Diffraction Theory for Images of Disk-Shaped Particles with Köhler Illumination

The distribution of the time-averaged energy density in the diffraction image of thin disk-shaped particles is derived from the diffraction theory of optical instruments for cases in which the particle is focused sharply by objectives of the idealized Airy type in a microscope adjusted for Köhler illumination and illuminated by unpolarized monochromatic light. Whereas the diffraction integrals are stated for any numerical aperture of the substage condenser, the solution is restricted to cases in which the numerical aperture of the substage condenser or illuminating system is set equal to the numerical aperture of the objective.