The calibration sources were observed either with PHT-P in a standard circular aperture that is defined per filter (23 arcsec for 3.3-7.7 microns, 52 arcsec for 10-16 microns, 79 arcsec for 20-25 microns and 180 arcsec for 60-100 microns), or with PHT-C in each pixel (43.5 and 89.4 arcsec pixelsize).
The flux range from 0.1 to 10,000 Jy is well covered by stars, planets and asteroids.
Model spectra are available for each of these stars, selected from the ISO Ground-Based Preparatory Programme (GBPP) and the Cohen, Walker, Witteborn et al. (CWW) absolute calibration programme. Models cover the wavelength range from 2 to 35-50 microns. Far infrared extrapolations also exist for some of them up to 300 microns that were provided by Martin Cohen using Engelke functions (Engelke 1992). In the range between 2 and 160 microns the SEDs have attributed uncertainties between 3 to 5%. Above 160 microns quoted errors are 5 to 6%. Both programmes used Kurucz model atmospheres of Sirius and Vega as common zero-point for their broadband photometry.
Some asteroids are well enough understood by thermophysical modelling
in order to be used as FIR standards. They can fill the gap at
intermediate flux levels, that appears at wavelengths between 45 and
200 microns, between planets and stars (see
Figure 1). Some
specific complications arise, since they are moving objects w.r.t.
the sky background and show periodic variations of their intensity
due to rotation and varying distance to the Earth and Sun. For the
actual photometric calibration Thermophysical Models (TPM)
(Mueller and Lagerros 1998) were produced which assume a rotating ellipsoid, thus
accounting for lightcurve variations, and parametrise heat
conduction, surface roughness and scattering in the regolith.
The accuracy of the predicted
asteroid fluxes is in general 10% in
the wavelength range from 24 to 500 microns, except for 106 Dione and 65
Cybele, where discrepancies between model and observations of 20-30% were
found. Table 2 lists the asteroids that were
actually used for ISOPHOT calibration.
Model SEDs are also available.
Note that the conversion factors used to derive the monocromatic
flux densities in Jy from
inband powers assume the spectral shape to be lambda x F_lambda = constant,
or equivalently nu x F_nu = constant. For each PHT filter a reference wavelength
is selected to which these flux densities are referred.
The result of this calculation stills need to be corrected
for the actual colour of the object, once this is known.
This causes a large uncertainty in the photometric calibration (up to 40%) if no corrections are made and a fixed responsivity for the PHT-S detectors is assumed.
In order to avoid this problem, as of OLP v8.4, a different approach was used to calibrate chopped PHT-S observations. The method is based on the direct comparison of the difference (on-off) signal of the source with the difference (on-off) signal of calibration standard stars of similar brightness.
For this, a number of faint calibration stars were selected with m_K = 1.65 to m_K = 7.54 to produce a database of chopped spectral response functions (SRFs) to be used for the absolute flux calibration of chopped PHT-S observations.
It should be noticed that there is a clear bias on the shape of the spectral energy distribution: the stellar spectra are always fainter towards longer wavelengths.
Table 3 lists the calibration observations used for the determination of the SRF of of chopped PHT-S observations. Their model SEDs are also available. They are taken from the ISO Ground-Based Preparatory Programme (GBPP).
A mean value for the chopped PHT-S SRF using inputs from all calibration standard measurements was derived from the ratio between the signal difference (on-off) observed and the predicted model flux for each calibration star. After this, a first-order correction was applied for all PHT-S pixels which takes into account for the systematic variations of the individual SRFs with the brightness of the calibration stars considered. This is just a consequence of the different relative intensity of the calibration sources with respect to the background (dominated by the Zodiacal Light at these wavelengths), which has to be considered since it is also affected by transients although it shows a time constant much longer than the integration time per plateau. Once this signal dependent correction is applied the so derived mean chopped SRF was used for the absolute flux calibration of PHT-S observations reaching in most cases the 10% level of accuracy.
The method, implemented first in PIA v7.3, and later in OLP 9.0, is based on a a direct comparison of the signal time evolution of the observed target with that of known calibrators.
The idea behind the method, suggested originally by Linda Cornwall (RAL) was worked out by Garzon and Hammersley (both IAC) and proposed to the PIA development team. The full implementation in PIA was performed by Jose Acosta Pulido (ESA/IAC) and later moved into OLP by Peter Abraham (MPIA).
The basic assumption of the dynamic calibration is that the transients behaviour (temporal response) of an individual pixel depends primarily on the flux level observed with a high reproducibility under a similar illumination history of the detector. The fact that PHT-S staring observations are always performed in the same way (source observation preceded by a short dark exposure), implies in most cases a very similar history and makes observations with this PHT subsystem specially suitable for this method.
A comparison of the signals achieved by the target to the ones achieved by different calibrators after same time intervals within an observation allows a discrimination of the most closed calibrators in flux to the target. The ratios obtained are then used for deriving the unknown target flux.
For this, a series of calibration measurements were performed on standard stars covering a range of magnitudes from m_K = -3.08 to m_K = 7.54. taking into account that preliminary tests had shown that the drift behaviour of a given pixel remains similar for a flux range of 0.5 magnitudes.
A complete list of the calibration observations performed with this purpose is given in Table 4 . The model spectra for each of these stars are also available. They are taken from the ISO Ground-Based Preparatory Programme (GBPP) and the Cohen, Walker, Witteborn et al. (CWW) absolute calibration programme.
The flux calibration is done in this method by taking the ratio between the signals from the target and the calibrator along the observing time and then deriving the mean and median values, which are scaled by the known flux from the calibrator chosen. The dark current subtraction should be performed previously to the dynamic calibration application.
Since the time evolution of the response for a given pixel is determined mainly by the illumination level NO background subtraction to the observed target should be done. Therefore the total flux (source plus background) of each calibrator has to be computed. The stellar models provided by P. Hammersley are used for computing the flux of the calibration stars while the background to be added was estimated from modelling Zodiacal Light (which is the dominating background at the PHT-S wavelengths) with an emission component (blackbody of T=267 K) plus a reflection component (BB of T=6000K). The relative scaling of the two components was done using COBE/DIRBE weekly averaged measurements at bands matching the PHT-S wavelengths.
The exposure time becomes naturally long at low illumination levels in order to get sufficient signal to noise ratio. Moreover, the response of the detector is extremely slow in these cases. Some observers have obtained observations of very faint targets, which are longer than the calibration observations. In order to extend the drift behaviour to the longest measurements obtained with PHT-S it was decided to include some of these measurements, listed in Table 5 in the database. The measurements which correspond to similar flux level were co-added at the signal level, producing average drift curves. In this way, the time evolution for each pixel is preserved and the signal to ratio improved. Then the average spectra are flux calibrated using the dynamic method and the best matching standard calibrators from Table 4. The method, as implemented in OLP v9.0, provides in most cases a final accuracy of 5-10%.