Python NET library validation

Summary

Upcoming features

• Add in realistic bandpass: Either bandpasses with a Chebychev ripple on top to mimic realistic bandpasses, or read in our real BK published bandpasses, or allow the user to input a real bandpass file.
• Check the results as a function altitude to verify that the NETs make sense for LDB or space loading.
• Place the code on github under git control.

Calculation details

Similarities

• Site: The spreadsheet is hard-coded for South Pole atmosphere, so I use that site. I checked and the spreadsheet uses the same atmospheric profile aswhat I'm using (the 10yr merra2-avg profile from Scott's tutorial, yields a PWV = 0.425mm)
• Bandpass: This initial comparison only checks the flat top hat bandpass model. More complicated bandpass will come in upcoming features.
• All NET are calculated for elevation = 45deg.
• Bolometers parameter are matched. The spreadsheet allows you to input: beta, the safety factor (sf) and the bolometer critical temperature (Tc). Additionally, NETlib.py allows you to specify the bath temperature (T0), R_tes and T_shunt (used to calculate NEP_tes and NEP_shunt)

Differences

• The main difference is in the way the optical loading is calculated. As described above, the python code sets up a 1D radiative transfer through a stack of cmb + atmosphere + instrument + detector layers to derive the total loading on the detector. The optical efficiency is an output of the code and depends on the input emissivities of the various instrument layers. The spreadsheet treats the layers more independantly as follows:

  The instrument is a set of layers each of the physical temperature (Ti) and emissivity (epsi)
  The instrument loading is simply:
      #   Trj_instr = Sum (Ti*epsi) 
  
  
  Then, the instrument loading is simply
          # dQinstr(v) = bandpass * oe * k * Trj_instr * dv
          # Qopt = Integral(dQinst dv) in pW
  Note that dQinstr above is a constant
  
  Given an atmospheric brightness temperature spectrm Trj_atm(v),  a tophat bandpass (bandpass = 0 outside the band 1 inside the band), an end-to-end optical efficiency (oe), and an elevation (el), the incident power from the atmosphere on the detector is
       # dQatm = bandpass * oe * k * Trj_atm(v) * dv /(sin el) 
       # Qatm = Integral(dQatm(v) dv) in pW
  
  And finally:
          # dQcmb = bandpass * (1-(1-Tx_atm(v))/sin el) * oe * h * v * dv / exp(hv/kTcmb)
          # Qcmb = Integral(dQcmb dv) in pW
  
  The total loading is then simply
          # Qtot = Qatm+Qinstr+Qcmb
  

  So from the description above, we expect some differences in the resulting Trj_instr, Qinstr, and Qatm and that the 1D radiative transfer is likely more correct as it treats the cumulative effects.
• Equation for Gc matches except that in the spreadsheet has T0 hard-coded to T0 = 0.250K. Only difference in Gc comes from differences in Q_tot.
• Same equation for NEP_shot noise. Only difference comes from difference in Q_tot.
• Same equation for NEP_bose noise contribution. Only difference comes from Q_tot.
• Same equation for NEP_phonon noise, except that spreadsheet has the value of F (which depends on Beta, T0 and Tc) hard-coded to 0.823, while it's explicitely re-calculated in the NETlib.py
• Detector noise in Jamie's spreadsheet only accounts for phonon noise and ignores shunt and tes noise contributions (which are indeed sub-dominant)

Below are the compared results for 4 specific cases. The bold results are from NETlib.py (as used by the online tool), the other from the spreadsheet.
We can see that the dPdT , Qcmb and Qatm match well, though for Qatm not as well as I would have expecte given the match in the atmospheric spectra. I will check why. I'm also not sure why dPdTcmb at v=40GHz differs so much given that it matches perfectly at other frequencies. I will also check. As expected, the largest differences come from the calculated instrument loading (Qinst). This difference obviously gets passed on to the NEP_shot and NEP_bose. The small difference in NEP_det comes from ignoring the tes and shunt noise in the spreadsheet.