Impact of Photon Counting Detector Spectral Response on Dual Energy Techniques

Photon counting detectors with energy discriminating capabilities offer the exciting prospect of dose efficient dual energy x-ray imaging. Several techniques have been proposed to form the energy-dependent detector measurements needed for dual energy. However, their performance depends on the limitations of the detectors, an important one being the detector's spectral response. Therefore, in this paper, we study the effect of a detector's spectral response on several dual energy techniques with photon counting detectors. We use a two-parameter model to characterize realistic spectral response functions, which exhibit a Gaussian photopeak trailed by a lower energy tail. The dual energy techniques compared all reduce the spectral data into two measurements using the following methods: (1) binning with an optimally chosen energy threshold; (2) a hybrid photon counting/energy integrating detector; (3) μ-weights, which have been shown to be optimal for ideal detectors. Their performances for different spectral responses are compared by evaluating the Cramer-Rao Lower Bound (CRLB) for estimating the unknown material thicknesses. We show that as the spectral response worsens, μ-weights rapidly deteriorate in performance while a hybrid detector's relative performance improves and consistently outperforms binning. Although the weighting functions are highly sensitive to a detector's spectral response, numerical optimization techniques can find two sets of weights whose performance is close to that of measuring the full detected spectrum.