Optimum Two-Dimensional Uniform Spatial Sampling for Microwave SAR-Based NDE Imaging Systems

Microwave imaging systems for nondestructive evaluation, based on 3-D synthetic aperture radar (SAR) techniques, utilize either a real aperture, composed of many antennas mounted next to one another, or a synthetic aperture, generated by raster scanning a single antenna. To obtain a quality SAR image, the spatial sampling must be dense enough to accurately sample the electric field reflected from a target. Conversely, the quantity of spatial samples may be optimally reduced, resulting in reduced system complexity and required resources for systems employing real apertures and reduced imaging time for synthetic aperture systems. In the literature, it has been reported that the optimum sampling step size is equal to the theoretical resolution, as per the Nyquist rate. It has also been reported that an image generated using a sampling step size equal to the theoretical resolution may not possess the same spatial resolution as predicted. Also, as expected and reported, resolution is dependent upon the distance between the target and the aperture, aperture dimensions, and antenna beamwidth. However, existing formulations of SAR resolution do not account for all of the physical characteristics of a measurement (e.g., 2-D limited-size aperture, electric field decreasing with distance from the measuring antenna, etc.). This paper presents a theoretical formulation of resolution and a study into optimum uniform spatial sampling by analyzing simulated 3-D SAR images according to metrics representing image quality, namely, half-power resolution and RMS error between practically sampled images and an ideally sampled image. The results of this simulation demonstrate optimum sampling given design requirements that fully explain resolution dependence on sampling step size. Also, it is found that there is additional widening of the 2-D spectral estimation of the data due to the aperture-limited nature of the measurements, which further influences the choice of sampling step size. Subsequently, the simulated results are compared to experimental results corroborating the efficacy of the formulation. Finally, design curves and procedures are proposed for selecting sampling step size as per resolution requirements.