Galaxy clusters are some of the largest known structures in the universe. Studying them observationally and theoretically can provide a lot of information on how these clusters form and are structured. One way to study them is through the so-called Sunyaev-Zel’dovich (SZ) effect, which is an interaction between the cosmic microwave background (CMB) and hot electrons in the cluster medium. The SZ effect can be further broken down into a thermal component (tSZ) arising from the random motion of the electrons, and a kinematic component (kSZ) arising from the bulk motion of the cluster medium, making it a good probe for several properties of the cluster. The SZ effect can be observed as a distortion of the CMB spectrum using submillimeter spectrometry. However, at many submillimeter frequencies radiation is absorbed strongly by the atmosphere. This makes it hard to interpret the measured SZ signal, and measurements require long observation times in order to reach a sufficient signal-to-noise ratio. In this thesis, we present a framework that simulates a submillimeter spectrometer observation of the tSZ effect including noise factors. It then fits a model tSZ signal to the noisy signal. This allows us to investigate the relation between observation time, noise and retrievability of cluster properties. We simulate a galaxy cluster with an electron temperature 𝑇𝑒 = 15.3 keV and central optical depth 𝜏𝑒 = 0.0172 with two simulated DESHIMA-type filterbanks spanning different frequency ranges. For each filterbank we perform 20 simulations with an observation time of 16 hours each, and 20 simulations of 32 hours. We fit every simulation separately, but average over simulations to obtain an expectation value for 𝑇𝑒 and 𝜏𝑒 given a filterbank and observation time. We also repeat each fit over rebinned copies of the noisy spectra, combining 7 data points into each bin. All tested combinations of filterbanks and observation times produce fits with results that are consistent with the input parameters. The 160-320 GHz filterbank consistently gives lower errors than the 220-440 GHz filterbank. From rebinning, we do not find any significant improvement or degradation of the quality of the fits. The estimates obtained from rebinned data deviate very little from the original estimates, by at most 5%, and show no change in consistency. From this result, we conclude that SZ observations using DESHIMA 2.0 could provide estimates on cluster parameters. These estimates are already consistent after 16 or 32 hours of observation time. However, we recommend a new filterbank design that covers 160-320 GHz since the error on estimates using this range are smaller than the errors obtained using the original 220-440 GHz filterbank. This is likely due to the atmosphere absorbing much less radiation at this frequency range. Additionally, the results from rebinning show that this new filterbank could contain fewer filters with a lower resolving power without degradation of fit quality.

A gas-cell-based calibration setup was designed to evaluate the wideband response of sub-millimeter spectrometers like DESHIMA (DEep Spectroscopic High-redshift MApper). The use of low pressure gas emission spectra allowed for accurate calibration of the absolute frequency response, and to test the detectability of faint emission spectra with long integration times. This is important to understand and evaluate systematic errors and noise profiles of sub-millimeter astronomical spectrometers before their telescope campaigns.

The setup consisted of a low pressure (~mbar) gas at room temperature in a high vacuum (<10^-3 mbar) chamber in front of a 77K N₂ background. A double-winged rotating chopper was used for signal modulation of the on- and off-source paths to reduce the low-frequency noise profile. The setup has been able to successfully detect the emission spectra of nitrous oxide at 30 mbar and methanol at 1 mbar in the frequency range of 332 to 377 GHz with the prototype DESHIMA spectrometer. Our models showed that lower pressures should be detectable over similar averaging times. The standing spectrum showed to be too irregular for detecting spectral lines in a single measurement. A second measurement was required to subtract the standing features, which extended the total time required beyond the current system stability.

Detailed analysis into optical resonances has shown the importance of anti-reflective (AR) coatings on the main optical interfaces to improve the detectability of the emission spectra. We adapted sub-wavelength pyramid gratings milled into TOPAS windows to reduce a standing wave in the output spectrum of the gas cell setup. Stability of the setup was shown for observation times of up to ~10³ seconds before environmental
noises became dominant. Extensive stability testing has shown the impact of key components in the setup. A two-stage post-processing algorithm was developed to successfully reduce instabilities in the data by removing linear drifts and by removing the common profile over simultaneous read-out data.