RESOLUTION IN LIGHT-MICROSCOPY STUDIED BY COMPUTER-SIMULATION

Microscopic resolution can be characterized by K = x . NA/lambda, where x is the distance between two objects, or the interval of a grating, just resolved with light of wavelength-lambda and an objective of aperture NA. Using a computer simulation of imaging the following K values were obtained on the Sparrow resolution criterion for line and grating objects and various imaging methods (figures for the Rayleigh criterion, which assumes a finite contrast-sensitivity of the light detector, are in parentheses). Several results appear to be novel. Due to limitations discussed in the text some data are only approximate. With a grating object K is 1.0 (1.0) for axial coherent illumination, 0.5 (0.5) for coherent illumination at an obliquity NA(obl) which just enters the objective aperture, 0.5 (about 0.53) for incoherent illumination, 0.5 (about 0.52) for illumination with a condenser aperture NA(c) equal to NA, 0.5 (about 0.515) for transmitted-light confocal scanning, and 0.25 (about 0.38) for fluorescent confocal scanning. If the object consists of two parallel lines K is about 0.68 (0.71) for axial coherent illumination, about 0.44 (0.5) for incoherent illumination, 0.375 (about 0.48) for optimal partially coherent illumination in which NA(c) may exceed NA, 0.44 (0.48) for transmitted-light confocal scanning, and 0.32 (0.41) for fluorescent confocal scanning. For inter-object distances of 1, 1.5 and 2 wavelengths, respectively, NA(c) values of about 0.69, 0.5 and 0.375 gave optimal contrast and resolution irrespective of NA. The practice of setting NA(c) to about two-thirds of the NA of a high-power objective is supported by the fact that a condenser aperture of about 0.69 gives excellent or optimum resolution and contrast for most inter-object distances and objective apertures tested, although with some distances and apertures reducing NA(c) improved contrast slightly. The rule (sometimes attributed to Abbe) that resolving power is proportional to the mean of NA and NA(c) is correct for oblique coherent illumination in the case of a grating object, provided NA(obl) does not exceed NA. In the case of two isolated objects the rule is only approximately correct, but applies even if NA(obl) is greater than NA. Coherent light at an obliquity of 0.5-lambda/x introduces a half-wavelength phase difference between two objects and permits their resolution (with perhaps an incorrect apparent inter-object distance) even with objective apertures approaching zero. In confocal scanning the width of the scanning spots has only a moderate effect on resolution, and two objects can sometimes be resolved with scanning spots wider than the inter-object distance provided the lens apertures are neither too small nor too large.