LC-SLM Selection and Performance Evaluation Method Based on Multi-parameter Coupled Constraint Model

Abstract

This invention relates to the field of precision optical inspection, and particularly to a method for selecting and evaluating the performance of an LC-SLM based on a multi-parameter coupled constraint model. The method includes determining the input variables of the inspection system based on the LC-SLM, which are divided into two main categories: parameters of the surface to be measured and basic requirements of the inspection system; determining the order of the blazed grating based on its diffraction efficiency requirements; determining the bit depth of the LC-SLM based on the accuracy requirements of the inspection system; determining the pixel parameters based on the wavefront modulation requirements of the LC-SLM; establishing a comprehensive error evaluation model for the inspection system; and calculating the total residual error, which is the square root of the sum of quantization error, pixel discretization error, LC-SLM surface shape error, nonlinearity error, and thermally induced phase drift error. This invention enables a systematic and quantitative design and evaluation of the hardware parameter selection, software configuration, and final compensation performance of the LC-SLM.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of precision optical detection, and particularly relates to an LC-SLM selection and performance evaluation method based on a multi-parameter coupling constraint model. BACKGROUND

[0002] Since the 21st century, complex optical curved surface elements have become the core components of high-end optical equipment in the fields of aerospace, high-end medical treatment, semiconductor lithography, etc. due to their core advantages of simplifying the structure of optical systems, improving imaging resolution and energy utilization. However, the elements have inherent characteristics such as non-rotationally symmetric surface, nonlinear curvature change, and high surface steepness, which lead to the problem that the standard spherical wavefront output by the interferometer cannot match the actual surface deviation of the element in the traditional interference detection technology, directly causing insufficient detection accuracy or even the inability to detect, which seriously restricts the industrialization process of complex optical curved surface elements.

[0003] To solve the above detection problems, the industry generally uses compensators to generate wavefronts that match the surface deviation of the elements to achieve accurate detection. Among them, the adaptive programmable compensation technology based on a spatial light modulator (such as a liquid crystal spatial light modulator, LC-SLM) can flexibly adjust the wavefront shape through programming to realize "one-to-many" detection adaptation, effectively overcoming the defects of high cost, long cycle, and poor universality caused by the "one-to-one" customization of traditional rigid compensators, and has become a research hotspot in the field of precision optical detection. However, the application range of this technology is limited, and the core bottleneck is the lack of a spatial light modulator compensation capability evaluation system. The traditional compensation evaluator based on a computer-generated hologram (CGH) is relatively mature, but there is a lack of systematic evaluation methods and quantitative models for the compensation performance of LC-SLMs, which makes it impossible to select appropriate devices from multiple LC-SLMs according to clear indicators in engineering practice, seriously hindering the engineering application of adaptive compensation technology.

[0004] In actual engineering applications, the above technical bottlenecks are specifically manifested in the following four aspects:

[0005] 1. Existing methods lack analysis of the influence of multi-parameter coupling: there is a strong coupling relationship between key hardware parameters such as the bit depth (n), pixel number (N), and pixel size (p) of LC-SLM, but existing technologies do not reveal the internal physical relationship;

[0006] 2. There is no basis for matching the order of blazed gratings: the order (k) of blazed gratings is commonly used in the industry to improve the first-order diffraction efficiency of LC-SLM, but its setting is mostly dependent on experience, and there is no matching model with the detection requirements of the measured curved surface, which may lead to problems such as excessive or insufficient order;

[0007] 3. Phase pattern is not related to the detection scene: the design of the phase pattern needs to be combined with the surface type characteristics of the measured surface (such as the maximum surface type deviation, surface type gradient) and the hardware characteristics of the LC-SLM, but the prior art does not clearly associate the two, so that the loaded phase pattern cannot fully exert the compensation ability of the LC-SLM;

[0008] 4. The input and output of the evaluation model are not clear: the existing evaluation system does not clearly define the input and output variables, lacks a standardized evaluation process, and engineers rely on experience for selection, making it difficult to start from the final detection accuracy and energy efficiency requirements to deduce the optimal hardware configuration and software parameters.

