Table of SPARO instrumental characteristics
Characteristic Value Units Notes
Detector Operating Temperature 285 mK measured at Northwestern
Beam FWHM predicted: 4.1
measured: < 6.0
arcmin predicted as follows: add (in quadrature) the pixel spacing (3.5 arcmin) and the diffraction-limited beam FWHM of approx. (0.45 mm/0.7 m)
Detector Noise 50 nV/Hz1/2 measured with spectrum analyzer at 3.1 Hz
Responsivity (S) 4 K blankoff wheel closed 5.0*108 V/W varies by about 20% from detector to detector
blankoff wheel open
300 K load
Austral Winter 2000: 3.8*108
after 2001 upgrade: 2.1*108
V/W varies by about 20% from detector to detector
blankoff wheel open
200 K load (theoretical; interpolated)
Austral Winter 2000: 4.1*108
after 2001 upgrade: 2.9*108
V/W Interpolated using result of empirical fit to pre-2001 vs. 2001 load curves that gives
(Sclosed - Sopen) = (const.)(load power)0.83
Noise Equivalent Power (atmospheric) Austral Winter 2000: 1.10*10-16[1-e-tau*sec(z)] 1/2
after 2001 upgrade:
1.88*10-16[1-e-tau*sec(z)] 1/2
W/Hz1/2 Fundamental noise from a 200K atmosphere with optical depth tau at 450 microns and zenith angle z
(detector) 1.2*10-16 W/Hz1/2 detector NEP = (det. noise)/S
Noise Equivalent Flux Density (atmospheric) Austral Winter 2000: 62*[e2*tau*sec(z)-etau*sec(z) ]1/2
after 2001 upgrade:
Jy/Hz1/2 theoretical estimates based on 4' beam
(detector) Austral Winter 2000: 68*etau*sec(z)
after 2001 upgrade: 17.4*etau*sec(z)
Jy/Hz1/2 theoretical estimates based on 4' beam
Instrumental Transmission (cold optics) Austral Winter 2000: 1.87
after 2001 upgrade: 5.5
% determined from load curves with BOW closed vs. BOW open (Note this is measured with unpolarized light, so a perfect polarimeter would have 50% transmission in each of the two corresponding orthogonally-polarized detectors.)
Overall Instrumental Transmission Austral Winter 2000: 1.12
after 2001 upgrade: 4.4
% Cold Optics transmission times warm optics transmission (pressure window [80%]; black polyethylene OVCS filter [75%] that was used in 2000 but not 2001). Again, 50% is theoretical maximum transmission.
Fractional Bandpass 0.1 (none) Bandpass centered at 450 microns

More detailed treatments of the following subjects are given below:

Responsivity (2000)
Instrumental transmission (2000)
Detector Noise

A chart of the relative gain matrix (2000) is also given.

These are the formulae used in determining NEP and NEFD

NEP = (5.5*10-14 WHz-1/2)[fBT*tc(em)]1/2(theta/theta0)*[lambda/micron]-1

NEFD = (3.3*1011 JyHz-1/2)[NEP/WHz-1/2][lambda/micron]{fB[Atel/m2]tctw}-1

And, substituting the top equation into the bottom, we get

NEFD = (1.8*10-2 JyHz-1/2)[(T*tc*em)1/2(theta/theta0)]/[A*twtc*(fB)1/2]


Note that tw = ta*tt*nch*nAC*twd, where