All ISOPHOT detectors are photoconductors. Therefore the crucial calibration measure is the photocurrent generated by the incident infrared photons. A detector is characterised by the detector responsivity R_det which is the ratio between the photocurrent I and in-band power P_src:

$\begin{displaymath} R_{det} = \frac{I}{P_{src}}~~~~~~~~~~~~~~~~(A/W).\end{displaymath}$

(4.1)

In the first stage of data collection the output voltage from an integrating amplifier is measured. From these data the signal or voltage increase per unit time is obtained, see Chapter 3. The in-band power can be derived from signal and responsivity if the capacitance of the integration capacitor, C_int, is known:

$\begin{displaymath} P_{src} = \frac{C_{int}s_{src}}{R_{det}}~~~~~~~~~~~~~~~~(W),\end{displaymath}$

(4.2)

where s_src is the source signal in V/s. The value for C_int depends on the detector used and is assumed to be constant throughout the mission. R_det, however, is not a constant and can depend on external parameters such as the strength of the ionizing radiation and flux history.

In principle, FCS measurements scheduled in all PHT-P and PHT-C AOTs should ensure that P_src can directly be obtained from the comparison between the sky and the FCS signal without knowledge of the exact value of R_det.

FCS measurements are obtained in all ISOPHOT AOTs except P40. However, for some observations the FCS measurements can be of insufficient quality, or, in the case of P40, completely absent. In such cases a default responsivity should be adopted.

The default detector responsivities were derived during the in-orbit calibration. The values of the default responsivities are provided in Cal G files, see section 13.11. The relationships between FCS heating power and the corresponding in-band power measured by the different detectors are also given in the Cal G files.

A detector is linear if Eqn. 4.1 is independent in-band power on the detector. Deviations from linearity introduce a bias when deriving the responsivity from the FCS measurement or when using a single (default) value for R_det. To avoid this bias the FCS signal is tuned close to the source signal by the AOT logic. This strategy may fail in the following cases:

In these cases the dynamic range of the signals is high whereas the calibration is performed by one or more FCS measurements using a single heating power.

In case of a PHT-S observation with AOT PHT40 no FCS measurement is performed (cf. section 3.5). The PHT-S signals are directly converted to fluxdensities assuming constant responsivities for each pixel. The Cal G file containing the conversion factors for each PHT-S pixel is described in section 13.16. The conversion factors for each pixel are derived by frequent observations of a number of calibration stars. Due to this procedure detector non-linearities can influence the PHT-S results. Currently, these effects are under investigation.

The above description of the detector responsivity is still idealised and is only valid for responsivity values averaged over timescales longer than the measurement time. On shorter timescales the responsivity can still vary. The stability of the responsivity depends on the radiation history including the history of ionisation radiation. Detailed descriptions of the most important phenomena are presented in the next section.

4.2.2 Transient behaviour after flux change

After an illumination change, the output signal of a PHT detector shows a systematic drift in time. Such a drift effect is also referred to as a detector transient. A common feature to all transient curves is the asymptotic approximation to a stable level. This typical slow response is due to the presence of low ohmic contact material necessary to connect the detector substrate with the metallic wires.

Typical drift curves are presented in Fig. 4.1. In case of a flux drop a signal decay and in case of increasing flux steps a signal rise (Fig. 4.1) is observed. The doped silicon detectors (SS, SL, P1, and P2) exhibit a hook response during the first 40 seconds after large positive flux steps (Fig. 4.1b). The signal shows a behaviour similar to a strongly damped oscillation around the asymptotic level. For even higher flux steps the signal behaviour can be restricted to an overshoot followed by a slow decay.

The characteristic stabilisation time scales depend on (1) the detector material, (2) the flux change, (3) the illumination level, and (4) the temperature of the detector. They vary from a few seconds up to several minutes.

Typical timescales for stabilisation after a given flux step for the PHT-SS/SL detectors are presented in Table 4.1. These timescales can be taken as approximate values for detector P2 and lower limits for P1. The stabilisation time is defined as the time after flux step to reach 90 % of the signal at $t=\infty$ ( $S_{\infty}$ ).

Note that a signal of 0.5 mV/s is very close to the dark signal and - in practice - cannot be determined accurately. The relative stabilisation time is faster for positive flux steps - cf. table values below the diagonal versus those above the diagonal. Flux steps at low flux levels will take more time to stabilise. However in such cases the S/N and the detector stability (see next section) might be more important.

