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4.4 Transients

The occurrence of transients in responsivity after changes in the incident photon flux is a well known problem of extrinsic infrared photodetectors (see Fouks 1992, [31]; Coulais et al. 2000, [23] and references therein). In general, the transient response of such detectors cannot be easily described because the responses are non-linear and non-symmetrical. The transient not only strongly depends on the detector material and on the level of the incident flux, but also on the prehistory on the detector illumination and, for matrix arrays, on the signal gradient between adjacent pixels. Both SW and LW detectors of CAM present strong responsive transient effects. Stabilisation after changes of incident flux was the main problem encountered with these arrays. After a change of incoming flux, several tens, hundreds or even thousands of readouts may be necessary to reach stabilisation at the new flux level. Because of this behaviour it was recommended for each measurement to let the signal stabilise for a number of readouts ( $\rm N_{stab}$ ), before recording the science exposures ( $\rm N_{exp}$ ). It was however, for most observations, impossible to reach a fully stabilised signal, so that methods had to be developed to correct the data for the transient behaviour. These methods will be discussed in the following subsections. The worst cases were the following: a) switching to illumination after having the detector in the dark (the dark position of the entrance wheel); or b) after a saturating flux. The first problem could be reduced for the LW array by keeping always light on the array (e.g. by configuring the instrument to the ISOCAM parallel mode (Section 3.6) when ISOCAM was not used in prime mode) and executing the observations in order of decreasing flux. Dark calibrations were placed at the end of the science observations, or in those revolutions with no ISOCAM science activity in prime mode. An extensive description of the responsive transients after flux steps for the two detector arrays will be described in the following subsections. The responsive transient effect is one of the most important sources of systematic error in ISOCAM data. Therefore, it is mandatory to understand something of the nature of these transient effects and to apply transient correction methods.

4.4.1 SW transients

For SW, which accounted for only 5% of all CAM observations, a detailed physical model of the transient behaviour is lacking. Tiphène et al. 2000, [60] claim that the evolution of the responsivity with accumulated signal is likely to be related to surface traps in the semi-conductor. Those traps have to be filled first with photon-generated charges before the well begins to accumulate signal. Starting from the observation that the lower the signal, the longer the corresponding time constant, Tiphène et al. 2000, [60] developed a model that reproduces quite well the transient behaviour, using only a small set of parameters. The model provides the asymptotic value of the stabilised signal. However, because of the limited number of test cases available it is difficult to judge whether the method is generally applicable to the full range of SW data.

4.4.2 LW transients

The transient behaviour of the LW channel has two main components: a short term drift with an amplitude of typically 40% of the total stabilised flux step, and a long term drift or transient (LTT in the following) with a typical amplitude of about 5% of the total flux step (Abergel et al. 1999, [1]). The short term response at a given time strongly depends on the illumination history of the detector, and also on the spatial structure of the sky field viewed. The LTT can affect the data for hours, but does not always occur. These effects will be described in the following subsections.

4.4.2.1 LW transients under uniform illumination

The short term transient (see Figure 4.7) of the LW channel has the following components: (1) an initial jump of about 60% of the total signal step and (2) a signal drift behaviour which depends on the flux history, on the amplitude of the current step, on the pixel position on the detector matrix and on the local spatial gradient of the illumination (Abergel et al. 1999, [1]; Coulais & Abergel 2000, [21]). Upward and downward steps are not symmetrical.

**Figure 4.7:** *Upward and downward steps of flux (Up : in-flight data, TDT 12900101, down : ground based test). These examples show that the transient response is clearly non-symmetrical.*
$\resizebox {7.5cm}{!}{\includegraphics{trace_up_linlin.eps}}$ $\resizebox {7.5cm}{!}{\includegraphics{trace_down_linlin.eps}}$

It has been shown in Coulais & Abergel 2000, [21] that under quasi-uniform illumination of the detector array the short term transient response of individual pixels can be described by an analytical model, with an accuracy of around 1% per readout (for all pixels except those near the edges of the array). This Fouks-Schubert model (FS model in the following) was initially developed for ISOPHOT Si:Ga detectors (Schubert et al. 1994, [53]; Fouks & Schubert 1995, [32]). This is not an empirical model, but a true physical model, based upon a detailed knowledge of the detector construction and properties. It is a `1-dimensional model', in the sense that: (1) the pixel surface is assumed to be uniformly illuminated; and (2) one pixel does not interact with other pixels (the cross-talk between adjacent pixels compensates each other). The following equation describes the response for an instantaneous flux step at time

