An artificial intelligence-based single-exposure absolute step-type error measurement method

Abstract

The application relates to the technical field of optical precision measurement and artificial intelligence, in particular to a single-exposure absolute step error measurement method based on artificial intelligence, which constructs an artificial intelligence algorithm model based on physical guidance, generates a virtual interferogram sequence of another wavelength based on a single-wavelength, single-exposure interferogram sequence, combines a synthetic wavelength principle to calculate the absolute phase of a measured surface, and then calculates the absolute step height, so as to solve the 2pi phase ambiguity problem in traditional interferometry and realize large-range and high-precision absolute step height measurement.

Description

Technical Field

[0001] This application relates to the interdisciplinary field of optical precision measurement and artificial intelligence, specifically to an artificial intelligence-based method for measuring absolute step error in a single exposure. Background Technology

[0002] In fields such as semiconductor manufacturing, micro / nano device inspection, and precision optical processing, accurate measurement of surface step height is crucial. Interferometry, due to its non-contact, high-precision, and full-field capabilities, has become the preferred technique for such measurements. Its basic principle is to invert the surface height by analyzing the phase distribution ϕ(x,y) of the interference fringes. The formula is as follows: Where λ represents the wavelength of the light source. However, all phase-based interferometry techniques face an inherent physical limitation: 2π phase ambiguity. Specifically, since interferometers can only measure the phase within the interval [−π,π), when the height change of the measured surface exceeds λ / 2, the phase jumps, making it impossible to directly obtain continuous, unambiguous absolute height information. For example, when using a 633 nm He-Ne laser, the theoretical maximum unambiguous measurement height is only about 316 nm. To overcome the measurement limitation caused by 2π phase ambiguity, traditional schemes typically employ the following methods:

[0003] 1. Phase Unwrapping: This method uses multi-frame, multi-wavelength, or spatial domain algorithms to stitch the wrapped phases into a continuous phase. However, this method is extremely sensitive to noise, occlusion, and steep edges, and is prone to failure on complex stair structures.

[0004] 2. Dual-wavelength / multi-wavelength interferometry: This method uses two different wavelengths to synthesize a longer equivalent wavelength, thereby expanding the unambiguous measurement range. However, this approach requires a complex light source system and multiple exposures, resulting in high cost, slow speed, and new limitations on the ambiguity cycle.

[0005] On the other hand, deep learning has been attempted to predict absolute phase directly from single-frame interferograms. However, existing methods often treat this as a purely image regression problem, ignoring the inherent physical constraints of the interferometric signal. This results in poor model generalization ability, especially when faced with step heights not covered by the training data or novel sample types, leading to unreliable predictions that fail to meet industrial metrological requirements.

[0006] Therefore, there is an urgent need for a new method for measuring absolute step error that can robustly and accurately measure the absolute step height under single exposure conditions, freeing it from the constraints of 2π ambiguity. Summary of the Invention

[0007] In view of this, this application discloses a single-exposure absolute step error measurement method based on artificial intelligence to solve the measurement accuracy problem caused by 2π phase ambiguity in existing interferometric measurement techniques, including:

[0008] S1. Using a single-wavelength interferometer, the sample containing the step structure to be tested is exposed and measured with a light source of wavelength λ1 to obtain an experimental interferogram set;

[0009] S2. Normalize and perform binary masking on the experimental interferogram set to obtain a preprocessed interferogram sequence;

[0010] S3. Establish an artificial intelligence algorithm model for virtual multi-wavelength step interferometry. The artificial intelligence algorithm model processes the preprocessed interferogram sequence to generate a virtual wavelength phase-shifted interferogram sequence. The artificial intelligence algorithm model is used to generate virtual multi-wavelength phase-shifted interferograms. The model is pre-trained before use.

[0011] S4. Based on the principle of dual-wavelength interference, calculate the absolute phase of the surface under test according to the experimental interferogram set and the virtual wavelength phase-shifted interferogram sequence;

[0012] S5. Calculate the absolute step height based on the absolute phase of the surface to be measured.

[0013] The beneficial effects of this application include:

[0014] This application constructs a physical-guided artificial intelligence algorithm model, which generates a virtual interferogram sequence of another wavelength based on the interferogram sequence obtained by a single wavelength and a single exposure. The absolute phase of the surface under test is calculated by the principle of synthetic wavelength, and then the absolute step height is calculated. This solves the 2π phase ambiguity problem in traditional interferometry and realizes large-scale, high-precision absolute step height measurement.

