The Deep Spectroscopic High-redshift Mapper, or DESHIMA, is an integrated superconducting spectrometer which measures the redshift of photons originating from submillimeter galaxies. These photons have to travel through the Earth's atmosphere before arriving at DESHIMA, but this atmosphere adds noise to the signal. Using a principal component analysis on still-sky measurement data, the influence of the atmospheric noise on these observations is analyzed. To achieve this, several principal component analyses are performed on still-sky observations, which are measurements of the brightness temperature of the sky, Tsky. These observations are assumed to be governed by three noise types: atmospheric noise, photon noise, and detector 1=f noise. A PCA on a still-sky observation reveals the effect of the most dominant noise sources. By creating an artificial data set, the physical origin of these noise sources can be found. This data set was produced by using an existing atmospheric model, based on the fluctuation of the precipitable water vapour, or PWV, in the atmosphere. A principal component analysis on this artificial data set reveals the effect of this PWV fluctuation on the data. The first principal component of the artificial data is found to represent the derivatives of the Tsky-PWV relations for every channel. The second principal component has a non-zero explained variance and is found to represent the second-order derivatives of the
Tsky-PWV relations for every channel, indicating that these relations are not linear. This can be explained by performing a Taylor expansion on the Tsky-PWV relation. Comparing the principal components of the real data to those of the artificial data shows that the first principal component generally has the same shape as the fist principal component of the artificial data, which represents the first-order PWV fluctuation, confirming that PWV fluctuation is the most dominant noise source for still-sky observations. It is also found that, when the PWV fluctuation is large, the second-order Taylor expansion term of the Tsky-PWV generally becomes more important in the real data. In this case, the first
principal component has a very high explained variance, and the second-order term is usually represented by the second principal component. Conversely, when the PWV range is small, the first-order term explains significantly less variance, and random noise like the photon noise becomes more dominant than the higher-order terms. The results show a few exceptions to this interpretation, so further research on these systematic errors is strongly recommended. In order to achieve better results, the experimental method can be improved by including the bandwidths of the channels and better estimation of the PWV fluctuation. This research can also be extended into a design of a random noise level and ultimately, the design of a better atmosphere calibration method for DESHIMA.