Superlens reverse design method

Abstract

The invention discloses a super lens reverse design method, and belongs to the technical field of optical equipment. The method comprises the following steps: S1, constructing a simulation data set containing paired structure images and spectral data; s2, a two-channel variational auto-encoder is adopted to encode the structure image and the spectral data to a low-dimensional submerged space; s3, constructing a reverse design single-step diffusion model, generating structural latent representation through single-step denoising under the condition of target spectrum latent representation, and decoding the structural latent representation into a structural image; s4, constructing a forward prediction single-step diffusion model, performing single-step denoising to generate spectral latent characterization under the condition of the structural latent characterization, and decoding the spectral latent characterization into spectral data; and S5, introducing a period consistency training mechanism, performing joint optimization on the two models through two closed loops of a structure period and a spectrum period, and forcing the models to keep physical consistency in round-trip mapping. Through the double-channel submerged space coding-bidirectional single-step diffusion-period consistency combined training closed-loop design, the model stability and the data utilization rate are improved.

Description

Technical Field

[0001] This application relates to the field of optical equipment and nanophotonics technology, and in particular to a reverse design method for superlenses. Background Technology

[0002] Inverse design of superlenses and metamaterials is a core challenge in nanophotonics. Traditional methods rely on experience and first-principles electromagnetic simulations (such as FDTD or COMSOL), which are computationally expensive, time-consuming, and unable to cover a broad design space. In recent years, deep learning, especially generative models, has been introduced to learn complex mappings between structures and spectra. However, existing methods typically train the forward and inverse models independently, resulting in the following problems: lack of periodic consistency, leading to inconsistencies between the design results and the target spectrum; unstable training and slow inference speed; and reliance on large amounts of paired labeled data, resulting in high data acquisition costs.

[0003] To address the aforementioned issues, no existing technology has proposed a reverse design framework that can simultaneously guarantee efficient inference, physical consistency, and support training on unlabeled data. Therefore, there is an urgent need for a novel cross-modal generative model that can achieve fast and diverse superlens reverse design while maintaining physical plausibility. Summary of the Invention

[0004] To address the aforementioned issues, this application provides a reverse engineering method for superlenses, which solves problems such as low inference efficiency, poor physical consistency, and strong data dependence in the prior art.

[0005] The first technical solution adopted in this application is: providing a reverse design method for a superlens, including the following steps: S1. Construct a simulation dataset containing paired structural images and spectral data; S2. Construct a dual-channel latent space representation framework, encoding the structural image and the spectral data into independent latent spaces respectively; S3. Construct a reverse design single-step diffusion model, using the latent representation of the target spectrum as a condition, generate the corresponding structural latent representation through single-step denoising, and decode it into a structural image; S4. Construct a positive prediction single-step diffusion model, using the latent representation of the structural image as a condition, generate the corresponding spectral latent representation through single-step denoising, and decode it into spectral data. S5. Introduce a periodic consistency training mechanism. By constructing two closed loops, structural period and spectral period, jointly optimize the reverse design single-step diffusion model and the forward prediction single-step diffusion model to force the model to maintain consistency in round-trip mapping.

[0006] In an optional embodiment, in step S2, the dual-channel latent space representation framework is implemented using two independent variational autoencoders, including: A structural variational autoencoder is used to encode a structural image into a first latent vector and reconstruct it; A spectral variational autoencoder is used to encode spectral data into a second latent vector and reconstruct it; The denoising processes in steps S3 and S4 are performed in the latent spaces of the first latent vector and the second latent vector, respectively.

[0007] In an optional embodiment, in steps S3 and S4, both the reverse design single-step diffusion model and the forward prediction single-step diffusion model are built based on the diffusion Transformer architecture.

[0008] In an optional embodiment, both the reverse design single-step diffusion model and the forward prediction single-step diffusion model perform single-step denoising operations at the noisiest fixed time step during the diffusion process during inference.

