The image-forming performance of multilayer positron tomographs for extended sources is evaluated analytically. The analysis is simplified by "rotation transform," by which three-dimensional photon detection problems are solved by two-dimensional treatment. Event rates of singles, unscattered true coincidence, and a single- and double-scattered coincidence are formulated for a uniform cylinder phantom as functions of various design parameters. Angle factors for Compton scattering and other parameters used in the evaluation are presented. Scatter components in projections and their effect on the reconstructed images are also evaluated. The scatter component in the reconstructed image depends critically on the detector ring radius, phantom radius, method of attenuation correction, etc. When the director radius is relatively small (40 or approximately 45 cm in diameter), the scatter/true ratio at the image center of a 20 cm diameter phantom may be larger than the scatter/true ratio in the event rates. Comparison with experimental data obtained with a head positron tomograph, POSITOLOGICA, showed reasonable agreement both in the total coincidence rates and in the scatter components in the images for a cylindrical phantom of 20 cm in diameter.