Abstract
Light distribution in an image is known to depend not only on the maximum deformation of actual wave-front from an ideal reference surface but also on the type of aberration. Marechal proposed a condition under which a system can be regarded as satisfactorily corrected for any aberration when the normalized intensity (Strehl definition) at the diffraction focus is greater than or equal to 0.8. Under this condition, he derived aberration tolerance values for various aberra-tions (any one aberration or any combination of aberrations). In his treatment of the permissible aberration in optical systems, small aberrations and uniform distribution of amplitude over the entire aperture of the optical system are assumed.
In the present paper, study is made as to how the aberration tolerances given by Mar6chal are affected when the amplitude distribution over the entire aperture is not uniform. The problem is in the context of Fraunhofer diffraction pattern of an incoherent point source. The amplitude distribution (amplitude filter) over the aperture is in the form of a paraboloid of revolution, by which the total energy passing through the aperture remains constant and the Strehl definition at the diffraction focus is kept unity when the system is free from aberrations. The results obtained for the effect of the amplitude aperture filter on the aberration tolerances are presented in figures for various aberrations as a function of the amplitude filter parameter. The results also show a close relation between the non-uniform amplitude aperture illumination and the Marechal aberra-tion tolerance values. It is shown what the maximum value of aberration tolerance will be for a given non-uniform amplitude filter and what form of the aperture filter is optimum for use.
