Generalized cascaded model to assess noise transfer in scintillator-based x-ray imaging detectors

Ho Kyung Kim
2006 Applied Physics Letters  
For a scintillator-based x-ray imaging detector, the conventional cascaded model is generalized to describe the direct x-ray induced quantum noise. The direct x rays are those that are unattenuated from a scintillator and that directly interact with photosensitive elements. The developed model is applied for an analysis of a photodiode array in conjunction with a phosphor screen and shows a good agreement with the measured noise-power spectrum. For a better design and assessment of x-ray
more » ... systems, linear-systems transfer theory is widely applied as it can represent a complex imaging system as a cascade of simple elementary processes, such as quantum amplification, binomial selection, deterministic blur, and quantum scatter. It therefore describes signal and noise transfer characteristics. 1 Various scintillator-based detectors have been evaluated with this Fourier-based linear-systems approach. 1,2 Since normally a scintillator has a finite thickness, the quantum detection efficiency is not always perfect. Instead, direct interactions of x rays transmitted through the scintillator within the subsequently located photosensitive elements, for example, photodiode array, may occur. Although these interactions are important signal and noise sources, there has been no sufficient attention paid to the conventional cascaded model analysis. In this study, to consider the direct x-ray induced noise, the cascaded model is generalized by incorporating an additional parallel cascading path for the signal and noise transfers due to the direct x rays. The theoretical framework is based on the parallel-cascade approach, 3 which successfully demonstrated the effect of characteristic x-ray reabsorption in a radiographic screen. The conventional cascaded model for the analysis of a scintillator-based x-ray imaging detector can be described by a number of elementary processes from the incident x-ray fluence q 0 to the addition of electronic noise add through the paths A, B, and C, as shown in Fig. 1 , designated by the solid lines. When q 0 interacts in a scintillator with a probability of ␣ ͑or quantum detection efficiency͒, path A describes a conversion process of the absorbed energy within the scintillator into the generation of optical photons, 2 while path B describes a conversion process when a characteristic x ray is produced. 3 Path C represents the generation of optical photons remotely due to the reabsorption of the characteristic x rays. 3 K and f K quantify the probabilities that a characteristic x ray will be produced and reabsorbed, respectively. A detailed description of the physical parameters used in this model is summarized in Table I . Noise transfers along each path prior to node 1 can be expressed as where u and v are the spatial-frequency conjugates to x and y in the Cartesian coordinates, respectively. m j is the mean number of secondary quanta and I j is the statistical or Swank factor corresponding to each amplification process along path j. As the branching between paths A and B is represented as a Bernoulli branch and the input quanta are statistically uncorrelated, the cross spectral density is NPS 1AB ͑u , v͒ = NPS 1BA ͑u , v͒ = 0. Similarly, NPS 1AC ͑u , v͒ = NPS 1CA ͑u , v͒ = 0. In contrast, the branching between paths B and C is a point selection process for identical input quanta, and the cross spectral density is therefore given by 3 NPS 1BC ͑u,v͒ = NPS 1CB ͑u,v͒ = q 0 ␣ K f K m B m C T K ͑u,v͒. ͑4͒ These noise spectra are transferred towards node 2 by experiencing successive elementary processes such as an optical quantum scattering in the scintillator and a conversion into the electronic signal charges in a readout-pixel photodiode. Referring to the formalism described in a previous work, 4 the resultant noise-power spectrum ͑NPS͒ prior to node 2 is NPS 20 ͑u,v͒ = q 0 ␣m 1 ͓1 + M K ͑u,v͒T scn 2 ͑u,v͔͒, ͑5͒ where a͒ Electronic mail: hokyung@pusan.ac.kr APPLIED PHYSICS LETTERS 89, 233504 ͑2006͒
doi:10.1063/1.2398926 fatcat:3au4aimh2fd2zaxqraxjnwsygi