When looking up to the sky and trying to detect the photons of far away stars that are still in formation, we can get access to knowledge we never had before. In order to do this, we must make sure we truly understand the nature of how photons behave in accordance to each other and to our detectors.In quantum optics we can see that these photons have a very dubious character. They are both particle and wave and neither. This makes studying how they are distributed over the spectrum of the submillimeter and millimeter wave astronomy a very big challenge. We know that this very particlewave duality is what makes up the noise that is fundamental to photons. This duality also makes them obey the BoseEinstein statistics. Hence due to their particlelike behavior, we have a noise component that resembles that of a Poisson distribution. Very much like raindrops falling down from the sky. On the other hand we have the wave nature of the photons, this causes them to arrive in bunches rather than these random raindrops. It is observed that photons arriving at a detector are corrrelated.
In this thesis we will be investigating how to incorporate the noise of the bunching of the photons into the model of TiEMPO. This model simulates the signal processing of a measurement done by the wideband spectrometer named DESHIMA. Due to the fact that DESHIMA operates in a wideband frequency range, we do theoretical research that explains the fundamental theory behind calculating the photon noise over this wideband range. We show that taking the wideband integral of the photon noise is mathematically equivalent of summing the narrowband approximation for infinitely many subbands and adding them up top each other. This approach is the previous method of calculating the photon noise over the wideband. Due to this method being valid, the question of how these variances over these smaller subbands can be additive?
Since we are dealing with the detection of photons which as previously stated is a correlated signal. By modeling a simplified version of wideband photon detection, we have come to the conclusion that due to the small coherence time these photons are independent in the wideband signal. The photons in these smaller subbands of the wideband signal can also be viewed as statistically independent. If we decrease the frequency bandwidth, we increase the coherence time. Thus measuring the signal over this subband equates to having a larger uncertainty in time. Hence when a photon is detected in this subband, due to the large coherence time we have that the knowledge of when this photon arrived is mostly lost. Making the time correlations irrelevant to a measurement of an integration time this long.

To study the aerosols in the atmosphere is an important aspect for getting a better understanding of climate change. Therefore, it is important to get accurate observations of aerosols in the atmosphere as well as accurate emission fluxes of aerosol species. Satellite instruments such as SPEXone are able to measure aerosol properties with a high accuracy. Unfortunately, the instrument has a low daily global coverage. To obtain full daily global coverage, methods such as data assimilation are used. However, these methods have a high computational cost. This report investigates the use of neural networks to obtain global daily coverage of aerosol properties and emission fluxes with a lower computational cost. Two networks are trained. One to get global coverages of the aerosol properties Aerosol Optical Depth at 550nm (AOD), Single Scattering Albedo at 550nm (SSA) and ̊Angstr ̈om Exponent between 550nm and 865nm(AE). The other network is trained for global emission fields of the species dimethylsulfide (DMS), sulfur dioxide (SO2), black carbon (BC), organic carbon (OC), sea salt (SS) and dust (DU). The results from these trained networks are compared to the results of a control experiment, which represents our prior knowledge on the aerosol fields and emissions, although not the truth. It is found that the network for aerosol properties has a significant decrease in errors compared to the control experiment. For both AOD and AE, the network has a large improvement, and for SSA the improvement is slightly smaller, likely due to a lower performance of the control experiment compared to AOD and AE. The network for the emissions also has a noticeable improvement over the control experiment for all species except DMS, where there is only a small improvement due to the already accurate DMS value for the control experiment. It is also found that the network for emissions overfits due to too little variation in training and testing data.

