input amplitude and input phase after optimization and update using the gradient method are:

[0029]

[0030] Among them, M A i and M A i+1 Indicates the input amplitude, M P i and M P i+1 represents the input phase, and the subscripts i and i+1 represent the iteration factor; Z A With Z P represents the amplitude profile and phase profile of the actual generated projection light field; M T-A With M T-P Represents the target amplitude pattern and target phase pattern of the target projected light field; Z′ A and Z′ P Indicates the contours exceeding the upper limit of amplitude and phase in the actual generated projected light field; Zeros represents the zero matrix; s A , s P , s A-shift , s P-shift They are the preset amplitude optimization step, phase optimization step, amplitude upper limit optimization step, and phase upper limit optimization step respectively; δ represents the partial derivative operation symbol.

[0031] According to another aspect of the present invention, a system for optimizing the mixing of amplitude and phase of a projected light field is provided, comprising:

[0032] A calculation module, used for calculating and actually generating a projection light field based on the input light field;

[0033] a judgment module, configured to substitute the parameters of the target projected light field and the parameters of the actually generated projected light field into an objective function model, and determine whether the calculated value of any function in the objective function model meets the corresponding preset threshold requirements; wherein the objective function model includes an amplitude objective function and a phase objective function, which are used to evaluate the accuracy of the amplitude and phase of the actually generated projected light field;

[0034] an optimization module configured to optimize and update the input amplitude and input phase of the input light field using a gradient method if the amplitude objective function and / or the phase objective function do not meet the corresponding preset threshold requirements, until both the amplitude objective function and the phase objective function meet the corresponding preset threshold requirements or the number of optimizations reaches a preset number.

[0035] In general, compared with the prior art, the above technical solutions conceived by the present invention provide a method and system for hybrid optimization of the amplitude and phase of a projection light field:

[0036] 1. Setting the amplitude objective function and the phase objective function to optimize the amplitude and phase of the actual generated projection light field respectively, so as to improve the amplitude accuracy of the actual generated projection light field while improving its phase accuracy. By alternating the optimization of the amplitude and phase, the amplitude and phase of the generated light field can be controlled simultaneously, so that the amplitude and phase of the generated light field both meet the target requirements, thereby comprehensively optimizing the generated light field, so that the projected light field can meet the high precision and complexity requirements required by more industries, and improve the applicability and application prospects of the projected light field;

[0037] 2. In the process of optimizing the amplitude and phase of the projected light field, a gradient method is used to determine the optimal optimization direction by determining the gradient direction of the complex large-scale light field. This method is suitable for large-scale, nonlinear optimization problems and has high computational efficiency and convergence speed.

[0038] 3. Adding an upper limit constraint objective function can limit the amplitude and phase of the optimized light field to a certain range, avoiding the problem of pathological convexity in the output light field during the optimization process. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of the projection light field amplitude and phase mixing optimization method provided by the present invention;

[0040] Figure 2 It is a schematic flow chart of the method for optimizing the mixed amplitude and phase of the projection light field in the specific example provided by the present invention;

[0041] Figure 3 is a schematic diagram of the initial input / target projection light field selected in the specific example provided by the present invention;

[0042] Figure 4is a schematic diagram of the amplitude and phase of a light field generated by using an initial input light field in a specific example provided by the present invention;

[0043] Figure 5 Schematic diagram of the amplitude of the input light field and the amplitude of the generated light field after optimization in a specific example provided by the present invention;

[0044] Figure 6 It is a schematic diagram of the phase of the optimized input light field and the phase of the generated light field in the specific example provided by the present invention. DETAILED DESCRIPTION

[0045] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0046] See also Figure 1 , this embodiment 1 provides a method for hybrid optimization of projection light field amplitude and phase, the method comprising:

[0047] The projection light field is actually generated based on the input light field calculation;

[0048] Substituting the preset parameters of the target projection light field and the parameters of the actually generated projection light field into an objective function model, and determining whether the calculated value of any function in the objective function model meets the corresponding preset threshold requirements; wherein the objective function model includes an amplitude objective function and a phase objective function, which are used to evaluate the accuracy of the amplitude and phase of the actually generated projection light field;

[0049] If the amplitude objective function and / or the phase objective function do not meet the corresponding preset threshold requirements, a gradient method is used to optimize and update the input amplitude and input phase of the input light field until both the amplitude objective function and the phase objective function meet the corresponding preset threshold requirements or the number of optimization cycles reaches a preset number. The hybrid optimization method for the projected light field amplitude and phase provided in this embodiment takes into account that in existing light field optimization processes, when adjusting the input amplitude, the phase of the generated light field will be distorted. The phase-shift masks used in advanced nodes and the phase-structured light field field field have strict requirements not only on the amplitude of the light field, but also on the phase of the light field.

