This paper introduces and analyzes a theory for a paraxial design of a hybrid catadioptric optical system with variable focal length, which uses focus tunable optical components. Compared to the conventional zoom lens system, the proposed hybrid optical system can be designed with a smaller length and weight than a lens system of similar characteristics. The hybrid system does not need the movement of individual elements for zooming. All necessary relations for the calculation of the paraxial parameters and the third-order spherical aberration of the hybrid optical system are derived. The presented theory helps to find out the optical power distribution of individual optical elements of the whole hybrid zoom system considering the requirement on the spherical aberration of the system. In addition, the procedure for the calculation of basic design parameters of such an optical system is shown by examples.
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