SCIAMACHY Product Handbook
Spatial Stray Light
where on the left hand side of the equation a scalar describes the light as detected by the instrument, and on the right hand side we have the polarisation sensitivity vector of the OBM, and the Mueller matrix defining the response of the scanner to the incoming light represented by another Stokes vector. The first element of this Stokes vector, I, denotes the total intensity of the light. Q is a measure for the polarisation along the x- or y-axis of a chosen reference frame and can be described as . U is a measure for the polarisation along the 45¿ direction and is defined as , and V is the circular polarisation component of the incoming light, which is negligibly small for atmospheric light. Note that the total intensity can be written as or . Often Q and U are normalised to the total intensity I. We will denote normalised fractions with q and u.The polarisation reference frame used in the calibration is defined w.r.t. the direction of the slit, at the plane of the slit: looking in the direction of the light entering the instrument after the scan mirrors, the +45¿ polarisation (u=1) direction is obtained by a 45¿ clockwise rotation from the long side of the entrance slit of SCIAMACHY (q=1). All calibration data use this reference frame.
All Mueller matrix elements are dependent on wavelength and on the incidence angle of the light on the scan mirror(s) or diffuser(s). In the calibration, ambient measurements on component level and instrument TV measurements have to be combined meaning that the actual instrument matrix has to be calculated by a multiplication of the matrix for the scanner (combination) and the OBM. Note that though the end-to-end circular polarisation sensitivity of the instrument is irrelevant when V is zero, the scanner may through its Mueller matrix introduce a circular polarisation component to the light, which requires the circular polarisation sensitivity of the OBM to be known. Though originally not foreseen for on-ground calibration, an update of the calibration concept introduced the circular polarisation sensitivity into the calibration equations. Defining the relative polarisation sensitivity vector of the OBM as:
the response of the instrument to polarised light becomes:
Combination of the polarisation response of the scanner and the OBM using
and making sure to normalise so that the first element remains unity, gives the equation describing the instrument response as expressed in total intensity and fractional linear polarisation (equ. 4-6)
where is the radiometric sensitivity of the instrument (with implicit dependence on wavelength for the main science channels, and determined as well for all 7 PMDs). The term in brackets is the inverse of the polarisation correction factor, c pol. It depends on the polarisation sensitivity of the instrument and the polarisation of the incoming light q and u.The instrument polarisation correction factor is thus with the definitions given above (equ. 4-7)
The problem of correcting the response of the instrument for polarisation can thus be divided into two parts: (1) determining the polarisation sensitivity of the instrument and (2) determining the polarisation of the incoming light during the science measurements in-flight.
The instrument response was measured on instrument level under TV conditions while the mirror and the mirror/diffuser combination were measured under ambient conditions. The Fresnel equations for reflection off a dielectric medium are used to describe the scanner withthe index of refraction determined from the ambient measurements, and hence used to calculate the Mueller matrix elements of the scanner for arbitrary angles used during TV measurements or in flight. While the OBM polarisation sensitivities (fig. 4-4) were derived during the on-ground calibration under thermal vacuum, from measurements with fully linearly polarised light at a range of polarisation angles.
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The second step, the determination of the polarisation of the incoming light is done by determining the ratio of the signal in the PMD channels – which is fully polarised due to the Brewster reflection at the pre-disperser prism (see chapter 3.2) – and the corresponding signal in the science channel for each individual measurement. During calibration this ratio was determined for different combinations of u- and q-polarised light. The comparison of the in-flight ratio with the calibration data gives 7 polarisation values for the whole spectrum, one for each PMD channel.
Polarisation values q are calculated from PMD A-F needing the corresponding value of u. The ratio u/q, which depends only on the polarisation angle, is assumed to be constant, such that (equ. 4-8)
In the original calibration concept, for UV-VIS wavelengths below 600 nm the polarisation angle from single scattering theory was planned to be used (see below), whereas for higher wavelengths the ratio u/q from PMD D and PMD 45°, both centred around 850 nm, had to be taken. The values of q and u here are derived by iteration, until the u needed to calculate q from PMD D and the q needed to calculate u from PMD 45°, match. In-flight it was noted that PMD 45° delivers systematically signals which are 10-15% higher than expected, even for unpolarised sources such as the sun. As there are indications that this PMD suffers from stray light, it remains currently unused. Instead, u/q is taken from single scattering theory for the complete wavelength range. From POLDER satellite measurements of u/q this appears to be a sufficiently accurate assumption (Schutgens et al. 2004). Note, that for small values of q, this ratio becomes very large, thereby amplifying small measurement errors on qmeasured into large measurement errors on umeasured. However, since the instrument is much more sensitive to q than to u, this has little impact on the radiometric calibration, even though u is notably unreliable. In limb, the calculated polarisation displayed an unexpected drift with increasing tangent height, which is probably due to increasing significance of the spatial stray light contribution as the limb intensity decreases. Therefore the PMD measurements are only used up to 30 km. Radiative transfer calculations show that above this height the depolarisation remains constant (Mc Linden et al. 2002), such that for higher limb tangent heights we are able to scale the measured polarisation at 30 km with a value obtained from single scattering theory.