# Terahertz Spiral Spatial Filtering Imaging
###### Abstract  
In this paper, we propose a terahertz (THz) spiral spatial filtering (SSF) imaging method that can enable image contrast enhancement. The related theory includes three main steps: (1) the THz image of the target is Fourier transformed to the spatial spectrum distribution; (2) the spatial spectrum is modulated by a spiral phase at the Fourier plane; (3) the filtered spatial spectrum is inverse Fourier transformed to the desired THz image. Meanwhile, analytic expression of the final THz image is derived. Due to the unique nature of the spiral phase, THz image contrast enhancement can be achieved and verified by various simulated target images with different contrasts. In our designed THz SSF imaging system, Fourier transform is carried out by the lens, and the spiral phase is acquired by the spiral phase plate (SPP). Proof-of-principle experiments with three different types of targets (carved metal letters, a high-density polyethylene (HDFE) piece with a scratch, and a leaf) were carried out, and the effectiveness of contrast enhancement and edge extraction on the THz reconstruction images was validated. terahertz imaging; spiral phase; contrast enhancement; edge detection +
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only in amplitude objects but also in phase objects [30]. Inspired by the SSF imaging demonstrated in the visible and infrared range of the electromagnetic spectrum, this technique can be extended to the THz band and is expected to present great opportunities for the enhancement of THz image contrast. SSF imaging originated from radial Hilbert transforms, which was demonstrated by [PERSON] et al. in 2000 [31]. Subsequently, the theories and experiments related to SSF imaging developed further. In 2005, [PERSON] et al. applied SSF imaging to light microscopy [32] and demonstrated that the spiral phase can improve the imaging contrast, with the experiments revealing good image quality. In 2006, [PERSON] et al. proposed a radial Hilbert transformation with Laguerre-Gaussian spatial filters (LGSF) [33] and demonstrated that the LGSF possesses various advantages in comparison with the conventional spiral phase. In 2018, [PERSON] et al. proposed an imaging method in nonlinear optics using a nonlinear spatial filter, where the phase objects--using invisible illumination--can be converted into visible high-contrast images [30]. An early attempt at enhancing THz image contrast was made in 2001 by [PERSON] et al. [34]. They proposed THz dark-field imaging based on the THz time-domain spectrometer (TDS) to enhance image contrast. The THz power was low in this system and the dark-field imaging resulted in the loss of most of the energy, which yielded a low signal to noise ratio (SNR) of the THz images. To improve the image contrast, [PERSON] et al. proposed the Bessel zone plate design based on silicon multi-phase diffractive optics, which was demonstrated in continuous wave mode at 0.6 THz [35]. Despite significant experimental and theoretical progress in this area, SSF imaging at the THz band is still not satisfactory. Here, we propose a THz SSF imaging technique that enables contrast enhancement of the target with low image contrast. THz SSF imaging inherits both the advantages of THz imaging and SSF imaging simultaneously, which is an effective way to enable THz high-contrast imaging. In our work, the SSF imaging principle at the THz frequency is analyzed. Based on such analysis, simulations and experiments were later carried out. From the simulated imaging results, it is noted that the proposed image technique can effectively enhance the image contrast of the target. In the experiments, we built a THz SSF imaging system based on a THz quantum cascade laser (THz-QCL) 4\(f\) imaging system. As it is a light source, the THz-QCL emits a power of 0.3 mW at 3.7 THz. In this 4\(f\) imaging system, a spiral phase plate (SPP) designed from high-density polyethylene (HDPE) at 3.7 THz is placed in the Fourier plane to obtain the spiral phase information.