[0015] A physics-guided artificial intelligence algorithm model architecture is provided. Through multi-stage processing, it focuses on the physical property constraints of the interferogram, the spatial domain features at different scales, and the frequency domain features, so as to achieve accurate generation of virtual wavelength interferograms with physical meaning.

[0016] Based on the artificial intelligence algorithm model architecture, a composite loss function design is provided, which includes pixel-level image reconstruction loss, phase-level loss and pixel-level loss, to ensure that the generated virtual graph is equally accurate in subsequent physical calculations.

[0017] It also provides a method for constructing the training dataset, which combines a small number of real-world interferograms (for background and modulation) with a large amount of simulation data generated based on Zernike polynomials (especially the piston term Z1, which is randomized in the range of 0-4.5 μm), thus balancing the realism and diversity of the dataset. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of an artificial intelligence-based single-exposure absolute step error measurement method in an embodiment of this application;

[0019] Figure 2 This is a schematic diagram of the artificial intelligence algorithm model in the embodiments of this application. Detailed Implementation

[0020] To make the objectives, technical solutions, features, and advantages of this application clearer and to facilitate a better understanding of the technical solutions of this application by those skilled in the art, the following detailed description of this application is provided in conjunction with the accompanying drawings and embodiments.

[0021] Example 1:

[0022] This embodiment includes an artificial intelligence-based method for measuring absolute step error in a single exposure, such as... Figure 1 As shown, it includes:

[0023] S1. Using a single-wavelength interferometer, the sample containing the step structure to be tested is exposed and measured with a light source of wavelength λ1 to obtain an experimental interferogram set.

[0024] The single-wavelength interferometer can be a Twyman-Green interferometer, a Mirau interferometer, or other interferometric measurement device used to acquire phase-shifted interferograms. A single exposure of the sample containing the step to be measured is performed using a light source with wavelength λ1. The measurement is based on a four-step phase shift to obtain a two-step phase shift, resulting in the interferometric image. ; or , representing the four interferograms corresponding to the four-step phase shift process, or the two interferograms corresponding to the two-step phase shift process. In some embodiments, only one interferogram I(x, y) may be acquired.

[0025] Furthermore, this embodiment adds noise to the experimental interferogram set to form surface morphology samples with different spatial frequency characteristics and amplitude distributions. The noise type is generally Gaussian noise, and the signal-to-noise ratio after adding noise is generally not less than 10dB. In this embodiment, the pupil of the measurement system is a circular region, and the surface morphology of the surface to be measured is modeled using Zernike polynomials, the formula of which is:

[0026]

[0027] in, Denotes the nth order Zernike polynomial. This represents the coefficients of the nth-order Zernike polynomial. The order N is chosen based on practical needs, generally not lower than order 10 and not higher than order 65. By analyzing the coefficients... Random sampling is performed to generate surface morphology samples with different spatial frequency characteristics and amplitude distributions.

[0028] S2. Normalize and perform binary masking on the experimental interferogram set to obtain a preprocessed interferogram sequence.

[0029] The normalization process normalizes the pixel values ​​of the interferogram to the range of [0, 1] or [-1, 1].

[0030] The binary masking process determines whether a specific pupil shape exists in the optical path, causing the acquired image to be outside the full field of view. If so, the binary mask is multiplied with the input interferogram to delineate the effective region, which is then used to inform the model for discrimination. If not, no additional processing is performed.

[0031] S3. Establish an artificial intelligence algorithm model for virtual multi-wavelength step interferometry. The artificial intelligence algorithm model processes the preprocessed interferogram sequence to generate a virtual wavelength phase-shifted interferogram sequence.

[0032] The artificial intelligence algorithm model is used to generate virtual multi-wavelength phase-shift interferograms. The model is pre-trained before use; the process of constructing the training dataset includes:

[0033] Step 1: Using a light source with wavelength λ2, conduct exposure measurement simulation based on complete experimental conditions, where λ2≠λ1. The obtained high-confidence samples are used as the simulation interferogram set; the high-confidence samples have physical consistency with the experimental interferogram set.

