Consider nine 1 cm × 1 cm PMTs arranged in 3 × 3 array (Figure P8.2). The output of each PMT to a scintillation event is modeled as
where (x, y) is the location of the scintillation event, and (xi, yi) is the center of the i-th PMT.
Figure P8.2 See Problem 8.8.
(a) Find the output of each PMT for a scintillation event that occurs at (−0.5, 0.5) cm.
(b) What is the estimated position of the scintillation event?
(c) Is the estimated position the same as its true position? If not, explain why