[0009] In an optional embodiment, the loss function used when training the reverse design single-step diffusion model and the forward prediction single-step diffusion model separately includes: The loss function for structural image reconstruction combines pixel-level mean square error and perceptual quality loss. The loss function for spectral data reconstruction uses mean square error.

[0010] In an optional embodiment, in step S5, the structural period is: the real structural image is reconstructed into a first reconstructed structure through forward prediction and then through reverse design, and the first period loss between the real structural image and the first reconstructed structure is calculated; The spectral period is defined as follows: the real spectral data is reconstructed into a first reconstructed spectrum through reverse design and forward prediction, and the second period loss between the real spectral data and the first reconstructed spectrum is calculated. The total loss function of the joint optimization includes the first periodic loss and the second periodic loss.

[0011] In an optional embodiment, both the first periodic loss and the second periodic loss are calculated using the L2 norm.

[0012] In an optional embodiment, the periodic consistency training mechanism supports self-supervised training using unlabeled data, wherein unlabeled data containing only structural images participates in the training of the structural periodicity, and unlabeled data containing only spectral data participates in the training of the spectral periodicity.

[0013] In an optional embodiment, a one-to-many reverse design step is also included: Potential characterization of the spectrum of a fixed target; Different Gaussian noises are sampled multiple times and input into the trained reverse design single-step diffusion model respectively; After denoising and decoding using the reverse-designed single-step diffusion model, multiple different metamaterial structure images are obtained.

[0014] In an optional embodiment, the multiple different metamaterial structure images are verified by the forward predictive single-step diffusion model, and the predicted spectral data are all consistent with the target spectrum within a preset tolerance.

[0015] Due to the adoption of the above technical solution, this application has at least one of the following beneficial effects compared with the prior art:

[0016] 1. By compressing high-dimensional data into the latent space through a dual-channel VAE and combining it with a single-step diffusion model, the inference speed of reverse design and forward prediction is significantly improved.

[0017] 2. By using a periodic consistency training mechanism, the forward and inverse models are forced to remain consistent in the closed loop, ensuring the physical rationality of the design results and the target spectrum.

[0018] 3. Utilize the randomness of the diffusion model to achieve one-to-many design and provide multiple feasible structural schemes.

[0019] 4. The Diffusion Transformer is adopted as the core architecture to enhance the model's expressive power and training stability. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 A schematic flowchart of a reverse engineering method for a superlens provided in an embodiment of this application; Figure 2 This is a schematic diagram of the bidirectional diffusion model of the reverse design method for a superlens provided in an embodiment of this application. Detailed Implementation

[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. It is understood that the specific embodiments described herein are only for explaining this application and not for limiting it. Furthermore, it should be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings, not all structures. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0022] The terms "first," "second," etc., used in this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0023] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0024] Existing methods for inverse design of superlenses typically rely on frameworks such as Generative Adversarial Networks (GANs), training forward prediction and inverse generation as two independent tasks. This results in a lack of physical consistency between models—that is, the structure generated inversely often fails to accurately reproduce the target spectrum after being validated by the forward model. At the same time, these methods are unstable in the training process, slow inference speed, and heavily rely on a large amount of paired labeled simulation data, making it difficult to utilize the widely available unpaired or single-modal data in reality, thus limiting their generalization ability.