[0034] Considering the potential difficulty in obtaining sufficient samples of different scenarios and degrees of the step to be tested in real-world situations, this embodiment adds a certain amount of noise to the samples in the simulated interferogram atlas to form new samples. The noise added in this embodiment is Gaussian noise, and the signal-to-noise ratio after adding noise is generally not less than 10dB. The method for adding noise in this embodiment includes: simulating the generation of two test surfaces on the samples in the simulated interferogram atlas, and forming a step by adjusting the height difference between the two surfaces.

[0035] The surface to be tested is generated through simulation in the following ways:

[0036] For samples with circular pupils, Zernike polynomials are used to simulate and generate the surface shape of the test surface; the order of the polynomial is selected according to the actual task, generally not less than 3 and not more than 10.

[0037] For samples with square pupils, the surface shape of the test surface is generated using Legendre polynomial simulation; the order of the polynomial can be selected according to the actual task, generally not less than 3rd order and not more than 10th order;

[0038] For samples of pupils in irregular regions, the surface shape of the test surface is generated by simulating Zernike polynomials or Legendre polynomials, and then the target region is defined by a 0-1 binary mask; the order of the polynomial is selected according to the actual task, generally not less than 3 and not more than 10.

[0039] Step 2: Construct model input data and model label data based on experimental and simulated interferometric atlases.

[0040] The model input data includes the interference image at the experimental wavelength λ1 (e.g., λ1 = 633 nm). As input data, M=2 or M=4 correspond to the two-step phase shifting method or the four-step phase shifting method, respectively.

[0041] The model label data will be the virtual interference image under the simulated wavelength λ2 (e.g., λ2 = 656 nm). As label data, k=2 or k=4.

[0042] Furthermore, the artificial intelligence algorithm model, such as Figure 2 As shown, the data processing includes:

[0043] S31. Obtain the interferogram sequence at wavelength λ1. Based on the multi-stage structure design, perform feature extraction or downsampling on the input interferogram to obtain the output features of different channels.

[0044] The design, based on a multi-stage structure and adapted to the image characteristics of interference fringes, employs one or more of the following unconventional, targeted designs:

[0045] To address the characteristic that the connected domains of the interferogram fringes extend across the entire image, a visual perception module or attention mechanism module with an additional receptive field is introduced into the spatial domain processing of the main stage of the multi-stage structure. For example, a large-sized convolutional kernel is added, typically with a size of no less than 10.

[0046] To address the physical nature of interference fringes satisfying the wave equation, implicit neural representation (INR) downsampling is introduced. First, the interference pattern is represented as... The implicit function, where, Represent the coordinates, then encode the amplitude A and phase. Finally, downsampling is converted into network parameter compression to achieve arbitrary resolution reconstruction during inference;

[0047] To address the uneven contrast of interference fringes (e.g., high at the center, low at the edges, or attenuation), contrast-aware channel attention is used to reduce or enhance features in low-contrast regions. Retinex style decomposition is introduced to decompose the interference pattern into fringe structure and slowly changing background, which are then processed separately.

[0048] To take advantage of the gradual change in brightness in the interferogram, frequency domain learning is performed at a specific stage of the multi-stage structure. The amplitude and phase maps are obtained by performing a Fourier transform on the input interferogram, and the amplitude and phase domain features are learned respectively.

[0049] S32. Perform scale unification, feature alignment, and feature fusion on the output features of each channel to obtain fused features.

[0050] S33. Perform conditional reasoning or upsampling on the fusion features to obtain a virtual phase-shifting interferogram.

[0051] The conditional inference or upsampling of the fused features, adapted to the image characteristics of the interference fringes, employs one or more of the following unconventional targeted designs:

[0052] To address the characteristic that the connected domain of the virtual phase-shifting interferogram fringe runs through the entire image, an additional visual perception module or attention mechanism with an extra receptive field is introduced into the spatial processing of the main stage structure. For example, a large-sized upsampling convolution kernel is added; the size of the large-sized upsampling convolution kernel is usually not less than 10.

[0053] To address the characteristic of gradual changes in brightness in the interferogram, the characteristic mapping relationships between the input interferogram and the phase-shifted interferogram in the amplitude and phase domains are learned respectively. Based on the inverse Fourier transform, the high-fidelity constraint on the generation of fringes in the output virtual phase-shifted interferogram is further strengthened in the frequency domain.

