METHODOLOGY FOR THE PARAMETRIC SYNTHESIS OF ZOOM-AFOCAL SYSTEMS BASED ON FIXED VARIOFOCAL LENSES

Background. Zoom optical systems utilising mechanically fixed, electrically controlled varifocal lenses cannot be regarded as having fixed optical components. The existing axial displacement of the principal points of varifocal lenses is associated with variations in their optical power; if ignored, this can have a negative impact on the functional parameters of the synthesised optical system. Therefore, the methodology for the parametric synthesis of such systems is a pressing scientific and engineering challenge. Objective. To develop a methodology for the parametric synthesis of zoom-afocal systems with fixed varifocal lenses, which allows the elimination of afocality violations in these systems caused by unaccounted-for shifts in the principal points of the varifocal lenses. Methods. Based on data regarding the variable design parameters of optical systems modelled as membrane and electrically wettable varifocal lenses , the positions of the principal points of the varifocal lenses were investigated as a function of their optical power. The research results were obtained using an analysis of the paraxial parameters of optical systems within the Zemax software in multi-configuration mode, whilst varying the data on the position and curvature of the interface between the working optical media of the varifocal lenses. Changes to the design parameters of the varifocal lens optical system were carried out within the actual operating range of variation in their optical power. The functional relationship identified between the shifts in the principal points of the studied varifocal lens models and their optical powers was approximated using the Mathcad mathematical editor. Results. It has been established that the axial position of the principal points in varifocal lenses is related to their optical powers, and that the shift of the principal points occurs in the direction of movement of the surface separating the working optical media of the varifocal lens as the optical power changes. Coefficients have been determined that relate the magnitude of the shift in the principal points to the optical power of the studied varifocal lens models. A methodology is proposed for the synthesis of zoom-afocal systems based on fixed varifocal lenses, which takes into account the established patterns of principal point displacement, thereby ensuring stable afocality of the systems across the entire operating range of angular magnification changes. Conclusion. The shifts in the principal points of varilenses, which are associated with changes in their optical powers, can significantly affect the paraxial parameters of the zoom systems in which they are used. Ignoring the shifts in the principal points of varifocal lenses, which make up zoom-afocal systems, leads to a loss of afocality in these systems. The method of parametric synthesis of zoom-afocal systems based on the Galileo or Kepler schemes, provided that the varifocal lenses remain stationary, ensures the preservation of the afocality of these systems throughout the entire operating range of angular magnification variation , as the method takes into account the actual shifts in the principal points of the varifocal lenses.