Diffraction Images of Disk-Shaped Particles Computed for Full Köhler Illumination

Abstract

Energy densities in the diffraction images of single uniform nonself-luminous disk-shaped particles are computed for cases in which the image of the source of light just fills the exit pupil of the object lens in a microscope adjusted for Köhler illumination. Curves are presented for several examples, including holes in an opaque screen and opaque particles in a transmitting surround. Two functions are developed and a table of values for each is given from which it is possible to calculate curves for many other examples. The functions are tabulated for particles 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, and 2.0 Airy units in radius. A hole 2 Airy units in radius in an opaque screen is found to produce a diffraction image the central energy density of which is less than 90% of what would be produced at the image plane if no screen were present. Similarly, the energy density at the center of the image of an opaque particle 2 Airy units in radius is found to be nearly 5% of the energy density in the image of the distant surround. Opaque particles about 1 Airy unit in radius, which previously were known to produce images containing a secondary Airy disk when narrow-coned, axial illumination is used, are found both experimentally and theoretically to produce images retaining that feature when the numerical aperture of the condenser equals that of the objective.