[0054] S34. Define the effective region of the virtual phase-shifting interferogram and output the interferogram sequence at wavelength λ2. That is, a sequence of phase-shifted interferograms of virtual wavelengths.

[0055] The internal architecture of an artificial intelligence algorithm model can be arbitrary, such as CNN, GAN, Transformer, etc., as long as it implements steps S31 to S34.

[0056] S4. Based on the principle of dual-wavelength interferometry, the absolute phase of the surface under test is calculated according to the experimental interferogram set and the virtual wavelength phase-shifted interferogram sequence to eliminate the inherent 2π periodic ambiguity problem in single-wavelength interferometry and obtain a globally unique phase distribution result. This includes:

[0057] S41. Calculate the wrapping phase of the true wavelength interferogram. For the interferogram with wavelength λ1... The corresponding package phase distribution is obtained by processing using the standard phase shift algorithm. .

[0058] The described phase distribution is a phase result limited to a 2π period range. It is only used to characterize the local phase change information of the surface under test and cannot be directly used to solve for the absolute height.

[0059] S42. Calculate the wrapping phase of the virtual wavelength interferogram. For a virtual interferogram with wavelength λ2... The corresponding package phase distribution is obtained by using a phase shift algorithm. ;

[0060] Since the virtual wavelength interferogram and the interferogram under the real wavelength originate from the same surface under test, their phase information maintains a consistent physical correspondence with the real morphology of the surface under test, and can be used as the second wavelength information in the dual-wavelength joint solution to participate in subsequent calculations.

[0061] S43. Calculate the absolute phase of the surface under test based on the enveloping phase of the real wavelength interferogram and the virtual wavelength interferogram.

[0062] First, based on the principle of dual-wavelength interferometry, the synthesized wavelength Λ is constructed, and its expression is:

[0063]

[0064] in, This represents the operating wavelength corresponding to the actual acquired interferogram. This indicates the target wavelength corresponding to the virtual interferogram.

[0065] Then calculate and The normalized difference between the phases of the two wavelengths is used to obtain the absolute phase of the surface under test. The formula is:

[0066]

[0067] Here, unwrap represents the phase unwrap operation.

[0068] Since the synthesized wavelength Λ is much larger than the single wavelength λ1 or λ2, the corresponding equivalent phase change is smoother, which can significantly reduce the risk of phase jumps during the phase unfolding process, thereby reducing the probability of unfolding errors and improving the stability and accuracy of absolute phase recovery.

[0069] Through the above steps, an equivalent dual-wavelength measurement process can be constructed using real wavelength interferograms and artificial intelligence-generated virtual wavelength interferograms without the need for an additional multi-wavelength hardware acquisition system, thereby achieving reliable recovery of the absolute phase of the surface under test.

[0070] S5. Calculate the absolute step height based on the absolute phase of the surface to be measured.

[0071] Based on the correspondence between phase and optical path difference in interferometry, the absolute phase is converted into a physical height distribution using the following formula:

[0072]

[0073] Where h represents the absolute height of the surface under test at each location, and λ1 represents the wavelength used to actually acquire the interferogram.

[0074] This allows us to obtain the absolute height distribution of the area under test and further obtain the absolute height value of the stepped structure. Since the height results are calculated based on absolute phase, they are not affected by 2π phase ambiguity and have global consistency and clear physical meaning.

[0075] Example 2:

[0076] This embodiment includes an artificial intelligence-based method for measuring absolute step error in a single exposure. The difference from Embodiment 1 is that this embodiment mainly describes the pre-training of the artificial intelligence algorithm model before its use.

[0077] Pre-training refers to the process of adjusting model parameters using training data, including but not limited to supervised learning, semi-supervised learning, unsupervised learning, and reinforcement learning modes; fixed learning rate or adaptive learning rate adjustment strategies can be used; the standard for completing model training is that the image metrics on the test set reach the expected level.