[0009] In the prior art, although some researches use Fresnel diffraction theory for grating diffraction efficiency calculation, they do not combine the dynamic characteristics of LC-SLM with the detection scene of the measured surface; at the same time, the order setting of blazed grating and the selection of LC-SLM still rely on experience, lacking systematic theoretical support. Therefore, it is urgent to propose an LC-SLM compensation performance evaluation method containing a blazed grating order matching strategy, clear input and output variables, and quantified system error, to fill the current technical gap and promote the engineering application of adaptive compensation technology in complex optical surface detection. SUMMARY

[0010] Therefore, the present application aims to provide an LC-SLM selection and performance evaluation method based on a multi-parameter coupling constraint model to solve the technical problem of the lack of compensation ability evaluation system of LC-SLM.

[0011] To achieve the above-mentioned purposes, the technical scheme of the present application is as follows:

[0012] An LC-SLM selection and performance evaluation method based on a multi-parameter coupling constraint model, comprising the following steps:

[0013] S1: determining the input variables of the detection system based on LC-SLM, which includes the maximum surface type deviation and the maximum local spatial slope of the measured surface, and the basic requirement parameters of the detection system, including the working wavelength λ, the target detection accuracy , the minimum first-order diffraction efficiency of LC-SLM required by the detection system and the environmental temperature fluctuation ;

[0014] S2: determining the order k of the blazed grating based on the diffraction efficiency requirement of the blazed grating, and the diffraction efficiency requirement of the blazed grating is constrained by the minimum first-order diffraction efficiency of LC-SLM required by the detection system, and the diffraction efficiency satisfies the minimum k value;

[0015] S3: determining the bit depth n of the LC-SLM based on the accuracy requirement of the detection system, the accuracy requirement of the detection system being the target detection accuracy of the detection system is the constraint, and the bit depth n satisfying is screened through the correlation between the bit depth and the quantization error ;

[0016] S4: determining the pixel parameters based on the wavefront modulation requirement of the LC-SLM, the pixel parameters including the pixel number N and the pixel size p, and screening N and p satisfying the conditions through the modulation range requirement and the modulation gradient requirement respectively, and establishing a multi-parameter coupling constraint model based on the order k of the blazed grating, the bit depth n, the pixel number N and the pixel size p;

[0017] S5: establishing a comprehensive error evaluation model of the detection system, and calculating the total residual error , the total residual error being the square root of the sum of the quantization error , the pixel discrete error , the LC-SLM surface error , the nonlinearity error and the thermal-induced phase drift error ;

[0018] .

[0019] Further, in step S2, the calculation formula of the diffraction efficiency is:

[0020] ;

[0021] wherein R represents the reflectivity of the LC-SLM;

[0022] The actual value of the reflectivity R of the LC-SLM is substituted into the calculation formula of the diffraction efficiency , the corresponding to different k values is calculated, and the minimum k value satisfying is selected as the order k of the blazed grating.

[0023] Further, in step S3, the calculation formula of the quantization error is as follows:

[0024]

[0025] The actual values of the order k of the blazed grating and the working wavelength λ are substituted into the calculation formula of the quantization error , the corresponding to different bit depths n is calculated, and the bit depth n satisfying bit depth n.

[0026] Further, in step S4, the modulation range requirement is filtered by the pixel number N through the following formula:

[0027]

[0028] The modulation gradient requirement is filtered by the pixel size p through the following formula:

[0029] .

[0030] Further, in step S5, the pixel dispersion error is calculated by the following formula:

[0031] .

[0032] Further, in step S5, the LC-SLM surface error is calculated by the following formula:

[0033]

[0034] wherein A represents the maximum static unevenness of the LC-SLM surface measured by the interferometer, x represents the position coordinate of the maximum unevenness A in the effective area of the LC-SLM, D represents the diameter or width of the effective area of the LC-SLM, represents the center point coordinate of the effective area of the LC-SLM.

[0035] Further, in step S5, the non-linear error is calculated by the following formula:

[0036] ;

[0037] wherein, represents the actual phase generated by the LC-SLM when the driving level is m, represents the actual phase generated by the LC-SLM when the driving level is m-1.

