Evaluation of optical aberrations in point images

Merit figures that are based on ray aberrations give different results from those based on wave-front aberrations. Here Zernike polynomials and a set of orthogonal polynomials that are based on the wave-front slope are used to study the transition from physical optics to geometrical optics. A knife-edge energy distribution is used to evaluate point images that are derived from both physical optics and geometrical optics. Parameters that are obtained from this evaluation are the radius of the major axis and the eccentricity of the irradiance distribution. A direct comparison of geometrical and physical aberrations through tenth order is made, based on geometrical–physical spot size, with the magnitude of the aberrations chosen in the transition region between physical and geometrical optics. Spot diagrams and diffraction images are shown side by side to the same scale with the diffraction images matched in exposure. This comparison shows that spot size, as determined by knife-edge scans, is a consistent measure of image quality for both spot diagrams and diffraction images. Furthermore spot size is a valid figure of merit down to the diffraction limit.