synthesis, the AT of the thinned array additionally depends upon the size of the array and the degree of thinning, which generally leads to a significant degradation in sensitivity over what can be achieved with a total power radiometer in a "stare" mode, because, as the physical collecting area is reduced, the signal-to-noise ratio is correspondingly reduced to the detriment of the radiometric sensitivity. Such a trade-off is discussed in (LeVine 1989) which concludes that the sensitivity obtained with aperture synthesis is proportional to that obtained with a total power radiometer of the same system temperature, bandwidth and integration time. The proportionality constant is the "fill" factor which is the ratio of the effective area of the synthesised antenna to the actual collecting area employed in the array. The reduction in sensitivity that this entails can be restored by a correspondingly increased integration time because the synthetic aperture does not need to scan as it collects energy from many independent, fixed antenna pairs.

A Microwave Imaging Radiometer with Aperture Synthesis (MIRAS) in two dimensions for earth observation applications from space based on the VLA configuration of Fig. 2 is presented in Fig. 5 (Tanner et al. 2006). MIRAS consists of a Y-array of microwave receivers located at the points of a hexagonal grid. Each pair of receivers forms a single particular baseline and the correlations of all baselines as a function of their relative position form the complex visibility function. Each sample of the visibility function measures a particular spatial harmonic of the brightness temperature image across the field of view. The brightness temperature can be recovered by an image reconstruction process which is similar to an inverse

Fig. 5 Two-dimensional Aperture Synthesis Concept: MIRAS has receivers along the main directions of a hexagonal grid (top-left); the correlations between all pairs of receivers (baselines) populate the spatial frequency domain (bottom); the image reconstruction provides the brightness temperature of the Earth, Spain (top-right)

Fig. 5 Two-dimensional Aperture Synthesis Concept: MIRAS has receivers along the main directions of a hexagonal grid (top-left); the correlations between all pairs of receivers (baselines) populate the spatial frequency domain (bottom); the image reconstruction provides the brightness temperature of the Earth, Spain (top-right)

Fourier transform. To save in complexity, the spacing between receivers can be made larger up to the point where the alias free field of view reaches the desired swath extent, as per Fig. 13. An extended alias free field-of-view is limited by the six-curved contours of the earth aliases, as seen in Fig. 5 (top-right). Moreover, the large field of view present in earth observation induces non-negligible effects of individual antenna patterns, obliquity factors and spatial decorrelation effects (Cor-bella et al. 2004). Experimental work on SMOS has shown that mutual effects of closely spaced antennas, as well as their individual matching, become important to fully understand the measurements. For SMOS, a complete re-formulation of the visibility function, including full antenna characteristics and interactions between receivers, was developed in the Corbella equation, a full derivation of which is contained in the Appendix. The main outcome is that when these effects are taken into account, the measured cross correlation between receiver output signals turns out to be proportional to the inverse transform of the difference between the brightness temperature of the source and the physical temperature of the receivers. This effect, which has never been taken into account in previous approaches, has an important impact on inversion techniques and also on instrument specifications and performance.

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