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5.2 Calibration strategy

5.2.1 Calibration strategy involving the FCS

An observation with PHT-P or PHT-C always includes a photometric reference measurement using one or both internal fine calibration sources (FCSs, see also section 3.5) which are assumed to be stable troughout the mission. The emission from an FCS can be changed by adjusting the FCS heating power. The FCS reference measurement assesses the actual detector responsivity at the time of the measurement.

The crucial photometric calibration as contained in the Cal G files is the relationship between heating power applied to the FCS as commanded by the AOT logic, and the resulting in-band power illuminated on the detector. This is the basis of the derivation of the detector responsivity which characterises the detector at a given time. The detector responsivity enables transfer of calibration between filters of the same detector and/or between apertures.

Transfer of calibration is in practice necessary in case of multi-filter photometry (PHT03, PHT22) or multi-aperture photometry (PHT04) where one FCS measurement is taken for combinations of several filters and apertures.

The FCS calibration itself is obtained empirically by comparing the signal of a designated celestial calibration target and signals of several FCS measurements. Based on the known flux of the calibration target, its signal, and the known instrument transmissions, the in-band power is derived for each FCS measurement. These in-band powers are then related to the FCS heating powers.

Three types of astronomical targets - all being point sources - have been used as prime calibrators for the FCSs:

stars
Stellar calibrators are most suitable for the 2.5 to 35 ${\mu}$ m wavelength range. A dedicated ground based preparatory programme for ISO calibration standards was carried out to provide the ISO mission with the most consistent and most accurate set of calibration stars, see Jourdain de Muizon and Habing 1992 [23], van der Bliek et al. 1992 [34], and Hammersley et al. 1998 [7]. Another set of calibrated stellar spectral energy distributions was provided by M. Cohen from an independent calibration programme (Cohen et al. 1995 [3]). The confidence in the absolute calibration of the calibration stars is about 3% in the 2.5 to 35 ${\mu}$ m wavelength range and better than 10% at longer wavelengths up to 300 ${\mu}$ m. The model spectral energy distribution (SED) for Vega ( ${\alpha}$ Lyr) has been used to define the zero point for both programmes.
asteroids
Asteroids are used to cover the 35 to 200 ${\mu}$ m wavelength range. An extensive ground and airborne based calibration programme was carried out to quantify the fluxes and to monitor the light curves of the prime asteroids 1 Ceres, 2 Pallas, 4 Vesta, and 10 Hygiea, and other asteroids that have been observed with ISO. For the current calibration the absolute fluxes of the asteroids were derived using a thermophysical model (Müller and Lagerros 1998 [22]). The accuracy of the predicted asteroid fluxes is in general $\pm$ 10% in the wavelength range from 24 to 500 ${\mu}$ m.
planets
Outer planets Neptune and Uranus were used for calibration at the longer wavelengths in the high flux density range up to 1000 Jy. The model SED's for a given time in the mission were provided by M. Abbas. Comparison with independent model predictions for Uranus showed a consistency of better than 20% in the wavelength range between 30 and 240 ${\mu}$ m. At shorter wavelengths the models become less certain.

The stability of both FCSs was monitored against the bright secondary standard NGC6543 as well as against a set of fainter stars. A full description of the ISOPHOT calibration involving the FCS can be found in Schulz et al. 1998 [30].

5.2.2 Absolute calibration of FCS

The FCS calibration against celestial standards has been determined for 25 filter bands over the full range of possible astronomical flux densities.

The ISOPHOT instrument dedicated team has measured fluxes of prime calibrators in each available filterband spanning 3-5 decades of flux range per filterband. For a given calibration target, the following measurements were obtained in a given filter:

measurement of the FCS for which zero heating power is applied (also referred to as `cold FCS measurement' or `FCS straylight measurement'),
measurement of the calibration target,
measurement of one or more background positions, and
measurement of one to several FCS illumination levels.

The cold FCS measurement provided the zero FCS signal level. All measurements of the celestial calibrators included an uncalibrated amount of background emission which had to be subtracted. The background level was determined by performing one or more separate background pointings in the same aperture. In the case of multiple FCS measurements, the FCS illumination levels were tuned such that their in-band powers span a range of about one decade around the power expected from the calibration target plus background emission. It is assumed that the responsivity is linear in the measured power range.

