Parabolic Equation Methods for Terahertz 3-D Synthetic Aperture Imaging

Terahertz (THz) imaging has shown great potential for nondestructive evaluation of a wide variety of manufactured products composed of nonpolar dielectric materials. Recent work by the authors and others has demonstrated the ability to produce three-dimensional (3-D) THz tomographic images of such objects using a single dataset collected in a 2-D synthetic aperture configuration. However, the irregular surface topographies of many objects of interest introduce refractive effects that distort the tomographic images of the object's interior. This paper presents a novel physics-based approach to correct these refractive effects using parabolic equation methods common to undersea acoustics, seismology, and recently adapted for ground-penetrating radar and biomedical ultrasound. The ability of this method to estimate the thickness of a curved dielectric layer in a specially designed 3-D printed test object is demonstrated using experimental data. The error due to approximations made in the method's derivation is also analyzed and used to select simulation test cases to examine the effect of the approximation error on the accuracy of the resulting thicknesses estimates.