[0025] In view of this, this application addresses the aforementioned drawbacks through a technical solution based on image-spectral cross-modal latent space, bidirectional single-step diffusion model, and a joint training mechanism of periodic consistency; such as Figure 1 , 2 As shown, Figure 1 This is a flowchart illustrating a reverse engineering method for a superlens provided in an embodiment of this application. Figure 2 This is a schematic diagram of a bidirectional diffusion model of a superlens reverse design method provided in an embodiment of this application. The superlens reverse design method includes the following steps: S1. Construct a simulation dataset containing paired structural images and spectral data. To build a high-quality simulation dataset, parametric scanning was performed using electromagnetic simulation software based on the finite element method, such as COMSOL Multiphysics. Specifically, key geometric parameters (such as height) of metamaterial units (e.g., nanopillars, open rings) were selected. ,diameter ,cycle The geometric parameters (such as material refractive index) are systematically sampled within the design space. For each set of geometric parameters, a corresponding two-dimensional or three-dimensional structural image is generated through rendering. (Usually grayscale or RGB images, size is) Simultaneously, electromagnetic simulations are run to calculate the spectral response (e.g., transmittance, reflectance, or phase) of the structure in the target frequency band (e.g., visible light, infrared band), obtaining one-dimensional spectral data. (length is) (vectors). Finally, collect Pairs of data And divide it into training set and test set in proportion (e.g., 8:2).

[0026] S2. Construct a dual-channel latent space representation framework, encoding structural images and spectral data into independent latent spaces. To reduce the computational cost of directly training the diffusion model in high-dimensional pixel / spectral spaces and to unify the representation of data from different modalities, a latent space representation strategy based on a variational autoencoder is adopted. Specifically, a dual-channel VAE framework is constructed: VAE structure: Contains encoder and decoder Encoder High-dimensional structural images Mapped to a low-dimensional, continuous latent vector Decoder Then try to from Reconstruct the original image The training objective is to minimize the reconstruction error and satisfy the prior distribution of the latent space, which includes the standard normal distribution.

[0027] Spectral VAE: Includes encoder and decoder Encoder one-dimensional spectral data Mapping to latent vector Decoder from Reconstructed Spectrum .

[0028] Two VAEs are pre-trained independently. After training, the subsequent diffusion, noise addition, and noise reduction processes all take place in their respective latent spaces. and This reduces the number of model parameters and computational complexity.

[0029] S3. Construct a single-step diffusion model for reverse design. Using the latent representation of the target spectrum as a condition, generate the corresponding structural latent representation through single-step denoising and decode it into a structural image. To achieve rapid reverse design from the target spectrum to the metamaterial structure, construct a single-step reverse design model (P→S) based on a Diffusion Transformer (such as J-DiT). Its core idea is to utilize the noisiest time step in the diffusion process. Perform single-step noise reduction.

[0030] Input: Target spectrum after latent representations obtained through encoding As a condition; a Gaussian noise sampled from a standard normal distribution. As the target to be denoised, its corresponding time step is fixed as follows: .

[0031] Model and Processing: The model (a J-DiT network) is based on... and conditions As input, it is trained to predict velocity (v-prediction). Then, the denoised structural latent characterization is directly calculated using the v-parameterization formula. : .

[0032] in, These are diffusion scheduling parameters.

[0033] Output: The result will be Decoder input to structure VAE In this process, the final image of the metamaterial structure can be reconstructed. Compared to the traditional denoising process that requires dozens or even hundreds of iterations, this single-step design significantly improves inference speed.

[0034] S4. Construct a forward prediction single-step diffusion model. Using the latent representation of the structure image as a condition, generate the corresponding spectral latent representation through single-step denoising and decode it into spectral data. Symmetrically, construct a single-step forward prediction model (S→P) to quickly predict the spectral response of the structure image, as a replacement or supplement to the physical simulator.

[0035] Input: Structural image after processing latent representations obtained through encoding As a condition; another Gaussian noise (The time step is also fixed as) () is the target to be denoised.

[0036] Model and Processing: Another J-DiT Network Given the given conditions, predict Then, the denoised spectral latent characterization was calculated. : .

[0037] Output: Decoder input to spectral VAE In the process, the predicted spectral data is reconstructed. .

[0038] S5. A cycle consistency training mechanism is introduced. By constructing two closed loops—structural cycle and spectral cycle—the reverse-design single-step diffusion model and the forward-predictive single-step diffusion model are jointly optimized to force the models to maintain consistency in round-trip mapping. To address the potential mapping inconsistency problem that may occur when independently trained reverse and forward models are concatenated, a cycle consistency training mechanism is introduced. This mechanism jointly optimizes the two models, constructing two data closed loops: Structural period ( ): Input the actual structure The predicted spectrum is generated using the forward model (S→P). The predicted spectrum is then input into the inverse model (P→S) to reconstruct the structure. Calculate the periodic consistency loss between the original structure and the reconstructed structure. .