[0078] For the interferogram generation task involved in this application, the core of training lies not only in pixel-level accuracy but also in the consistency of fringe structure and physical response. Therefore, the loss function can include: spatial domain loss function, frequency domain loss function, phase loss function, and Piston loss function. Specifically:

[0079] The spatial loss function is used to constrain the consistency between the generated interferogram and the real interferogram in the spatial domain, ensuring accurate reconstruction of grayscale distribution and local structure. In addition to pixel-level differences, gradient constraints and structural similarity constraints can be further introduced to enhance the model's ability to preserve fringe orientation, edge positions, and local morphology. Through spatial constraints, the generated result can closely approximate the real interferogram in both grayscale values ​​and fringe structure.

[0080] The frequency domain loss function is used to constrain the consistency of the generated interferogram's spectral distribution, ensuring that the periodic structure and overall frequency characteristics of the fringes match the real interferogram. Specifically, constraints can be applied to the amplitude information, phase information, and overall differences in the complex domain, thereby simultaneously considering fringe density, directional distribution, and structural positional relationships. Through frequency domain constraints, the generated result can have the correct fringe morphology in the spatial domain while also conforming to the physical laws of interferometric imaging in the frequency domain.

[0081] The phase loss function and the piston loss function are used to ensure the accuracy of the generated virtual interferogram in subsequent physical calculations. The phase loss function is used to constrain the consistency between the phase result calculated from the virtual interferogram and the true phase; the piston loss function is used to constrain the composite wavelength phase (i.e., the overall optical path difference component) calculated jointly by the true wavelength interferogram and the virtual wavelength interferogram.

[0082] By applying the above constraints, the model can not only generate reasonable interference fringes, but also maintain good physical consistency in phase retrieval and absolute height measurement tasks.

[0083] Pre-trained artificial intelligence algorithm models are used to generate inference.

[0084] If the four-step phase shift method is used to solve the problem, typical reasoning scenarios include:

[0085] 1. Model input: Phase shift at wavelength λ1 =m (m= Single-frame interferogram Model output: Phase shift at wavelength λ2 =m single-frame interferogram .

[0086] 2. Model input: Phase shift at wavelength λ1 ={ 4-frame interferogram Model output: Phase shift at wavelength λ2 ={ 4-frame interferogram .

[0087] If the two-step phase shift method is used to solve the problem, typical reasoning scenarios include:

[0088] 1. Model input: Phase shift at wavelength λ1 =m (m= Single-frame interferogram Model output: Phase shift at wavelength λ2 =m single-frame interferogram .

[0089] 2. Model input: Phase shift at wavelength λ1 ={ } 2-frame interferogram { , , , Model output: Phase shift at wavelength λ2 ={ } 2-frame interferogram { , , , }

[0090] Finally, it should be noted that the above description only depicts some embodiments of this application. For those skilled in the art, various changes, modifications, substitutions, and variations can be conceived of these embodiments without departing from the principles and spirit of this application. The scope of protection of this application is defined by the appended claims and their equivalents, and all the above-mentioned behaviors should be covered within the scope of protection of this application.

Claims

1. A method for measuring absolute step error in a single exposure based on artificial intelligence, characterized in that, include: S1. Using a single-wavelength interferometer, the sample containing the step structure to be tested is exposed and measured with a light source of wavelength λ1 to obtain an experimental interferogram set; S2. Normalize and perform binary masking on the experimental interferogram set to obtain a preprocessed interferogram sequence; S3. Establish an artificial intelligence algorithm model for virtual multi-wavelength step interferometry. The artificial intelligence algorithm model processes the preprocessed interferogram sequence to generate a virtual wavelength phase-shifted interferogram sequence. The artificial intelligence algorithm model is used to generate virtual multi-wavelength phase-shift interferograms. The model is pre-trained before use. The process of constructing the training dataset includes: Step 1: Using a light source with wavelength λ2 as the simulation condition, perform exposure measurement simulation, where λ2≠λ1, and obtain high-confidence samples as the simulation interferogram set; Step 2: Based on the experimental interferogram set and the simulation interferogram set, construct the model input data and model label data; The pre-training process uses loss functions including: spatial domain loss function, frequency domain loss function, phase loss function, and Piston loss function. The spatial domain loss function is used to constrain the consistency between the generated interferogram and the real interferogram in the spatial domain. The frequency domain loss function is used to constrain the consistency of the generated interferogram in the spectral distribution; The phase loss function and the piston loss function are used to constrain the consistency between the phase result calculated from the virtual interferogram and the real phase, and the piston loss function is used to constrain the composite wavelength phase calculated from the real wavelength interferogram and the virtual wavelength interferogram. S4. Based on the principle of dual-wavelength interference, calculate the absolute phase of the surface under test according to the experimental interferogram set and the virtual wavelength phase-shifted interferogram sequence; the calculation of the absolute phase of the surface under test includes: S41. Calculate the wrapping phase of the true wavelength interferogram; S42. Calculate the wrapping phase of the virtual wavelength interferogram; S43. Calculate the absolute phase of the surface under test based on the enveloping phase of the real wavelength interferogram and the virtual wavelength interferogram; S5. Calculate the absolute step height based on the absolute phase of the surface to be measured.