Using the total optical transmission of the instrument and detector chain, the in-band power from the calibration source on the detector was computed using Eqn 5.6 below. By relating the in-band power of the calibration target to its corresponding signal, the FCS signals were converted to in-band powers. These together with the commanded FCS heating powers were used to derive the FCS power calibration tables. Assuming a measurement for a given aperture in case of PHT-P or pixel in case of PHT-C:

$\begin{displaymath} P_{fcs}^f(h) = P_{cal}{\cdot}\frac{(S_{fcs}^{f}-S_{str})}{S_{cal}} ~~~~~~(W),\end{displaymath}$ (5.1)

where

P_fcs^f(h): the in-band power in W for filter f and FCS heating power h in mW;
P_cal: in-band power in W of the celestial calibrator;
S_cal: measured signal in V/s of the prime calibrator after subtraction of the background signal;
S_fcs^f: measured FCS signal in V/s;
S_str: measured dark FCS signal (straylight) in V/s.

It is assumed that the difference signal between calibration source and background scales linearly with the signals from FCS measurements. Consequently, the accuracy of the absolute calibration of the background level depends on the linearity of the detector from zero to the background level and on the suppression of parasitic flux, such as straylight. Uncertainties become higher for flux levels close to the astronomical background because of the absence of reliable celestial calibrators that are faint.

Eqn. 5.1 is a simplification of the relation used to determine the actual FCS power tables. For PHT-P the tables are normalized to the aperture area, and for PHT-C the tables refer to a pixel, after correction for inhomogeneous FCS illumination (cf. section 5.2.3).

The FCS calibration makes the observation independent of long term responsivity drifts. However, on measurement time scales of order of 32-2048 s, detector transients (sect. 4.2.2) due to flux changes occur and have to be corrected for. For the determination of the overall FCS calibration drift corrections have been applied to estimate the signal level of the asymptotic limit.

5.2.3 Photometry with PHT-P and PHT-C

The FCS measurement together with the FCS power calibration tables (cf. section 13.10) are used to determine the detector responsivity. In the following derivations a separation will be made between single detector, multi-aperture, and multi-filter subsystems PHT-P and the multi-filter detector arrays PHT-C.

For a given PHT-P FCS measurement taken with detector det, filter f', and aperture a', the responsivity R_det is derived from:

$\begin{displaymath} R_{det} = \frac{S_{fcs}(a)C^{det}_{int}} {P^{f'}_{fcs}(h)A(a){\alpha}^{f'}(a)} ~~~(A/W)\end{displaymath}$ (5.2)

For a given PHT-C FCS measurement taken with detector det and filter f', and for pixel i, the responsivity R_det is derived from:

$\begin{displaymath} R_{det}(i) = \frac{S_{fcs}(i)C^{det}_{int}} {P^{f'}_{fcs}(h){\Gamma}^{f'}(i){\chi}^{f'}(i)} ~~~(A/W)\end{displaymath}$ (5.3)

where the prime (') indicates the FCS measurement configuration and

S_fcs: the signal in V/s from the FCS measurement after subtraction of dark signal or FCS straylight (only possible with PHT05 and PHT25);
C^det_int: the integration capacity in A/(V/s) (=farad) associated with detector det (see Fig. 3.2 and Table 13.5);
P^f'_fcs(h): the in-band power in W for filter f' and FCS heating power h in mW as obtained from the FCS power table, for PHT-P the power is per mm², for PHT-C per pixel;
A(a): the area of aperture a in mm²;
${\alpha}^{f'}(a)$ : dimensionless correction for inhomogeneous illumination of PHT-P aperture a by the FCS in filterband f;
${\Gamma}^{f'}(i)$ : dimensionless correction for PHT-C pixel i due to inhomogeneous illumination of the array by the FCS;
${\chi}^{f'}(i)$ : dimensionless correction for pixel i for non-uniform filter-to-filter responsivity of the PHT-C pixels.