[0050] Based on this, this embodiment sets an amplitude objective function and a phase objective function to optimize the amplitude and phase of the actual generated projection light field respectively, so as to improve the amplitude accuracy of the actual generated projection light field while improving its phase accuracy. By alternately optimizing the amplitude and phase, it is possible to achieve simultaneous control of the amplitude and phase of the generated light field, so that both the amplitude and phase of the generated light field meet the target requirements, thereby comprehensively optimizing the generated light field, so that the projected light field can meet the high precision and complexity requirements required by more industries, and improve the applicability and application prospects of the projected light field.

[0051] In the process of optimizing the amplitude and phase of the projected light field, the gradient method is used to determine the optimal optimization direction by determining the gradient direction of the complex large-scale light field. This method is suitable for large-scale, nonlinear optimization problems and has high computational efficiency and convergence speed.

[0052] The method in this embodiment aims to achieve higher degrees of freedom in complex amplitude control of the light field by simultaneously controlling both the amplitude and phase distributions of the generated light field through hybrid optimization of the light field's amplitude and phase. Compared to existing technologies, this method offers the technical advantage of simultaneously controlling both the amplitude and phase of the generated light field, eliminating the significant distortion of the light field's phase that occurs when optimizing the amplitude distribution alone.

[0053] In some specific embodiments, the target projection light field is a complex amplitude field, and the parameters of the target projection light field include a target amplitude pattern and a target phase pattern. The parameters of the actually generated projection light field include an actual amplitude pattern and an actual phase pattern. The target projection light field should be expressed as a complex amplitude M T , to ensure that the amplitude and phase of the subsequent target projection light field can be correctly extracted, such as M T =M T-A *exp(i*M T-P ); the grid size g and the number of grids m and n are not restricted. The target projected light field is usually set as the initial input value in the iterative optimization process.

[0054] In some specific embodiments, the amplitude target function includes an amplitude difference function, and the amplitude difference function is used to represent the error between the actual amplitude pattern of the actually generated projection light field and the target amplitude pattern of the target projection light field;

[0055] The phase target function includes a phase difference function, and the phase difference function is used to represent the error between the actual phase pattern of the actually generated projection light field and the target phase pattern of the target projection light field.

[0056] Specifically, the amplitude difference function F A and the phase difference function F P Defined as:

[0057]

[0058] Among them, M T-A With M T-P Represents the target amplitude pattern and target phase pattern of the target projected light field, Z A With Z P represents the amplitude profile and phase profile of the projected light field actually generated after inputting the light field pattern M. The right side of the equation is the standard two-norm calculation.

[0059] Furthermore, the amplitude target function further includes an amplitude upper limit function, and the amplitude upper limit function is used to limit the upper limit of the actual amplitude pattern of the actually generated projection light field;

[0060] The phase target function further includes a phase upper limit function, and the phase upper limit function is used to limit the upper limit of the actual phase pattern of the actually generated projection light field.

[0061] Preferably, in order to limit the amplitude and phase of the optimized light field to a certain range and avoid the problem of pathological convexity in the output light field during the optimization process, that is, the amplitude and phase of the light field are infinite or infinitely small, it is necessary to add a set of amplitude upper limit objective functions, namely the amplitude upper limit function F′ A And the phase upper limit objective function is the phase upper limit function F′ P :

[0062]

[0063] Among them, Z′ A and Z′ P It represents the contours exceeding the upper limit of amplitude and phase in the actually generated projected light field; Zeros(m,n) represents the zero matrix of m*n dimension.

[0064] The method of the present invention improves the existing light field optimization method. By carrying out amplitude optimization and phase optimization in parallel and adding light field convex feature restrictions in opposite directions, it can generate a light field with arbitrary target amplitude and phase distribution in combination with a projection system.

