The price of tomography: SNR comparisons of acquisition strategies for x-ray fluorescence imaging

We have been working to develop and implement faster synchrotron-based X-ray fluorescence computed tomography (XFCT) methods for the mapping of trace metals in biological samples. As practiced now, the XFCT image acquisition process is slow (on the order of 1 or more hours per slice), which severely limits the ability to perform 3D imaging and to image multiple samples for sake of comparison and improved experimental statistics. This is because the data needed for tomographic reconstruction are acquired line-by-line in a first-generation tomographic geometry. Recently, we have been demonstrated the feasibility of using emission tomography systems for synchrotron X-ray fluorescence computer tomography. The proposed detection system combines high-resolution semiconductor detectors with multiple-pinhole apertures. The most promising acquisition mode involves using a sheet-collimated beam to illuminate a single plane through the object, which can then be directly imaged through the pinholes without need for tomographic reconstruction. Monte Carlo and experimental studies demonstrated the potential for order-of-magnitude improvements in SNR or imaging speed using this strategy. Some have found this surprising since the use of a pinhole collimator greatly reduces the detection efficiency of the system. In the present paper, we derive analytic figures of merit based on the ideal observer signal to noise ratio for the two geometries. These FOMs provide simple analytic insight into the reason for the improvement obtained with the pinhole-based system: the low detection efficiency is more than compensated for by avoiding the ill-posedness of tomographic reconstruction. The derived FOMs also provide a basis for performing system optimization.