本研究針對微型單光子放射電腦斷層掃描系統，完成正向投影之快速針孔穿隧計算以及拼貼式伽瑪相機之訊號讀出方法表現分析。 針對刀口式的圓形針孔和脊椎式的圓形針孔，以直接光線追跡的方式建立針孔穿隧模型，所得結果與文獻相較可避免使用泰勒展式近似解的誤差，且具備針孔位移和旋轉之功能。另一方面，藉由SCOUT模擬工具，獲得拼貼式伽瑪相機16×16個陽極訊號輸出的偵測器平均響應函數(MDRF)，並加總換算成16+16個欄列訊號的MDRF，使用包含多變數常態分佈和帕松分佈的訊號機率模型，依最大可能性原理建立費雪訊息矩陣和偵測器解析度的克拉馬-羅下限，評斷偵測器訊號讀出方法的優劣。 模擬結果顯示，多變數常態分佈模型的解析度優於帕松模型，推測原因為多變數常態分佈模型描述了陽極之間的訊號相關性，因此更貼近實際的訊號輸出情況。另一方面，使用所有陽極的輸出訊號，會比欄列加總的訊號輸出方式保留更多的資訊，因此也獲得較佳的空間解析度。綜合此結果，使用所有陽極的輸出訊號建立的多變數常態分佈模型將擁有最好的空間解析度。 ;In this study, a speedy forward projection model is built up for micro-SPECT systems to perform the pinhole penetration calculations. The performance of the signal readout methods for tiled gamma cameras are also analyzed through simulations. The pinhole penetrations of knife-edge and kneel-edge pinholes are calculated by ray tracing. The model is straightforward, avoids the approximate error of Taylor series expansion, and has the functions of pinhole displacement and rotation. In addition, the mean detector response functions (MDRFs) of tiled gamma cameras are generated by the SCOUT simulation tool, including the outputs of 1616 individual anodes and 1616 row/column signals. Both the multivariate normal model and Poisson model are employed as the signal probability models. The resolution performance of the detectors with different signal readout methods are judged by the Fisher information matrix and Cramer-Rao lower bound based on the maximum likelihood principle. According to the simulations results, the resolution with the multivariate normal model is better than that with the Poisson model. The reason is that the multivariate normal model accounts for the signal correlations among the anodes and hence better represents the signal outputs. Moreover, using the signal outputs of all anodes keeps more information than using just the row/column signal outputs, and hence yields better spatial resolution. In conclusion, utilizing the multivariate normal model built with the signal outputs of all anodes would attain the best spatial resolution.
