## 2 Peculiarities of ATR Measurements
### Combined Spectral Filters and Polarisers  
A toolbox of spectral filters and polarisers are required to fully explore the potential of spectroscopy for material characterisation. Such a toolbox is less developed for the THz spectral range. However, due to the low-resolution photolithography required for longer sub-millimetre wavelengths, spectral filters can be easily made based on a square lattice (Figure 8a). Here, we introduce the concept of filter multiplexing for control over the transmission wavelength, bandpass, and amplitude. Such comb filters can be made by direct laser cutting [37] from a metal foil or by standard photolithography. For the chosen wavelength \(\lambda_{THz}\) [\(\mu\)m], the period \(P=0.78393\times\lambda_{THz}\), the length of cross opening \(L=0.50897\times\lambda_{7 Hz}\), and the width of the opening \(W=0.1482\times\lambda_{7 Hz}\)[38; 39]. The typical 10-15% bandwidth \(\Delta\lambda/\lambda_{0}\) for the geometry defined above becomes smaller as the \(P/L\) and \(P/W\) ratios are increased, while the centre frequency of the band-pass filter is mainly dependent on the cross-member length \(L\). It is demonstrated that transmission \(T>0.9\) can be obtained using micrometer-thick Cu-foil within the 0.5-2 THz spectral range, using the presented scaling [38]. With the known spectral profile of the synchrotron source (inset of Figure 8b), it is possible to design a transmission mask, which filters spectral bands and sets their intensities. Such filters are numerically designed to produce a comb of THz frequencies (five for the pattern shown in Figure 8b). As is known, it is desirable to have a uniform spectral response such that the gain of the bolometer can be precisely set in advance. The spectral profile can be precisely engineered by spatially multiplexing cross-filter designs corresponding to different wavenumbers. The first method is a super-pixel type spatial multiplexing, where every pixel of the mask is formed by the mosaic of the building block of the different filters. A super-pixel design with \(5\times 5\) elements is shown in Figure 9a. This is the most straightforward approach, but results in undesirable diffraction orders due to the periodic configuration. The second approach uses a random phase mask. In principle, any random phase mask will work, but in order to allow at least certain number of crosses of the same type, it is crucial to engineer the scattering ratio of the random phase mask. Such quasi-random phase masks can be synthesized using the well-known Gerchberg-Saxton algorithm (GSA) by giving the scattering ratio as the input [41]. The schematic of the GSA is shown in Figure 9b. The algorithm begins with a complex amplitude consisting of a uniform amplitude and random phase function at Plane 1, which is Fourier transformed. The amplitude in Plane 2 is replaced by a uniform amplitude within a predefined area, which decides the scattering degree given as \(\sigma=d/D\), where \(d\) is the length of the predefined area and \(D\) is the length of the total area. The output of the GSA is a quasi-random phase mask, consisting of grey levels from 0 to \(2\pi\). As the area of every different phase level is equal, different grey level ranges can be set to different filters. By controlling the relative ranges, the relative intensity responses can be manipulated. The images of a section of spatially randomly multiplexed cross-filters for \(\sigma=0.1\), \(\sigma=0.15\) and \(\sigma=0.2\) are shown in Figure 9c-e, respectively. The use of photolithography on thick 20-500 \(\upmu\)m SU8 laminates (SUEX from DJ Microlaminates Ltd.) is particularly appealing, due to the possibility of retrieving free-standing mesh filters. With a gold (or any other metal) coating, this completes the filter. The SEM images of the mosaic type comb type and randomly multiplexed cross-filters on gold-coated SU8 films on silicon substrate are shown in Figure 9f,g, respectively.