[0039] Spectral period ( Input the true spectrum. The predicted structure is generated through the inverse model (P→S). The predicted structure is then input into the forward model (S→P) to reconstruct the spectrum. Calculate the periodic consistency loss between the original spectrum and the reconstructed spectrum. .

[0040] The total loss function for joint training is the sum of the individual reconstruction losses and the periodic consistency loss: ,in These are the weighting coefficients.

[0041] In step S2, the dual-channel latent space representation framework is implemented through two independent variational autoencoders, including: A structural variational autoencoder is used to encode a structural image into a first latent vector and reconstruct it; A spectral variational autoencoder is used to encode spectral data into a second latent vector and reconstruct it; The denoising processes in steps S3 and S4 are performed in the latent spaces where the first latent vector and the second latent vector reside, respectively.

[0042] The specific architecture of a dual-channel VAE can be designed according to the data characteristics. For a structured VAE, its encoder... Convolutional neural networks (CNNs) can be used to extract spatial features from images, and the decoder... Image reconstruction is performed using transposed convolution or upsampling layers. The loss function typically includes pixel-level reconstruction loss (such as MSE or L1 loss) and KL divergence loss to normalize the latent space distribution. For spectral VAEs, the encoder... Spectral curves can be processed using one-dimensional convolutional layers or fully connected layers; the decoder... Symmetrically use one-dimensional transposed convolutions or fully connected layers. The training of the two VAEs is independent and parallel. Through this design, high-dimensional image and spectral data are compressed into a low-dimensional, dense latent space (e.g., 64-dimensional or 128-dimensional), enabling subsequent diffusion models to perform generation and denoising operations more efficiently in the latent space.

[0043] In steps S3 and S4, both the reverse-engineered single-step diffusion model and the forward-predicted single-step diffusion model are built based on the diffusion Transformer architecture; this application preferably uses Diffusion Transformer (DiT) or its variants (such as J-DiT) as the core architecture of the single-step diffusion model. Compared with the traditional U-Net, the Transformer architecture has stronger global modeling capabilities and scalability. In specific implementation, noisy latent vectors (such as...) are used... ) and conditional latent vectors (such as The inputs are concatenated or fused via a cross-attention mechanism and fed into multi-layer Transformer blocks. Each block contains a multi-head self-attention mechanism and a feedforward neural network. The model is trained to predict added noise or velocity (v-prediction); this Transformer-based single-step diffusion architecture, combined with latent space operations, enables extremely fast inference speed while maintaining generation quality.

[0044] Both the reverse-engineered single-step diffusion model and the forward-predicted single-step diffusion model perform single-step denoising at the noisiest fixed time step during inference. In the standard diffusion model, generation requires denoising from pure noise. Begin with gradual noise reduction. Step to get This application fixes the time step to a maximum value. (i.e., the noisiest state), and train the model to directly predict from arrive The transformation. During training, the model learns how to transform the noisiest latent vector in one step, given the conditions. Translated into clean latent vectors or During inference, only one random noise sample is needed. By combining the target conditions, the generated result can be obtained through a single forward propagation of the model, achieving an order-of-magnitude speed improvement.

[0045] The loss functions used when training the reverse design single-step diffusion model and the forward prediction single-step diffusion model separately include: The loss function for structural image reconstruction combines pixel-level mean square error and perceptual quality loss. The loss function for spectral data reconstruction uses mean square error.

[0046] A task-specific loss function was designed.

[0047] Structural Image Loss The precise geometry of the structural image is crucial. Therefore, the loss function combines pixel-level L2 loss (MSE) and perceptual loss (such as LPIPS). MSE ensures the accuracy of pixel values, while LPIPS loss compares differences in the feature space of the image through a pre-trained neural network (such as VGG), better preserving the visual quality and details of the structure. The formula is expressed as: .

