The natural units for a direct detection spectrometer such as SPIFI are the NEP and NEF as defined above. Currently SPIFI is only background limited at modest resolving powers (R < 3000), so that the NEP is only weakly dependent on R: NEP = 7.48 ´ 10-16×(sqrt(1.28 + 1000/R)) W-Hz-1/2. In the near future, through improvements in the cold electronics and system transmission, we expect to become background limited at all resolving powers, so that NEP µ R-1/2. For point sources, the minimum (1s) detectable line flux (MDLF) then given by:
MDLF = sqrt(N)×NEP/{(A×htel×hMB×hsky)×sqrt(2×tint)}
Where N is the number of spectral resolution elements in the scan, htel is the receptive efficiency of the telescope (= 65%, JCMT web page), and hMB is the fraction of the forward beam that couples into the main beam (= 30%, JCMT web page). Note that ha = htel×hMB. The transmission of the atmosphere along the line of sight, hsky is given by: hsky = exp(-tzenith×sec(q)), where tzenith is the zenith opacity, and q is the angle from the zenith to the source.
It is instructive to compare our sensitivity to current heterodyne receivers. It is difficult to compare the two directly since the figure of merit for heterodyne receivers is Trec(DSB), which translates in very subtle ways to our NEF listed above. {The primary complication is that the NEF includes the shot noise contribution of the background Tbac, while Trec does not. Therefore, at the telescope the relevant noise for heterodyne receivers is Trec + Tbac, while for a background limited direct detection system, like SPIFI at small R, Trec ® 0, so that the relevant noise is Tbac}. A more straightforward method, is to convert SPIFI's NEF to a system temperature on the telescope by comparing the detected power to a main beam rms noise, TMB(rms), then converting TMB(rms) back to Tsys. From the JCMT web page:
NEF [W-m-2Hz-1/2 ] = 2×kTMB(rms)/l2×{Dn×Wbeam}
TMB(rms) = 2×Tsys×k/(Dn×t)1/2/hMB
where Wbeam is the beam solid angle (= 1.28 ´ 10-9 sr at 370 mm), Dn is the resolution bandwidth (Dn = p/2×n/R = 1.29 ´ 109 Hz, for R = 1000), k is the backend degradation factor (= 1.15 for a 2-bit digital correlator), and the integration time, t, is ½ second. For hsky= 40%, hMB = 30%, and htel = 65%, SPIFI has an equivalent Tsys = 800 K for R = 1000 at 370 mm. If SPIFI were background limited at all resolutions, Tsys would be independent of R (since TMB µ (Dn) µ R1/2 for that case). We are working towards, but have not yet reached this goal. Figure 1 below plots the expected Tsys for SPIFI on JCMT as function of R for both today's system and the limit we expect to reach (the "goal" system). For the "goal" system, SPIFI's sensitivity will improve by a factor of 1.5 at the lowest resolutions, and up to a factor of 3.7 at R ~ 10,000. This Tsys gives the minimum detectable line flux per resolution element if we do not spectrally scan. This is only appropriate for very deep line searches where the line to continuum ratio is expected to be large. Normally we will need to spectrally scan, typically 5 resolution elements to form a spectrum, so we also plot the effective Tsys for this case as well.
Recall that Tsys is related to TA*(rms), TR*(rms), and TMB*(rms) by (cf. JCMT web page):
TA* = 2×Tsys×k/(Dn×tint)1/2;
TR*(rms) = TA*(rms)/hfss;
TMB(rms) = TA*/hMB.
The "antenna temperature", TA*(rms) is that actually measured at the telescope after corrections for telescope and antenna losses, while TR*(rms) is the internationally accepted scale obtained by correcting the forward spillover and scattering efficiency, hfss (~ 0.60, JCMT web page).
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