PSF simulation system and method based on tolerance digital twinning

Abstract

According to the tolerance digital twinning-based PSF simulation system and method provided by the invention, on the basis of the diffraction theory, a full-system optical transfer model based on the Huygens-Fresnel principle is constructed, and simplified processing of high-order aberration and diffraction terms by traditional geometric ray tracing is avoided; and then system error parameters are introduced as digital twin modeling variables, so that simulation models are in one-to-one correspondence with actual optical system parameters and have the capability of representing error ranges, and the limitation that in an existing method, a PSF model is separated from a real structure of an optical system and cannot cover a real error source of the system is overcome; high-fidelity PSF modeling of a specific optical system can be realized, and the method can be applied to high-precision imaging simulation and debugging verification.

Description

Technical Field

[0001] This invention belongs to the field of optical system simulation technology, and particularly relates to a PSF simulation system and method based on tolerance digital twin. Background Technology

[0002] In recent years, digital twin technology, as a physical model-based and data-driven technique, has been increasingly applied to the modeling and simulation of optical systems. By establishing a virtual model corresponding to the actual optical system, digital twins can reflect the dynamic changes of the system in real time and accurately simulate and optimize the performance of the optical system in a virtual environment. However, existing digital twin models still have certain limitations in the tolerance analysis of optical systems, especially in simulations considering multiple optical components, complex tolerance propagation, and system-level effects. Achieving accurate simulation of the point spread function (PSF) remains a technical challenge. For example, the paper "Afast PSF model for optical system evaluation using wavefront coding and deep learning" (OpticsExpress, Vol. 31, No. 26, 2023) uses the digital twin's point spread function for image prediction and reconstruction, but it focuses on the rapid reconstruction of the PSF in the imaging chain.

[0003] Existing research on PSFs of actual optical systems has simplified the modeling of the physical error sources of PSFs of actual optical systems. It lacks systematic embedding of factors such as assembly and adjustment errors, manufacturing errors, and higher-order aberrations. Furthermore, the restored PSFs trained based on deep learning networks do not have the ability to continuously evolve the system (i.e., they are not adapted to the system's state changing over time, such as temperature changes or alignment state changes).

[0004] In other words, existing methods generally suffer from the following problems in PSF modeling:

[0005] 1. Incomplete error modeling: Failed to systematically consider the superposition effect of various optical errors (such as lens geometric errors, assembly and adjustment deviations, higher-order aberrations, etc.) on PSF.

[0006] 2. Lack of dynamic adaptability: The simulation model cannot be dynamically adjusted as manufacturing and assembly data are acquired, lacking real-time performance and updateability.

[0007] 3. Lack of simulation pathways for engineering closed-loop design: Existing simulation methods are difficult to embed into the design-manufacturing-testing closed loop, which limits the role of PSF simulation in high-performance optical system engineering practice. Summary of the Invention

[0008] To address the aforementioned issues, this invention provides a PSF simulation system and method based on tolerance digital twins, which can achieve high-fidelity PSF modeling for specific optical systems and can be applied to high-precision imaging simulation and debugging verification.

[0009] A PSF simulation method based on tolerance digital twin includes the following steps:

[0010] Determine the systematic error parameters of the optical system to be simulated, including manufacturing error, assembly error, and higher-order aberrations;

[0011] The error range and tolerance distribution of the system error parameters are set according to the actual production process and quality control standards.

[0012] A random number model is used to sample the error range and tolerance distribution corresponding to machining error, assembly error, and higher-order aberrations, so that machining error, assembly error, and higher-order aberrations have different values.

[0013] By arranging and combining different values ​​of machining error, assembly error, and higher-order aberrations, different samples of systematic error parameters are obtained;

[0014] Each error parameter sample is input into the diffraction optical tracing model corresponding to the optical system to be simulated, and the point spread function (PSF) of the optical system to be simulated under each error parameter sample is obtained.

[0015] The point spread function (PSF) corresponding to all error parameter samples is fitted into a single PSF according to the set weights. The fitted PSF is the prior PSF digital twin library of the optical system to be simulated.

