Paraxial design method based on an analytic calculation and its application to a three-group inner-focus zoom system

A paraxial design method based on an analytic calculation is presented to overcome the problems of the conventional approaches in initial zoom lens design. We analytically derive a set of available zoom equations for a three-group inner-focus zoom system by using the matrix representation for paraxial ray tracing. We also develop a program tool to obtain the powers of the lens groups and total track length from the zoom equations. These powers of the lens groups are used to calculate the zoom locus; then the powers of the lens groups and the zoom locus are evaluated to see if the constraints are satisfied. If not, the power of each lens group is changed to meet the constraints. The stability of this iterative paraxial design method has been confirmed and applied to the initial design for a three-group inner-focus zoom system having a focal length of 3.0 to 9.0 mm. The total track length of this zoom lens is 12.37 mm at all zoom positions, and the apertures are F/3.5 at the wide and F/4.5 at the tele positions. In conclusion, this design procedure results in a 3x compact zoom lens system useful for a mobile camera.