MUSCAT system temperature

Mexico-UK Submillimetre Camera for Astronomy (MUSCAT) is being built for the LMT Observatory. MUSCAT is an LEKID (Lumped Element Kinetic Inductance Detector) instrument. It covers the frequency range between 250 and 300 GHz. It is designed as a broadband instrument with a 50 GHz bandwidth. (See Tapia et al. 2020 for more details.) To allow for some flexibility, it is set-up in the sensitivity calculator to cover bandwidths from 10 to 80 GHz. MUSCAT is being used to demonstrate the capabilities of a KID based continuum camera that can observe at these frequencies on AtLAST.

As a KID instrument, the sensitivity is calculated slightly differently to the generic instrument description as Poisson noise and quasiparticle recombination noise are important in addition to the wave noise, as described in detail in this note. Re-arranging the equations, we find that we can incorporate this instrument into our sensitivity calculation by determining an equivalent system temperature that is dependent on the Noise Equivalent Power (NEP) as follows:

\[T_{sys} = \frac{\mathrm{NEP}}{k\,\eta_\mathrm{chip}\,\eta_\mathrm{co}\,\eta_\mathrm{eff}\,\mathfrak{t}\,\sqrt{2n_\mathrm{pol}\,\Delta\nu} }\]

where

  • \(\eta_\mathrm{eff}\) is the forward efficiency

  • \(\eta_\mathrm{chip}\) is the pixel efficiency

  • \(\eta_\mathrm{co}\) is the cold optics optical efficiency due to the Lyot stop illumination

  • \(\mathfrak{t}\) is the atmospheric transmittance, defined as \(\mathfrak{t} = \textrm{exp}^{(-\tau_{atm})}\)

The Noise Equivalent Power is the square root of the sum of the Poisson noise, bunching (wave) noise and quasiparticle recombination noise and calculated as:

\[\mathrm{NEP} = \sqrt{2\,P_\mathrm{KID}\,h\,\nu+2\,P_\mathrm{KID}^2/(n_\mathrm{pol}\Delta \nu)+4\,\Delta_\mathrm{g}\,P_\mathrm{KID}/\eta_{pb}}\]

where

  • \(\Delta_\mathrm{g}\) is the gap energy of the superconductor

  • \(\eta_\mathrm{pb}\) is the pair-breaking efficiency

  • \(P_\mathrm{KID}\) is the power received by the KID.

The power received by the KID (\(P_\mathrm{KID}\)) is dependent on the power spectral density (\(PSD_\mathrm{KID}\)), which is the sum of the contributions of the noise sources and calculated as:

\[ \begin{align}\begin{aligned}P_\mathrm{KID}(\nu_\mathrm{0}) = \int^{\nu_\mathrm{max}}_{\nu_\mathrm{min}} PSD_\mathrm{KID}(\nu)\:n_\mathrm{pol}\: d\nu \sim PSD_\mathrm{KID}(\nu_\mathrm{0})\:n_\mathrm{pol}\: \Delta \nu\\\begin{split}PSD_\mathrm{KID}(\nu) = & k(\eta_\mathrm{chip}(1-\eta_\mathrm{co})\cdot O(\nu, T_\mathrm{co})\\ &+ \eta_\mathrm{chip}\,\eta_\mathrm{co}(1-\eta_\mathrm{eff})\cdot O(\nu, T_\mathrm{amb})\\ &+ \eta_\mathrm{chip}\,\eta_\mathrm{co}\,\eta_\mathrm{eff}(1-t_\mathrm{r})\cdot T_\mathrm{sky})\end{split}\end{aligned}\end{align} \]

where

  • \(T_\mathrm{sky}\) is the sky temperature (in terms of a Rayleigh-Jeans brightness temperature) calculated from the model grid described in Weather Calculations

  • \(T_\mathrm{amb}\) is the ambient temperature.

Here, \(O(\nu, T)\) converts a physical temperature to a Rayleigh-Jeans brightness temperature:

\[O(\nu, T) = T\frac{h\nu/kT}{\exp(h\nu/kT)-1}.\]

For MUSCAT, the constants are expected to have the following values (based on information provided by the MUSCAT team):

  • \(\eta_\mathrm{chip} = 0.7\)

  • \(\eta_\mathrm{co} = 0.35\)

  • \(\Delta_\mathrm{g} = 200\,\mu\mathrm{eV}\)

  • \(\eta_\mathrm{pb} = 0.4\)

  • \(T_\mathrm{co} = 0.3\,\mathrm{K}\)