The use of optical aberration coefficients.

An extensive theory of aberration coefficients of symmetrical optical systems has been developed by Buchdahl in his monograph \Optical Aberration Coefficients -(hereafter called M) and 3‚Äö99. extended in subsequent papers2 The advantages resulting from the use of these coefficients rest in two important properties. Firstly the one set of coefficients characterise systems of rays that is they apply simultaneously to all rays that traverse the optical system. Secondly the aberration coefficients are the suns of corresponding coefficients computed for each surfaceof the system (the contributions to the coefficients). This enables the action of the system on all rays to be analysed surface by surface and it is this that places a powerful tool in the hands of the designer. Now although there is only one set of coefficients for each system it is an infinite set. Obviously the calculation of them all is impossible. So far computing schemes have been designed for the computation of all the third fifth and seventh order monochromatic coeff1cients 4 the coefficients of ninth5 and eleventh9 order spherical aberration and several of the more important chromatic coefficients (M Chapter XIII). Naturally the aberrations of a system are not completely described by only these coefficients. The object of this thesis is to examine the effectiveness of the first three orders of the monochromatic coefficients in the description of the aberrations of optical systems. As well as enabling a detailed analysis of a system the coefficients and their surface contributions are of considerable use in the differential correction of a system following the initial design. The effectiveness of the coefficients in this field is also examined here. The work has been restricted to monochromatic coefficients since after the initial design the majority of design is carried out in monochromatic light. Also the systems studied here have been restricted to those containing spherical surfaces only. The extension of the work to aspherical surfaces is a matter of detail and not of method; as mentioned in M Section 55 the only change is that the \"intrinsic\" coefficients (Section 5 6 of this thesis) contain additional terms which depend on the \"extra-axial\" curvatures of the aspheric surfaces. These additional terms in no way affect the general theory or the application of the coefficients. The aberration coefficients in no way indicate whether the system they represent is aspheric or not. However in the construction of computing schemes for the coefficients many simplifications can be introduced if only spherical surfaces are being considered resulting in comparatively short schemes e.g. compare M 81.3 with 84.2333 44."