Wavelet-Enhanced Physics-Informed Complex-Valued CNN for Satellite Camera Alignment using Interferograms

To acquire diffraction-limited imagery, high-resolution satellite camera systems must be precisely aligned. Optical aberrations caused by misalignments, often detected using interferometry, can significantly degrade performance. We propose an enhanced deep learning framework for real-time alignment correction that combines a Complex-Valued Convolutional Neural Network (Complex CNN) architecture with wavelet-based preprocessing. First, interferograms are decomposed using a discrete wavelet transform to separate amplitude and phase components, enabling more effective extraction of their intrinsic complex characteristics. The classical CNN architecture is then reformulated into a fully complex-valued structure by modifying both the feedforward and backpropagation stages to properly handle complex-valued inputs and gradients. To further improve performance and interpretability, Zernike polynomial coefficients—mathematical descriptors of optical aberrations—are incorporated as additional inputs, creating a physics-informed learning process. Using a simulated dataset of satellite interferograms, we evaluate the proposed Wavelet-Enhanced Zernike Complex CNN and demonstrate its robustness and accuracy in predicting and correcting optical misalignments.