We present a theoretical framework describing projections obtained from computed tomography systems considering physics of each component consisting of the systems. The projection model mainly consists of the attenuation of x-ray photons through objects including x-ray scatter and the detection of attenuated/scattered x-ray photons at pixel detector arrays. X-ray photons are attenuated by the Beers-Lambert law and scattered by using the Klein-Nishina formula. The cascaded signal-transfer model for the detector includes x-ray photon detection and light photon conversion/spreading in scintillators, light photon detection in photodiodes, and the addition of electronic noise quanta. On the other hand, image noise is considered by re-distributing the pixel signals in pixel-by-pixel ways at each image formation stage using the proper distribution functions. Instead of iterating the ray tracing over each energy bin in the x-ray spectrum, we first perform the ray tracing for an object only considering the thickness of each component. Then, we assign energy-dependent linear attenuation coefficients to each component in the projected images. This approach reduces the computation time by a factor of the number of energy bins in the x-ray spectrum divided by the number of components in the object compared with the conventional ray-tracing method. All the methods developed in this study are validated in comparisons with the measurements or the Monte Carlo simulations.
We have developed a novel sandwich-style single-shot (single-kV) detector by stacking two indirect-conversion flat-panel detectors for preclinical mouse imaging. In the sandwich detector structure, extra noise due to the direct x-ray absorption in photodiode arrays is inevitable. We develop a simple cascaded linear-systems model to describe signal and noise propagation in the flat-panel sandwich detector considering direct x-ray interactions. The noise-power spectrum (NPS) and detective quantum efficiency (DQE) obtained from the front and rear detectors are analyzed by using the cascaded-systems model. The NPS induced by the absorption of direct x-ray photons that are unattenuated within the photodiode layers is white in the spatial-frequency domain like the additive readout noise characteristic; hence that is harmful to the DQE at higher spatial frequencies at which the number of secondary quanta lessens. The model developed in this study will be useful for determining the optimal imaging techniques with sandwich detectors and their optimal design.
Detectors for computed tomography (CT) typically consist of scintillator and photodiode arrays which are coupled using optical glue. Therefore, the leakage of optical photons generated in a scintillator block to neighboring pixel photodiodes through the optical glue layer is inevitable. Passivation layers to protect the silicon photodiode as well as the silicon layer itself, which is inactive to the optical photons, are another causes for the leakage. This optical crosstalk reduces image sharpness, and eventually will blur CT images. We have quantitatively investigated the optical crosstalk in CT detectors using the Monte Carlo technique. We performed the optical Monte Carlo simulations for various thicknesses of optical components in a 129 × 129 CT detector array. We obtained the coordinates of optical photons hitting the user-defined detection plane. From the coordinate information, we calculated the collection efficiency at the detection plane and the collection efficiency at the single pixel located just below the scintillator in which the optical photons were generated. Difference between the two quantities provided the optical crosstalk. In addition, using the coordinate information, we calculated point-spread functions as well as modulation-transfer functions from which we estimated the effective aperture due to the optical photon spreading. The optical crosstalk was most severely affected by the thickness of photodiode passivation layer. The effective aperture due to the optical crosstalk was about 110% of the detector pixel aperture for a 0.1 mm-thick passivation layer, and this signal blur was appeared as a relative error of about 3-4% in mismatches between CT images with and without the optical crosstalk. The detailed simulation results are shown and will be very useful for the design of CT detectors.
The modulation transfer function (MTF) is a typical parameter to measure the spatial resolution, which is an essential
factor for evaluating the performance of computed tomography (CT) systems. It is known that the CT system does not
follow the shift-invariant manner because of the cone-beam geometry and the transformation from the cylindrical
coordinates to the axial coordinates when the image reconstruction is employed. Several studies reported that if the
position of impulse receded from the center of a region of interest (ROI), the MTF degraded continuously. In this study,
the trend of shift-variant characteristics of CT systems was measured and analyzed using a novel multi-cylindrical
phantom. This study used to determine a point spread function (PSF) and MTF of a CT system using a simple cylindrical
phantom. First of all, the optimal diameter of cylinder phantoms was experimentally determined as 70 mm to obtain
reliable PSFs. Two kinds of field of views (FOVs), 40 cm and 60 cm, were used to vary reconstructed pixel sizes. The
shift-variant MTF curves were acquired at five off-center positions per FOV. For the effective analysis of MTF shiftvariance,
the integrated MTF values were calculated and used. In the result, the MTF slightly decreased as diameter
increased from CT center in the central region within the distance of 10 cm. Moreover, a considerable MTF decrease
suddenly occurred around the distance of 15 cm in the actual FOVs. The decreasing trend of the off-center spatial
resolution of CT cannot be neglected in recent radiologic and radio-therapeutic fields requiring high degree of image
precision, especially in sub-mm images. It is recommended that the ROI is laid on the CT center as close as possible. A
novel cylindrical phantom was finally suggested to effectively measure PSFs with optimal diameters for clinical FOVs in
this study. This phantom is cheap and convenient to use because it was only made of acryl with simple geometry. It is
expected that the spatial resolution of CT can be easily monitored using our methodology in clinical CT sites.