We mathematically analyze the phase-only hologram constructed by taking the phase corresponding to the linear combination of two weighted phase functions. We show that this phase-only hologram may be written as a new linear combination for the original phase functions with new weights. Expressions for the new weights are developed to control the performance of the hologram. Also, some nondesired new terms appear and are written in terms of the original phase functions. The particular case of a bifocal lens is analyzed. © 1995, Optical Society of America.