[0065] In some specific embodiments, calculating and actually generating the projection light field according to the input light field specifically includes:

[0066] The vector imaging model is used to calculate the complex amplitude of the projected light field actually generated after the input light field propagates to the image plane;

[0067] Based on the complex amplitude of the actually generated projection light field, an actual amplitude pattern and an actual phase pattern of the actually generated projection light field are extracted.

[0068] In some specific embodiments, the complex amplitude of the actually generated projection light field is obtained by the following formula:

[0069] The vector imaging model used in this embodiment can be simplified as the kernel function H, as follows:

[0070] Furthermore, T g-g is the coordinate mapping relationship between the input field and the generated field, W is the window function of the projection system, and the expression is:

[0071]

[0072] Where H represents the kernel function of the vector imaging model; Represents the convolution operation; E image Represents the complex amplitude of the actual generated projection light field; M i Indicates that the input light field is a complex amplitude field, the subscript i represents the iteration factor, and the initial input of the iteration is M1 = M T ; m, n represent the number of grids; T g-g is the coordinate mapping relationship between the input field and the generated field; W is the window function of the projection system; NA represents the numerical aperture of the imaging lens; α, β, and γ are the frequency domain coordinates on the lens plane, and the subscripts en and ex represent the entrance and exit pupils, respectively. The coordinates are process parameters in the light field formation process and can be obtained by actual measurement.

[0073] In some specific embodiments, the actual amplitude pattern includes an amplitude profile of the actually generated projected light field and a profile exceeding an amplitude upper limit in the actually generated projected light field;

[0074] The actual phase pattern includes the phase profile of the actually generated projected light field and the profile exceeding the phase upper limit in the actually generated projected light field. Specifically, the profile Z and the upper limit profile Z′ are calculated using the Sigmoid function, which are specifically obtained by the following formula:

[0075]

[0076]

[0077] Among them, Z A With Z P Represents the amplitude profile and phase profile of the actual generated projection light field; Z′ A and Z′ P Indicates the contours exceeding the upper limit of amplitude and phase in the actual generated projected light field; E image Represents the complex amplitude of the actual generated projection light field; a A 、a P , a′ A and a′ P Expressed as steepness factor; b A 、b P , b′A and b′ P Expressed as a threshold, usually b A Smaller than the target amplitude value, b P Smaller than the target phase value, b′ A Larger than the target amplitude value, b′ P Greater than the target phase value; angle represents the phase angle of the calculated complex number. The target value is set according to the target projected light field.

[0078] In some specific embodiments, if the amplitude objective function and / or the phase objective function does not meet the corresponding preset threshold requirements, the gradient method is used to optimize and update the input amplitude and input phase of the input light field, specifically including: if the amplitude objective function does not meet the corresponding preset threshold requirements, and the phase objective function meets the corresponding preset threshold requirements, the input amplitude of the input light field is optimized and updated, and the input phase is selectively optimized and updated (that is, the input phase may be optimized and updated or not); if the phase objective function does not meet the corresponding preset threshold requirements, and the amplitude objective function meets the corresponding preset threshold requirements, the input phase of the input light field is optimized and updated, and the input amplitude is selectively optimized and updated (that is, the input amplitude may be optimized and updated or not); if both the amplitude objective function and the phase objective function do not meet the corresponding preset threshold requirements, then both the input amplitude and input phase of the input light field are optimized and updated.

[0079] After any parameter of the input light field (input amplitude and / or input phase) is updated, it is necessary to re-judge whether the amplitude objective function and the phase objective function meet the preset threshold value, until both the amplitude objective function and the phase objective function meet the corresponding preset threshold requirements or the number of optimizations reaches the preset number.

[0080] In some specific embodiments, optimizing and updating the input amplitude and input phase of the input light field using the gradient method specifically includes: calculating and obtaining the gradient of the amplitude objective function and the gradient of the phase objective function, and optimizing and updating the input amplitude and input phase of the input light field based on the gradient of the amplitude objective function and the gradient of the phase objective function. The gradient of the amplitude objective function is the partial derivative of the amplitude objective function with respect to the input light field; the gradient of the phase objective function is the partial derivative of the phase objective function with respect to the input light field.

