An analysis and a description of methods for a paraxial design of rifle scopes with a four-element image-erecting zoom system is performed. It is described a method of the calculation of basic design parameters of the rifle scope with the four-element image-erecting zoom system, where two inner elements are movable for ensuring zooming of the rifle scope. The method is demonstrated on two examples of the rifle scope design with the zoom factor 10×. Moreover, the possibility to design the rifle scope with the fixed position of the exit pupil using the four-element image-erecting zoom system with three movable elements is analyzed. The method of the initial paraxial design is demonstrated on two examples of the calculation of the basic rifle scope design parameters. The calculated parameters from proposed methods can be used in the aberration analysis and the optimization of the rifle scope parameters in optical design software.
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