2. The method for measuring absolute step-type error in a single exposure based on artificial intelligence according to claim 1, characterized in that, The binary mask processing determines whether there is a specific pupil shape in the optical path that makes the acquired image not a full field of view; if so, the binary mask is multiplied with the input interferogram to divide the effective region and inform the model for discrimination; if not, no additional processing is performed.

3. The method for measuring absolute step error in a single exposure based on artificial intelligence according to claim 1, characterized in that, The simulated interferogram set also incorporates noise into the samples to form new samples; The methods used to add noise include: simulating two test surfaces on the sample of the simulated interferogram atlas, and forming a step by adjusting the height difference between the two surfaces; The surface to be tested is generated through simulation in the following ways: For samples with circular pupils, the surface profile of the test surface is generated using Zernike polynomial simulation; For samples with square pupils, the surface profile of the test surface is generated using Legendre polynomial simulation; For samples with irregularly shaped pupils, the surface shape of the test surface is generated by Zernike polynomial or Legendre polynomial simulation, and then the target area is defined by a 0-1 binary mask.

4. The method for measuring absolute step error in a single exposure based on artificial intelligence according to claim 3, characterized in that, The order of the polynomial is no less than 3 and no more than 10.

5. The method for measuring absolute step error in a single exposure based on artificial intelligence according to claim 1, characterized in that, The data processing methods of artificial intelligence algorithm models include: S31. Obtain the interferogram sequence at wavelength λ1. Based on the multi-stage structure design, perform feature extraction or downsampling on the input interferogram to obtain the output features of different channels. S32. Perform scale unification, feature alignment, and feature fusion on the output features of each channel to obtain fused features; S33. Perform conditional reasoning or upsampling on the fusion features to obtain a virtual phase-shifting interferogram; S34. Define the effective region of the virtual phase-shifting interferogram and output the interferogram sequence at wavelength λ2.

6. The method for measuring absolute step error in a single exposure based on artificial intelligence according to claim 5, characterized in that, The multi-stage structural design adopts one or more of the following designs: In the spatial processing of the main stage of the multi-stage structure, an additional receptive field visual perception module or attention mechanism module is introduced. Introducing implicit neural representation for downsampling, the interferogram is first represented as... The implicit function is then used to encode the amplitude A and phase. Finally, downsampling is converted into network parameter compression to achieve arbitrary resolution reconstruction during inference; Contrast-aware channel attention is used to deweight or enhance features in low-contrast regions; Retinex style decomposition is introduced to decompose the interferogram into stripe structures and slowly changing backgrounds, which are then processed separately. Frequency domain learning is performed at a certain stage in the multi-stage structure. The amplitude map and phase map are obtained by performing Fourier transform on the input interferogram, and the amplitude domain features and phase domain features are learned respectively.

7. The method for measuring absolute step error in a single exposure based on artificial intelligence according to claim 5, characterized in that, The conditional inference or upsampling of the fused features may employ one or more of the following designs: Introduce additional receptive fields in the spatial processing of the main phase structure, such as visual perception modules or attention mechanisms. Learn the characteristic mapping relationships of the input interferogram and the phase-shifted interferogram in the amplitude domain and phase domain, respectively.

8. The method for measuring absolute step error in a single exposure based on artificial intelligence according to claim 1, characterized in that, The calculation of the absolute phase of the surface under test includes: constructing a synthesized wavelength based on the principle of two-wavelength interferometry; calculating... and The normalized difference between the phases of the two wavelengths is used to obtain the absolute phase of the surface under test.

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