Analytical results are presented showing improved detection and location performance of point sources in a staring sensor using a hexagonal detector array or having the capability to adjust the size of its blur spot (variable focus). Square and hexagonal detector arrays are compared for detection probability versus focus, for location accuracy versus focus and signal-to-noise ratio, and for location accuracy versus blur size and detector array fill factor. We find that hexagonal detectors provide better detection probability when the point source lies near a corner of the detector, but otherwise the two detector types give comparable performance. Hexagonal detectors generally give better location accuracy than square detectors. Variable focus is shown to be advantageous for maximizing performance for both detection and location of point sources.