Abstract: The theory of canonical coordinates, developed by Prof. H. H. Hopkins, is introduced and the formation of the coordinates discussed. The introduction of reference spheres on the pupils establishes a simple and precise Fourier transform relation between the pupil function and the point spread function, which facilitates the image assessment of an optical system. It also enables the establishment of an one to one correspondence between the entrance and exit pupil, and this makes it possible to use the variance of wave aberration as the merit function in the optimization calculation. Methods of implementing the advantages of the theory in an optical design software are considered, so as to improve its effectiveness and calculation accuracy.