A rapid method of determining the coefficients of the monochromatic aberration polynomial of an optical system is described and tables of the universal coefficients for eleven polynomial types are given for ready use by an appropriate routine of a computer ray-trace programme. Results on the accuracy of aberrations represented by the polynomials so constructed are given for some optical systems. Applications of the method to image assessment and automatic optical design are discussed. Similar methods of calculating the integrated radius of gyration of the geometrical point-spread function and for determining the coefficients of a chromatic aberration polynomial are suggested.