Once the detector responsivity is known, measurements of a celestial source with filters of the same detector in a multi-filter photometry observation can be calibrated. For a given PHT-P measurement, the in-band power P_src^f(a) for filter f and aperture a is:

$\begin{displaymath} P_{src}^{f}(a) = \frac{[S_{src}(a)-S^{det}_{dark}]C^{det}_{int}} {R_{det}}~~~~~(W)\end{displaymath}$ (5.4)

For a given PHT-C measurement, the in-band power P_src^f(i) for filter f and for pixel i is:

$\begin{displaymath} P_{src}^{f}(i) = \frac{[S_{src}(i)-S^{det}_{dark}]C^{det}_{int}} {R_{det}{\chi}^{f}(i)}~~~~~(W)\end{displaymath}$ (5.5)

where S_src-S^det_dark is the source signal in V/s after dark signal subtraction. Note that the correction ${\chi}^f(i)$ cancels out for a PHT-C source measurement taken in the same filter band as for the FCS measurement. To convert from in band power to point source flux density on the sky, the following relation is used for PHT-P:

$\begin{displaymath} \frac{F_{\nu}^{f}}{k_f} = \frac{P_{src}^{f}(a)}{C1^f f_{PSF}^{f}(a)}~~~~~(Jy),\end{displaymath}$ (5.6)

and for PHT-C:

$\begin{displaymath} \frac{F_{\nu}^{f}}{k_f} = \frac{\sum_{pix i}P_{src}^{f}(i)}{C1^f f_{PSF}^{f}}~~~~~(Jy),\end{displaymath}$ (5.7)

where:

$F_{\nu}^{f}$ : the source flux density in Jy for an assumed spectral energy distribution ${\nu}f_{\nu}$ = constant;
k_f: the colour correction;
C1^f: constant in ${\rm m^2Hz}$ describing the transmission of the whole optical path for a given filter. The effective size of the primary mirror, reflections, filter transmission, spectral response of the detector, etc. are included;
f_PSF^f: (dimensionless) fraction of the ISO point spread function entering the field aperture in case of PHT-P or falling onto the entire array in case of PHT-C for filter f.

$F_{\nu}^{f}$ is also referred to as the flux density at the reference wavelength of the filter band and is the value of the flux density computed by OLP. It is required that the constant C1^f is identical to the one used in the determination of the FCS power tables.

5.2.4 Spectro-photometry with PHT-S

In the short wavelength range below 10 ${\mu}$ m very high FCS heating powers are required to get a reasonable in-band power. Due to the wavelength coverage of PHT-S no single FCS power can illuminate both SS and SL arrays without causing saturation in the SL array. Therefore, the PHT-S measurements (PHT40) are not accompanied by any FCS measurement. It is assumed that the PHT-S responsivity is sufficiently stable throughout the ISO mission.

The flux calibration for point sources is carried out by direct comparison between the signals (in V/s) of the PHT-S pixels and the flux (in Jy) of the calibration target. Only stars have been used for the determination of the PHT-S spectral response function. The responsivity was monitored on a weekly basis using calibration stars. The flux density $F_{\lambda}(i)$ of pixel i is derived as follows:

$\begin{displaymath} {F_{\lambda}(i)}= 10^{-20} \frac{[S_{src}(i)-S_{dark}(i)]}{C... ...}(i)}{\cdot}\frac{c}{{\lambda}^2(i)} ~~~~~(Wm^{-2}{\mu}m^{-1}),\end{displaymath}$ (5.8)

where

S_src(i)-S_dark(i): the source signal in V/s of a PHT-S pixel after dark signal subtraction;
C_s,pnt(i): the conversion in (V/s)/Jy from signal to point source flux density in Jy;
c: is the speed of light in m/s;
${\lambda}(i)$ is the central wavelength of the PHT-S pixel.

similarly, for extended sources:

$\begin{displaymath} {I_{\lambda}(i)}= 10^{-26} \frac{[S_{src}(i)-S_{dark}(i)]}{C... ...cdot}\frac{c}{{\lambda}^2(i)} ~~~~~(Wm^{-2}{\mu}m^{-1}sr^{-1}),\end{displaymath}$ (5.9)

where C_s,ext(i) is the conversion in (V/s)/(MJy/sr) from signal to point source flux density in MJy/sr.

Monitoring of the PHT-S responsivity at the beginning and end of each revolution has shown that the daily responsivity variation is at most 10% depending on the space weather conditions. Relative variations along a revolution and from revolution to revolution can be inferred by comparison with the PHT-S responsivity checks performed in the activation and de-activation windows at the begin and end of a revolution. Shorter time scale responsivity variations are mainly due to detector transients which can be corrected using a transient model.

Next: 5.3 Point sources versus Up: 5 Calibrations Previous: 5.1 Overview

ISOPHOT Data Users Manual, Version 4.1, SAI/95-220/Dc