Background. Parametric synthesis of zoom-afocal optical systems for zoom lenses. Development of an algorithm for dimensional calculation of three-component zoom-afocal systems when accounting overall limitations, providing the desired range of changes in the angular magnification and field of view of the zoom lens, the allowable vignetting of the extreme beams of light when the field of view changes over the entire specified range. Synthesis of an afocal system for a stationary lens, the entrance pupil of which is located behind the afocal system. Objective. The purpose of the paper is to create a universal analytical and suitable for computer automation algorithm for calculation of the optical and overall parameters of the components of zoom-local three-component zoom systems. Methods. The zoom-afocal system is represented by subtle components. A system of equations is compiled in which the distances between the components are unknown. From the equations, the values of these distances are recovered, which provide the necessary values of the angular magnification and zero optical power of the afocal system. In this case, the magnitudes of the optical powers of the components and their ratios should ensure positive values of the distances between them. Using the formulae of the angles and heights of the zero rays on the components of the system, taking into account the permissible vignetting of the beam of rays from the edge of the field of view, the required light diameters of the components are determined. Results. The obtained analytical dependences allow us to determine the focal distances of the afocal system components and their mutual location over the entire required range of changes in the angular magnification using the original data on the allowable longitudinal and transverse dimensions of the afocal system. It is shown that afocal systems have a maximum axial length with the angular increase of one. The largest light diameter has the first component. The diameter of this component reaches its greatest value as the value of the angular increase is close to one. Conclusions. The obtained results allow analytically performing parametric synthesis of three-component zoom-afocal systems, taking into account the requirements for their dimensions, the range of changes in the angular magnification and permissible vignetting of beams of rays from the edge of the visual field.
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