A portable non-contact tonometer (2) for measuring Intra-Ocular Pressure (IOP) of subject's eye is presented. Tonometer (2) is designed to be operated by the subject himself. It is housed in a hand-held case (4) which contains compressed air source (40), eye alignment detectors (12, 14), cornea applanation detector system (8, 10), a pressure sensor (32) and optical system for presenting gaze target (48). The animated gaze target (48) advantageously draws subject's attention to itself and keeps his eye (62) in alignment long enough for the measurement to take place, while optionally displaying system status and operating instructions. An audio annunciation system (16) guides the subject in the operation of the tonometer and prepares him for the actual procedure. The timing of the air puff is randomized to prevent subject's conditioning. The overall operation of the tonometer is controlled by a built-in microprocessor (50) system. A 3-D map of cornea is computed and a technique to compute the IOP derived from the difference of 3-D corneal maps before and during the air puff application is disclosed.