Analytic determination of pinhole collimator sensitivity with penetration

Pinhole collimators are widely used to image small organs and animals. The sensitivity of knife-edge pinhole collimators has been previously estimated using an "effective diameter" formulation and experimentally described using a sin ^∞ θ fit, where θ is the angle between the line segment from the center of the aperture to the photon source and its projection onto the plane of the aperture. An analytic form of the sensitivity of the pinhole collimator is derived in this paper. A numerical formula for predicting the sin ^∞ θ form of the sensitivity is calculated from the analytic form. Experimental data are compared with the theoretical estimate and the sin ^∞ θ prediction. The agreement is excellent.