TIFUUN system temperature

Terahertz IFU with Universal Nanotechnology (TIFUUN) is being built for the ASTE Observatory. TIFUUN is an MKID (Microwave Kinetic Inductance Detector) instrument. It covers the frequency range between 90 and 360 GHz. It is set-up to cover channel spacings from 180 MHz to 10 GHz. (See Rybak et al. 2024 for more details.)

TIFUUN is being used to demonstrate the capabilities of a KID based integral field unit (IFU) instrument 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 chip optical efficiency

  • \(\eta_\mathrm{co}\) is the cold optics optical efficiency

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

TIFUUN is a versatile instrument. It contains two IFUs. In principle, these could be set-up to cover the same bandwidth range but different polarisations, making this a dual-polarisation instrument. However, this would come at the cost of total bandwidth and so in general TIFUUN should be set-up as a single-polarisation instrument by ensuring that \(n_\mathrm{pol}=1\).

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

  • \(T_\mathrm{co}\) is the temperature of the cold optics

  • \(T_\mathrm{sky}\) 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 TIFUUN, the constants are expected to have the following values (based on information provided by the TIFUUN team):

  • \(\eta_\mathrm{chip} = 0.26\)

  • \(\eta_\mathrm{co} = 0.65\)

  • \(\Delta_\mathrm{g} = 188\,\mu\mathrm{eV}\)

  • \(\eta_\mathrm{pb} = 0.4\)

  • \(T_\mathrm{co} = 4\,\mathrm{K}\)