Log-periodic temporal apertures for grating lobe suppression in k-space tomography

Millimeter-wave (mmW) imaging receivers have demonstrated the ability to sense radio-frequency (RF) waves using traditional phased antenna array techniques, and, through a coherent photonic up-conversion process, image these waves using free-space optical systems. Building upon the idea of coherent up-conversion, k-space tomography extends the functionality of the millimeter-wave imaging receiver as a two-dimensional spatial processing unit to three-dimensional sensing with the addition of frequency detection. In this configuration, an arrayed waveguide grating, or temporal aperture, is implemented following the photonic up-conversion of RF signals received by the phased array. These waveguides of varying length add a spectral beam-forming network to the existing spatial beam-forming of the mmW-imaging receiver. The introduction of three-dimensional phase information to the imaging system disrupts the ability to directly image the RF signal distribution on a photo-detector array, requiring the application of tomographic algorithms to reconstruct the power distribution of the received signals. In order to receive and properly recover the spatial-spectral distribution of RF sources, the antenna array and temporal array must be sampled adequately to avoid introduction of grating artifacts into the system response. Grating lobes, an artifact of regular spacing of elements within a grating, restrict the alias-free field of regard for antenna arrays, or the free spectral range for time-delay based arrays, thus limiting the spatial-spectral monitoring of RF sources via the k-space imaging modality. To alleviate this constraint, we present a non-uniform log-periodic array sampling for the k-space tomographic time-delay based aperture, greatly increasing the free spectral range of the system while maintaining the number of existing channels.