This thesis describes new techniques for the evaluation and design of high quality optical systems, based on the application of canonical pupil variables, and employing the Strehl ratio as the criterion of image quality. Marechalls treatment of tolerance theory shows that, in designing high quality systems, one should aim at minimising the mean squared deviation, E, of the wave surface from the spherical form, and this approach has been adopted in the present work. As part of the investigation, a numerical integration procedure has been used to obtain the Strehl ratio, and the accuracy and range of usefulness of the Marechal's criterion have been studied. A brief account is given of traditional design methods and automatic design techniques. The advantages of using modern techniques of image-assessment as the criterion of image quality is stressed. Using the canonical pupil variables, the exit-pupil co-ordinates of any ray are equal to the entrance pupil co-ordinates, at least in a nominally corrected system. For this reason, the wave-aberration of an optical system may be expressed as a function of the entrance pupil co-ordinates, and used in this form directly in the diffraction integrals. The exploration and specification of the pupil shape in terms of these co-ordinates are also described, it being shown that the vignetted pupil shape may be well approximated by an ellipse, which is then 'scaled' to correspond to a circular aperture. The wave-aberrations may then be expressed as a polynomial in the corresponding equivalent circular pupil co-ordinates, and pattern of rays traced can then remain the same for different image fields and for different systems of the same class.