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Figure 10: Noise maps before (left) and after (right) the processing. For this observation 1 ADU/g/s corresponds to 0.242 mJy/pix |
From the comparison of the final maps of the two GRB observations (Figs. 8D and 8E) we can estimate the reliability of our processing. At first glance we see that the structure of the diffuse emission is very similar in both maps; the LTT correction applied seems to restore properly the large scale structure. Furthermore, almost all point like structures are present in both maps, giving confidence in our bad pixel identification.
The difference of the two final sky images is shown in Fig. 8F.
It is dominated by small-scale structure noise but large-scale structures are also apparent.
These are probably due to error in the LTT correction.
Extra noise is seen at point source positions. This was expected as memory effects
are not fully corrected on point sources and as we are undersampling the point
spread function (PSF).
One also notices that the noise level is higher at the edges of
the difference map, due to less redundancy in these regions.
The standard deviation of the difference map (Fig. 8F) in the central part
of the field is 0.06 ADU/g/s.
Therefore, the noise on each GRB final map can be estimated at
ADU/g/s.
It is clear from the difference map (Fig. 8F) and from the impact of the LTT
on the sky image that noise is present at all scales. The processing presented in this paper
affects the signal at various scales. To characterize the noise as a function of angular scale
we use the structure function of second order:
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(12) |
The goal of this section is to show that the high spatial frequency noise of our maps is close to the optimal value obtained with stabilized ground calibration data with no glitches. The data are affected by many sources of noise. First, there are the classical quantum photon noise and the detector readout noise which have been extensively studied in the pre-launch calibration phase (Perault et al. 1994). A conservative value of the readout noise is given in the ISOCAM cookbook: 1.5 ADU/g. Secondly, memory effects (short term transient, long term transient and slow glitches) and fast glitches with small amplitudes substantially increase the noise level. These non-Gaussian events may prevent to reach the optimal sensitivity.
The noise level is measured on the flux history of pixels for which fast glitches have been removed. We have selected pixels not affected by slow glitches. We quantify the noise using the standard deviation of the high frequency component of the pixel flux history. We see in Table 2 that the noise level of the two GRB observations is in total agreement with the readout and photon noise estimated from calibration data (for a 41.5 ADU/g/s flux).
The flux
at a given position in the final sky image is the average of N independent
flux measurements. The error
on
can be estimated by
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(13) |
For each sky image of Fig. 8, Table 2 lists
the median error ,
the median redundancy N and the median standard deviation of the N
flux measurements averaged at each sky position. The first thing to notice is that the noise level
decreases gradually through the processing.
In the final sky image, the median
is only 5%
above the noise calibration measurement for the GRB1 observation. The noise in the
GRB2 observation is exactly the one obtained with stabilized ground calibration data with no glitches.
The dispersion of the difference between the two final maps (divided by )
is 0.04 ADU/g/s (see Sect. 6.1)
which is 35% above the noise level computed on each final map (0.03 ADU/g/s - see Table 2).
This 35% difference is partly due to the increased noise on point sources
and to the imperfection of the LTT correction. Nevertheless, considering
the amplitude of the instrumental effects (3 ADU/g/s for the LTT) we think
that the comparison between the two GRB observations
is a strong validation of the whole processing.
Finally we conclude from the numbers of Table 2 that the noise level in our final maps are dominated by the readout and photon noise. The other instrumental effects are corrected in the data reduction. Such ISOCAM sensitivity has been obtained in recent point source extraction studies (Desert et al. 1999; Aussel et al. 1999) where the low frequency diffuse emission is removed. It is the first time that such a sensitivity is reached for the emission structure on all scales.
Sky Image | ![]() |
Nb | ![]() |
|
GRB1 | Before LTT correction | 0.062 | 76 | 2.72 |
After LTT correction | 0.053 | 76 | 2.32 | |
Variable Flat Field | 0.046 | 76 | 2.01 | |
Final map | 0.031 | 58 | 1.21 | |
GRB2 | Final map | 0.030 | 60 | 1.15 |
a Median error value of each sky image (in ADU/g/s).
b Median redundancy of each sky image (in number of readouts).
c
(in ADU) = Error
Integration time.
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