next up previous contents index
Next: 5.3 Dark Current Subtraction Up: 5. Photometric Calibration Previous: 5.1 Introduction


5.2 Photometric Model

This section describes the model used for converting measured slopes in $ \mu $V/s, (see Chapter 2.4) to absolutely calibrated flux densities (in Jy). The measured slope, $ S$, is a linear combination of the source flux incident on the detectors, instrumental gain $ G$, the dark current $ D$ and the Flux conversion factor $ G_c$. This is described by the following equation:
$\displaystyle F(\lambda)$ $\displaystyle =$ $\displaystyle G(t, block, det, aotband, \lambda ) \cdot G_{c}(aotband) \cdot ( S(t,\lambda) - S_d(t) )$ (5.1)

where $ t$ is the time of the observation, $ block$ is the detector block, $ det$ the detector number, $ aotband$ is the unique combination of detectors, apertures, and orders to describe a wavelength range, and $ \lambda$ is the specific wavelength. The different types of detectors (e.g., In:Sb) are grouped into 6 different blocks. Blocks 1 through 4 refer to the grating detectors and each block has 12 detectors. Blocks 5 and 6 are Fabry-Pérot detectors and each of these blocks only has 1 active detector.

Note that in Equation 5.1 it is implicitly assumed that all memory effects (see section 9.2) can be neglected or have been removed.

The instrumental gain is split into several orthogonal components:

$\displaystyle G(t, block, det, aotband, \lambda )$ $\displaystyle =$ $\displaystyle G_{p}(t,block) \cdot$  
    $\displaystyle G_{f}(det, aotband) \cdot$  
    $\displaystyle G_{r}(detector, \lambda , aotband)$ (5.2)

$ G_{p}$ accounts for time variations in the detectors response at the time of observation but is assumed constant within the observation. This correction brings the measurement to a standard time determined by the Cal-G 41. The correction is calculated from observations of the internal grating calibrator. Traditionally these observations are called `photometric checks'.

$ G_{f}$ corrects for the response of an individual detector relative to the average of the detectors. This gain brings the response of all the detectors (within a band) to that of one average detector. The flat-field coefficients are found in the Cal-G 43. The Fabry-Pérots do not have any flat-fielding values applied since they are single detectors and not in blocks.

$ G_{r}$ corrects for the response of a detector at wavelength $ \lambda$ (anywhere within the band) relative to the response of that detector at an optimum system response wavelength of the band. The gain factor, $ G_{r}$, is called the Relative Spectral Response Function (RSRF).

The Relative Spectral Response Function characterises the wavelength dependent response of SWS. The wavelength range of the grating section of the ISO-SWS is covered in 15 overlapping spectral bands. Each of these channels, sometimes also referred to as AOT-bands, are characterised by a unique combination of the instrument aperture, the grating order, the detectors used and a set of order selection filters in the light path. Therefore every detector has a different RSRF in every band. In each band, a block of 12 detectors is used. Thus, the complete RSRF behaviour of the SWS grating section is characterised by $ 12~\times~15$ RSRF functions. The RSRF functions are retained in calibration files Cal-G 25_xx.

In each of the 10 independent SWS gratings and 5 independent SWS Fabry-Pérot (FP) bands a wavelength and a bandpass have been chosen where the RSRF is at its maximum, and where the spectra of the calibration standards are featureless. These so-called `key wavelengths' (listed in Table 5.3) were used for determining the scaling constants between signal ($ \mu $V/s) to flux density (Jy). The grating calibration made use of SWS06 observations of astronomical standards centred at these `key wavelengths' over the corresponding passbands.

$ G_{c}$ is the conversion factor from corrected signal in $ \mu $V/s to flux density units in Jy. These numbers are retained in calibration file Cal-G 42.

For the Fabry-Pérot mode, sources considered to be continuum in their emission at the FP key wavelengths were observed. They are listed in Morris 1999, [30].

Following Equation 5.1 the actual source flux $ F(\lambda)$ is reconstructed by first subtracting the dark current from the measured slopes, and subsequently applying the instrumental gain and the flux conversion to convert the signal within the band to flux in Jy.

next up previous contents index
Next: 5.3 Dark Current Subtraction Up: 5. Photometric Calibration Previous: 5.1 Introduction
ISO Handbook Volume V (SWS), Version 2.0.1, SAI/2000-008/Dc