Relaxation of Alignment Errors and Phase Calibration in Computational Frequency-Diverse Imaging using Phase Retrieval

We demonstrate a computational, frequency-diverse, phaseless imaging technique at microwave frequencies that minimizes the impacts of phase calibration and alignment errors on image reconstruction. Phase calibration error is introduced by means of misaligning the sub-antennas forming an aperture, causing unwanted phase shifts between the forward model and adjoint operation. It is shown that by leveraging phase retrieval techniques, distinguishable images can still be reconstructed in the presence of significant phase errors, while complex-based reconstructions - those relying on measurement of both phase and amplitude - produce heavily corrupted images. Using a frequency-diverse imaging system consisting of a cavity-backed metasurface antenna that operates at microwave frequencies in the K-band (17.5-26.5 GHz), we demonstrate the complex-based and phaseless images of various objects, from a simple subwavelength conducting element to more complex metal structures. We verify that the combination of the phase retrieval approach with the frequency-diverse imager significantly improves the robustness of the composite imaging system to phase errors. While frequency-diverse computational imaging systems have significant advantages in terms of hardware, their reliance on a near-exact forward model places heavy requirements on system calibration. The phase retrieval approach developed here has the potential to alleviate this reliance, increasing the feasibility of such systems.