[0038] Further, in step S5, the thermal phase drift error is calculated by the following formula:

[0039]

[0040] wherein, represents the thickness of the liquid crystal substrate of the LC-SLM, represents the temperature coefficient.

[0041] After step S5, the following steps are further included:

[0042] S6: judging the total residual error calculated whether the set target detection accuracy is met ; if met, the selection of the LC-SLM is successful; if not met, return to execute steps S2-S4 to reselect the LC-SLM, and perform error analysis again until the total residual error meets the set target detection accuracy .

[0043] Compared with the prior art, the present application can achieve the following beneficial effects:

[0044] 1. The transition from experience dependence to model driving is realized, and the selection process is scientific and quantitative. The present application first constructs a systematic evaluation model with clear input and output, and changes the selection and performance evaluation of the LC-SLM from relying on the personal experience of engineers to scientific calculation based on physical models and mathematics. By clearly defining 2 types of 6 core input parameters, a quantitative mapping relationship from detection requirements to hardware parameters and software configuration is established, completely changing the previous dilemma of fuzzy selection process without any basis.

[0045] 2. The resource allocation and trade-off mechanism of the blaze grating order k is revealed, and the problem of blind setting of the blaze grating order is solved. The present application not only gives the quantitative relationship between the blaze grating order k and the diffraction efficiency, but more importantly, proposes the optimization criterion of the minimum k value that meets the diffraction efficiency requirement. This reveals the core trade-off role of the k value between guiding light energy (efficiency) and sacrificing spatial resolution (modulation ability), effectively avoids the waste of modulation ability caused by excessive order or the problem of too low diffraction efficiency caused by insufficient order, and realizes the optimal configuration of LC-SLM pixel resources.

[0046] 3. A multi-parameter coupling constraint model for LC-SLM selection is established, avoiding the wood barrel effect in selection. The present application innovatively couples key hardware parameters such as bit depth n, pixel number N and pixel size p with core performance indicators such as wavefront modulation range, modulation gradient and quantization error. By determining N through modulation range constraint, determining p through modulation gradient constraint, and determining n through modulation precision constraint, an optimization closed loop of mutual correlation and mutual restriction is formed, ensuring that the selected LC-SLM can meet the detection requirements in all performance dimensions, and avoiding the substandard system performance caused by the short board of a single parameter.

[0047] 4. A comprehensive and quantitative integrated error assessment model was constructed, resulting in high reliability in predicting compensation accuracy. For the first time, the total residual error was systematically decomposed into five independent error sources: quantization error, pixel discretization error, LC-SLM surface shape error, nonlinearity error, and thermally induced phase drift error. A physically meaningful and calculable quantitative formula was provided for each error. This model covers almost all major error sources, from digital sampling and inherent device defects to environmental stability, making the prediction of the final compensation accuracy more comprehensive and reliable. This provides a solid basis for error allocation and tolerance design in high-precision detection tasks.

[0048] 5. Highly practical for engineering applications, with output results directly guiding procurement and configuration. This method fully considers the actual situation of commercial LC-SLM products, and the output selection results are specific, clear, and available in the market. They can be directly used for equipment procurement list formulation and system software parameter preset, greatly shortening the R&D and debugging cycle of the detection system and promoting the engineering implementation of adaptive compensation technology.

[0049] 6. The optimized process has a clear logical structure and good versatility and scalability. The standardized process proposed in this invention—efficiency k → accuracy n → capability N and p → comprehensive error analysis—has a clear logical hierarchy and interconnected steps, providing a unified and reusable technical path for LC-SLM selection and evaluation in different application scenarios (such as semiconductor lithography, aerospace, and high-end medical). This framework can also be extended as LC-SLM technology develops by introducing new error terms or correcting the calculation formula, demonstrating good foresight and adaptability. Attached Figure Description

[0050] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0051] Figure 1 A flowchart illustrating the LC-SLM selection and performance evaluation method based on a multi-parameter coupled constraint model as described in the embodiments of the present invention;

[0052] Figure 2 The blazed grating order k and diffraction efficiency described in the embodiments of the present invention Relationship diagram;

