A Wavenumber Domain Consistent Imaging Method Based on High-Order Fourier Series Fitting Compensation for Optical/SAR Co-Aperture System

Optical and SAR image registration and fusion are pivotal in the remote sensing field, as they leverage the complementary advantages of both modalities. However, achieving this with high accuracy and efficiency remains challenging. This challenge arises because traditional methods are confined to the image domain, applied after independent image formation. They attempt to correct geometric mismatches that are rooted in fundamental physical differences, an approach that inherently struggles to achieve both precision and speed. Therefore, this paper introduces a co-designed system and algorithm framework to overcome the fundamental challenges. At the system level, we pioneer an innovative airborne co-aperture system to ensure synchronous data acquisition. At the algorithmic level, we derive a theoretical model within the wavenumber domain imaging process, attributing optical/SAR pixel deviations to the deterministic phase errors introduced by its core Stolt interpolation operation. This model enables a signal-domain compensation technique, which employs high-order Fourier series fitting to correct these errors during the SAR image formation itself. This co-design yields a unified processing pipeline that achieves direct, sub-pixel co-registration, thereby establishing a foundational paradigm for real-time multi-source data processing. The experimental results on both multi-point and structural targets confirm that our method achieves sub-pixel registration accuracy across diverse scenarios, accompanied by a marked gain in computational efficiency over the time-domain approach.