SMOS In-Orbit External Calibration and Validation (2005)

SMOS is ESA’s second Earth Explorer mission with the objective of producing global maps of Soil Moisture and Ocean Salinity over the Earth. The launch date is expected in September 2007. The only instrument on-board SMOS is an L-band Microwave Imaging Radiometer with Aperture Synthesis (MIRAS). This paper describes what is believed to be the optimum strategy to calibrate and validate MIRAS in-orbit using external targets. Central to the method are the flat target response and the flat target transformation of the Corbella equation. The paper includes the application of the technique to image reconstruction and some illustrative simulations. Introduction The Flat Target Transformation (FTT) has been derived based on the Corbella equation, which correctly describes how MIRAS works [1]. The proposed in-orbit calibration and validation approach is thus fully based on this equation. The main objective of the FTT is to minimize the impact of antenna errors, as they are outside the internal calibration loop. In a markedly different way to the point target response method used to calibrate other imaging systems, the FTT is essentially based on measuring a flat (uniform) target as the cold sky near the galactic poles. The original motivation to deviate from the classical impulse response calibration resides on the fact that no emitters are allowed in the protected radio-frequency band of MIRAS. The Corbella Equation The fully-polarimetric Corbella equation of the visibility function V was derived in [2] and reads as follows: V pq ij (u, v) = 2kB √ BiBj αiαj × 1 √ ΩiΩj ∫∫ ξ2+η2≤1 F n,i (ξ, η)F β,q∗ n,j (ξ, η) T B (ξ, η) − δαβTr √ 1− ξ2 − η2 rij ( − + vη fo ) e−j 2π(uξ+vη) dξ dη (1) where p and q are the polarisations (in the antenna reference frame) that are selected in each of the two receivers i and j involved in the particular baseline, (u,v) the baseline in wavelengths (λo=c/fo), (ξ,η) the direction cosines, kB=1.38×10-23 J/K is the Boltzmann constant, B the equivalent noise bandwidth of the receiver, α the peak voltage gain of the receiver (including antenna losses) –not to be confused with the polarisation superscript–, Ω the solid angle of the corresponding antenna, Fnα,p the normalised voltage antenna pattern in α polarisation when p polarisation is selected, TBαβ the brightness temperature in αβ polarisation, Tr the receiver physical temperature (assumed the same for all receivers), r the fringe-washing function and δαβ the Kronecker delta. Eq.1 assumes Einstein’s sum convention over the repeated α and β indices, meaning implicit summation over them as in the following example, where the same selected polarisation p is assumed in both receivers: F n,i F β,p∗ n,j ( T B − δαβTr ) ≡ F p,p n,i F p,p∗ n,j (T pp B − Tr) + F p,p n,i F q,p∗ n,j T pq B + F q,p n,i F p,p∗ n,j T qp B + F q,p n,i F q,p∗ n,j (T qq B − Tr) (2) where Fnp,p and Fnq,p are the coand cross-polar normalised voltage antenna patterns respectively, when the p polarisation is selected. The Corbella equation fully describes the behaviour of an aperture synthesis microwave radiometer as MIRAS and predicts that antenna errors are critical since they scale with the temperature contrast (difference) between the brightness temperature of the target and the receivers physical temperature. Ocean salinity retrieval in SMOS is thus challenging. 530 Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26 MIRAS Flat Target Response A flat target is defined as follows: one which is completely unpolarised, with the same brightness temperature in every direction and constant over time. Excellent realisations of such reference flat targets at the spatial resolution of MIRAS are the cold sky near the galactic poles and the absorber wall of an EMC anechoic chamber that is at a known physical temperature. In the case of the cold sky around the galactic Pole [3] T v P = T h P = 3.5 K (3a) T vh P = T hv P = 0 K (3b) The visibility function of a flat target at To can be derived from Eq.1: V pq ij (u, v; To − Tr) = (To − Tr) V αα,pq ij (u, v; 1) (4) where V αα,pq ij (u, v ; 1)≡ 1 √ ΩiΩj ∫∫ ξ2+η2≤1 F n,i (ξ, η)F α,q∗ n,j (ξ, η) 1 √ 1− ξ2 − η2 rij ( − + vη fo ) e−j2π(uξ+vη)dξdη (5) will be called the flat target response of the instrument from now on. Flat Target Transformation The impact of antenna errors would be minimized if, in the Corbella equation, the receiver temperature were replaced by the average temperature of the scene, that is: ⌣ V pq ij (u, v) ≡ 2kB √ BiBj αiαj × 1 √ ΩiΩj × ∫∫ ξ2+η2≤1 F n,i (ξ, η)F β,q∗ n,j (ξ, η) T B (ξ, η)− δαβ T B (ξ, η) √ 1− ξ2 − η2 rij ( − + vη fo ) e−j 2π(uξ+vη) dξdη (6) The FTT achieves this objective through the following transformation ⌣ V p q ij (u, v) = V p q ij (u, v)−∆V p q ij (u, v) (7)