[0053] Figure 3 A schematic diagram illustrating the limitations of pixel size p and blazed grating order k on gradient compensation capability as described in the embodiments of the present invention;

[0054] Figure 4 The bit depth n and blazed grating order k described in the embodiments of the present invention affect the quantization error. A schematic diagram illustrating the coupling effects. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0056] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0057] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0058] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "assembly," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0059] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0060] like Figure 1 As shown in the figure, this invention provides a method for selecting and evaluating the performance of LC-SLM based on a multi-parameter coupled constraint model, including the following steps:

[0061] S1: determining the input variables of the detection system composed of LC-SLM, which are divided into parameters of the surface to be measured and basic requirements of the detection system, the parameters of the surface to be measured including the maximum surface type deviation of the surface to be measured and the maximum local spatial slope , the basic requirements of the detection system including the working wavelength λ, the target detection accuracy , the minimum first-order diffraction efficiency of the LC-SLM required by the detection system and the environmental temperature fluctuation .

[0062] In order to solve the problem that the existing evaluation theory does not clearly define the input variables, in order to facilitate the establishment of the evaluation system of the standardized SLM used for the compensation detection of complex optical curved surface, it is necessary to clearly define the input variables of the detection system (2 categories and 6 items), which are divided into two categories:

[0063] Parameters of the surface to be measured: the maximum surface type deviation of the surface to be measured (unit: μm), the maximum local spatial slope of the surface to be measured (unit: rad).

[0064] The physical meaning of the maximum surface type deviation of the surface to be measured is the maximum deviation of the surface to be measured from the ideal reference surface (such as the designed spherical surface or the plane), which reflects the "shape accuracy" of the curved surface and is one of the core indicators of the detection.

[0065] The physical meaning of the maximum local spatial slope of the surface to be measured is the maximum value of the curvature change rate of the surface to be measured, which reflects the steepness of the curved surface. The greater the slope, the more intense the change of the curved surface, and the higher the requirements for the resolution of the detection system and the modulation capacity of the LC-SLM.

[0066] Basic requirements of the detection system: working wavelength λ (unit: μm), target detection accuracy (unit: μm), minimum first-order diffraction efficiency of LC-SLM , environmental temperature fluctuation .

[0067] The physical meaning of the working wavelength λ is the wavelength of the laser used for interference detection. The wavelength of the laser determines the pitch of the interference fringes and the scale of the detection accuracy.

[0068] The physical meaning of the target detection accuracy is the maximum detection error allowed when the surface to be measured is detected by interference, which reflects the maximum acceptable deviation of the detection result from the true surface type of the curved surface and is the core indicator for judging whether the detection result meets the detection requirements of the surface to be measured.

[0069] The minimum first-order diffraction efficiency of LC-SLM The physical meaning of the minimum first-order diffraction efficiency of LC-SLM is the lower limit value of the first-order diffraction efficiency that the LC-SLM must reach to ensure that the entire interferometric detection system can work normally. The minimum value of the first-order diffraction efficiency of the LC-SLM needs to be determined in combination with the structure (optical path design) of the interferometric detection system, the reflectivity of the mirror to be measured, and the sensitivity of the image sensor. The minimum first-order diffraction efficiency of the LC-SLM The minimum value needs to be determined to ensure the feasibility of detection.

[0070] Environmental temperature fluctuation The physical meaning of the environmental temperature fluctuation is the temperature variation range of the working environment of the LC-SLM during operation. Temperature variation will cause the performance drift of the LC-SLM liquid crystal layer and the thermal expansion and contraction of optical elements, thereby introducing thermal-induced errors, which is an environmental factor that needs to be quantified in error analysis.

[0071] S2: Determine the order k of the blazed grating based on the diffraction efficiency requirement of the blazed grating, and select the blazed grating with a diffraction efficiency that meets the minimum k value of the LC-SLM.

[0072] The purpose of step S2 is to find the minimum k value that meets the requirement of The purpose of the minimum k value is to ensure the least occupation of total pixel resources and reduce the sacrifice of spatial resolution.