[0016] Furthermore, the processing errors include geometric dimension errors, shape errors, and material property errors of the optical elements.

[0017] Furthermore, the assembly and adjustment errors include installation errors of optical components and alignment errors during the assembly process.

[0018] Furthermore, the higher-order aberrations include spherical aberration, astigmatism, coma, and field curvature.

[0019] Furthermore, the system error parameters that have a greater impact on the imaging quality of the simulated optical system have a larger weight.

[0020] Furthermore, the tolerance distribution includes the standard deviation of the error, the offset, and its distribution characteristics.

[0021] Furthermore, a PSF simulation method based on tolerance digital twins also includes the following steps:

[0022] Based on the values ​​of the error parameter samples corresponding to the spread function PSF at any point, the optical system corresponding to the current point spread function PSF is compensated for the corresponding system error parameters, thereby improving the imaging performance of the current optical system.

[0023] Furthermore, a PSF simulation system based on tolerance digital twin includes a parameter setting module, an interval setting module, a sampling module, a combination module, a simulation module, and a fitting module;

[0024] The parameter setting module is used to determine the system error parameters of the optical system to be simulated, wherein the system error parameters include manufacturing error, assembly and adjustment error, and higher-order aberrations;

[0025] The interval setting module is used to set the error range and tolerance distribution for the system error parameters according to the actual production process and quality control standards.

[0026] The sampling module is used to sample the error range and tolerance distribution corresponding to the processing error, assembly error, and higher-order aberration using a random number model, so that the processing error, assembly error, and higher-order aberration have different values.

[0027] The combination module is used to arrange and combine different values ​​of processing error, assembly error, and higher-order aberrations to obtain different system error parameter samples;

[0028] The simulation module is used to input each error parameter sample into the diffraction optical tracing model corresponding to the optical system to be simulated, and obtain the point spread function (PSF) of the optical system to be simulated under each error parameter sample.

[0029] The fitting module is used to fit the point spread function (PSF) corresponding to all error parameter samples into a single point spread function (PSF) according to a set weight. The PSF obtained by fitting is a priori PSF digital twin library of the optical system to be simulated.

[0030] Beneficial effects:

[0031] 1. This invention provides a PSF simulation method based on tolerance digital twins. Based on diffraction theory, it constructs a full-system optical transfer model based on the Huygens-Fresnel principle, avoiding the simplification of higher-order aberrations and diffraction terms in traditional geometric ray tracing. Subsequently, system error parameters are introduced as digital twin modeling variables, so that the simulation model corresponds one-to-one with the parameters of the actual optical system and has the ability to characterize the error range. This overcomes the limitations of existing methods where the PSF model is detached from the real structure of the optical system and cannot cover the real sources of system error. It can achieve high-fidelity PSF modeling for specific optical systems and can be applied to high-precision imaging simulation and debugging verification.

[0032] 2. This invention provides a PSF simulation method based on tolerance digital twins. By constructing a physical simulation model under the synergistic effect of multiple error sources, and combining diffraction optical tracing and statistical error perturbation techniques, a dynamically updatable PSF database is established to achieve high-precision prediction and engineering optimization support for the imaging performance of actual optical systems. This invention can be used to generate PSF image datasets covering typical processing and working states, which can be used to assist in image reconstruction algorithms or system debugging tolerance design.

[0033] 3. This invention provides a PSF simulation system based on tolerance digital twin, which can comprehensively consider factors such as processing errors, assembly and adjustment errors and higher-order aberrations, and optimize the imaging performance of the optical system through compensation methods. This system not only improves the design and simulation accuracy of the optical system, but also can accurately predict the imaging effect in the actual processing process by updating the digital twin model in real time, providing effective support for the optimized design and performance control of the optical system. Attached Figure Description

[0034] Figure 1 A flowchart of a PSF simulation method based on a tolerance digital twin model provided by the present invention;

[0035] Figure 2 The flowchart shows the PSF digital twin library obtained based on diffraction optical tracing.

[0036] Figure 3 The PSF image is obtained from typical diffraction optical tracing.

