In automatic optical design it is customary to minimize the mean square value of the aberrations along selected rays. This leads in different cases to different ‘best forms of correction’ of primary and higher-order aberration terms. Image evaluation theory, on the other hand, shows that it is the variances of the wave-aberration and of an aberration difference function which determine the tolerances on aberrations, and the best forms of correction, according to the Strehl intensity ratio and transfer function theory respectively. The consequences of using different criteria of image quality are investigated, and it is shown that significantly poorer image quality can result from using more ‘ad hoc’ criteria instead of those based on diffraction theory. It is then shown how the use of canonical variables makes possible the simple use of the appropriate variances as diffraction-based criteria of image quality for optical systems. To optimise the system using least squares techniques then requires new forms of the normal equations. This procedure is described, it being shown that the method of damped least squares, and the Lagrange method of undetermined multipliers, may still be applied to the problem.