It is shown that polynomials related to the desired magnification and shift of focus of a zoom system may be used to derive a continued fraction related to a family of lenses having the desired properties. This is used to develop the method for first-order design of linearly compensated zoom systems outlined by William Peck at the 1961 Spring Meeting of the Optical Society of America. It is also shown that certain types of designs are apt to be very difficult to achieve with optical compensation, yet readily achieved with linear compensation. Numerical calculations illustrating the design procedure are carried out.
RICHARD J. PEGIS and WILLIAM G. PECK, "First-Order Design Theory for Linearly Compensated Zoom Systems," J. Opt. Soc. Am. 52, 905-909 (1962)