2 ISOCAM transients description

2.1 Global description

The transient behavior of the LW ISOCAM detector has been analyzed during ground-based observations at IAS (Pérault et al. 1994; Abergel & Pérault 1994) and the current understanding after the mission is detailed in Abergel et al. (1999). We see in Fig. 1 that going from the dark level to an uniform illumination, the response is made up of a short-term transient followed by a long-term drift, with typical time constants equal to one minute and one hour respectively. This paper is focused on the short term transient.

Figure 1: Response of the central pixel after a flux step going from the dark level to the zodiacal emission observed with the LW10 broad-band filter ($8-15~\mu$m and centered to 11.5 $\mu$m, coinciding to the 12 $\mu$m IRAS band). The integration time of each frame is 2.1 s. This observation was taken at the beginning of a revolution of ISO, just after the switching on of the camera. Upper panel: First frames showing the short-term transient (see the text). Lower panel: Whole observation showing the long-term drift. (Fig. from Abergel et al. 1999)

The short term transient is made (1) of a jump of about 60% of the total step and (2) of a signal behavior which depends on the flux history, the amplitude of the current step, the pixel position on the detector matrix and the local spatial gradient illumination (Abergel et al. 1999). Upward and downward steps are not symmetrical (compare Figs. 2 and 3). The model systematically used up to now to process most of the data (Abergel et al. 1996) does not produce any asymmetry in the response curve, so the final precision cannot be better than $\sim$ 10$\%$.

The short term transient is extremely reproducible (the same history gives exactly the same response curve), so experimental data give very strong constrains for new models.

2.2 Short transient asymmetry

The asymmetry of the response is analyzed using data obtained during the preflight characterization (Pérault et al. 1994) and the revolution 16 of the Performance Verification phase (PV phase) of ISO. Uniform extended fields were observed (integrated spheres during preflight test, zodiacal background during revolution 16). The data presented in this paper correspond to individual pixels or mean values inside the 11 $\times$ 11 central square. Moreover, the signals measured by the camera are given using the internal output units of the camera ("ADU'': Analog to Digital Unit) divided by the electronic gain and the integration time (units: ADU/G/s). To convert these numbers into physical units, see Blommaert (1998). For example, with the LW1 filter, 1 ADU/G/s $\simeq$ 1 mJy.

The response to upward step from an initial level close to the dark level to a high level of illumination presents an inflection point (Fig. 2). This inflection point appears for all observations starting from levels not too far from the dark level and going to a final flux above $\sim$ 5 ADU/G/s. Its temporal position strongly depends on the initial and final fluxes (see also Sect. 3.2). For small steps of flux (typically below $\sim$10 ADU/G/s) this inflection point can be hidden by the noise. For upward steps higher than $\sim$ 50 ADU/G/s, a long term drift may also be visible (see Fig. 1). For a low ratio of steps of fluxes, this inflection point does not exist.

For downward steps from a high and uniform illumination to the dark level (Fig. 3), the inverse of the response increases linearly with time. So, the general shape of the downward steps is hyperbolic rather than exponential. The value of the slope depends on the initial flux. There is neither an inflection point nor long term drift.

Finally, ground-based data have indicated that the time constants (up and down) for each pixel and for any step of flux are at a first order inversely proportional to the current illumination.

Figure 2: Upward step of flux. These data were take during in-flight observations (tdt 12900101). Upper panel: Data (+, central pixel) and the Fouks-Schubert model (solid line) in linear scales. Lower panel: Derivative of the data (+) and the model (solid line). The levels before the step of flux is constant and stabilized. Therefore, we used Eq. (1), with: $\beta =0.55$, $\lambda = 551.$ ADU/G, $J_0 ^{\infty } = 4.4$ ADU/G/s and $J_1 ^{\infty } = 91.6$ ADU/G/s. In the difference between the data and the model, we can see the errors are below $\sim$ 3%

Figure 3: Downward step to dark level (data taken during the preflight measurements). Upper panel: mean central pixel (+) and Fouks-Schubert model (line) in linear scales. Lower panel: inverse of the data (+) and the model (line) in order to show the quasi linear shape of the downward step. The level before the flux change is constant and stabilized. The level after is the dark level (very close to zero). Therefore we used Eq. (2), with: $\beta =0.55$, $\lambda = 400.$ ADU/G, $J_0 ^{\infty } = 90.$ ADU/G/s and $J_1 ^{\infty } = 0.$ ADU/G/s. Preflight and in-flight values of $\lambda$ and $\beta$ are different (compare with 2) due to a different setup of the detector

2.3 Modeling of the short-term transient

A lot of models have been already proposed to describe ISOCAM-LW transients. The simplest ones use simple exponential formulae to describe the response starting from a stabilized level to a new one (e.g. Delattre et al. 1996). However, such an approach generally fails because (1) it does not take into account the whole history of illumination and (2) observed upward and downward responses are not symmetrical.

In previous studies (Abergel et al. 1996; Abergel et al. 1999), we have proposed an integral description of the response to take into account the history of illumination. This model ("the old IAS model'') has been systematically used during the last two years, but it fails to reproduce the asymmetry. Finally non linear models (see for instance (Ganga et al. 1998b; Ganga et al. 1998a) and the IRA model (Lari 1997) are more promising. However at the present time, none of these models have been systematically tested and compared with ISOCAM observations.