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--- cso:instruments:heterodyne:obstime [2013-12-01 07:19]
sradford
+++ cso:instruments:heterodyne:obstime [2014-04-15 00:05] (current)
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@@ Line 1: / Line 1: @@
+====== 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]].