[0073] The order k of the blazed grating is a periodic tilt phase superimposed on the compensation phase map in software, which is a core software configuration parameter. It defines the number of pixels occupied by the phase wrapping from 0 to 2π. The larger the k value, the smoother the phase change, and the closer to the ideal blazed grating shape. The blazed grating concentrates most of the light energy to a specific order (such as +1 order) through phase tilting, thereby increasing the diffraction efficiency. However, the total pixel resources of the LC-SLM are fixed. When a blazed grating is loaded, it is equivalent to using these pixels to do two things: generating tilt and generating compensation wavefront. It can be considered that the control over the diffraction angle is exchanged for the sacrifice of spatial resolution to enhance the first-order diffraction efficiency.

[0074] The diffraction efficiency can be calculated by the following formula:

[0075] ;

[0076] wherein R represents the reflectivity of the LC-SLM.

[0077] Substitute the actual value of the reflectivity R of the LC-SLM into the calculation formula of the diffraction efficiency , and calculate the diffraction efficiency corresponding to different k values. , select the minimum k value satisfying as the order k of the blazed grating.

[0078] diffraction efficiency With the change of the order k of the blazed grating, as shown in Figure 2 , it is shown that the diffraction efficiency monotonically increases with the increase of k value, but the growth trend gradually saturates. The optimization method of the present application is that: according to the minimum first-order diffraction efficiency of the LC-SLM input by the detection system, find the corresponding minimum k value through this curve, so as to maximize the spatial resolution of the LC-SLM while meeting the energy demand of the detection system, for wavefront modulation. Effectively avoid the common problem of excessive order in engineering, which leads to waste of modulation capacity, or insufficient order which leads to low diffraction efficiency, and realize the optimal allocation of LC-SLM pixel resources.

[0079] S3: Determine the bit depth n of the LC-SLM based on the accuracy requirement of the detection system, and the accuracy requirement of the detection system is the target detection accuracy of the detection system as the constraint, through the correlation between bit depth and quantization error , select the bit depth n satisfying .

[0080] Substitute the actual values of the order k of the blazed grating and the working wavelength λ into the calculation formula of the quantization error , calculate the corresponding to different bit depths n, and select the bit depth n satisfying .

[0081] In hardware, the bit depth n represents the resolution of the voltage signal driving each liquid crystal cell. An 8-bit driver means there are 2 8 =256 different voltage levels; 10 bits have 1024 levels. In software, the bit depth n determines the fineness of the voltage level applied to each pixel electrode, and determines the phase control accuracy. Since the bit depth n is limited, the quantization error introduced is:

[0082]

[0083] The quantization error must satisfy:

[0084]

[0085] The coupling effect of the bit depth n and the order k of the blazed grating on the quantization error is shown in Figure 4 , under the same bit depth n, increasing the k value will cause the quantization error to worsen; while to meet a certain target detection accuracy The (n, k) parameter combination must be selected below its horizontal line. Figure 4 The internal trade-off between light energy guidance (efficiency) and phase control (accuracy) in the parameter optimization process is deeply revealed, which provides a key basis for the quantification of the bit depth n.

[0086] Unlike the order k of the blazed grating, large bit depth does not affect the modulation ability at all, but higher bit depth of LC-SLM will bring the price increase, and currently 10bit and 8bit are the popular bit depth values in the market.

[0087] S4: Determine the pixel parameters based on the wavefront modulation requirements of LC-SLM, the pixel parameters including the pixel number N and the pixel size p, filter N and p that meet the conditions through the modulation range requirement and the modulation gradient requirement, and establish a multi-parameter coupling constraint model based on the order k of the blazed grating, the bit depth n, the pixel number N and the pixel size p.

[0088] Based on the determination of the order k and the bit depth n of the blazed grating in the first two steps, step S4 determines the spatial sampling characteristics of LC-SLM to meet the wavefront modulation requirements, which is also the step that has the greatest impact on the selection of LC-SLM.

