Performance optimization of indirect x-ray detectors requires proper characterization of both ionizing (gamma) and optical photon transport in a heterogeneous medium. As the tool of choice for modeling detector physics, Monte Carlo methods have failed to gain traction as a design utility, due mostly to excessive simulation times and a lack of convenient simulation packages. The most important figure-of-merit in assessing detector performance is the detective quantum efficiency (DQE), for which most of the computational burden has traditionally been associated with the determination of the noise power spectrum (NPS) from an ensemble of flood images, each conventionally having 107 − 109 detected gamma photons. In this work, the authors show that the idealized conditions inherent in a numerical simulation allow for a dramatic reduction in the number of gamma and optical photons required to accurately predict the NPS.
The authors derived an expression for the mean squared error (MSE) of a simulated NPS when computed using the International Electrotechnical Commission-recommended technique based on taking the 2D Fourier transform of flood images. It is shown that the MSE is inversely proportional to the number of flood images, and is independent of the input fluence provided that the input fluence is above a minimal value that avoids biasing the estimate. The authors then propose to further lower the input fluence so that each event creates a point-spread function rather than a flood field. The authors use this finding as the foundation for a novel algorithm in which the characteristic MTF(f), NPS(f), and DQE(f) curves are simultaneously generated from the results of a single run. The authors also investigate lowering the number of optical photons used in a scintillator simulation to further increase efficiency. Simulation results are compared with measurements performed on a Varian AS1000 portal imager, and with a previously published simulation performed using clinical fluence levels.
On the order of only 10–100 gamma photons per flood image were required to be detected to avoid biasing the NPS estimate. This allowed for a factor of 107 reduction in fluence compared to clinical levels with no loss of accuracy. An optimal signal-to-noise ratio (SNR) was achieved by increasing the number of flood images from a typical value of 100 up to 500, thereby illustrating the importance of flood image quantity over the number of gammas per flood. For the point-spread ensemble technique, an additional 2× reduction in the number of incident gammas was realized. As a result, when modeling gamma transport in a thick pixelated array, the simulation time was reduced from 2.5 × 106 CPU min if using clinical fluence levels to 3.1 CPU min if using optimized fluence levels while also producing a higher SNR. The AS1000 DQE(f) simulation entailing both optical and radiative transport matched experimental results to within 11%, and required 14.5 min to complete on a single CPU.
The authors demonstrate the feasibility of accurately modeling x-ray detector DQE(f) with completion times on the order of several minutes using a single CPU. Convenience of simulation can be achieved using GEANT4 which offers both gamma and optical photon transport capabilities.
This paper was partially supported by Academic-Industrial Partnership Grant No. R01 CA138426 from the NIH. The authors wish to thank Dr. Kevin Holt and Dr. Peter Munro for helpful discussions.
II.A. Monte Carlo modeling environment
II.B. NPS from a flood image ensemble
II.B.1. Expectation of qNNPS
II.B.2. Simulation error, χ2
II.C. MTF and NPS from a point-spread function (PSF) ensemble: Fujita-Lubberts-Swank (FLS) method
II.D. Modeling optical transport
II.E. Validation studies
II.E.1. 1D multilayer model
II.E.2. Pixelated scintillator simulation
II.E.3. AS1000 EPID measurements
II.E.4. AS1000 EPID simulations
III.A. 1D multilayer Lubberts model
III.B. Wang pixelated detector: Flood image ensemble
III.C. Wang pixelated CSI detector: FLS simulation
III.D. AS1000 portal imager: Simulation vs experiment
III.E. Computation times
- Image sensors
- Modulation transfer functions
- Medical imaging
- X-ray detectors
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