VI.B.3 Photometry of Extended Emission

IRAS Explanatory Supplement
VI. Flux Reconstruction and Calibration
B. Determination of Relative Flux
B.3 Photometry of Extended Emission

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  1. Determination of F[TFPR]
  2. Determination of the TFPR Annual Variation

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:

  1. 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
  2. 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
  3. 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.

TFPR Model Parameters1
Table VI.B.1
Parameter:2 Effectivewavelength (µm)
12 25 60 100
B0 (MJy/sr)3 13.527.67.78.3
statistical uncertainty5
total uncertainty6
B1 (MJy/sr)3 1.402.30.580
statistical uncertainty5
total uncertainty6
(day)4 -23.8-22.3-26-
statistical uncertainty5
total uncertainty6
  1. The parameters have been converted to sky brightness (MJy sr-1) in order to illustrate the relative magnitudes of the parameters. The parameters were originally derived relative to the flashes of the internal reference source.
  2. At a time t in days the model assumes BTFPR to be:
    BTFPR = B0 + B1 × sin((2pi/365.25) × ( t - )]
  3. The usual convention of using a flat spectral distribution for the sources was followed in deriving the flux densities.
  4. l983 January 1 (UT) is day 1.
  5. The statistical uncertainty corresponds to a 1- deviation in the fit to the observations.
  6. The total uncertainty incorporates the estimated systematic uncertainties: 5, 6, 7 and 10% in the absolute calibration at 12, 25, 60, and 100 µm respectively; 5% for the frequency response and 10% for the solid angle. Note that these uncertainties are estimated to apply at the TFPR; they are clearly exceeded in other places in the sky.
  7. 3- upper limit.

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:

Vtia[TFPR,1] = R[1] × F[TFPR] + Vtia[off]
Vtia[TFPR,2] = R[2] × F[TFPR] + Vtia[off]

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:

(Vtia[IRS,1]) = R[1] × FIRS


(Vtia[IRS,2]) = R[2] × FIRS

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:

Equation (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.

B.3.b Determination of the TFPR Annual Variation

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.

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