A NEW CONCEPT OF THEORETICAL RESOLUTION OF AN OPTICAL-SYSTEM, COMPARISON WITH EXPERIMENT AND OPTIMUM CONDITION FOR A POINT-SOURCE

A new concept and a definition of spatial resolution of an optical system, taking into account the signal-to-noise ratio, are introduced. The resolution of an optical system corresponding to the Rayleigh criterion is defined in terms of an abeffation-free optical system having the same quality of image as the image produced by the actual system. The quality of an optical image is evaluated based on the theory of the mean information content of an optical image, formulated by Shannon. The theory has been applied to evaluate the performance of an actual optical system, the field emission scanning electron microscope Hitachi S-900. Good agreement has been found with the experimented data. A general method based on the mean information content of an optical image is presented for determining the optimum focusing condition, its tolerance, and the attainable resolution of an optical system for a point source under the conditions of arbitrary coefficients of spherical and chromatic aberrations, and the beam energy distribution. The effect of the signal-to-noise ratio of the system plus specimen is also taken into account. The optimum value of the beam convergence angle is defined as that at which the density-of-information passing capacity of an optical system is maximized. The tolerance on the optimum beam-convergence angle is defined by the angles where the density-of-information passing capacity of an optical system has fallen to 90% of its maximum.