[0037] Figure 4 A typical PSF diagram after incorporating lens tolerances;

[0038] Figure 5 This is a composite PSF diagram of the combined tolerance range in a digital twin library under typical tolerances. Detailed Implementation

[0039] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0040] In the process of designing and evaluating the performance of complex optical systems, the traditional PSF simulation method cannot accurately consider key factors such as actual processing errors, assembly and adjustment errors and higher-order aberrations, resulting in a significant deviation between the simulation results and the actual imaging performance. This makes it difficult to meet the consistency requirements of high-precision optical systems for imaging quality prediction and design verification.

[0041] Based on this, the present invention provides a PSF simulation method based on a tolerance digital twin model, aiming to accurately simulate the point spread function (PSF) of an optical system by considering various factors such as manufacturing errors, assembly errors, and higher-order aberrations of optical surfaces, thus providing a scientific basis for the design, debugging, and optimization of optical systems; specifically, such as Figure 1 As shown, it includes the following steps:

[0042] S1: Determine the systematic error parameters of the optical system to be simulated, including manufacturing error, assembly error, and higher-order aberrations;

[0043] It should be noted that, as Figure 2 As shown, this invention first establishes a diffraction optical tracing model of the optical imaging system based on its geometric structure and the characteristics of its optical components. This model accurately calculates the diffraction effect of the optical system on light of different wavelengths by analyzing the propagation process of the light beam within the optical system, and simulates the beam propagation and imaging distortion during the imaging process, such as... Figure 3 As shown, this model provides the foundation for subsequent error analysis and PSF simulation. Diffraction optical tracing is just one general method; the key feature of this invention is the application of a reasonable system parameter offset during the diffraction optical tracing process. Combined with the characteristics of diffraction optical tracing, this allows for rapid acquisition of the PSF.

[0044] Based on this, this invention introduces processing errors into the optical system according to actual processing requirements and precision standards. These processing errors include geometric dimensional errors, shape errors, and material property errors of the optical elements. These errors, through modeling the shape of the optical elements, affect the imaging quality of the optical system, such as… Figure 4 As shown.

[0045] Next, considering the errors that may occur during the actual assembly and adjustment of the optical system, a model is built based on the assembly and adjustment errors of the optical system. These errors typically originate from the installation errors of optical components, alignment errors during assembly, and other processing and assembly errors such as lens thickness errors, surface shape errors, positional deviations, and assembly and adjustment pose errors. By introducing assembly and adjustment errors into the model, the simulation accuracy of the optical system is further refined.

[0046] Furthermore, based on the processing capabilities and characteristics of the optical system, this invention introduces higher-order aberrations into the optical surface. Higher-order aberrations simulated using Zernike polynomials or other aberration characterization methods include various aberration terms such as spherical aberration, astigmatism, coma, and field curvature. These aberrations cause certain imaging distortions during the imaging process, such as… Figure 5 As shown. By conducting a detailed analysis of the processing and assembly accuracy of each optical element, different types of higher-order aberrations can be introduced into the model, and optimized by adjusting various parameters.

[0047] S2: Set the error range and tolerance distribution for the system error parameters based on the actual production process and quality control standards;

[0048] It should be noted that, to make the model more consistent with reality, this invention sets the error range and tolerance distribution by referring to processing experience and test results. Specifically, based on actual production processes and quality control standards, the statistical distribution of various errors (such as processing errors, assembly errors, and higher-order aberrations) is set, including the standard deviation, offset, and distribution characteristics of the errors. Through this step, various error combinations that the optical system may encounter during actual processing and assembly can be simulated, and the sampling accuracy of the PSF image within a certain error range can be improved by using a range error composite PSF.

[0049] S3: Using a random number model that conforms to the processing statistical distribution, such as Gaussian or equidistant, to sample the error range and tolerance distribution corresponding to processing error, assembly error, and higher-order aberrations, so that processing error, assembly error, and higher-order aberrations have different values.

[0050] S4: Arrange and combine different values ​​of machining error, assembly error, and higher-order aberrations to obtain different samples of system error parameters;

[0051] S5: Input each error parameter sample into the diffraction optical tracing model corresponding to the optical system to be simulated to obtain the point spread function (PSF) of the optical system to be simulated under each error parameter sample;

[0052] S6: Fit the point spread function (PSF) corresponding to all error parameter samples into a single point spread function (PSF) according to the set weights. The fitted PSF is the prior PSF digital twin library of the optical system to be simulated.

