A theoretical and experimental study of lens centring errors and their influence on optical image quality

Abstract

Any small decentring of a surface of an optical system may be resolved into an angular tilt of the surface about its intersection with the optical axis and a second-order displacement along the axis. A simple method is described for calculating the lateral shift and coma of the axial image resulting from a surface tilt, and also the contribution of this axial coma to the variance of the wavefront aberration. This leads to a system of tolerances for the tilt and eccentricity of any simple or compound component, and for cementing errors in the latter case. The applications of the resulting formulae are illustrated with examples. An optical unit has been constructed, with which the tilt error of each surface of a compound system may be measured. The axial coma of a decentred system may be measured using a wavefront-reversing interferometer which is also described. The decentring errors of a badly mounted microscope objective have been measured, and the axial coma expected from the theory determined interferometrically. Good confirmation of the theory was obtained, and star images further confirm the order of magnitude of the axial coma.