5 Limitations and work in progress

5.1 Flux history before the observation

One critical problem with the correction methods comes from the difficulty to estimate properly the flux history before the first readout of the observation to be processed. Especially at low levels, strong memory effects due to the unknown history may affect the whole observation.

Practically, an observation is made, for all pixels, of N readouts: J _n (t), for n going from 0 to N-1. Whatever the correction method is, the first corrected value $J _{0} ^\infty$ is computed from J ₀ (t), $J _{-1} ^\infty$ and $J _{-1} ^{{\rm end}}$ (Eq. 6), where $J _{-1} ^\infty$ and $J _{-1} ^{{\rm end}}$ are the input flux during the integration before the first one and the measured signal at the end of this integration respectively. We see that the state of the pixel before the first integration (number 0) is fully contained in $J _{-1} ^\infty$ and $J _{-1} ^{{\rm end}}$(if stabilization, $J _{-1} ^\infty = J _{-1} ^{{\rm end}}$). Therefore to correct the response measured by one pixel, it is mandatory to estimate as properly as possible these two numbers.

Actually, two alternative methods can be used to estimate the flux history before the observation:

• If the first readouts seem stabilized, it is assumed that $J _{-1} ^\infty$ and $J _{-1} ^{{\rm end}}$ are equal to an averaged value of the first readouts for each pixel;
• If the first readouts are not stabilized then if we can supposed that (1) the flux is constant at the beginning of the observation and during a significant number of integrations and (2) the flux before staring the observation was also constant, then it is possible to apply the fitting techniques presented in Sect. 3.4 to estimate $J _{-1} ^\infty$ and $J _{-1} ^{{\rm end}}$.

It is obviously much more difficult to recover a realistic history at low level than at high level because of longer time constants and smaller signal to noise ratio. This point can be critical for CVF observations.

5.2 Time discontinuities in data set

In the ideal case, the data should be corrected without any time discontinuity. The observing time of ISO was shared between the four focal plane instruments. However, even when ISOCAM was not the prime observing instrument, it was still active and data were transmitted with a low telemetry rate (Siebenmorgen et al. 1996), except during 6 hours per revolution when the instruments are switched off.

Temporal discontinuities in the data flow come from: (1) turn on at the begin of each revolution, (2) from time to time, telemetry was canceled, (3) problems due to on board software when filter wheel motors are commanded, (4) instantaneous glitches (one or few readouts lost), (5) data splitting due to data proprietary protection.

The transient correction works without any problems induced by glitches (which are actually substituted by a local median value). Points (2) and (3) are equivalent to the glitches problem (4). Point (5) should disappear in the next future since the data can now be processed revolution by revolution.

Figure 9: Corrections of transients with the old IAS method (upper panel) and our new method (lower panel). The data are the same as in Fig. 6

Figure 10: Comparison between CVF reconstructions with the old IAS method and the new one, for downward and upward scanning. Upper panel: one full scan CVF (downward (solid line) and upward (dots)), original data; middle panel: inversion with the old IAS method; bottom panel: inversion with the new method we propose, based on the Fouks-Schubert model. (1) the shape of the downward scan is correct over the full range, even at the beginning of the observation (we start at 17.5 $\mu$m) and (2) upward and downward are quasi superposed over the full range

5.3 Accuracy of the dark correction

We have shown in Sect. 3.2 and in Fig. 4 that the FS model is very sensitive to the absolute level. This is critical near the dark level, since the time constants of the response are inversely proportional to the current observed flux. Moreover, 0 is a singular point in the model (we have seen in Sects. 3.2 and 3.3 that if we have for one readout $J^\infty= J^{{\rm end}}$= 0, then the response for all the following readouts is $\beta J^\infty$). Negative values may induce long term divergence in the correction. Therefore for observations with low input fluxes (especially with the CVF), the accuracy of the dark correction is critical.

At the present time, a dark image computed using the estimator of the time behavior of the dark signal (Biviano et al. 1998) is subtracted for each readout. In some cases, the dark subtraction is not perfect since some negative values may appear. For data containing significant upward steps of flux, the FS model can be used to refine the determination of the absolute dark level.

5.4 Long term drift

The correction method we have presented does not correct the long term drift (see Fig. 1 and Sect. 2) which generally affects the data after a positive upward step. The physical origin of this drift is still not understood.

For large scale mapping obtained by successive pointings of the satellite (raster mode), a powerful correction method is proposed by Miville-Deschênes (1999). This method uses the redundancy of the observation since in raster mode a significant fraction of the sky positions is observed by different pixels at different times.

  
5.5 The problem of point sources

When the observed field contains high spatial gradients, the FS model cannot describe the observations and the corrections we propose in this paper generally fail. This is critical for point sources since the responses measured for bright sources are actually never properly corrected.

For the same initial and final levels (after stabilization), the response of all pixels of the point source departs from the uniform illumination response. For the brightest pixel the response is (1) generally non monotonous, (2) is faster than the FS one and (3) a peak appears for strong sources (brightest pixel at least 80 ADU/G/s above the background). The brighter the source, the higher that peak.

The model we present in this paper is developed for low contrasted illumination of the detector. The cross talk between pixels (Fouks 1992; Fouks et al. 1994) and non linear effects due to a non uniform illumination of the pixel (the PSF is under-sampled for a large fraction of observations) have been neglected. We are currently working on these problems.

  
5.6 Oscillations in the response curve

We have seen (Sect. 3.5) that for typically 10% of the pixels, the FS model does not allow us to describe properly the response because of temporal oscillations in the response curve. Most of these pixels are close to the detector's edges and corners (Abergel et al. 1999). In a first order, the higher the amplitude of the flux step, the higher the amplitude of the oscillations. For these pixels, the correction obviously fails. However, at low levels (few tens of ADU/G/s) the mean error remains generally limited (a few $\%$) after transient correction.

One possible explanation could be cross talk between pixels since the gradient of charge distribution is higher near the edges than in the central part of the detector. However, Fouks (1997) has suggested an improvement of the FS model to deal with these oscillations without cross talk. But first attempts with this model fail to reproduce the oscillations observed in ISOCAM LW data.