[0053] S7: Based on the values ​​of the error parameter samples corresponding to the spread function PSF at any point, compensate for the corresponding system error parameters of the optical system corresponding to the current point spread function PSF to improve the imaging performance of the current optical system. It should be noted that the compensation process includes adjusting the optical surface parameters to restore PSF performance.

[0054] In other words, after considering the aforementioned error factors, this invention further introduces compensation methods for actual processing. By compensating and adjusting the optical system (such as optical surface correction and assembly adjustment), the imaging performance of the system is improved. Compensation methods include adjustment strategies during processing, feedback adjustment based on measurement data, and real-time correction of processing errors. Using these compensation methods, a priori PSF digital twin library of the optical system is established. This library can be gradually optimized and provides more accurate simulation results as processing measurement data accumulates.

[0055] Therefore, this invention categorizes error sources into three types: ① machining errors (curvature, thickness, surface shape, etc.); ② assembly and adjustment errors (position and attitude deviations); ③ higher-order aberrations (Zernike term modeling). A perturbation distribution model (such as Gaussian, uniform, equidistant, etc.) is defined for each type of error and introduced step-by-step into the simulation for PSF simulation. This solves the problem that existing models cannot distinguish error types and are difficult to study the cumulative effect of errors, helping the system achieve error feedforward compensation and improve design robustness during the design phase.

[0056] The following section uses a diffraction PSF based on Huygens PSF as an example to further illustrate the PSF simulation method based on tolerance digital twin of the present invention.

[0057] For the unit vector is propagating light

[0058]

[0059] For a circle with center O on the optical axis l A spherical lens P with surface properties of (0,0,l) satisfies;

[0060] x P 2 +y P 2 +(z P -l) 2 =R 2

[0061] Solving the simultaneous equations into a quadratic equation yields the optical path t of the ray on the sphere. P At this time t P The point closest to the object plane should be selected.

[0062] When light ray r propagates in a medium with refractive indices n1 and n2, it obeys Snell's law:

[0063]

[0064] Vector of light Substituting this in, we can see that the ray vector propagating backward from point P... exist:

[0065]

[0066] right Its unit vector can be obtained by taking the modulus.

[0067]

[0068] At this time, Substituting three unit vectors located in the same plane into the above formula, we can obtain the following solution:

[0069]

[0070] The optical path L of a ray originating from any point on the object surface and exiting onto any surface of the optical system can be calculated using this method. x,y :

[0071] L x,y =∑|d n |×n n

[0072] Where, d n For the light along a path during a tracking process The distance traveled in the direction, n n This represents the refractive index of the medium during this tracking process.

[0073] For optical systems with large aberrations, using the exit pupil position as the reference wavefront can provide more accurate information. The spherical diverging field U0(x0,y0) at a point (x0,y0,z0) in the pupil satisfies:

[0074]

[0075] in, For different image points to this point;

[0076] According to simplified Kirchhoff diffraction, its field distribution U on the image plane after propagation along the optical axis is... i (x0, y0; x i ,y i )satisfy:

[0077]

[0078] Therefore, the response of the composite field at the image plane satisfies:

[0079]

[0080] In actual energy calculations, to simplify the calculations, the composite field U... i The calculation of (x,y) should use the summation of the pupil sampling points, and its energy I(x) i ,y i )satisfy:

[0081] I(x i ,y i )=|U i (x i ,y i )| 2

[0082] To preserve the energy characteristics of the dataset, we assume the PSF is the impact response from the object point, therefore:

[0083]

[0084] After considering the wavelength response of the actual imaging detector, the PSF response after wavelength integration can be used as the original response.