[0089] Modulation range requirement: the maximum phase delay that LC-SLM can produce Must be sufficient to cover the maximum deviation of aspheric surface or the maximum wavefront PV that needs to be modulated in other scenarios. Must meet:

[0090]

[0091] It is derived that the required pixel number N must meet:

[0092]

[0093] Modulation gradient requirement: according to the Nyquist sampling criterion, there must be at least 2 pixels in each period of the wrapped phase displayed on the LC-SLM, which determines the maximum local spatial slope that LC-SLM can generate LC-SLM must be able to produce a phase change gradient that matches the maximum local spatial slope , that is:

[0094] ;

[0095] It is derived that the required pixel size p must meet:

[0096]

[0097] Diffractive efficiency ​As the order k of the blazed grating changes as shown in Figure 2

[0098] The limitation of pixel size p and the order k of the blazed grating on the compensation ability of gradient is shown in Figure 3 For the same pixel size p, the smaller the k value, the larger the maximum local spatial slope that the LC-SLM can produce, that is, the stronger the ability to compensate steep gradients. For the same k value, the smaller the pixel size p, the larger the maximum local spatial slope that the LC-SLM can produce.

[0099] The maximum surface gradient that the LC-SLM can compensate is simultaneously constrained by the coupling of the pixel size p and the order k of the blazed grating. To meet the compensation requirements of the maximum local spatial slope of the surface to be tested , the (p, k) parameter combination located above the horizontal line must be selected.

[0100] The present application establishes a multi-parameter coupling constraint model for LC-SLM selection, avoiding the bucket effect in selection. The present application innovatively couples key hardware parameters such as bit depth n, pixel number N and pixel size p with core performance indicators such as wavefront modulation range, modulation gradient and quantization error. By determining N through modulation range constraint, determining p through modulation gradient constraint, and determining n through modulation precision constraint, an optimized closed loop is formed, which ensures that the selected LC-SLM can meet the detection requirements in all performance dimensions, avoiding the substandard system performance caused by the short board of a single parameter.

[0101] S5: Establish a comprehensive error evaluation model of the detection system to calculate the total residual error , which is the square root of the sum of the quantization error , pixel discrete error , LC-SLM surface error , nonlinear error and thermal phase drift error .

[0102] The quantization error , pixel discrete error , LC-SLM surface error , nonlinear error and thermal phase drift error are five independent error sources of the total residual error , and the total residual error is calculated by the following formula:

[0103] ​​​​.

[0104] quantization error : derived from the joint limitation of bit depth and blaze order.

[0105] pixel discrete error : fitting error caused by limited number of pixels, which can be characterized by the following formula:

[0106]

[0107] SLM surface error : static surface flatness error of LC-SLM device itself, which is measured by interferometer and brought into the system, static surface flatness error can be characterized by the following formula:

[0108]

[0109] wherein A represents the maximum static unevenness of LC-SLM surface measured by interferometer, x represents the position coordinate of the maximum unevenness A in the effective area of LC-SLM, D represents the diameter or width of the effective area of LC-SLM, represents the center point coordinate of the effective area of LC-SLM.

[0110] nonlinear error : phase difference between adjacent gray levels after gamma correction, which can be characterized by the following formula:

[0111]

[0112] wherein, represents the actual phase generated by LC-SLM when the driving level is m, represents the actual phase generated by LC-SLM when the driving level is m-1, and the difference between generally 1 / 1000λ after gamma correction.

[0113] thermal phase drift error : phase output instability caused by device heating. Thermal phase drift error can be characterized by the following formula:

[0114]

[0115] wherein, represents the thickness of the liquid crystal substrate of LC-SLM, which is commonly about 3 represents the temperature coefficient, assuming good heat dissipation of the substrate, the temperature coefficient is 1.0×10 -4 / ℃, and the error is generally <0.03nm.

[0116] This invention constructs a comprehensive and quantitative integrated error assessment model, achieving high reliability in predicting compensation accuracy. For the first time, it systematically decomposes the total residual error into five independent error sources: quantization error, pixel discretization error, LC-SLM surface shape error, nonlinearity error, and thermally induced phase drift error. For each error, a physically meaningful and calculable quantitative formula is provided. This model covers almost all major error sources, from digital sampling and inherent device defects to environmental stability, making the prediction of final compensation accuracy more comprehensive and reliable. This provides a solid basis for error allocation and tolerance design in high-precision detection tasks.