[0048] Spectral data loss Spectra are continuous 1D signals, requiring high smoothness and numerical accuracy. Using a simple mean squared error (MSE) as the loss function is sufficient to achieve good results, and is computationally efficient and stable. The formula is expressed as: .

[0049] In step S5, the structural period is: the real structural image is reconstructed into the first reconstructed structure through forward prediction and then through reverse design, and the first period loss between the real structural image and the first reconstructed structure is calculated. The spectral period is as follows: the real spectral data is reconstructed into the first reconstructed spectrum through reverse design and forward prediction, and the second period loss between the real spectral data and the first reconstructed spectrum is calculated. The total loss function of the joint optimization includes the first-cycle loss and the second-cycle loss.

[0050] The first and second period losses are both calculated using the L2 norm.

[0051] Periodic consistency loss is the core of the joint optimization phase, such as Figure 2 As indicated by the arrow, it establishes a two-way constraint between the two models.

[0052] Structural periodicity loss: measures the reconstructed structure after a closed loop of "structure → spectrum → structure". With the original structure The difference is calculated using the L2 norm (MSE): .

[0053] Spectral periodicity loss: measures the reconstructed spectrum after a closed loop of "spectrum → structure → spectrum". Compared with the original spectrum The difference. The L2 norm is also used for calculation: .

[0054] The total periodic loss is the sum of the two: L2 loss is sensitive to outliers and can effectively punish large inconsistencies, thus strongly promoting the two models to learn the relationship of inverse mapping of each other and ensuring physical consistency.

[0055] The periodic consistency training mechanism supports self-supervised training using unlabeled data, where unlabeled data containing only structural images participates in the training of structural periods, and unlabeled data containing only spectral data participates in the training of spectral periods.

[0056] For a batch of images containing only structural data If no corresponding spectral data is available, it can be input into the forward model (S→P) to generate a "pseudo-spectrum," which can then be input into the inverse model (P→S) to reconstruct the structure and calculate the structural periodicity loss. In this process, the model uses its learned knowledge for self-supervision, which helps improve its generalization ability.

[0057] Similarly, for a batch of data that only contains spectral data... For data lacking a corresponding structure, it can be input into the inverse model (P→S) to generate a "pseudo-structure," and then input into the forward model (S→P) to reconstruct the spectrum and calculate the spectral period loss. .

[0058] This mechanism greatly reduces the reliance on large-scale, perfectly matched simulation data, enabling models to learn from richer and more readily available single-modal data, thus enhancing their robustness in real-world applications.

[0059] It also includes a one-to-many reverse design step: Potential characterization of the spectrum of a fixed target; Different Gaussian noises are sampled multiple times and input into the trained reverse-engineered single-step diffusion model respectively; After reverse design of a single-step diffusion model, noise reduction and decoding were performed to obtain multiple images of different metamaterial structures.

[0060] Multiple images of different metamaterial structures were verified by a forward predictive single-step diffusion model, and the predicted spectral data were consistent with the target spectrum within the preset tolerance.

[0061] When the user has a target spectral response At that time, it first passes through the encoder of the spectral VAE. Obtain its latent characteristics Then, fix this. As a condition, perform the following operation M times: sample a different random Gaussian noise vector. ( ), and combine it with fixed Input the pre-trained reverse-engineered single-step diffusion model (P→S) together. Each time, the model outputs a different structural latent vector. via decoder After decoding, M different images of the metamaterial structure that may achieve the target spectrum are obtained. .

[0062] To ensure the effectiveness of the generated structures, these M structures can be sequentially subjected to rapid spectral prediction using a forward predictive single-step diffusion model (S→P) to obtain the corresponding predicted spectra. Since the model has undergone periodic consistency training, these predicted spectra should theoretically all be consistent with the original target spectra. High consistency. In practical applications, a preset tolerance (such as the mean square error of the spectrum being less than a certain threshold) can be set to screen out qualified candidate structures.