[0081] The input amplitude and input phase of the input light field are optimized and updated based on the gradients of the amplitude objective function and the phase objective function. Specifically, the input amplitude is linearly updated stepwise based on the gradient of the amplitude objective function, and the input phase is linearly updated stepwise based on the gradient of the phase objective function. In other words, the updated input amplitude is the input amplitude before the update minus the product of the gradient of the amplitude objective function and the preset step size. The updated input phase is the input phase before the update minus the product of the gradient of the phase objective function and the preset step size.

[0082] Specifically, the gradient of the amplitude objective function includes the gradient of the amplitude difference function and the gradient of the amplitude upper limit function;

[0083] The gradient of the phase objective function includes the gradient of the phase difference function and the gradient of the phase upper limit function.

[0084] Specifically, the amplitude gradient of the amplitude difference function is calculated as follows:

[0085]

[0086] The calculation method of the phase gradient of the potential difference function is:

[0087]

[0088] The gradient corresponding to the contour exceeding the upper limit is calculated using the same expression as above, replacing the variables containing the Z symbol with the corresponding variables. Specifically, the amplitude gradient of the amplitude upper limit function is calculated as:

[0089]

[0090] The phase gradient of the phase upper limit function is calculated as:

[0091]

[0092] Furthermore, if the amplitude objective function and / or the phase objective function does not meet the corresponding preset threshold requirements, the input amplitude and input phase of the input light field are optimized and updated according to the gradient of the amplitude objective function and the gradient of the phase objective function, and the input amplitude and input phase after optimization and update are respectively:

[0093]

[0094] Among them, M A i and M A i+1 Indicates the input amplitude, M P i and M P i+1represents the input phase, and the subscripts i and i+1 represent the iteration factor; Z A With Z P represents the amplitude profile and phase profile of the actual generated projection light field; M T-A With M T-P Represents the target amplitude pattern and target phase pattern of the target projected light field; Z′ A and Z′ P Indicates the contours exceeding the upper limit of amplitude and phase in the actual generated projected light field; Zeros represents the zero matrix; s A , s P , s A-shift , s P-shift They are the preset amplitude optimization step, phase optimization step, amplitude upper limit optimization step, and phase upper limit optimization step respectively; δ represents the partial derivative operation symbol.

[0095] Furthermore, this second embodiment further provides a projection light field amplitude and phase mixing optimization system, which is used to implement the projection light field amplitude and phase mixing optimization method described in any of the above embodiments. The system can be understood by reference to the above methods, and the system includes:

[0096] A calculation module, used for calculating and actually generating a projection light field based on the input light field;

[0097] a judgment module, configured to substitute the parameters of the target projected light field and the parameters of the actually generated projected light field into an objective function model, and determine whether the calculated value of any function in the objective function model meets the corresponding preset threshold requirements; wherein the objective function model includes an amplitude objective function and a phase objective function, which are used to evaluate the accuracy of the amplitude and phase of the actually generated projected light field;

[0098] an optimization module configured to optimize and update the input amplitude and input phase of the input light field using a gradient method if the amplitude objective function and / or the phase objective function do not meet the corresponding preset threshold requirements, until both the amplitude objective function and the phase objective function meet the corresponding preset threshold requirements or the number of optimizations reaches a preset number.

[0099] Further, refer to Figure 2 This embodiment provides a method for optimizing the mixed amplitude and phase of a projected light field. In some specific examples, the method includes:

[0100] Step 1: Input the target projection light field;

[0101] Step 2: construct an objective function F to evaluate the error between the generated projected light field and the target projected light field;

[0102] Step 3: Extract the phase pattern and amplitude pattern corresponding to the target projection light field.

[0103] Specifically, the amplitude M in the initial input complex amplitude light field is extracted T-A With phase M T-P , as the initial input for iterative optimization of amplitude and phase. Figure 3 As shown in the figure, a set of structured light fields with both amplitude and phase spatial distribution characteristics is used as the target projection light field. The spatial characteristics are array rectangles, where the amplitude of the black area is 0 and the phase is 0, and the amplitude of the white area is 1 and the phase is pi / 2. The characteristic size of the spatial distribution of the target projection light field on the image plane is 500×100nm, which is smaller than the optical diffraction limit.

[0104] Step 4: Calculate the complex amplitude of the generated projected light field and extract the generated phase and generated amplitude.