[0117] Following step S5, the following steps are also included:

[0118] S6: Determine the calculated total residual error Does it meet the set target detection accuracy? If the conditions are met, the LC-SLM selection is successful; otherwise, return to steps S2-S4 to reselect the LC-SLM, re-determine k, n, N, and p), and recalculate the total residual error using the comprehensive error assessment model. until the total residual error Meets the set target detection accuracy until.

[0119] Taking a high-precision semiconductor lithography objective lens compensation detection as an example, note that this example mainly pursues picometer-level accuracy, which correspondingly sacrifices diffraction efficiency and compensation capability. In different application scenarios, it is necessary to reasonably set the evaluation index formula based on the detection requirements and select the appropriate blazed grating order and spatial light modulator type.

[0120] Step 1: Determine the input variables of the detection system based on LC-SLM.

[0121] , ; , , , .

[0122] Step 2: Determine the software order k of the blazed grating based on the diffraction efficiency requirements.

[0123] The reflectivity of a reflective LC-SLM is generally around 95%, so here we take R=95% and substitute it into the formula.

[0124] according to Looking for needs that can satisfy The required minimum value of k is k=2.

[0125] Step three: determine the bit depth n based on the accuracy requirement.

[0126]

[0127] The quantization error must satisfy:

[0128] .

[0129] When n = 8, .

[0130] When n = 10, .

[0131] Conclusion: the quantization error of n = 8 and n = 10 is much smaller than Although 8bit is slightly lower in cost, but for the high accuracy detection of the target, the error distribution is considered, the choice of 10bit bit depth (n = 10) is more prudent and recommended, leaving more margin for other unavoidable non-quantization error. 10bit LC-SLM is currently more common, and the price premium is within a reasonable range.

[0132] Step four: determine the pixel parameters (pixel number N and pixel size p) based on the wavefront modulation capability requirement.

[0133]

[0134]

[0135] Step five: establish a comprehensive error evaluation model of the detection system.

[0136]

[0137] Calculate each independent error:

[0138] Quantization error : , n = 10, = 0.04nm.

[0139] Pixel discrete error :

[0140] LC-SLM surface error :

[0141]

[0142] Substitute A = 0.7nm, = 0.8 into the above formula, we get = 0.8nm.

[0143] Nonlinear error : , ideally, take 1 / 1000 lambda as a representation, that is .

[0144] Thermal-induced phase shift error :

[0145] Total residual error :

[0146] In the ideal case, the total residual error calculated theoretically is 1.001 nm, which is less than the set target detection accuracy 1.2 nm, and the selection of LC-SLM meets the standard.

[0147] It should be understood that the various forms of flow shown above can be used to reorder, add or delete steps. For example, the steps described in the present disclosure can be executed in parallel, sequentially or in a different order, as long as the desired results of the technical solutions of the present disclosure can be achieved, which is not limited herein.

[0148] The above detailed description does not constitute a limitation on the scope of protection of the present application. Those skilled in the art should understand that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A method for LC-SLM selection and performance evaluation based on multi-parameter coupling constraint model, characterized in that, Comprising the following steps: S1: determining input variables of a detection system composed of an LC-SLM, the input variables being divided into parameters of a surface to be measured and basic requirement parameters of the detection system, the parameters of the surface to be measured including maximum surface type deviation of the surface to be measured and maximum local spatial slope , the basic requirement parameters of the detection system including working wavelength λ, target detection accuracy , minimum first-order diffraction efficiency of the LC-SLM required by the detection system and environmental temperature fluctuation ; S2: determine the order k of the blazed grating based on the diffraction efficiency requirement of the blazed grating, the diffraction efficiency requirement of the blazed grating being constrained by the minimum first-order diffraction efficiency required by the detection system for the LC-SLM, and screening the diffraction efficiency that meets the minimum k value; S3: determining the bit depth n of the LC-SLM based on the accuracy requirement of the detection system, the accuracy requirement of the detection system being in terms of the target detection accuracy of the detection system To constrain, through the correlation between the bit depth and the quantization error , the bit depth n that satisfies is screened; S4: determining pixel parameters based on the wavefront modulation requirements of the LC-SLM, the pixel parameters comprising a pixel number N and a pixel size p, screening N and p meeting the conditions through modulation range requirements and modulation gradient requirements respectively, and establishing a multi-parameter coupling constraint model based on the order k, the bit depth n, the pixel number N and the pixel size p of the blazed grating; S5: Establishing the comprehensive error evaluation model of the detection system, calculating the total residual error , the total residual error is the sum of the square roots of the quantization error , the pixel discrete error , the LC-SLM surface shape error , the nonlinear error and the thermal-induced phase drift error ​ 。 2. The LC-SLM selection and performance evaluation method based on multi-parameter coupling constraint model according to claim 1, characterized in that, In step S2, the diffraction efficiency is calculated by the formula: ； Wherein, R represents the reflectivity of the LC-SLM; The actual value of the reflectivity R of the LC-SLM is substituted into the calculation formula of the diffraction efficiency , the corresponding of different k values are calculated, and the minimum k value satisfying is selected as the order k of the blazed grating.

