A general analysis for the first-order design of a three-lens afocal z
oom system with one lens fixed is presented. The reasonable solution a
reas in the focal length diagrams with positive or negative magnificat
ion are derived and shown graphically. The relation between the two se
parations of the three lenses in zooming is found to be a hyperbola. A
ccording to the different locations of hyperbola centers, four cases a
re analyzed. From the four hyperbolic graphs, we get five different ty
pes of zoom systems. For each zoom type, we find the maximum range of
magnification and the position where the maximum or minimum system len
gth occurs during zooming. The zoom loci for the first or second lens
fixed are also discussed. (C) 1997 Society of Photo-Optical Instrument
ation Engineers.