SPIRE Flux Calibration:
Implementation
George J. Bendo
and the SPIRE-ICC
Basic Equations
Derivative of flux calibration curves (from empirical analysis):
K2
f (V )  K1 
V  K3
Flux calibration curve (integral of above equation):
Vm  K 3 
S  K1(Vm V0 )  K 2 ln

V0  K 3 
•
V0 is a zero-point voltage that is selected to match the
background in dark sky.
• K1, K2, and K3 are unique parameters for each bolometer that are
derived using the techniques discussed here.
• An additional K4 term is used to scale the RSRF-weighted flux
density to produce monochromatic flux densities (assuming υFυ
is constant).
Calibration Strategy
• PCal flash observations taken against backgrounds
with different surface brightnesses give the relation
between V and 1/ΔV. These data can then be used
with the derivative of the flux calibration curve to
give unscaled versions of K1 and K2 and a scaled
value of K3.
• Fine scan observations in which each bolometer
scans over Neptune are used to scale the K1 and K2
parameters.
PCal Flash Observations
• Instrument was pointed at a
series of locations near Sgr A*
during PCal flash observations to
get 1/ΔV vs V measurements.
Each bolometer falls within a
region that should be ~75% of the
peak surface brightness.
• Additional PCal flash
measurements against dark sky
were used to constrain the part
of the curve near V0.
Results: Unscaled Derivatives of
Calibration Curves
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)
Results: Unscaled Derivatives of
Calibration Curves
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)
Results: Unscaled Derivatives of
Calibration Curves
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)
Neptune Fine Scan Observations
• In these observations, each bolometer in SPIRE passed across Neptune in
a very fine pattern. This gave measurements of the peak and background
voltages that could be used to scale the calibration curves.
• To derive the peak and background voltages, we fit the timeline data (not
the map data) with two dimensional Gaussian functions. An example is
shown below.
Results: Scaled Calibration Curves
Solid line: V3-0 flux calibration
Dotted line: V2-3 flux calibration
Results: Scaled Calibration Curves
Solid line: V3-0 flux calibration
Dotted line: V2-3 flux calibration
Results: Scaled Calibration Curves
Solid line: V3-0 flux calibration
Dotted line: V2-3 flux calibration
Problematic Bolometers
• Some of the dead, noisy, and slow bolometers could not be calibrated
because of difficulties with performing analysis on the sample. The
following number of bolometers were not calibrated:
PSW
7
PMW 1
PLW
1
• 16 bolometers in PSW and 7 bolometers in PMW saturated on Neptune.
To calibrated these bolometers, we used fine scan observations of 3C 273.
We calibrated the signal from 3C 273 for the “good” bolometers, and then
used the signal from 3C 273 to scale the bolometers that saturated on
Neptune.
Sources of Uncertainty
(Individual Bolometers)
• Uncertainty from fits to PCal flash data.
• Uncertainty in scaling terms.
• Uncertainty in model flux densities of
calibration source.
Uncertainty from PCal Fits
Because of degeneracy problems with the nonlinear equation fit to the PCal
flash data, we cannot derive simple uncertainties in the K parameters from
the fit.
Instead, we used a Monte Carlo approach to create plots that show the
uncertainty in the calibration curves as a function of voltage.
The typical fractional uncertainties from the PCal flash fits derived this way
are ~0.0002. The maximum uncertainties do not supercede 0.005.
Uncertainty from PCal Fits
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)
Uncertainty from PCal Fits
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)
Uncertainty from PCal Fits
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)
Uncertainty from Scaling Terms
The table below lists the uncertainties for the scaling of the calibration
curves for individual bolometers based on the uncertainty in the peak
voltage measurements of Neptune or 3C 273.
Array
Mean Fractional
Uncertainty
Maximum Fractional
Uncertainty
PSW
0.0098
0.11
PMW
0.010
0.12
PLW
0.0016
0.040
The maximum fractional uncertainties in the PSW and PMW arrays are for
bolometers that saturated on Neptune. Most other bolometers have
uncertainties much closer to the mean.
Tests of Flux Calibration
The new Flux Calibration Product was used to process standard large and
small scan map data for two sources:
• Neptune (primary calibrator)
• Gamma Dra (secondary calibrator)
The results can be used to gauge the random uncertainty in the flux
calibration as well as variations in the flux calibration over time.
Measurements of the flux densities were performed on the timeline data.
Mapping the data increases the dispersion in the flux density measurements,
as binning the data into map pixels will effectively blur the data. The source
extraction tools currently included in HIPE (DAOPHOT and Sussextractor)
both systematically undermeasure flux densities, and Sussextractor also
functions very poorly for >100 mJy sources.
Neptune Measured/Model
Flux Densities
Triangles: Small scan map
Squares: Large scan map
Neptune Measured/Model
Flux Densities
Triangles: Small scan map
Squares: Large scan map
Neptune Measured/Model
Flux Densities
Triangles: Small scan map
Squares: Large scan map
Neptune Measured/Model
Flux Densities
Array
Measured/Model Flux Density Ratios
All
Large Map
Small Map
PSW
0.995 +/- 0.007
0.996 +/- 0.009
0.994 +/- 0.003
PMW
0.993 +/- 0.010
0.997 +/- 0.013
0.992 +/- 0.004
PLW
1.001 +/- 0.003
1.000 +/- 0.003
1.002 +/- 0.003
Gamma Dra Measured Flux Densities
Triangles: Small scan map
Squares: Large scan map
Gamma Dra Measured Flux Densities
Triangles: Small scan map
Squares: Large scan map
Gamma Dra Measured Flux Densities
Triangles: Small scan map
Squares: Large scan map
Gamma Dra Measured Flux Densities
Measured Flux Densities (mJy)
Array
Model Flux
Density (Jy)
All
Large Map
Small Map
PSW
251
258 +/- 3
260 +/- 2
258 +/- 4
PMW
127
139 +/- 4
140 +/- 5
138 +/- 4
PLW
61
74 +/- 5
75 +/- 5
73 +/- 5
These are monochromatic flux densities without color corrections (and without a u in
color).
Conclusions
• Although a few individual bolometers have
calibration uncertainties of >5%, each array as a
whole can measure flux densities with the following
accuracies:
PSW
1.5%
PMW
1.7%
PLW
0.5%
• The accuracy of the flux calibration for >100 mJy
sources will primarily be limited by the Neptune
models.