3. The LC-SLM selection and performance evaluation method based on multi-parameter coupling constraint model according to claim 1, characterized in that, In step S3, the quantization error The calculation formula is as follows: Substitute the actual values of the order k and the working wavelength λ of the blazed grating into the calculation formula of the quantization error , calculate the corresponding of different bit depths n, and select the bit depth n satisfying .

4. The LC-SLM selection and performance evaluation method based on multi-parameter coupling constraint model according to claim 1, characterized in that, In step S4, the modulation range requirements screen the pixel number N through the following formula: The modulation gradient requirements screen the pixel size p through the following formula: 。 5. The LC-SLM selection and performance evaluation method based on multi-parameter coupling constraint model according to claim 1, characterized in that, In step S5, the pixel discrete error The calculation formula is as follows: 。 6. The LC-SLM selection and performance evaluation method based on multi-parameter coupling constraint model according to claim 1, characterized in that, In step S5, the LC-SLM face form error The calculation formula is as follows: wherein A represents a maximum static unevenness of the LC-SLM surface measured with an interferometer, x represents a position coordinate of the maximum unevenness A occurring in the effective area of the LC-SLM, D represents a diameter or width of the effective area of the LC-SLM, denotes the center point coordinate of the effective area of the LC-SLM.

7. The LC-SLM selection and performance evaluation method based on multi-parameter coupling constraint model according to claim 1, characterized in that, In step S5, the non-linear error is calculated according to the following formula: ； wherein, φmrepresents the phase actually generated by the LC-SLM when the driving stage number is m, φm-1represents the phase actually generated by the LC-SLM when the driving stage number is m-1.

8. The LC-SLM selection and performance evaluation method based on multi-parameter coupling constraint model according to claim 1, characterized in that, In step S5, the thermal phase shift error is calculated as follows: wherein represents the liquid crystal substrate thickness of the LC-SLM, represents the temperature coefficient.

9. The LC-SLM selection and performance evaluation method based on multi-parameter coupling constraint model according to claim 1, characterized in that, After step S5, the following steps are further included: S6: determining the pixel parameters based on the wavefront modulation requirements of the LC-SLM, the pixel parameters comprising a pixel number N and a pixel size p, screening N and p meeting the conditions through modulation range requirements and modulation gradient requirements respectively, and establishing a multi-parameter coupling constraint model based on the order k, the bit depth n, the pixel number N and the pixel size p of the blazed grating; Wherein, R represents the reflectivity of the LC-SLM; In step S6, the modulation range requirements screen the pixel number N through the following formula: The modulation gradient requirements screen the pixel size p through the following formula: In step S6, the modulation range requirements screen the pixel number N through the following formula: The modulation gradient requirements screen the pixel size p through the following formula: S6: judging whether the total residual error calculated whether the set target detection accuracy is met ; if met, the selection of the LC-SLM is successful; if not met, return to execute steps S2-S4 to reselect the LC-SLM, and again perform error analysis until the total residual error meets the set target detection accuracy .

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