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: 27*[e2*tau*sec(z)-etau*sec(z)]1/2	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)[f_BT*t_c(em)]^1/2(theta/theta0)*[lambda/micron]^-1

NEFD = (3.3*10¹¹ JyHz^-1/2)[NEP/WHz^-1/2][lambda/micron]{f_B[A_tel/m²]t_ct_w}^-1

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

NEFD = (1.8*10^-2 JyHz^-1/2)[(T*t_c*em)^1/2(theta/theta0)]/[A*t_wt_c*(f_B)^1/2]

Where,

• lambda = bandpass center = 450 microns
  
• f_B = fractional bandpass = 0.1
  
• T = atmospheric temperature = 200K for Austral winter at Pole
  
• em = atmospheric emissivity = 1 - e^-tau*sec(z)
  
• t_c = transmission of all cold optics
  
• t_w = transmission of all 200K elements
  
• A_tel = Area of telescope = (pi/4)*(0.7m)² for SPARO on Viper
  
• theta = beam size on sky = 4'
  
• theta0 = diffraction limited beam size = 2.7'
  

Note that t_w = t_a*t_t*n_ch*n_AC*t_wd, where

• t_a = atmospheric transmission = e^-tau*sec(z)
• t_t = telescope transmission = 80% from Ruze scattering for telescope rms of 17.5 microns
• n_ch = chopper duty cycle, approximately 85%
• n_AC = detector responsivity gain comparing S_AC to S_DC, about 90%
• t_wd = transmission of warm dewar components (= 60% in 2000, 80% in 2001)