IRAS Explanatory Supplement
VI. Flux Reconstruction and Calibration
B. Determination of Relative Flux
B.3 Photometry of Extended Emission
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Since there were neither on-board calibration techniques to establish the electronic offset voltage directly for each detector under zero photon flux conditions nor celestial sources of known total sky brightness, it was necessary to follow a special procedure to determine a Vtia[off]. The procedures can be summarized as follows:
- An area of the sky with a smoothly varying sky brightness, free from
point sources and near the north ecliptic pole and NGC6543, was selected
to serve as a secondary calibration source for the diffuse emission. The
area was called the total flux photometric reference or TFPR. Since the
viewing geometry of the TFPR through the zodiacal dust cloud varied throughout
the duration of the mission, the signal from this area of the sky varied
with time.
Figure VI.B.1.1 The variation of total sky brightness at 12 and 25 µm at the north ecliptic pole is shown as a function of day number of the year (1983, January 1 (UT) is day 1). See Section VI.B.3.b for explanation of the symbols.
larger largest - On several occasions during the mission direct measurements of
Vtia[off] were obtained while pointing at the TFPR.
These yielded direct comparisons of the flux from the TFPR,
FTFPR, with flashes from the internal reference source (see
Section B.3.a below). Hence values for the total sky
brightness, BTFPR, were obtained using measured values for
the solid angles in each band. More accurate and more frequent measures
of the annual variation of BTFPR were obtained by
differencing the fluxes from the north and south ecliptic poles obtained on
individual scans which passed over both poles (see
Section B.3.bbelow). These data are shown in
Fig. VI.B.1 along with the best fit models for the
annual variation. Table VI.B.1 gives the
parameters for the model in each band and summarized the errors of
measurement.
Figure VI.B.1.2 The variation of total sky brightness at 60 and 100 µm at the north ecliptic pole is shown as a function of day number of the year (1983, January 1 (UT) is day 1). See Section VI.B.3.b for explanation of the symbols.
larger largest - In order to update the values of Vtia [off] as needed for regular processing of the survey data, observations of the TFPR were made twice daily and the signals for each detector derived from the model of BTFPR versus day number were subtracted.
(day)
/365.25)
× ( t - 
deviation in the fit to the
observations.
B.3.a Determination of FTFPR
The determination of FTFPR was based on thee possibility of changing the detector responsivity, and hence the total photocurrent, while leaving the offset voltage Vtia[off] unchanged. In the case of the 12 µm detectors, the responsivity change was easily achieved since two bias voltage levels were available within the operating range of the detectors; see Section II.C.5. In the other wavelength bands, where the second bias levels resulted in channel saturation, the required change in responsivity was obtained as a result of passage through a dense portion of the SAA uncorrected by bias boosting (see Section IV.A.7), and the change in responsivity was achieved by applying bias boost while the TFPR was still observable. The special sequences to do this were started and ended by 13/16 second and 15 second multiple flashes of the internal reference source.
The reduction of the special calibration observations is illustrated with the equations representing the voltage at the trans-impedance amplifier as:
where the symbols [1] and [2] indicate high responsivity and low responsivity
conditions of the detector. FTFPR and
Vtia[off] are assumed constant during the
observation.
R[1] and R[2], the responsivities in the two states, can
be determined from the differential responses to the internal reference
source:
and
where FIRS is the source strength of the internal reference
source. The effects of the backgrounds and offsets cancel out since the
measurements are differential. In practice, the flashes used for these
special measurements were 15 seconds long; they therefore had to be calibrated
relative to the 13/16 seconds flashes normally used.
The relative source strength of the TFPR can now be found from:
(VI.B.3)
The quality of these special calibration observations varied with the
wavelength band; see Fig. VI.B.1. At 12 µm the
observations yielded a smooth sine wave which agreed in phase and amplitude
with measurements of the ecliptic polar differences seen in pole-to-pole
scans; see below. At 25 µm it was necessary to use only one of the two
detector modules (module 2A) since bias boosting altered the electronic
offset appreciably compared to the relatively small change in responsivity
produced by a 2 to 3 minute bias boost. Module 2A had been modified to
overcome pre-flight wiring failures inside the dewar and, fortunately, these
modifications greatly reduced the effects of bias boosting on
Vtia[off].
Some independent information concerning the zero point for each detector
was available during the first week of the mission when the cryogenically
cooled cover was still in place. This afforded essentially zero background
conditions for the 12 and 25 µm detectors and allowed their
electronic offsets to be measured directly. These measurements agreed with
the results of the special calibration measurements described above within
6% and 10% at 12 and 25 µm respectively. Unfortunately the internal
dewar background was not low enough with the cover in place at 60 and 100
µm to give useful results.
At 60 and 100 µm the change in responsivity of the detectors
as a result of the SAA dose and a short bias boost application was substantial
and it was possible to obtain useful data on a number of occasions by delaying
the bias boost until the telescope was pointed at the TFPR. All detectors
responded well to this procedure and repeatable results were obtained even
though the data are not as well behaved as those obtained in the 12 µm
band (see Fig. VI.B.1); in part this is due to the fact
that the sky brightness at 60 and 100 µm is considerably lower than at
shorter wavelengths.