The doped germanium detectors P3 and C100 tend to stabilise faster than the doped silicon detectors. C200 shows the shortest transient time scales. Typical time scales are 100 sec for P3 and C100 and 40 sec for C200.

**Table 4.1:** Stabilisation times for a given flux step in seconds. The first row lists the initial signal, the first column the final signal in V/s
	5.e-4	0.001	0.01	0.1	1	10
5.e-4	...	6800	11500	11880	11900	11900
0.001	4070	...	5570	5900	5960	5960
0.01	1500	1220	...	560	592	595
0.1	240	210	122	...	55	59
1	32	30	21	12	...	5
10	4	4	3	2	1	...

**Figure 4.1:** Examples of P1 detector transients. Upper panel (A): multi-filter observation of the star HR6705, filter sequence P_16 (64 sec integration), P_3.6 (64 sec) followed by the P_3.6 (32 sec) FCS measurement. Both the P_16 as well as the P_3.6 FCS measurement show a downward drift, with a longer stabilization time for the fainter P_16 signal. Lower panel (B): 4 transient curves after a flux step overplotted in the same graph for comparison, the highest curve corresponds to the largest positive flux step. In all cases the signal prior to each step was the same and had a strength of about 35 V/s. For these flux steps a signal overshoot is detected followed by a strongly damped oscillation.
$\begin{figure} \begin{center} \begin{tabular} {c} {\epsfxsize=10cm \epsfbox{driftfig1.eps}} \\ \end{tabular}\end{center}\end{figure}$

For chopped measurements the same drift behaviour description applies. Due to the chopper modulation, the signal evolution on each chopper plateau can be regarded as a drift curve after a flux step. Consequently, the difference signal between the on- and off-target chopper plateaux is not only a function of flux step but also a function of chopper frequency. Without applying drift corrections use of the difference signal seriously underestimates the actual flux of the target. It has been observed that the signal differences between neighbouring chopper plateaux remain stable, even in case of a measurement containing a general drift (see section 4.2.3), provided that the flux difference between the chopper plateaux is less than 50% of the total signal. An example of a chopped measurement with P2 is presented in Fig. 4.2.

**Figure 4.2:** Examples of P2 detector transients induced by the chopper modulation on a very high source-background contrast. Upper panel (A): slow (32 sec per chopper plateau) chopped measurement on a high source-background contrast. Lower panel (B) same source-background contrast as under (A) but with a a higher chopper frequency (8 sec per plateau). Note the strong overshoot in the first higher plateau; a straight signal average per chopper plateau would underestimate the background subtracted source signal in both cases
$\begin{figure} \begin{center} \begin{tabular} {c} {\epsfxsize=10cm \epsfbox{chopfig1.eps}} \\ \end{tabular}\end{center}\end{figure}$

PHT32 uses the chopper in the sawtooth mode to obtain oversampled maps. Detector transients of bright sources can introduce ghost images in neighbouring areas. This can happen when a bright source is observed at the end of a sawtooth sweep. When the chopper is directed back to the starting point the transient causes an increased signal which is measured at the beginning of the next chopper sweep. The signal decays with the relevant time scale thereby mimicing a point source detection. Consequently, the ghost is always displaced from the bright source by 180'' (=amplitude of the chopper sweep) in Y-direction.

The study of transients have led to the development of an PHT AOT logic which should minimise disturbing effects by detector transients:

Not every measurement will last long enough to provide a stabilised signal. Laboratory and in-flight measurements showed that the transient curves are reproducible under the same flux conditions. Methods to correct for these transient drifts based on physical models as well as on empirical results are currently under development by the PHT instrument dedicated team.

For the present OLP software (Version 7) no sophisticated treatment of transients is applied. Instead, an algorithm is used which determines per chopper plateau whether a significant signal drift is present. In case such a drift is found, the last stable part of a chopper plateau is used (see also section 7.3.5).

A description of detector transients tested against the doped silicon detectors (PHT-S and PHT-P) can be found in Schubert et al. 1995 [27]) and Acosta-Pulido et al. 1999 [1]. C200 detector transients have been studied by Wilke [36]). A study of in-orbit transients and descriptions of correction methods and practical recipes are presented in Acosta-Pulido et al. 1999 [1].

4.2.3 Drift behaviour of responsivity

Besides the transient behaviour, the responsivity of a detector can vary or drift on timescales ranging from less than an hour up to the entire science window of 16 hours (see ISO Satellite and Data Manual [17]). Responsivity drifts are mainly observed for the doped germanium detectors (P3, C100 and C200) and are a result of both the illumination history of the detector as well as the rate of ionising radiation falling on the detector, see also section 4.4.

