Apodization for minimizing the second moment of the intensity distribution in the fraunhofer diffraction pattern. III

For pt.II see ibid., vol.7, p.305 (1976). The apodization is solved for determining the pupil function (amplitude distribution over the exit pupil) which minimizes the second moment of the intensity distribution in the Fraunhofer diffraction pattern of a point object, on the conditions that the total energy passing through the aperture is specified in advance to a certain value less than that for the standard Airy-type optical system without filter and that the optical system is passive. The problem is treated for a rotationally symmetric optical system without aberrations and solved by using the calculus of variations of unconventional type involving the constraint of inequalities due to the passivity of the optical system. A detailed derivation of the optimum pupil function is given and the resultant pupil function is shown graphically.