Simultaneous, maximum-likelihood determination of focal length and source position for point-source experiments with pinhole collimation

A simple procedure to determine the focal length of a pinhole collimator is presented, which is important for planar and SPECT imaging. The procedure involves the use of a point source and three linear stages. The source is moved by carefully controlled relative shifts in two dimensions to a number of different positions within a plane nearly perpendicular to the detector's plane. For each position a projection is acquired. The focal length is calculated from the shift in the centroid of the projections via a maximum-likelihood fit. A useful byproduct of the procedure is calibration of the position of the source, which can then be used for planar imaging studies such as sensitivity and point-spread function. This calibration maps the coordinate system of the stages to the coordinate system of the aperture. The method was experimentally validated for three different focal lengths.