[0105] Specifically, the wavelength of the projection imaging system is set to 423 nm and the numerical aperture is 0.9. The initial complex amplitude M T In the input vector imaging model, the complex amplitude of the output light field is obtained as Figure 4 As shown, both the amplitude distribution and the phase distribution are degraded, and the rectangular characteristics of the amplitude and phase in the target projected light field are lost.

[0106] Step 5: Determine whether optimization is needed based on the objective function. If optimization is needed, proceed to the subsequent steps.

[0107] Specifically, the numerical solutions of the objective function and the upper limit objective function are calculated, and the numerical solutions are compared with the preset thresholds. If optimization is required, the subsequent steps are displayed. If optimization is not required, jump to step 9 and end the process.

[0108] Step 6: Optimize the input light field using the optimal gradient method, calculating both the phase gradient and the amplitude gradient. Specifically, by determining the gradient direction of a complex, large-scale light field, the optimal optimization direction is determined. This method is suitable for large-scale, nonlinear optimization problems and has high computational efficiency and convergence speed.

[0109] Step 7: Update the input phase pattern and amplitude pattern.

[0110] In steps 6 and 7, two phase gradients and two amplitude gradients need to be calculated, respectively. These are the phase gradient and the upper limit phase gradient, and the amplitude gradient and the upper limit amplitude gradient. The target pattern for the gradients is the initial input target pattern, while the target pattern for the upper limit gradients is the zero matrix.

[0111] Step 8: Repeat steps 4 to 7 until the objective function reaches a preset threshold or the number of iterative optimizations reaches a preset upper limit.

[0112] Specifically, when the numerical results of the objective functions corresponding to the four sets of gradients are all better than the corresponding preset thresholds, the optimization ends, or when the number of optimization iterations reaches the preset upper limit, the optimization ends and the amplitude and phase of the optimized input light field are output.

[0113] Step 9: Optimization is completed, and the optimized input amplitude and phase are output.

[0114] Specifically, Figure 5 The left side shows the optimized input amplitude, and the right side shows the corresponding output light field amplitude. Figure 6 The optimized input phase is shown on the left, and the corresponding output light field phase is shown on the right. The amplitude and phase of the optimized output light field retain the good rectangular spatial distribution characteristics of the array, indicating that the optimization method has a good effect.

[0115] The present invention proposes a hybrid optimization method for the amplitude and phase of the projected light field, which for the first time discloses the proximity effect of the amplitude and phase of the projected light field of any target in the projection system. During the joint optimization process, the amplitude and phase are optimized alternately, and upper and lower penalty terms are added to suppress the optimization results within the tolerance range, ultimately achieving the control of the amplitude and phase of the generated light field.

[0116] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing the mixed amplitude and phase of a projected light field, characterized in that: include: The projection light field is actually generated based on the input light field calculation; Substituting the parameters of the target projected light field and the parameters of the actually generated projected light field into an objective function model, and determining whether the calculated value of any function in the objective function model meets the corresponding preset threshold requirements; wherein the objective function model includes an amplitude objective function and a phase objective function, which are used to evaluate the accuracy of the amplitude and phase of the actually generated projected light field; If the amplitude objective function and / or the phase objective function do not meet the corresponding preset threshold requirements, the input amplitude and input phase of the input light field are optimized and updated using a gradient method until both the amplitude objective function and the phase objective function meet the corresponding preset threshold requirements or the number of optimizations reaches a preset number; The actual generation of the projection light field based on the input light field calculation specifically includes: The vector imaging model is used to calculate the complex amplitude of the projected light field actually generated after the input light field propagates to the image plane. extracting an actual amplitude pattern and an actual phase pattern of the actually generated projection light field based on the complex amplitude of the actually generated projection light field; The complex amplitude of the actual generated projection light field is obtained by the following formula: ； ； ； ； in, H Kernel function representing the vector imaging model; Represents the convolution operation; E image Represents the complex amplitude of the actual generated projection light field; M i Indicates the input light field, subscript i represents the iteration factor; m 、 n Indicates the number of grids; T g-g is the coordinate mapping relationship between the input field and the generated field; W is the window function of the projection system; NA Indicates the numerical aperture of the imaging lens; α 、 β 、 γ is the frequency domain coordinate on the plane, with the subscript en 、 ex They represent the entrance pupil and exit pupil respectively.

