====== Observing Time ======


For heterodyne observations, estimate the sensitivity with the radiometer equation: 
  * //T//<sub>rms</sub> = //K// //T//<sub>sys</sub> (//t ∆f //)<sup>-1/2</sup>, 
where //T//<sub>sys</sub> is the system temperature, //t// is the integration time, //∆f// is the channel width, and //K// ≈ 2, depending on the switching scheme and observing strategy. Invert this equation to estimate the necessary observing time. Do not neglect to add overhead for setup, pointing, calibration, etc.  


===== System Temperature =====


Estimate system temperature on the //T//<sub>A</sub><sup>*</sup> scale with: 

  * //T//<sub>sys</sub> [SSB, //T//<sub>A</sub><sup>*</sup>] = [exp(//τA// ) / //α//] × 2 × (//T//<sub>rx</sub> [DSB] + //α// [1 - exp(-//τA// )] //T//<sub>atm</sub> + (1 - //α// ) //T//<sub>spill</sub> ) ,

where
  * //τ// is the atmospheric optical depth at the observing frequency, see [[http://cso.caltech.edu/atm|model atmospheric spectra]],
  * //A// is the airmass = secant (zenith angle),
  * //α// is the hot spillover efficiency = 1 - (fraction of power falling on ground, etc.), ≈ 93%,
  * //T//<sub>atm</sub> is the atmospheric temperature, ≈ 280 K,
  * //T//<sub>spill</sub> is the warm spillover temperature, ≈ 280 K, and
  * the Cosmic (Microwave) Background Radiation has been ignored.

For the above parameters and //T//<sub>Rx</sub> = 40 K [DSB], the approximate SSB system temperature at 230 GHz is:\\
{{tsys-230.png?600}}


If you're observing small sources, further adjust for the main beam efficiency.

If the atmospheric optical depth in the two sidebands is different, please review the discussion of [[calibration#sideband correction]].