The next step in our analysis is to estimate the total absorbed optical power
Q, and the change in absorbed optical power ∆Q resulting from a change in the external radiation field. We begin by taking a pair of load curves with the spectrometer first exposed to an ambient temperature (T = 280 K) radiation field, and then with the instrument entrance window filled with a cold (T = 78
K) load. A sample pair of such load curves is shown in Figure 4.3, along with a theoretical Q = 0load curve created from the thermal model. The bolometer temperature, and therefore its electrical impedance, depends only on the sum
P+Q. Therefore if we change the optical loading by an unknown amount∆Q
Figure 4.2: Dark Load Curves. Top: Series of dark load curves taken with vary- ing sink temperatureT0. A fit to the T0 = 225mK curve with the values of R∗
andTg obtained from the bottom plot are used to deriveβandgs, and these pa-
rameters are used to overlay models for the other 5 curves. Bottom: Plot of the zero-bias impedanceR0vs. T0, used to obtain estimates ofR∗andTg.
Table 4.1: ZEUS Bolometer Parameters
Parameter Symbol 450µm half (1−16) 350µm half (17−32) Units
Quantum Efficiency ηdqe 0.58−0.76 0.68−0.82
Sink Temperature T0 230 230 mK W(T,T0)=gs Tβ+1−Tβ+1 0 β 1.23−1.46 1.42−1.58 gs 420−670 536−864 pW/Kβ+1 R(T )=R∗exp pTg/T R∗ 1.44−2.80 1.17−1.67 kΩ Tg 19.2−22.5 19.1−23.3 K Operating Impedance R 9.6−15.1 8.0−17.7 MΩ Operating Temperature T 260−280 250−270 mK
Dynamic Thermal Conductance Gd 186−254 166−273 pW/K
Optical Loading Qa 4.2−4.7 2.8−3.9 pW
Electrical Responsivity SE 2.6−4.5 2.6−4.8 108V/W
Photon Noise NEPPhotonb 2.0−3.5 3.3−4.4 10−17W/
√
Hz
NEVPhoton 5.9−15.3 9.5−21.3 nV/
√
Hz
Johnson Noise NEVJohnson 8.8−9.6 7.9−9.8 nV/
√
Hz
Thermal Noise NEPthermalb 2.4−2.8 2.2−2.8 10−17W/
√
Hz
NEVthermal 7.3−10.8 6.9−12.3 nV/
√
Hz
Thermistor 1/f Noise at 2 Hz NEV1/f 3.5−6.5 3.2−8.4 nV/
√
Hz
Electrical Noise NEVFET+Amp ≈14 ≈14 nV/√Hz
Total Noise NEVtotal ≈20−26 ≈20−31 nV/
√
Hz
Measured Noise NEVmeasuredc 28 28 nV/
√
Hz aAveraged over each half of the array.
bRefers to detected (rather than incident) power.
cMeasured at the centers of the telluric windows during the March 2008 observing run. In subsequent runs in December 2008 and March 2009
the electrical noise was reduced and the responsivity increased, thereby bringing the system noise closer to the background photon limit.
Table 4.1 (Continued)
Note. – Detectors1−16operate in the450µm band, and detectors17−32operate in the350µm band. Unless otherwise noted, the ranges specified for each parameter include variations both with detector and with operating wavelength in theλ≈430−470µm andλ≈ 340−370µm regions in which the bandpass filters are highly transmissive. The parameters ηdqe andNEPphoton are assumed to be detector-independent, and are calculated over the same spectral bands. The ranges
specified forβ,gs,R∗, andTgrefer to variations with detector.
Figure 4.3: Pair of unblanked load curves with different optical loading, along with simple model fits used to interpolate between data points. Also shown is a theoretical load curve calculated for no optical loading. Differencing any two curves gives the differential loading∆Qbetween the two configurations.
impedance is unchanged, we have∆P = −∆Q. Differencing any pair of curves in Figure 4.3 at fixedRtherefore gives the change in optical loading between the two configurations.
As an example, it takes 2.1, 3.7, and 6.3 pW of electrical power to fix the bolometer atR= 16MΩwhen exposed to a280K external load, a78K external load, and when blanked off, respectively. This implies that when the tempera- ture of the external radiation field increases from78K to 280K the optical load increases by∆Q=3.7−2.1= 1.6pW, and the total optical loading under normal operation isQ= 6.3−2.1=4.2pW. This estimate ofQis included in Table 4.1.
defined as the change in output voltage with respect to a small change in the optical loading (SE = dV/dQ). The responsivity can be determined from the
shape of a single load curve by [80]
SE = − 1 2I 1− Z R R L Z+RL , (4.4)
where the dynamic impedance is Z = dV/dI. Estimates of SE derived in this
manner from the 280 K load curves are included in Table 4.1, and typical values areSE ≈ 3.6×108V/W.
A second estimate ofSE may be obtained by fixing the bias voltage and mea-
suring the change in output voltage∆V resulting from a change in the external radiation field. Dividing this by the corresponding estimate of ∆Q obtained above allows us to compute SE ≈ ∆V/∆Q. We note that changing the external
radiation temperature by the large value of≈ 200 K will change the operating condition of the bolometer in a way that changing the radiation temperature by a small amount (as when chopping between a source and blank sky during nor- mal operation) won’t. This ’large-signal’ responsivity may therefore be some- what different than the ’small-signal’ responsivity estimated from the shape of the load curve. The two methods generally agree to within 10%, however, so we consider this latter estimate as supporting the accuracy of the first method.
The bolometer operating temperatureT is derived from the measured resis- tance and equation 4.2. We are then able to calculate the dynamic conductance of the thermal link, defined asGd(T ) =dW/dT = gs(β+1)Tβ. The estimates ofR,
T, andGd are included in Table 4.1, and are used in section 4.6.2 to estimate the