Studies of the variation of Vtia[off] throughout
the mission in each of the bands show similar behavior; the relatively
smooth long term drift appears to be well correlated with measured changes
in the temperatures of the warm electronics boxes.
It must be kept in mind that no tests were available to validate the
design goal that the instrumental background would be negligible at 60
and 100 µm. The tests carried out to measure the out of field
radiation, however, indicate that stray radiation from the Sun and Earth
were negligible (see Section IV.C.3). It is assumed
that no significant radiation from within the instrument was able to reach
the detectors.
As discussed by Hauser et al. (1984)
the component of the sky brightness produced by the zodiacal dust emission
varies as the Earth makes its way through the interplanetary dust cloud.
It was possible to measure this variation without knowledge of the electronic
offset voltage by assuming that Vtia[off] changes
negligibly on the time scale of half an IRAS orbit. The observed difference
between the brightness of the north and south ecliptic poles on a single
scan is therefore a measure of the true difference in the sky brightness.
This difference was found to vary seasonally and to be well represented
in all wavelength bands except at 100 µm by a sinusoidal modulation
of half amplitude B1 TFPR, where the phase angle does
not vary with wavelength.
The pole-to-pole differences determined the time dependence of the TFPR
brightness much more accurately than the special calibration measurements.
The polar difference data were used to determine the phase angle and
modulation amplitude of the TFPR variation, while the special calibrations
provided the average DC brightness B0[TFPR]. The best fit
sinusoidal models in each band are presented in
Fig. VI.B.1, along with the half values of the ecliptic
polar differences. B0 was determined by a least squares fit
of the special calibration data to the independently determined sinusoidal
model for the annual variation.
In Fig. VI.B.1 the solid dots represent half of the observed difference
between the north and south ecliptic poles measured on single pole-to-pole
scans. The total sky brightness measured with the special calibration
observations is shown by solid squares for the north calibration polar region
(TFPR) and by solid triangles for the south polar region. The polar difference
data were positioned vertically by fitting them to the north polar special
calibration observations. The model of sky brightness variation derived
from these data and given in Table VI.B.1 is shown
as the solid curves. The special calibration observation data for the south
polar region was inverted in phase before plotting in the figure. The dotted
curve at 100 µm shows the best fit sine function. The open diamonds
show the TFPR brightness after the cover was ejected, assuming the telescope
background with the cover on was zero at 12 and 25 µm.
At 100 µm the annual variation was so small that the polar
differences were dominated by small variations resulting from small
differences in scan tracks passing over "cirrus" clouds near the
poles (see Low et al. 1984). As a result,
the value of B1[TFPR] at 100 µm was taken to be zero.
An upper limit to the value of B1[TFPR] at 100 µm
was found by fitting a sinusoid of the same phase found at shorter wavelengths
to the special calibration data. As can be seen in
Fig. VI.B.1, the result is a poor fit to the data and
the 30 upper limit is listed in Table VI.B.1.
Over half of the observations of the survey went through two passes
of processing. The first pass of the data reduction was used to determine
parameters of the model for the time dependent behavior of the TFPR. Once
the values for B1 and B0 listed in
Table VI.B.1 were derived as described above, they were
used during the second pass to recompute the twice daily determinations of Vtia[TFPR] which were then used to correct all of the survey
observations for small variations in the electronic offsets. No attempt was
made to include higher order terms in the model for the annual variation.
Systematic uncertainties in the value of B(TFPR) remain due to the limitations
of the total flux calibration procedure in fixing the average value of
the TFPR brightness, the assumption of sinusoidal time variation of the
TFPR, the methods used to determine the amplitude of the variation, the
ratio of point source to DC responsivity (Section
IV.A.4) and the effective detector solid angles
(Section IV.A.3). The statistical uncertainties
listed in Table VI.B.1 are derived from the fits to the
observations. The total uncertainties listed in
Table VI.B.1 include the
uncertainties in the absolute calibration
(Section VI.C.2.c), an estimated 5% uncertainty
in the frequency response for sources as bright as the TFPR, and a 10%
uncertainty in the determination of the solid angles. The uncertainty in
determining the average value of the TFPR brightness using the
responsivity-switching procedures is difficult to estimate, but the
comparison with the cover on/cover off test suggests this may be on the
order of 10% at 12 and 25 µm. No independent corroboration is available
at 60 and 100 µm. Refer to Section V.G for
a discussion of additional effects in directions other than the ecliptic
poles, such as the fixed pattern noise and corrections for the variations
caused by motion through the zodiacal cloud.
and
Vtia[TFPR,2] = R[2] ×
F[TFPR] + Vtia[off]
(Vtia[IRS,1]) = R[1] × FIRS
(Vtia[IRS,2])
= R[2] × FIRS
B.3.b Determination of the TFPR Annual Variation
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