Ionising radiation causes the detector responsivity to increase in time. This increase can be as high as 80%, 100% and 30% for P3, C100, and C200, respectively. The responsivity drift for these detectors is steeper at the end of the science window where the amount of ionizing radiation rapidly increases. Long integrations with the same detector can be affected by this effect. Examples are multi-filter photometry with PHT22 and multi-aperture photometry with P3 in PHT04. For large (raster) maps available in AOTs P03, P22, P32, and in the sparse map modes P17/18/19 and P37/38/39, the responsivity drift can be assessed from the two FCS measurements collected at the beginning and end of each map. For polarisation observations the polarisers are cycled with a cycle time of at most 128 sec per polariser to assess the long term stability of the detector during the observation.

On the other hand, very high flux levels in excess of 5 V/s for P3 and C100, and 10 V/s for C200 can cause the detector to cure during the measurement (see also section 4.2.4). The resulting effect is a decrease of the detector responsivity during the measurement. This decrease can amount to several percent up to a factor 1.5 of the initial responsivity. Such drifts are very difficult to correct for.

The observed responsivity drifts for the doped silicon detectors P1, P2 and PHT-SS/SL are less than 20% over the entire science window.

4.2.4 Curing Procedures

Due to the high ionizing radiation during perigee passage of ISO the responsivities and noise levels of the ISOPHOT detectors are strongly increased before the beginning of the new science window. Therefore different curing procedures have been designed for different detectors to restore the nominal responsivities. The procedures are applied after switch-on before the beginning of the science window.

For the doped germanium detectors (P3, C100 and C200) a combination of bias boost (absolute increase of the bias voltage) and two to three infrared flashes using one of the FCSs are applied. For the doped silicon detectors (SS, SL, P1, and P2) curing is achieved by exposing the detector to a higher temperature at a reduced bias voltage for a defined period of time. In addition, P1 undergoes a flash curing.

The doped germanium detectors are much more susceptible to drifts caused by accumulating effects of the high energy radiation impacts (section 4.4). In order to keep their responsivities within the nominal range a second curing procedure is applied around apogee passage in the hand-over window when the satellite control is switched from VILSPA (Madrid) to Goldstone (California) (see [17]). More about the effects of ionizing radiation inside the science window is described in section 4.4.

**Figure 4.3:** The relative variation of the responsivity of the P1 detector with respect to the mean value as a function of revolution number for the first 500 ISO revolutions. Each revolution lasts to good approximation 23 hours and 56 min.
$\begin{figure} \begin{center} \begin{tabular} {c} {\epsfxsize=10cm \epsfbox{p1trend.eps}} \\ \end{tabular}\end{center}\end{figure}$

Trend analysis of responsivity measurements performed immediately after the curing procedures indicates that the nominal responsivities are reestablished with $\pm$ 2% accuracy for all detectors if the space environment conditions are stable.

The doped silicon detectors are not very sensitive to geomagnetic storms. Typical responsivity variations for detector P1 are shown in Fig 4.3. It shows that the responsivity can be restored to better than 2% off the mean value. A long term variation can be noticed which is possibly correlated with the position of the Earth with respect to the Sun.

The doped germanium detectors are more sensitive to the space environment with variations in the responsivity between 20-50% during geomagnetic storms. A striking example is given in Fig 4.4 where the C200 responsivity variations are shown. C200 responsivity peaks can last for several revolutions. They are correlated in time with the geomagnetic storm activity induced by solar flares.

**Figure 4.4:** The relative variation of the C200 detector responsivity with respect to the mean value as a function of revolution. The responsivities of the 4 detector pixels have been averaged
$\begin{figure} \begin{center} \begin{tabular} {c} {\epsfxsize=10cm \epsfbox{c200trend.eps}} \\ \end{tabular}\end{center}\end{figure}$

4.2.5 Dark Signal and Noise

Dark current in the detector assembly adds a spurious dark signal to the source signal. Dark signals for the different detectors have been measured by means of dedicated observations in dark instrument configuration. These observations have been collected frequently throughout the mission. The in-orbit dark signals were found to be several factors higher than expected from pre-flight data. For all detectors except P3, the dark signals increased by a factor 2-3. For P3 the dark signal is up by a factor $\leq$ 50. The increase is attributed to the effects of ionizing radiation on the detectors.