[0085]

[0086] After building the diffraction optical tracing model, the actual machining tolerance range is further introduced to generate a tolerance-based digital twin PSF (point spread function). In this process, the tolerance range can be strictly defined according to the specific requirements of the design drawings and adjusted based on errors in the actual manufacturing and assembly process. Tolerance perturbations can be introduced using classic random number methods or more precise Gaussian random numbers. Furthermore, they can be set in conjunction with actual test data and measurement errors, making the simulation model more closely resemble the actual production process.

[0087] For example, when modeling optical components, lens thickness errors are reflected by introducing a variation in the radius of the sphere P in the diffraction optics tracing model. This variation directly affects the light propagation path and its diffraction effect, thus impacting the final image quality. By adjusting this variation, the specific impact of lens thickness errors during manufacturing on the optical system can be simulated.

[0088] After introducing machining tolerances, higher-order aberration perturbations can be superimposed on the image plane composite field to further improve the simulation accuracy of the digital twin model. Higher-order aberrations include various aberration terms (such as spherical aberration, astigmatism, coma, field curvature, etc.), and these aberrations can be simulated by introducing random distributions to simulate aberration variations that may occur during actual machining and assembly. For example, by superimposing a Zernike aberration model that conforms to machining randomness on the composite field, the random fluctuations of higher-order aberrations during machining can be simulated, which helps improve the model's prediction accuracy for actual imaging distortion.

[0089] After introducing higher-order aberrations, typical tolerance compensations such as image plane spacing are further added to the model. To better reflect the uncertainties in the actual assembly and adjustment process, random variations should be introduced into the compensation. These random variations should use equally spaced random numbers to better match the tolerance distribution in the actual assembly process. These variations can simulate the impact of errors that may occur during assembly and adjustment on the imaging performance of the optical system, ensuring that the simulation results are more consistent with the performance in the actual application environment.

[0090] Thus, through tolerance modeling and perturbation introduction under the aforementioned multiple conditions, the final generated PSF diagram constitutes a complete digital twin PSF database. This database can be updated in real time and continuously optimized as data accumulates during manufacturing and assembly, providing accurate predictions for the design, debugging, and performance evaluation of optical systems. This tolerance-based digital twin PSF simulation method effectively reflects and resolves various error problems encountered by optical systems in actual working environments, providing strong support for the design optimization and subsequent image processing of high-precision optical systems.

[0091] Furthermore, the present invention also provides a PSF simulation system based on tolerance digital twin, including a parameter setting module, an interval setting module, a sampling module, a combination module, a simulation module, and a fitting module;

[0092] The parameter setting module is used to determine the system error parameters of the optical system to be simulated, wherein the system error parameters include manufacturing error, assembly and adjustment error, and higher-order aberrations;

[0093] The interval setting module is used to set the error range and tolerance distribution for the system error parameters according to the actual production process and quality control standards.

[0094] The sampling module is used to sample the error range and tolerance distribution corresponding to the processing error, assembly error, and higher-order aberration using a random number model, so that the processing error, assembly error, and higher-order aberration have different values.

[0095] The combination module is used to arrange and combine different values ​​of processing error, assembly error, and higher-order aberrations to obtain different system error parameter samples;

[0096] The simulation module is used to input each error parameter sample into the diffraction optical tracing model corresponding to the optical system to be simulated, and obtain the point spread function (PSF) of the optical system to be simulated under each error parameter sample.

[0097] The fitting module is used to fit the point spread function (PSF) corresponding to all error parameter samples into a single point spread function (PSF) according to a set weight. The PSF obtained by fitting is a priori PSF digital twin library of the optical system to be simulated.

[0098] In summary, this invention first introduces three types of real-world error modeling mechanisms: processing errors (such as lens thickness and curvature variations), assembly errors (such as displacement and tilt deviations), and higher-order aberrations (Zernike aberration distribution). These are progressively superimposed in the simulation to achieve PSF simulation under realistic error scenarios. Secondly, this invention constructs a priori PSF twin library based on statistical perturbations and measurement data, setting the error distribution as Gaussian, isometric, or measured driving perturbations. This generates a large number of physically consistent PSF sample libraries and supports iterative updates through feedback optimization, improving the model's dynamic adaptability and actual predictive capabilities. Finally, this invention introduces an error compensation mechanism for performance recovery simulation. Assembly compensation (such as position fine-tuning and attitude correction) modeling is integrated into the simulation process to analyze the recoverability of imaging performance, providing a basis for subsequent error tolerance design and debugging strategy formulation.

