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Algebraic reconstruction techniques (ART) for 3-dimensional reconstruction from electron microscope data have been developed and implemented in this laboratory. These methods are an alternitive to the Fourier method of de Rosier and Klug and have several advantages over it, such as:relatively few views are required (about 6-12)limited angular ranges give useful reconstructions (+/-30°)no presumption of symmetry is necessary for facile implementingcomputation is fasterthe computation is stable in the presence of noiseThe dimensionality of the problem may be reduced from three to two by tilts about a single axis, so that planes perpendicular to the axis of tilt are independent of each other. This is not absolutely necessary, but is by far the most tractable mode computationally. A typical input data set, then, consists of m≥6 photos of the same region of the specimen at several known angles of tilt about the same axis. In general the direction of the tilt axis is not known.