[0063] In the several embodiments provided in this application, it should be understood that the disclosed methods and devices can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed.

[0064] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0065] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0066] The above description is merely an embodiment of this application and does not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for reverse engineering a superlens, characterized in that, Includes the following steps: S1. Construct a simulation dataset containing paired structural images and spectral data; S2. Construct a dual-channel latent space representation framework, encoding the structural image and the spectral data into independent latent spaces respectively; S3. Construct a reverse design single-step diffusion model, using the latent representation of the target spectrum as a condition, generate the corresponding structural latent representation through single-step denoising, and decode it into a structural image; S4. Construct a positive prediction single-step diffusion model, using the latent representation of the structural image as a condition, generate the corresponding spectral latent representation through single-step denoising, and decode it into spectral data. S5. Introduce a periodic consistency training mechanism. By constructing two closed loops, structural period and spectral period, jointly optimize the reverse design single-step diffusion model and the forward prediction single-step diffusion model to force the model to maintain consistency in round-trip mapping.

2. The reverse engineering method for a superlens according to claim 1, characterized in that, In step S2, the dual-channel latent space representation framework is implemented through two independent variational autoencoders, including: A structural variational autoencoder is used to encode a structural image into a first latent vector and reconstruct it; A spectral variational autoencoder is used to encode spectral data into a second latent vector and reconstruct it; The denoising processes in steps S3 and S4 are performed in the latent spaces of the first latent vector and the second latent vector, respectively.

3. The reverse engineering method for a superlens according to claim 1, characterized in that, In steps S3 and S4, both the reverse design single-step diffusion model and the forward prediction single-step diffusion model are built based on the diffusion Transformer architecture.

4. The reverse engineering method for a superlens according to claim 3, characterized in that, Both the reverse design single-step diffusion model and the forward prediction single-step diffusion model perform single-step denoising operations at the noisiest fixed time step during the diffusion process during inference.

5. The reverse engineering method for a superlens according to claim 1, characterized in that, When training the reverse design single-step diffusion model and the forward prediction single-step diffusion model separately, the loss functions used include: The loss function for structural image reconstruction combines pixel-level mean square error and perceptual quality loss. The loss function for spectral data reconstruction uses mean square error.

6. The reverse engineering method for a superlens according to claim 1, characterized in that, In step S5, the structural period is: the real structural image is reconstructed into a first reconstructed structure through forward prediction and then reverse design, and the first period loss between the real structural image and the first reconstructed structure is calculated. The spectral period is defined as follows: the real spectral data is reconstructed into a first reconstructed spectrum through reverse design and then forward prediction, and the second period loss between the real spectral data and the first reconstructed spectrum is calculated. The total loss function of the joint optimization includes the first periodic loss and the second periodic loss.

7. The reverse engineering method for a superlens according to claim 6, characterized in that, Both the first period loss and the second period loss are calculated using the L2 norm.

8. The reverse engineering method for a superlens according to claim 1 or 6, characterized in that, The periodic consistency training mechanism supports self-supervised training using unlabeled data, wherein unlabeled data containing only structural images participates in the training of the structural period, and unlabeled data containing only spectral data participates in the training of the spectral period.

9. The reverse engineering method for a superlens according to claim 1, characterized in that, It also includes a one-to-many reverse design step: Potential characterization of the spectrum of a fixed target; Different Gaussian noises are sampled multiple times and input into the trained reverse design single-step diffusion model respectively; After denoising and decoding using the reverse-designed single-step diffusion model, multiple different metamaterial structure images are obtained.

10. The reverse engineering method for a superlens according to claim 9, characterized in that, The multiple different metamaterial structure images were verified by the forward prediction single-step diffusion model, and the predicted spectral data were all consistent with the target spectrum within a preset tolerance.

Images