More insight has been gathered on the performance of the SPLITTER (Stationary spectrum Plus Low-rank Iterative TransmiTtance EstimatoR) algorithm as developed by Brackenhoff for denoising data gathered from observations of high-redshift galaxies. By using matrix decomposition to split the gathered data into a low-rank atmosphere matrix and a sparse matrix with the signal and photon noise, the algorithm avoids the subtraction of two noisy signals, and therefore the factor of √2 additional noise that comes with it. The algorithm was specifically developed for DESHIMA 2.0 (DEep Spectroscopic HIgh-redshift MApper), a wideband spectrometer that achieves a bandwidth from 220 to 440 GHz, using 347 spectral channels. Previous performance tests of the algorithm included the comparison of the weighted root mean square error between SPLITTER and the usual technique of Direct Subtraction on realistic data simulated using the TiEMPO (Time-dependent End-to-end Model for Post-process Optimization) software package. This resulted in a ~1.7 improvement factor for the whole spectrum and ~1.3 in the emission line area. The performance of SPLITTER on two key components of the spectrum have been analyzed separately. First, the measurement of the continuum has been analyzed by using TiEMPO to create realistic simulations of the observation of custom spectra with a linear continuum. SPLITTER showed to be more precise as the noise level was lower, but less accurate, as there was a systematic offset in the estimated continuum. Using a modified black body model for the continuum and assuming the relative offset is independent of the strength of the continuum, the observed offsets and errors were propagated to offsets in estimations of dust temperature $T_{dust}$ and spectral emissivity of the dust $eta$. Because of the offset, SPLITTER also showed a systematic offset in estimated $T_{dust}$, but as the algorithm is more precise, it performed better at estimating $eta$, since $eta$ determines the shape of the spectrum and has less influence on the strength. Second, to test the detection of emission lines, custom spectra have been created containing the same linear continuum and single spectral line at four different frequencies. Each line was set to have a known signal to noise ratio compared to the photon noise in its frequency bin. The retrieved signal to noise ratio as compared to noise of neighboring bins showed an improvement of ~1.9 for SPLITTER compared to Direct Subtraction for bright lines. Weak lines did not show any improvement in SNR. There seemed to be no correlation between continuum overestimation and emission line measurements. Conclusion is that SPLITTER definitely shows improvement in noise reduction, but comes with an overestimation of the continuum. The consequences of this are that Direct Subtraction is still preferred for estimating dust temperature, but for estimations of spectral emissivity and detection of emission lines, SPLITTER is more robust.

To better understand the formation of stars in dusty star-forming galaxies (DSFGs), and the evolution of this type of submillimeter galaxies (SMGs), it is of high significance to perform submillimeter/far-infrared surveys. The Deep Spectroscopic High-redshift Mapper 2.0 (DESHIMA2.0) on the ASTE telescope in Chile has been designed to observe the redshifted emission lines of these DSFGs to measure both their (spectroscopic) redshifts and molecular compositions. DESHIMA2.0 is designed to observe across the 220-440 GHz frequency band using its 347 channel integrated superconducting spectrometer (ISS) chip. The current DESHIMA2.0 instrument has been tested in the lab. Its 332 filter channels with center frequencies in the range of 204-391 GHz have a spectral resolution of f/δf ≈ 340. Their coupling efficiencies can be approximated by Lorentzian functions. The gravitationally lensed ultraluminous high-redshift DSFG J1329+2243 with redshift z = 2.04 shows emission lines of molecular gases like CO and H2O in the frequency band of DESHIMA2.0. Using the Time-dependent End-to-end Model for Post-process Optimization (TiEMPO), an 8-hour observation of the J1329+2243 galaxy has been simulated for both the lab-measured chip and the designed chip. Two measures of sensitivity, the noise equivalent flux density (NEFD) and the minimum detectable line flux (MDLF), are theoretically derived and subsequently used to be compared with the results of the simulations. The results yielded from these simulations are ultimately used to report on the overall performance of the lab-measured chip. To run a TiEMPO simulation using the lab-measured chip, adaptations had to be made to the model for it to accept customizable chip data. Within TiEMPO, variable spectral resolutions and coupling efficiencies had to be introduced as well as a crucial addition to enable the creation of a new filterbank. Given the results of the simulations, it can be stated that this implementation of the lab-measured chip has been successful. After applying an ON-OFF (dual) sky chopping technique to the simulated observation to cancel fluctuations of the atmospheric transmission, the atmosphere-corrected antenna temperature of the J1329+ 2243 galaxy could be found. The standard deviation of the noise showed to be scaling inversely proportional to the square root of the integration time. For five separate emission lines of the galaxy within the range of 200-310 GHz, a signal-to-noise ratio (SNR) analysis was performed and compared to the estimated theoretical proportionality to the square root of the integration time. For lines that show overlap in the spectrum, the detection was proven to be more difficult. Optimizations in the strategy used to define these signal-to-noise ratios would improve this finding. The performance of the current DESHIMA2.0 instrument is sufficient to detect (SNR≥5) the bright CO(7-6) line of an ultraluminous high-redshift galaxy like J1329+2243 after 5.5 minutes of observation time. After 50 minutes of observation time, it is also capable of identifying the CO(6-5), the H2O(211-202), the [CI](2-1), and the CO(8-7) emission line.

DESHIMA (the Deep Spectroscopic High-Redshift Mapper) is a 347 channel superconducting spectrometer with spectral resolution R =500 that operates in the range of 220GHz to 440GHz and can therefore accurately measure the frequency of spectral lines in order to calculate redshift z. This report investigates the sensitivity of DESHIMA-like spectrometers by investigating photon noise due to Poisson and bunching effects. It gives a broad overview of photon statistics and explains, through an analogous model, that photon bunching occurs due to an underlying change in the probabilistics, rather than the act of detecting itself. After that I investigate photon and quasiparticle recombination noise for a DESHIMA-like spectrometer with Lorentzian filters and find a closed form equation for NEP per channel for a constant power spectral density arriving at the filters. Previously the bandwidth of the filters was assumed to be negligible, resulting in an overestimation of the bunching. Because the photons that are impinging on the detector span a bigger bandwidth, the bunching is a factor of π/2 smaller than previously approximated. This NEPτ is defined at an integration time of τ=0.5s. For other integration times this is scalable, however this will only hold while the integration time is much bigger than the coherence time τ≫tcoh. Because of the correlation between photons arriving shorter than a coherence time apart, the scaling of the NEPτ drops in cases when τ≫̸tcoh. Finally I propose and describe modifications to the sensitivity model DESHIMA uses. The following features have been be improved and added: - Integrate over the entire power spectrum when calculating photon noise - Use arbritatry filter designs loaded from a file - Improve estimations of the quantities that express sensitivity I compare the proposed modifications to the old model, which has previously been compared with measurement results, and use it to validate the changes. Other than the previously mentioned factor of π/2 for the bunching term and the smoothing out in local extrema, the modified simulation results are similar to the old model. This is because the Lorentzian filters have a small bandwidth ν≫Δν, such that the previous narrowband approximation held for most non-extreme cases.