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.