4.2 Science-grade Arrays
4.2.8 Responsivity
Table 4.8: Median background loading, calculated using detectors of the specified band on the A2 and B2 arrays. All temperatures are referred to the cryostat window. Texc is determined from the hot/cold data,Tspill
is determined from the skydip data, and Tsky is determined from the FTS bandpass measurements and the ATM model assumingCPW=1.3 mm. These three temperatures sum to give the total loadingTload. Poptis the equivalent optical power incident on the MKID.
Band Texc[K] Tspill[K] Tsky[K] Tload[K] Popt[pW]
0 30 45 10 85 3.3
1 20 30 20 70 5.5
2 25 30 25 80 3.9
3 40 55 70 165 4.9
The flux of the source is then calculated as S=Ωsource
RFTS(ν)ATM(ν,e)I(ν)dν
RFTS(ν)ATM(ν,e)dν , (4.6)
whereFTS(ν)denotes the measured bandpass and ATM(ν,e) is the atmospheric transmission at the CSO at elevatione. The atmospheric transmission at zenith is calculated using theATMmodel with the mm of precipitable water vapor determined from the tipper measurement ofτ225at the time of the observation. The zenith transmission is then scaled to elevationeusing the relationshipATM(ν,e) = [ATM(ν,90◦)]1/sine. Since the solid angle of Uranus varies with observation epoch, we calculateΩsourceat the time of the observation using the JCMT FLUXES software.
The predicted response is given by rsrc=
∂(δfres/fres)
∂S
=
∂(δfres/fres)
∂nqp
∂nqp
∂Popt,ant
∂Popt,ant
∂Tload,ant
∂Tsrc
∂S
, (4.7)
where the terms on the second line are obtained by taking the appropriate partial derivative of Equations (2.59), (2.131), (2.105), and (2.9) from left to right. Doing so results in the following expression:
rsrc=α κ2ηphηopt,ant(1−fspill,ant)e−τant/sineAeff∆νmm,ant
4V∆(2Rnqp+τmax−1) , (4.8)
which we can evaluate directly using the best fit model parameters for each resonator. We determine τant
from Equation (4.3) using the value ofτ225reported by the CSO at the time of the observation to infer the atmospheric transmission. Fromτantwe can determine the background loading which sets the quasi-particle densitynqpin the above equation.
We have collected 55 observations of Uranus for flux calibration purposes over the course of our Au- gust/September 2013 observing run. The median value of the column density of precipitable water vapor for this set of observations isCPW=1.66 mm, which is approximately equal to the historical median. We calcu- late the median ratio of measured to predicted response for each resonator over the 55 observations. This is shown in Figure 4.12 as a function of the microwave powerPgused to probe each resonator relative to the critical powerPcritat which that resonator bifurcates. Note that the ratioP/Pcrit=awas estimated by fitting the pre-observation IQ sweep to a model for the transmission near resonance that includes a nonlinear kinetic inductance. We expect to see a slight degradation in detector responsivity with increasing power due to the nonlinear kinetic inductance and also (possible) microwave heating of the quasi-particle population. Since all of the calibration measurements are collected at low readout power, this effect is not included in our model and hence not included in the predicted response. We do indeed see a degradation in the ratio of measured to predicted response as we move to larger values ofPg/Pgcrit, decreasing by∼35% between the low power
Figure 4.12: Response comparison. Light blue diamonds denote the ratio of measured to predicted response to an unresolved astronomical source (in this case Uranus). Orange circles denote the ratio of measured to predicted response to small changes in airmass. Blue and red lines are linear fits to the data.
limit and the critical power. These values are consistent with more direct measurements of the degradation in frequency response with readout power for detectors on our engineering-grade arrays [161].
In the low power limit — where we expect our model to hold — we measure a response to Uranus that is a factor of [0.40, 0.50, 0.45, 0.40] times the predicted response for the four observing bands. One possible cause for this discrepancy is that a significant portion of our beam is making it to the sky but is not part of the main beam (i.e., sidelobes or a diffuse wide-angle beam). Another possibility is that we have an incomplete understanding of the detector physics. The instrument model is constrained using only large signal response:
for the hot/cold measurements we use the difference between a 77 K and room temperature load and for the sky dip measurements we use the difference between a sky load and room temperature load. Perhaps the large signal response does not translate into small signal response in the way described by the instrument model presented in Chapter 2.
In order to distinguish between these two possibilities, we examined the detector response to small changes in elevation. As the telescope scans in elevation there is a small change in the airmass, which in turn causes a small change in the background loading. The majority of our science observations are collected using a lissajous scan strategy, where the azimuth and elevation of the telescope are modulated with sine waves of different periods. This places the signal due to changing airmass at the specific frequency with which we are driving the telescope in the elevation direction. By examining the correlation coefficient be- tween the detector timestreams and the elevation track of the telescope in a narrow window centered on the fundamental scan frequency, we are able to detect this small signal response to a beam-filling calibrator.
Specifically we examine re=
∂(δfres/fres)
∂e
=
∂(δfres/fres)
∂nqp
∂nqp
∂Popt
∂Popt
∂Tload
∂Tload
∂e
=
∂(δfres/fres)
∂nqp
∂nqp
∂Popt
∂Popt
∂Tload
(1−fspill,ant)τantTatme−τant/sinecos(e)
sin2(e) , (4.9) where the terms on the second line are obtained by taking the appropriate partial derivative of Equations (2.59), (2.131), (2.105), and (2.9), from left to right. The ratio of the measured to predicted value ofreis presented in Figure 4.12. This was determined from over 400 observations of faint sources. In Band 1 and Band 2, the measured and predicted response are in good agreement in the low-power regime. However, in Band 0 the measured response is 35% larger than predicted and in Band 3 the measured response is 10% smaller than predicted. The agreement of Band 1 and Band 2 strongly suggest that our understanding of the MKID small-signal response is correct and the discrepancy for unresolved sources is due to a significant fraction of the beam being dispersed to wide angles. We discount Band 3 because of the systematics in the model discussed earlier. The excess response in Band 0 is not currently understood, but points in the same direction
as the implications of the Band 1 and Band 2 analysis. The measured Band 0 values are noisy due to the fact that the atmosphere is relatively transparent at these frequencies, and hence the response to changes in elevation is small.