The typical equivalent fluxes to dark signals for a number of detector/filter combinations are listed in Table 4.2. A flat power spectrum is assumed in the derivation of the dark flux values. In case one would like to know the typical dark flux for a different filter of the same detector one should multiply the values in the table with the factor C1(table_filter)/C1(new_filter) where C1 is the transmission parameter described in section 5.2.3. The values in Table 4.2 were derived by assuming default responsivities for the detectors (given in section 13.11). Note that pixel 6 of the C100 array shows a factor 3-7 higher dark signal than the other pixels in the C100 array.

**Table 4.2:** Dark signal equivalent fluxes
Detector ID	Filter ID	Dark Flux
		(mJy)
P1	P_11p5	41
P2	P_25	410
P3	P_60	48
C100(1)	C_100	55
C100(2)	C_100	116
C100(3)	C_100	81
C100(4)	C_100	50
C100(5)	C_100	100
C100(6)	C_100	395
C100(7)	C_100	48
C100(8)	C_100	56
C100(9)	C_100	95
C200(1)	C_160	34
C200(2)	C_160	36
C200(3)	C_160	27
C200(4)	C_160	35

The pixels of the PHT-S arrays have dark signals that show systematic variations with wavelength. Improper dark signal subtraction could cause the presence of spurious features in the spectrum. The dark signals for a number of PHT-SS detectors can be negative, this is not due to a negative dark current but due to a CRE effect. The equivalent flux to the dark signal in PHT-SL is typically 50 mJy for pixel 65 up to 250 mJy for pixel 128.

Trend analysis of dark calibration observations shows for all detectors a systematic variation as a function of orbital position. The dark signal gradually rises by a few percent per hour, accumulating nearly factor 2 towards the end of the revolution. Around 18 hours after perigee, in the last few hours of the science window, the dark signal steeply increases. This effect is caused by the rapidly increasing amount of ionizing radiation at the end of the science window. The germanium doped detectors (P3, C100 and C200) exhibit the largest increase of up to a factor 2-3. Dark signal corrections depending on orbital position has been included in OLP Version 7.

The dark signals can be higher for all detectors during a geomagnetic storm. If there are suspicions that observations may be affected by space weather activity it is advised to check the planetary ``K-index''. This parameter is strongly correlated with the space weather conditions. If within the 48 hours previous to a given measurement or on the same day the K-index is larger or equal than 4, it is possible that the measurement has been affected by the space weather. Tables of the K-index during the ISO mission will be made available in the future.

For differential observations the dark signal cancels out if the observations were taken close in time (<1 hour). Possible uncertainties in the target signal caused by the dark signal are in such cases automatically removed. For absolute photometry measurements in which the total sky flux must be determined the dark signal contribution can be important. For these observing modes (PHT05 and PHT25) PHT has offered the possibility to include a dedicated dark signal measurement.

All standard observations with PHT-S (AOT PHT40) is preceeded by a measurement in dark instrument configuration of 32 sec. This ``pseudo dark'' measurement cannot be used to subtract PHT-S dark signals, but offers the possibility to assess remaining detector transients from an earlier PHT-S observation, see section 5.6.7.

Average dark signal values obtained from many calibration observations are stored in a Cal G file (see section 13.7). These values are used to remove the dark signal from each measurement during SPD level processing.

4.2.6 Detector flat-fields

The pixels of the C100 and C200 arrays can be regarded as a number of individual detectors with their own responsivities. The detector flat-field gives the relative variation of the responsivites among the pixels with respect to the average responsivity over the array. The flat-fields measured in-orbit were found to be wavelength dependent. Therefore for each C-detector/filter combination a separate flat-field is necessary.

For those observations where the associated FCS measurement is done with the same filter, the flat-field correction is included in the responsivity values derived from the FCS measurements after correction for illumination variations (see section 4.5.4). However, observations with different filters compared to the FCS measurement need additional correction for the wavelength dependence of the flat field. See also section 7.4.3.

4.2.7 Detector Saturation

In rare cases, for very bright targets the power on the detector can be too high causing the detector to go into break-through condition. This means that the detector goes into a low ohmic stage and a high current is flowing onto the amplifier. In case such an event occurs all readouts will be saturated, and the observation should have been aborted by the instrument controllers. Illumination levels higher than $5{\times}10^{-10}$ W can be potentially harmful to the detector/CRE chain of the PHT-P1 and PHT-S detectors. Safety resistors have been built into the circuits in order to limit the amount of the current. To avoid any risk only a few astronomical targets are forbidden to be observed with P1: IRC+10216, 07 Car, VY CMa. Jupiter observations cannot be scheduled for P1 and PHT-S.