Proc. SPIE. 5368, Medical Imaging 2004: Physics of Medical Imaging
KEYWORDS: Fiber optics, Imaging systems, Sensors, Interference (communication), Fiber optics sensors, Medical imaging, Monte Carlo methods, Digital imaging, Modulation transfer functions, Signal detection
Cascaded-systems analyses have been used successfully by many investigators to describe signal and noise transfer in quantum-based x-ray detectors in medical imaging. However, the Fourier-based linear-systems approach is only valid when assumptions of linearity and shift invariance are satisfied. Digital detectors, in which a bounded image signal is spatially integrated in discrete detector elements, are not shift invariant in their response. In addition, many detectors make use of fiber optics or structured phosphors such as CsI to pass light to a photodetector-both of which have a shift-variant response. These issues raise serious concerns regarding the validity of Fourier-based approaches for describing the signal and noise performance of these detectors.
We have used a Monte Carlo approach to compare the image Wiener noise power spectrum (NPS) with that predicted using a Fourier-based approach when these assumptions fail. It is shown that excellent agreement is obtained between Monte Carlo results and those obtained using a Fourier-based wide-sense cyclostationary analysis, including the description of noise aliasing. A simple model of a digital detector coupled to a fiber optic bundle is described using a novel cascaded cyclostationary approach in which image quanta are integrated over fiber elements and then randomly re-distributed at the fiber output. While the image signal sometimes contains significant non-stationary beating artifacts, the Monte Carlo results generally show good agreement with Fourier models of the NPS when noise measurements are made over a sufficiently large region of interest.
Theoretical models of the detective quantum efficiency (DQE) provide insight into fundamental performance limitations and standards to which particular systems can be compared. Over the past several years, cascaded models have been developed to describe the DQE of several flat panel detectors. This article summarizes the governing principles of cascaded models, and conditions that must be satisfied to prevent misuse. It is shown how to incorporate: a) poly-energetic x rays; b) Swank noise; c) the Lubberts effect; d) reabsorption of K x rays from photo-electric interactions; e)secondary quantum noise; and, f)noise aliasing. Cascaded models involve cascading theoretical expressions of the noise-power spectrum (NPS) through multiple stages. Most expressions involve two or three terms, requiring the manipulation of algebraic expressions consisting of hundreds of terms. This practical limitation is alleviated using MATLAB's Simulink programming environment and symbolic math manipulations. It is shown that even for an 'indirect' detector, noise aliasing reduces the DQE by up to 50 percent at the cut-off frequency. Secondary quantum noise is generally a small effect, but reabsorption can reduce the DQE by 20-25 percent over a wide range of spatial frequencies.
For x-ray detectors, Compton interactions deposit photon energies along the paths of recoil electrons, which are not isotropic about the primary interaction sites. Light from each interacting x-ray is only generated near the path of a recoil electron. In this study, Compton scatter is modeled as an input-labeled cascade of the amplification and scattering processes to describe the transfer relationship of signal and noise in frequency space. The output of the model is the spatial distribution of secondary quanta generated by Compton recoil electrons. We determine the spatial dependence and statistical correlation of secondaries from the initial energy of the recoil electron and its range, resulting in the 'Compton' modulation transfer function (MTF) and noise power spectrum (NPS), respectively. Then the 'Compton' MTF and NPS are used to calculate the 'Compton' detective quantum efficiency (DQE). The probability density function of scattering angle of Compton recoil electron is developed using the Klein-Nishina coefficients. Results are applied to the description of a portal imaging system at 6 approximately MV where non-Compton interactions can be ignored. The MTF results are compared with a Monte Carlo calculation. This is the first model of how Compton interactions in the metal-plate/phosphor combination degrade image quality in terms of signal and noise. It is shown that Compton MTF depends on energy of x-ray photon in a complex way, and Compton scatter imposes a fundamental limitation on both the MTF and DQE of x-ray imaging system.