On The Sampling In Imaging Microwave Radiometers

In imaging radiometer systems the necessary sampling time is dependent on the dwell time per foot-print. Traditionally two different approaches are seen: either a sampling time equal t o the dwell time per foot-print, or sampling twice per dwell time. The correct sampling is between these two extremes: a sampling time of 70% of the dwell time per foot-print is required for realistic antenna patterns. clude that, a s i t is a completely unreal pattern having negative sidelobes! (IMPORTANT: we are dealing with power pattems as the brightness temperature to enter the antenna is a power measure). The reason is purely academic and will emerge a little later. The two next curves represent far more realistic patterns namely a (sin X / X ) ~ having -13 dB side lobes and (sin X / X ) ~ with 26 dB first side lobes. This statement is supported by an investigation of the normalized pattems of two actual antennas: one with a 140 h aperture (1.4 m a t 30 GHz f.ex.) and one with a 600 h aperture (2 m of 90 GHz f.ex.). When plotted on Figure 1, (not done here a s i t tends to obscure the figure), the two curves lie nicely between curves C and D. Finally curve E is a Gaussian pattern also sometimes used as a reference for overview considerations. In an imaging radiometer system the antenna foot-print moves across the scene to be sensed, and the dwell time per foot-print is defined as the time i t takes the antenna beam to move a distance of one foot-print. When the antenna beam scans a scene with a certain brightness temperature distribution, this results in a cer. tain variation in the input signal to the associated radiometer, hence there are certain requirements to the sampling in that radiometer . Quite clearly the spectrum associated with these input variations to the radiometer heavily depends on the dwell time per foot-print: the faster the scan, the quicker the variations or to say i t differently: the wider the spectrum. But, a s it will be shown in the following, also the actual shape of the antenna pattern plays an important role. In mathematical terms the sensing by the moving antenna of the scene corresponds to a convolution of the antenna pattem with the brightness temperature distribution of the scene. Hence, to find the transfer function H(D associated with that process i t is assumed that the antenna beam sweeps across a delta function in the scene distribution. Then H(0 is simply found as the Fourier transform of the antenna pattern (transformed to the time domain by means of the scan velocity or the dwell time per foot-print). Figure 1 shows a host of idealized antenna patterns. The pattems have been normalized to have equal 3 dB width, and without loss of generality this has been assumed to be 2 sec (i.e. the foot-print dwell time is 2 sec). Curve A represents a sector shaped pattem often used for overview considerations. B is the main beam of a sin x/x pattern. I t may seem odd to inA ; Sector sin 1.9 t R' 1.9 t . -3 -