2. The projection light field amplitude and phase hybrid optimization method according to claim 1, characterized in that: The target projection light field is a complex amplitude field, and the parameters of the target projection light field include a target amplitude pattern and a target phase pattern; The parameters of the actually generated projection light field include an actual amplitude pattern and an actual phase pattern.

3. The projection light field amplitude and phase hybrid optimization method according to claim 2, characterized in that: The amplitude target function includes an amplitude difference function, and the amplitude difference function is used to represent the error between the actual amplitude pattern and the target amplitude pattern; The phase target function includes a phase difference function, and the phase difference function is used to represent the error between the actual phase pattern and the target phase pattern.

4. The projection light field amplitude and phase hybrid optimization method according to claim 3, characterized in that: The amplitude target function further includes an amplitude upper limit function, wherein the amplitude upper limit function is used to limit the upper limit of the actual amplitude pattern; The phase target function further includes a phase upper limit function, which is used to limit the upper limit of the actual phase pattern.

5. The projection light field amplitude and phase hybrid optimization method according to claim 1, wherein: The actual amplitude pattern includes an amplitude profile of the actually generated projection light field and a profile exceeding an amplitude upper limit in the actually generated projection light field; The actual phase pattern includes a phase profile of the actually generated projected light field and a profile exceeding a phase upper limit in the actually generated projected light field; It is obtained by the following formula: ； ； ； ； in, Z A and Z P Indicates the amplitude profile and phase profile of the actually generated projected light field; and Indicates the contours exceeding the upper limit of amplitude and the upper limit of phase in the actually generated projected light field; E image Represents the complex amplitude of the actual generated projection light field; 、 、 and Expressed as steepness factor; 、 、 and Expressed as a threshold, usually Smaller than the target amplitude value, Smaller than the target phase value, Larger than the target amplitude value, Larger than the target phase value; angle Computes the phase angle of a complex number.

6. The projection light field amplitude and phase hybrid optimization method according to claim 4, characterized in that: The step of optimizing and updating the input amplitude and input phase of the input light field using the gradient method specifically includes: calculating and obtaining the gradient of the amplitude objective function and the gradient of the phase objective function, and optimizing and updating the input amplitude and input phase of the input light field according to the gradient of the amplitude objective function and the gradient of the phase objective function; The gradient of the amplitude objective function includes the gradient of the amplitude difference function and the gradient of the amplitude upper limit function; The gradient of the phase objective function includes the gradient of the phase difference function and the gradient of the phase upper limit function.

7. The projection light field amplitude and phase hybrid optimization method according to claim 6, characterized in that: The input amplitude and input phase after gradient optimization are: ； ； in, and represents the input amplitude, and Indicates the input phase, subscript i and i+1 represents the iteration factor; Z A and Z P Indicates the amplitude profile and phase profile of the actually generated projected light field; M T-A and M T-P representing a target amplitude pattern and a target phase pattern of a target projected light field; and Indicates the contours exceeding the upper limit of amplitude and the upper limit of phase in the actually generated projected light field; Zeros represents the zero matrix; s A , s P , s A-shift , s P-shift They are the preset amplitude optimization step, phase optimization step, amplitude upper limit optimization step, and phase upper limit optimization step respectively; δ represents the partial derivative operation symbol.

8. A projection light field amplitude and phase hybrid optimization system, characterized in that: The method for optimizing the mixed amplitude and phase of a projection light field according to any one of claims 1 to 7 comprises: A calculation module, used for calculating and actually generating a projection light field based on the input light field; a judgment module, configured to substitute the parameters of the target projected light field and the parameters of the actually generated projected light field into an objective function model, and determine whether the calculated value of any function in the objective function model meets the corresponding preset threshold requirements; wherein the objective function model includes an amplitude objective function and a phase objective function, which are used to evaluate the accuracy of the amplitude and phase of the actually generated projected light field; an optimization module configured to optimize and update the input amplitude and input phase of the input light field using a gradient method if the amplitude objective function and / or the phase objective function do not meet the corresponding preset threshold requirements, until both the amplitude objective function and the phase objective function meet the corresponding preset threshold requirements or the number of optimizations reaches a preset number.

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