Abstract
This paper reveals a counterintuitive, non-monotonic dependence of terahertz coded-aperture imaging (TCAI) performance on the imaging range. This phenomenon stems from phase-induced spatiotemporal correlations in the reference-signal matrix (RSM), governed by the wavefront phase interactions between the coded-aperture elements and scatterers on the imaging plane. Image quality deteriorates noticeably when a specific dimensionless criterion, which is defined mathematically and physically in this work, precisely reaches integer values. Under such conditions, the relative phase difference concentrates or clusters into discrete values determined by the imaging range, leading to strong column and row correlations in RSM that compromise the spatiotemporal independence essential for high-quality reconstruction. For imaging ranges exceeding the critical threshold determined by the number of grid points along one dimension of the imaging plane, two degradation mechanisms emerge: increased correlation between RSM columns mapping to directly adjacent scatterers and phase coverage reduction in wavefront encoding. Both effects intensify as the imaging range increases, resulting in a monotonic deterioration of imaging performance. Crucially, reconstruction fails primarily when strong correlations involve dominant scatterers, whereas correlations among non-dominant (dummy) scatterers have a negligible impact. The Two-step Iterative Shrinkage/Thresholding (TwIST) algorithm demonstrates superior robustness under these challenging conditions compared to some other conventional methods. These insights provide practical guidance for optimizing TCAI system design and operational range selection to avoid performance degradation zones.