, from the constant level $J_0^\infty$ to the constant level $J_1^\infty$ :

$\displaystyle J(t) = \beta J_1^\infty + { (1-\beta) J_1^{\infty} J_0^\infty \over J_0^{\infty} + (J_1^\infty - J_0^{\infty}) \exp(-t/\tau)}$

(4.1)

$J_1^\infty$ is the stabilised photocurrent measured at time $t=+\infty$ . It is also directly related to the observed flux, since a linear relationship is assumed between the flux and the photocurrent after stabilisation. The parameter $\beta$ characterises the instantaneous jump just after the flux change. The theory gives a simple relationship between the time constant $\tau$ and $J_1^\infty$ over several orders of magnitude: $\tau=\lambda / J_1^\infty$ . Yet, the time constant is $\lambda$ . This non-linear and non-symmetrical FS model describes well the detector behaviour in response to both upward and downward flux steps, for a large range of flux changes. The description of the physics of the model, and the relevant hypotheses and simplifications are detailed in Fouks & Schubert 1995, [32] and the application to the ISOCAM LW detector is described in Coulais & Abergel 2000, [21]. Characteristic simulated outputs of the FS model are shown in Figure 4.8. The transient effect described by the FS model is sometimes called the `short term' transient in contrast to the long term drift (LTT). But at low input flux levels this short term transient can be very long. (e.g. CVF observations with signals exceeding the dark level by only 5 ADU/s). The FS model is fully characterised by two parameters for each pixel: i) the amplitude of the instantaneous jump $\beta$ , and ii) a constant $\lambda$ in the exponential term. No significant changes of these parameters were observed during the whole lifetime of ISO, so that only one 32 $\times$ 32 map for each parameter is provided (CCGLWTRANS, Section 6.1.10). The FS model is used in the transient correction applied in the ISOCAM Auto Analysis (Section 7.2.5). The application of this transient correction method to ISOCAM data (including a list of frequently asked questions about the FS model) is discussed in Coulais & Abergel 2002, [22]. Further details can be found in Coulais & Abergel 2000, [21] and Coulais et al. 2000, [23].

**Figure 4.8:** Simulated transient responses in the Fouks-Schubert model for upward and downward flux steps. Upward steps of flux from a constant level to a constant level occur at time s and downward steps from to occur at s. We have taken: = 0.01, 0.1, 1.0, 2.0 and 5.0 ADU/G/s, and = 10 ADU/G/s. For all these simulations, the values of the parameters $\beta$ and $\lambda$ are constant. We see that this model is very sensitive to the initial level for the upward steps : curves from 0.01, 0.1 and 1.0 ADU/G/s are very different. When the dark level is poorly estimated, such non-linear effect can allow us to estimate the value of .
$\rotatebox {90}{\resizebox{!}{14.5cm}{\includegraphics{fouks_theoric.eps}}}$

4.4.2.2 LW transients for point sources

In the LW array, the pixels are defined by the electric field applied between the upper electrode and the bottom 32 $\times$ 32 contacts (Vigroux et al. 1993, [63]). As a consequence of this electrical design of the array, adjacent pixels are always affected by cross-talk. Under uniform illumination, the instances of cross-talk compensate for each other. But this is not the case when the input sky exhibits strong fluctuations with angular scales around the pixel size (e.g. point sources with gradients between pixels typically higher than 20 ADU/s). The 1-D FS model, described in Section 4.4.2, fails for such point sources, and 3-D models are required. A new 3-D physical model has recently been developed by Fouks & Coulais 2002, [33]. In order to test this model and compare it with the observed transient responses for CAM point sources, a simplified 2-D model, using symmetry properties of the detector array and of the point sources was derived. Under uniform illumination, this 2-D model was carefully compared with the 1-D model and both were found to give the same transients. Without any modification, using the same ( $\beta$ , $\lambda$ ) parameters as for a uniform illumination, the new model immediately gave also the correct shape for the transients of the sharpest point sources which are very different from the transient responses predicted by the 1-D model (see Figure 4.9).