[0099] In other words, the simulation process of this invention generates a PSF dataset under large-scale perturbation conditions, forming a "prior PSF digital twin library." Subsequently, the digital twin library can be matched, corrected, or updated based on test data (such as interferometer measurements, star map imaging, MTF testing, etc.). The simulation model has state tracking capabilities, realizing an iterative closed loop of "prediction-feedback-update," achieving timeliness consistency between the PSF model and the system state. Because the PSF dataset is correlated with optical system parameters, optical system parameters can be predicted by obtaining measured PSF data, and the system's PSF imaging state can be predicted by using optical system parameters from actual fabrication and testing.

[0100] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A PSF simulation method based on tolerance digital twin, characterized in that, Includes the following steps: Determine the systematic error parameters of the optical system to be simulated, including manufacturing error, assembly error, and higher-order aberrations; The error range and tolerance distribution of the system error parameters are set according to the actual production process and quality control standards. A random number model is used to sample the error range and tolerance distribution corresponding to machining error, assembly error, and higher-order aberrations, so that machining error, assembly error, and higher-order aberrations have different values. By arranging and combining different values ​​of machining error, assembly error, and higher-order aberrations, different samples of systematic error parameters are obtained; Each error parameter sample is input into the diffraction optical tracing model corresponding to the optical system to be simulated, and the point spread function (PSF) of the optical system to be simulated under each error parameter sample is obtained. The point spread function (PSF) corresponding to all error parameter samples is fitted into a single PSF according to the set weights. The fitted PSF is the prior PSF digital twin library of the optical system to be simulated.

2. The PSF simulation method based on tolerance digital twin as described in claim 1, characterized in that, The processing errors include geometric dimension errors, shape errors, and material property errors of the optical elements.

3. The PSF simulation method based on tolerance digital twin as described in claim 1, characterized in that, The assembly and adjustment errors include installation errors of optical components and alignment errors during the assembly process.

4. The PSF simulation method based on tolerance digital twin as described in claim 1, characterized in that, The higher-order aberrations include spherical aberration, astigmatism, coma, and field curvature.

5. The PSF simulation method based on tolerance digital twin as described in claim 1, characterized in that, The greater the impact of a system error parameter on the imaging quality of a simulated optical system, the greater its weight.

6. The PSF simulation method based on tolerance digital twin as described in claim 1, characterized in that, The tolerance distribution includes the standard deviation of the error, the offset, and its distribution characteristics.

7. The PSF simulation method based on tolerance digital twin as described in claim 1, characterized in that, It also includes the following steps: Based on the values ​​of the error parameter samples corresponding to the spread function PSF at any point, the optical system corresponding to the current point spread function PSF is compensated for the corresponding system error parameters, thereby improving the imaging performance of the current optical system.

8. A PSF simulation system based on tolerance digital twin, characterized in that, It includes a parameter setting module, an interval setting module, a sampling module, a combination module, a simulation module, and a fitting module; The parameter setting module is used to determine the system error parameters of the optical system to be simulated, wherein the system error parameters include manufacturing error, assembly and adjustment error, and higher-order aberrations; The interval setting module is used to set the error range and tolerance distribution for the system error parameters according to the actual production process and quality control standards. The sampling module is used to sample the error range and tolerance distribution corresponding to the processing error, assembly error, and higher-order aberration using a random number model, so that the processing error, assembly error, and higher-order aberration have different values. The combination module is used to arrange and combine different values ​​of processing error, assembly error, and higher-order aberrations to obtain different system error parameter samples; The simulation module is used to input each error parameter sample into the diffraction optical tracing model corresponding to the optical system to be simulated, and obtain the point spread function (PSF) of the optical system to be simulated under each error parameter sample. The fitting module is used to fit the point spread function (PSF) corresponding to all error parameter samples into a single point spread function (PSF) according to a set weight. The PSF obtained by fitting is a priori PSF digital twin library of the optical system to be simulated.

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