## 4 Discussion  
With the above results, we present a versatile technique for THz spectral imaging. In the following, we will discuss several aspects in view of future use. Two scanning methods were used, either scanning the sample very close to the aperture or scanning at a distance and using holographic reconstruction. The use of a small aperture close to the sample was key to a decent resolution, including the longer wavelengths. It allows us to overcome the resolution limit given by the wavelength and the small numerical aperture of the setup. Apart from the wavelength, the limiting factors for resolution are mask aperture, sample distance, and sample thickness. Estimated resolutions extracted from the images in Figures 5-7 are summarized in Table 1. They illustrate that, using an aperture mask, the resolution is not governed by the limit given by Equation (3) but rather by the size of the aperture mask. The presented simulation of the imaging method is in good agreement with the measurements. It can be used to optimize the setup for a specific imaging task. The annual ring structure of wood samples is imaged nicely, and the polarisation-dependent images are consistent with a structured birefringent material. The increasing \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **0.5 THz** & **1.0 THz** & **1.5 THz** & **2.0 THz** \\ \hline without mask & & 1.69 mm & 1.23 mm & 0.95 mm \\ \hline \(d_{\text{mask}}=0.5\) mm, \(\Delta z=0.5\) mm & 0.90 mm & 0.80 mm & 0.58 mm & 0.48 mm \\ \hline \(d_{\text{mask}}=0.5\) mm, \(\Delta z=5.0\) mm (holographic reconstruction) & 0.97 mm & 0.76 mm & 0.66 mm & 0.62 mm \\ \hline resolution limit (Equation (3)) & 2.14 mm & 1.07 mm & 0.71 mm & 0.54 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Resolutions for selected frequencies compared to resolution limit. Figure 9: Intensity (top row) and phase images (bottom row) at 0.5 THz for wood sample #2 for measurements at different polarizer orientations [\(P_{1}\), \(P_{2}\)]: **a)** [45\({}^{\circ}\), 45\({}^{\circ}\)]; **b)** [135\({}^{\circ}\), 135\({}^{\circ}\)]; **c)** [135\({}^{\circ}\), 45\({}^{\circ}\)]; **d)** [45\({}^{\circ}\), 135\({}^{\circ}\)]. absorption of THz radiation with frequency puts an upper limit of about 2 THz for imaging wood structures. A local mapping of refractive indices and extinction coefficients is not straightforward due to diffraction and interference effects within a sample of a thickness exceeding the wavelength. Here, modelling using multilayer field propagation could give more insights. The use of holographic reconstruction has the potential for imaging structures embedded in a homogenous matrix or a micro-fluidic device. Furthermore, it allows reconstruction to curved sample surfaces from a planar scan. In order to increase the accuracy of the reconstruction, the illuminated region of the sample could be increased. However, this might negatively impact the intensity passed through the aperture. One may argue that the scanning of a sample close to a mask does not correspond to a holographic data collection. This would only be the case if the sample were illuminated by an infinite plane wave. In this case, scanning a sample before a fixed mask would be equivalent to scanning a mask (representing a pixel of a camera) before a fixed sample. However, the reconstruction works well for a focusing illumination of limited spot size. If holographic reconstruction is used, the spot size on the sample can be optimized in order to allow for proper reconstruction, but still maintaining enough intensity hitting the aperture. A spot size in the order of \(\Delta z\) seems reasonable. The use of the robot is a new approach compared to traditional XY stages, where only the sample can be scanned. It offers a more flexible way to position the sample. It allows changing the distance to the aperture mask, and the sample can be put in different orientations with respect to the polarization of the incident light.