Effect of Particle Size on the Diffraction Image in Microscopy with Narrow-Coned, Axial Illumination

The distribution of energy density is derived for the diffraction image produced by an Airy type objective of a single, uniform, opaque or transmitting particle located in a uniform, transmitting surround and illuminated by a narrow cone of axial illumination. It is shown that for a large class of particles the diffraction image can have an irregular variation in energy density in addition to a regular variation and that these variations are in accord with experiments performed with opaque particles. The irregular variation can appear as a secondary Airy disk located well within the regular Airy disk. The development of the diffraction image with increasing radii of disk-shaped particles is described. The equations which govern this development are adapted to the determination of the radius of the particle from linear or photometric measurements upon the diffraction image. The smallest measurable radii are restricted by practical limits rather than by physical limits as in the resolution of two particles. The practical limit is about 0.6 Airy unit for the linear measurements but may fall below 0.3 Airy unit with photometric measurements.