1 Introduction

Because of the low brightness of the sky and their very low operating temperatures (typically a few K), the extrinsic photo-conductors used in infrared astronomy generally present systematic memory effects of the response. The response after a flux variation is not instantaneous and strongly depends on what has been observed before. The response can never be stabilized, and the final photometry is biased by a factor as high as several 10$\%$. Systematic corrections of these transient effects are generally necessary (1) to remove the trails due to the displacement of bright sources (2) to improve the photometric accuracy and (3) to reduce the observing times.

All the detectors of the four instruments on board the ISO satellite (Kessler et al. 1996) are extrinsic photo-conductors and are affected by this problem at various levels. Several examples of those transient effects have been published for the different detectors of ISO (see Table 1). The response curves are classified in three main families from the behavior after upward step of flux. A detector has a "normal'' behavior if the response to an instantaneous increase of the input flux increases monotonously after a quasi instantaneous jump. If the response presents a quasi instantaneous jump followed by a decrease and then by a monotonous increase, we have a "hook'' behavior (Fouks 1992). The detector of the SW channel of ISOCAM has an "other'' behavior since it does not present any instantaneous jump (but only a monotonous increase).

 

 

Table 1: Table of main families of low background IR detector (non exhaustive) on board ISO satellite. See type definition in Sect. 1

Type	Detector	Reference
normal	CAM Si:Ga LW	(Pérault et al. 1994; Abergel et al. 1999)
	PHT Si:Ga linear detector of PHT-S	(Fouks & Schubert 1995)
	SWS Ge:Be and Si:Ga single detectors of the grating section	(Wensink et al. 1992)
	LWS Ge:Be detectors of channel SW1 and stressed Ge:Ga of LW2	(Church et al. 1992b; Church et al. 1992a)
hook	PHT Si:Ga single detector of the channel P1	(Groezinger et al. 1992)
	SWS Si:Sb single detectors of the Fabry-Pérot section	(Wensink et al. 1992b; Church et al. 1992a)
	LWS unstressed Ge:Ga detector of the LW1 channel	(Church et al. 1992b; Church et al. 1992a)
other	CAM In:Sb SW	(Tiphène et al. 1999)

The ISOCAM camera (Cesarsky et al. 1996) operates in the $2.5-18~\mu$m range using two channels, the Short Wavelength one (SW) going from 2.5 to 5.5 $\mu$m, and the Long Wavelength one (LW) from 4 to 18 $\mu$m. The channels are selected using a wheel holding Fabry mirrors. The observing configuration is defined for each channel with a lens wheel to select the field of view per pixel (1.5, 3, 6 and 12''), and a filter wheel to select the spectral band pass. The operating temperature of the camera in flight is around 3 K. The integration times allowed in flight are 0.28, 2., 5., 10. and 20. s.

This paper is focused on the LW channel of ISOCAM. The filter wheel of this channel contains 10 broad band filters and two Continuously Variable Filters (CVF). The detector is a single crystal made of Si:Ga photo-conductor connected by Indium bumps to direct voltage readout circuits (Agnèse et al. 1989; Cesarsky 1992). 32 $\times$ 32 square pixels are electrically defined with a pitch of 100 $\mu$m. The crystal is 500 $\mu$m thick. The doper concentration of the bulk p is $\sim 5.~10^{16}$ cm^-3. The temperature inside the bulk is $\sim$3 K. The applied voltage was $\sim$20 V during the flight. The precise characteristics of the p⁺ contacts are not known. The quantum efficiency is $\sim$0.25.

The transient behavior of the LW channel has two components (Abergel et al. 1999): a short-term one which affects typically 40$\%$ of the total step and a very long-term drift which affects typically $5-10\%$ of the flux. Actually, the long-term component is not fully understood (we do not know whether it is predictable) and there is no method to correct it without using the redundancy of the observations (Miville-Deschênes et al. 1999). By contrast the short-term transient is perfectly predictable for uniform illuminations, and we present in Sect. 2 its main properties. In several cases (especially near the dark level), upward and downward steps are extremely different, which strongly constrains the models of the response used to develop correction algorithms. The model which has been used during the first two years of the mission, from 1996 to 1998, to process most of the data (Abergel et al. 1996) is not able to produce the observed asymmetry.

From a theoretical point of view, the Suris-Fouks- Vinokurov team has studied low background photo detectors during the last two decades (Suris & Fouks 1978; Suris & Fouks 1980; Fouks 1981a; Fouks 1981b; Vinokurov & Fouks 1991; Fouks 1992; Fouks 1996). Using solid state and semiconductor physics, they have derived several analytical models from the physical equations. The key parameters for such a detector are the doper concentration of the bulk p, the thickness of the bulk, the temperature inside the bulk, the contact properties (the dopant concentration of the p⁺ contacts) and the applied voltage. One very important hypothesis in these models is that the illumination of the pixel surface is uniform.

We describe in Sect. 3 one of these models developed by Fouks and Schubert (1995) for the Si:Ga detector of the PHT-S channel of ISOPHOT. Because several approximations can be made for this kind of detector, this model is one of the simplest non-linear models that Vinokurov & Fouks (1991) have developed. In Sect. 3, we show that this model allows us a remarkable adjustment of experimental data obtained for uniform illumination of the LW channel of ISOCAM, both for upward and downward steps. Each pixel is characterized by only two parameters (Sect. 3.5). We propose in Sect. 4 an original inversion method to correct systematically the data without any fitting. Limitations and works in progress are described in Sect. 5. Finally, we suggest in Sect. 6 extending our approach to other extrinsic photo-conductors of ISO and further experiments (especially to the normal ones, see Table 1).