Systems and methods for optically determining the direction of an object, such as a pointer, relative to an imaging system, particularly systems where triangulation is employed to determine the location of a pointer within a generally planar viewing field, such as a touch screen. Rather than employing focused imaging systems to produce a sharp image at the plane of a photodetector, and to thus define the visual pen for finger position, a deliberately diffuse or blurred image is employed. The diffusion produces a characteristic "bell-shaped" or Gaussian intensity distribution. By recognizing the characteristic intensity distribution, the position of the maximum intensity, and thus the direction of the object, can be determined to a small fraction of the distance between sample points, with an accordingly much higher resolution than focused systems. In a preferred embodiment, the position location system is incorporated into a computer system as a touch screen apparatus and a cursor is displayed on the screen as soon as a pointer is detected above the display.