In this thesis we are interested in distinguishing patterns of mesoscale cloud patterns in the trades. Specifically, whether Sugar, Gravel, Fish and Flowers patterns can objectively be identified using physical quantities. For this purpose, we use cloud fraction data attained by the CORAL Ka-Band cloud radar at the Barbados Cloud Observatory during the boreal winter seasons of 2018, 2019 and 2020. These cloud fraction data represents the curves up until a height of 4 km for a given 6-hour interval of time. We do this to see if these clusters match up with the labels assigned to each cloud fraction curve obtained from a classification model used in Schulz (2021). Firstly, we map the cloud fraction curves onto points on a finite dimensional space using functional principal component analysis. We subsequently apply K-means, Gaussian Mixture Models and Mean Shift clustering onto the pre-processed dataset to identify any robust clusters. We have been able to attain robust Sugar-like clusters for K-means for 3 and 4 partitions and Mean Shift with bandwidth λ ≈ 585. This provides evidence that we are able to use cloud fraction data to distinguish Sugar. However, the same can not be said for Gravel, Fish and Flowers as we have not been able to identify them in our analysis. It is suggested for future research to do sensitivity analysis in the height interval of the cloud fraction data, that outliers are omitted and that the labeled data from Schulz (2021) are used instead of the mean and spread of the data pertaining to those labels.

Ultra-wideband submillimeter observations are crucial to study the process of star and galaxy formation and for characterizing cosmic dust in the interstellar medium. The Deep Spectroscopic High-redshift Mapper 2.0 (DESHIMA 2.0) will use an integrated superconducting spectrometer chip with a 220-440 GHz band coverage and a spectral resolution of f/df = 500, enabling submillimeter observations with an unprecedented instantaneous band coverage.

However, the octave bandwidth of DESHIMA 2.0 poses a challenge: the atmospheric transmission is highly nonlinear in the broad frequency window of DESHIMA 2.0, complicating the removal of atmosphere noise from the signal.

In this thesis, I present the Time-dependent End-to-end Model for Post-process Optimization (TiEMPO). TiEMPO provides realistic time-dependent simulations of high-redshift galaxy observations. It consists of the following components:
Galaxy model. A galaxy is modeled using a two-component modified blackbody spectrum as a template. The model outputs the flux density, which is converted to power spectral density using the frequency-dependent effective aperture area of the telescope.
Atmosphere model. TiEMPO makes use of atmosphere model ARIS, which models a spatially and dynamically varying atmosphere and outputs Extra Path Length. TiEMPO converts this to precipitable water vapor using a relation that was found with the Smith-Weintraub value of the Extra Path Length and the ideal gas law.
Telescope beam. TiEMPO can be adapted to use any arbitrary beam shape for the near-field telescope beam. The far-field beam is modeled using the effective aperture area. Finally, the output of TiEMPO is given at multiple positions, enabling simulations of sky chopping and nodding in two directions.
Radiation transfer. A static model of the sensitivity of DESHIMA, determining the attenuation and the emission of the atmosphere and transmitting the signal through each component of the telescope and instrument.
Spectrometer chip. TiEMPO can adopt any filter transmission of the channels inside a spectrometer chip. In this work, they are approximated with Lorentzian curves. The photon and recombination noise are modeled with the NEP and the noise distribution is approximated with a normal distribution. The noise is incorporated with an integration over the filter response, treating photon-bunching over the wide bandwidth of DESHIMA 2.0 accurately.
Conversion to sky temperature.Finally, the power measured in the chip is related to the sky temperature with an interpolation made with a skydip simulation in the radiation transfer model.

We compare the first TiEMPO simulations to observation data by comparing the time signal, power spectral density and noise equivalent flux density. Apart from a small offset in the power spectral density, the simulation data closely resembles the observation data. TiEMPO allows us to test algorithms for atmosphere removal and galaxy detection, to study the effect of different weather conditions and to evaluate the performance of different observing techniques. TiEMPO is modular, making it usable for the original DESHIMA instrument and its successor DESHIMA 2.0. The use of TiEMPO can be extended to other spectrometers besides DESHIMA 2.0, like a grating spectrometer, and other telescopes, such as the promising 50m-aperture AtLAST/LST telescope.