Developing terahertz imaging equation and enhancement of the resolution of terahertz images using deconvolution

This paper introduces a novel reconstruction approach for enhancing the resolution of the terahertz (THz) images. For this purpose the THz imaging equation is derived. According to our best knowledge we are reporting the first THz imaging equation by this paper. This imaging equation is universal for THz far-field imaging systems and can be used for analyzing, describing and modeling of these systems. The geometry and behavior of Gaussian beams in far-field region imply that the FWHM of the THz beams diverge as the frequencies of the beams decrease. Thus, the resolution of the measurement decreases in lower frequencies. On the other hand, the depth of penetration of THz beams decreases as frequency increases. Roughly speaking beams in sub 1.5 THz, are transmitted into integrated circuit (IC) packages and the similar packaged objects. Thus, it is not possible to use the THz pulse with higher frequencies in order to achieve higher resolution inspection of packaged items. In this paper, after developing the 3-D THz point spread function (PSF) of the scanning THz beam and then the THz imaging equation, THz images are enhanced through deconvolution of the THz PSF and THz images. As a result, the resolution has been improved several times beyond the physical limitations of the THz measurement setup in the far-field region and sub-Nyquist images have been achieved. Particularly, MSE and SSIḾ have been increased by 27% and 50% respectively. Details as small as 0.2 mm were made visible in the THz images which originally reveals no details smaller than 2.2 mm. In other words the resolution of the images has been increased by 10 times. The accuracy of the reconstructed images was proved by high resolution X-ray images.