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.