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The purpose of the frameless stereotaxic operating microscope is to display computed tomography (CT) or other image data in the operating microscope in the correct scale, orientation, and position without the use of a stereotaxic frame. A nonimaging ultrasonic rangefinder allows the position of the operating microscope and the position of the patient to be determined. Discrete fiducial points on the patient's external anatomy are located in both image space and operating room space, linking the image data and the operating room. Physician-selected image information, e.g. tumor contours or guidance to predetermined targets, is projected through the optics of the operating microscope using a miniature cathode ray tube and a beam splitter. Projected images superpose the surgical field, reconstructed from image data to match the focal plane of the operating microscope. The algorithms on which the system is based are described, and the sources and effects of errors are discussed. The system's performance is simulated, providing an estimate of accuracy. Two phantoms are used to measure accuracy experimentally. Clinical results and observations are given.