During the assembly and adjustment process of an off-axis three-mirror optical system, a KAN-Transformer-based (Kolmogorov-Arnold network-Transformer-based) misalignment prediction model is developed to address issues such as the mutual coupling of aberrations due to misalignment, low calculation accuracy, and inefficiency in small-scale misalignments. The model uses 1 to 9 fringe Zernike coefficients derived from system wavefront decomposition across multiple fields of view as inputs. It employs the KAN-Transformer model to predict system misalignment values, which are then iteratively adjusted to complete the assembly process. Experimental results from 1000 misalignment calculations demonstrate that the KAN-Transformer model achieves an average error reduction of 0.0095, 0.0065, and 0.0048 mm compared to back-propagation (BP), KAN, and Transformer models, respectively. This improved accuracy allows precise misalignment calculations, avoids local optima, and better captures the nonlinear relationships between mirror misalignments and system wavefront aberrations in complex optical systems. The method described enhances calculation accuracy under small-scale misalignments by approximately 0.00618 mm. Mean square error (MSE) and mean absolute error (MAE) for the KAN-Transformer model are improved by 44.6% and 73.7%, respectively, compared to BP networks, and by 25.3% and 34.6%, respectively, compared to Transformer networks.

The computer-aided assembly technique for large and complex optical systems utilizes simulations to calculate misalignment values for each optical component, guiding actual assembly and improving efficiency. This approach provides a more precise and efficient solution for assembling and debugging optical systems and is widely used in aerospace, military, and photolithography applications. The prediction model utilizes fringe Zernike coefficient data obtained from the wavefront decomposition of the optical system through an interferometer. It calculates the initial system misalignment using a trained prediction network and subsequently adjusts the optical system with precision to meet design specifications. To improve the accuracy of system misalignment predictions, a large dataset of misalignment values corresponding to the first to ninth fringe Zernike coefficients across five fields of view is proposed. The KAN module replaces the linear transformation layer in the Transformer architecture, resulting in the KAN-Transformer model, which facilitates faster and more accurate calculations of the system’s initial misalignment.

Firstly, a KAN-Transformer neural network model is developed (Fig. 4) and jointly debugged using Zemax and Python. An API script is written to generate a dataset, yielding 10000 sets of imbalanced data for training. The network is trained on this dataset and subsequently used to simulate the installation and adjustment of an off-axis three-mirror optical system. The KAN-Transformer neural network achieves an average absolute error of 0.0012 mm in the case of small-scale misalignment (Fig. 9). After incorporating the misalignment values into the off-axis three-mirror model, the wavefront aberrations are found to be 1.129λ, 1.260λ, and 0.975λ (Fig. 11). When these misalignment values are introduced into the neural network solution, the wavefront aberrations improve significantly to 0.066λ, 0.078λ, and 0.035λ (Fig. 12), meeting the system design requirements. Further analysis of 1000 different networks reveals that installation and adjustment prediction errors are significantly larger with the BP neural network, which has an average error of 0.0104 mm. The KAN neural network shows an average error of 0.0057 mm, while the Transformer neural network has an average error of 0.0074 mm. The KAN-Transformer neural network outperforms all others with the smallest average error of 0.0009 mm (Fig. 13). To verify whether the model can effectively guide real-world installation and adjustment, 1000 sets of simulated F(0°, 0°), F(0°, 2°), F(2°, 2°) field-of-view PV error values and RMS error values of the off-axis three-mirror optical system are analyzed. The results indicate that compared to the central field of view, the PV error and RMS errors increase in the F(2°, 2°) and F(0°, 2°) fields of view. As the field-of-view angle increases, changes in the specular reflection direction cause greater deviations in the light propagation path, resulting in the gradual accumulation of wavefront errors and higher error values. However, these errors remain within acceptable limits, demonstrating that the KAN-Transformer misalignment prediction model provides sufficient accuracy to guide the actual installation and adjustment process (Fig. 14).

The traditional sensitivity matrix method establishes the relationship between misalignment and aberration, solving it using mathematical models. In contrast, neural networks train on large datasets to understand the influence of misalignment on image quality, enabling non-analytical misalignment calculations. This approach avoids relying on exact representations of imaging forms and misalignment parameters, making it better suited for the increasingly complex tuning of optical systems. To achieve more accurate misalignment calculations after initial adjustments and reduce the number of iterations required, we propose an optical system misalignment prediction model based on KAN-Transformer. By integrating the KAN structure into the Transformer neural network, the model’s nonlinear representation capability is enhanced, improving accuracy for small-scale misalignment calculations and enabling non-analytical system misalignment determination. The MSE and MAE mean values of the KAN-Transformer model are 41.2% and 62.4% of those for the KAN neural network and 22.2% and 50.7% of those for the BP neural network, respectively, demonstrating superior prediction accuracy and generalization ability. For small-scale misalignments, the KAN-Transformer achieves a calculation accuracy of about 0.0008 mm, outperforming the Transformer model. Simulations and adjustments of off-axis three-mirror optical systems verify that the KAN-Transformer provides significantly higher accuracy, proving its ability to effectively guide actual assembly.