Cramer–Rao lower bound optimization of an EM-CCD-based scintillation gamma camera

Abstract

Scintillation gamma cameras based on low-noise electron multiplication (EM-)CCDs can reach high spatial resolutions. For further improvement of these gamma cameras, more insight is needed into how various parameters that characterize these devices influence their performance. Here, we use the Cramer-Rao lower bound (CRLB) to investigate the sensitivity of the energy and spatial resolution of an EM-CCD-based gamma camera to several parameters. The gamma camera setup consists of a 3 mm thick CsI(Tl) scintillator optically coupled by a fiber optic plate to the E2V CCD97 EM-CCD. For this setup, the position and energy of incoming gamma photons are determined with a maximum-likelihood detection algorithm. To serve as the basis for the CRLB calculations, accurate models for the depth-dependent scintillation light distribution are derived and combined with a previously validated statistical response model for the EM-CCD. The sensitivity of the lower bounds for energy and spatial resolution to the EM gain and the depth-of-interaction (DOI) are calculated and compared to experimentally obtained values. Furthermore, calculations of the influence of the number of detected optical photons and noise sources in the image area on the energy and spatial resolution are presented. Trends predicted by CRLB calculations agree with experiments, although experimental values for spatial and energy resolution are typically a factor of 1.5 above the calculated lower bounds. Calculations and experiments both show that an intermediate EM gain setting results in the best possible spatial or energy resolution and that the spatial resolution of the gamma camera degrades rapidly as a function of the DOI. Furthermore, calculations suggest that a large improvement in gamma camera performance is achieved by an increase in the number of detected photons or a reduction of noise in the image area. A large noise reduction, as is possible with a new generation of EM-CCD electronics, may improve the energy and spatial resolution by a factor of 1.5.

Impact of fano factor on position and energy estimation in scintillation detectors

“…The expression for the score for x for the model described in Section III involves taking the logarithm of a sum of an expression containing a number of factorials (see (13,19)). To calculate the elements of the Fisher information matrix, covariance of the score must be averaged over all the values of for the given value of .…”

“…To calculate the elements of the Fisher information matrix, covariance of the score must be averaged over all the values of for the given value of . As a result, a general analytical solution to (19) with an expression for the Fisher information matrix as a function of the Fano factor is extremely challenging, if not impossible. (19) However, we can analytically calculate the elements of the Fisher information matrix for two special cases: F N = 0 and F N = 1.…”

“…As a result, a general analytical solution to (19) with an expression for the Fisher information matrix as a function of the Fano factor is extremely challenging, if not impossible. (19) However, we can analytically calculate the elements of the Fisher information matrix for two special cases: F N = 0 and F N = 1. Both calculations were done for the 3 × 1 geometry shown in Fig.…”

Impact of the Fano Factor on Position and Energy Estimation in Scintillation Detectors

“…The CRB has been widely used for evaluating the performance of gamma-ray detectors [17], [18]. The CRB has also been used to optimize gamma-camera design [19], [20], evaluate different readout strategies [21], and calculate the theoretical bound on timing resolution [22]. …”