This work outlines the design and construction of a single-photon emission computed tomography imaging system based on the concept of synthetic collimation. A focused multi-pinhole collimator is constructed using rapid-prototyping and casting techniques. The collimator projects the centre of the field of view (FOV) through 46 pinholes when the detector is adjacent to the collimator, with the number reducing towards the edge of the FOV. The detector is then moved further from the collimator to increase the magnification of the system. The object distance remains constant, and each new detector distance is a new system configuration. The level of overlap of the pinhole projections increases as the system magnification increases, but the number of projections subtended by the detector is reduced. There is no rotation in the system; a single tomographic angle is used in each system configuration. Image reconstruction is performed using maximum-likelihood expectation-maximization and an experimentally measured system matrix. The system matrix is measured for each configuration on a coarse grid, using a point source. The pinholes are individually identified and tracked, and a Gaussian fit is made to each projection. The coefficients of these fits are used to interpolate the system matrix. The system is validated experimentally with a hot-rod phantom. The Fourier crosstalk matrix is also measured to provide an estimate of the average spatial resolution along each axis over the entire FOV. The 3D synthetic-collimator image is formed by estimating the activity distribution within the FOV and summing the activities in the voxels along the axis perpendicular to the collimator face.