**Figure 4.9:** Data taken from the TDT 35600501 (filter LW5, lens 3 $^{\prime \prime }$ ). Brightest pixel: (10,15). Left panel: the data, and overplotted the 1-D Fouks-Schubert model to be used for uniform illumination case. For all the curves, the black lines are for the brigthes pixels, the blue line is the mean value of the $3\times 3$ pixels, the red lines are the 4 closest pixel to the brightest, and the green lines represent the 4 diagonal pixels. Right panel: the data, and overplotted with the new model for point source transients. Since in this configuration a narrow PSF is obtained, a good agreement between the data and the new model is expected. In both cases the same $\lambda$ and $\beta$ values are used. The unknown parameters are J and J.
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The new model works best for narrow PSFs. The model can still be improved for configurations in which the PSF is wide, for instance in the case of 1.5 $^{\prime \prime }$ and the long wavelength filters. An example of the present status of the correction for a wide PSF, is given in Figure 4.10. The transient response of the mean value of the $3\time3$ pixels centered on the brightest pixel is accurate up to the percent-level. For the individual pixels the accuracy achieved is a few percent. The new 3-D model is not used in the CAM OLP but is made available together with further information on request either by directly contacting Alain Coulais (currently at LERMA, Observatoire de Paris-Meudon) or through the ISO Helpdesk ( helpdesk@iso.vilspa.esa.es).

**Figure 4.10:** Data taken from the TDT 02201001 (filter LW10, lens 1.5 $^{\prime \prime }$ ). The different colours represent data from different pixels as explained in Figure 4.9. In this configuration, the point source has one of the largest possible FWHM of the PSF. For such a configuration the 2-D model gives a worse agreement between the data and the model on a pixel per pixel base than is found for smaller PSFs as in Figure 4.9. A better agreement is obtained for the $3\times 3$ mean value. The brown curve shows a second order correction term (which may be an improvement of the method, but which has not been extensively tested yet). It should be noted that these data are difficult to process because the illumination before the observation of the source is not uniform. As usual with such non-linear models, the results are very sensitive to the initial level, and, in this case, to its profile. Here, only a mean value was used, which may produce some error for the brightest pixel.
$\rotatebox {90}{\resizebox{11cm}{14.5cm}{\includegraphics{extra02201001.ps}}}$

4.4.2.3 LW long term transients

The LW array is also affected by long term transients (LTT). After an upward flux step, a drift becomes apparent generally after the stabilisation of the short term transient, while all the instrument parameters and the input flux are constant. This drift is characterised by a long term variation of the measured signal by a few percent (2 to 5%, see Figure 4.11). No LTT has been observed for downward steps. The LTT has never been modelled and it is not clear whether or not it may be stochastic. From ground based data, it seems that:

This drift always exists for steps higher than hundreds of ADUs;
The lower the initial level, the higher the drift amplitude.

A similar drift effect was predicted by Vinokurov & Fouks 1991, [62]. Their physical model has been compared to several ground based data sets (Coulais et al. 2001, [24]). However, the parameters of the model have to be separately adjusted for each data set, making it unsuitable for general application. The main technical problem comes from the large uncertainty in determining the absolute dark level.

**Figure 4.11:** This CAM LW in-flight observation starts just after the switch-on at the begin of a revolution. We clearly see the two components of the transient response: the short term transient from time $\sim$ 0 s to $\sim$ 50 s, which is the transient response described by the Fouks-Schubert model and, from $\sim$ 100 s to the end, the response change due to the long term drift (LTT). In this observation, the LTT amplitude is $\sim$ 7% which is especially strong for in-flight data.
$\resizebox {13cm}{!}{ \includegraphics*[5,5][480,330]{fig1_transient_long.eps}}$

The characterisation of in-flight LTT is even more complicated, and, up to now, no reproducible effects have been found. At the present time, since physical models cannot be used to describe the data affected by LTT, empirical dedicated processing methods have been developed. Two approaches exist for the extraction of reliable information from raster observations affected by LTT. For the case of faint point sources, as in cosmological surveys, source extraction methods are discussed in Starck et al. 1999b, [59] and Désert et al. 1999, [29]. For raster maps with low contrast large-scale structure (as in the case of diffuse interstellar clouds) an LTT correction method is now available in CIA. This method was developed by Miville-Deschênes et al. 2000, [41] and is based on the use of the spatial redundancy of raster observations to estimate and to correct for the LTT (see Figure 4.12). A further description of this method can be found in Appendix F.

**Figure 4.12:** When the contrast of the observed object is very low, and when the observations suffer from the Long Term Transient effect, it is important to use a correction method based on the spatial redundancy of raster observations. In the present case, the structure of a low contrast diffuse interstellar cloud is recovered (see Miville-Deschênes et al. 2000, [41] for more details).
$\resizebox {15cm}{!}{\includegraphics{ESA_info_note.ps}}$

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ISO Handbook Volume II (CAM), Version 2.0, SAI/1999-057/Dc