Optical Resolution – the Diffraction Limit
Optical magnification instruments are meant to make tiny objects visible. For that reason, the objects are magnified to cover a sufficient area of our retina. Optical magnification is achieved by a single lens (magnifier) or lens systems (compound microscope). The compound microscope consists of an objective lens and an eyepiece. In modern microscopes, the “objective lens” may contain some 20 individual lenses – needed to correct for many kinds of optical aberrations. Beside the optical magnification, electronic magnification is also important. Here, a pixelated image is magnified e.g. on a computer screen, printer or beamer by increasing the pixel size.
Obviously, electronic magnification by changing pixel size does not alter the resolution. The information in the image is not changed; the structural features are only displayed on a different scale. Nevertheless, the apparent resolution may be improved by inflating the information until our eyes can recognize it.
Optical imaging (the step before electronic imaging) has an inherent capability to resolve structural details. This resolution power depends on two parameters only (for ideal optical systems): the wavelength and the solid angle the lens clips from a full sphere. In circular optical systems, this fraction is described by the numerical aperture (NA). The NA is a technical property of the objective lens and engraved in the lens barrel.
An infinitesimally small object (that is: a point) would be represented by an optical imaging system (e.g. a compound microscope) as an extended structure. In circular optical systems this structure is the Airy pattern, a pattern that is caused by the light waves diffracted at the fringes of the optical lens. (Usually, these fringes are introduced by “apertures”, i.e. diaphragms that confine the circular beam area.)
The faintest structure that is resolved by an optical imaging system is therefore in the range of the size of that diffraction pattern. The pattern may be described by the diameter of the inner disc (which is defined by the first zero of the intensity), by the full-width-half-maximum, by 1/e of the maximum intensity or other choices. These parameters are arbitrary and consequently the “resolution power” is also defined by convention. The most prominent convention was first given by Ernst Abbe in 1874 and reads: