Optical Resolution - Lateral Resolution

Lateral Resolution

Resolution depends on the distance between two distinguishable radiating points. The sections below describe the theoretical estimates of resolution, but the real values may differ. The results below are based on mathematical models of Airy discs, which assumes an adequate level of contrast. In low-contrast systems, the resolution may be much lower than predicted by the theory outlined below. Real optical systems are complex and practical difficulties often increase the distance between distinguishable point sources.

The resolution of a system is based on the minimum distance at which the points can be distinguished as individuals. Several standards are used to determine, quantitatively, whether or not the points can be distinguished. One of methods specifies that, on the line between the center of one point and the next, the contrast between the maximum and minimum intensity be at least 26% lower than the maximum. This corresponds to the overlap of one airy disk on the first dark ring in the other. This standard for separation is also known as the Rayleigh criterion In symbols, the distance is defined as follows

where

is the minimum distance between resolvable points, in the same units as is specified

is the wavelength of light, emission wavelength, in the case of fluorescence,

is the index of refraction of the media surrounding the radiating points,

is the half angle of the pencil of light that enters the objective, and

is the Numerical aperture

This formula is suitable for confocal microscopy, but is also used in traditional microscopy. In confocal laser-scanned microscopes, the full-width half half-maximum (FWHM) of the point spread function is often used to avoid the difficulty of measuring the Airy disc. This, combined with the rastered illumination pattern, results in better resolution, but it is still proportional Rayleigh-based formula given above.

Also common in the microscopy literature is a formula for resolution that treats the above-mentioned concerns about contrast differently. The resolution predicted by this formula is proportional to the Rayleigh-based formula, differing by about 20%. For estimating theoretical resolution, it may be adequate.

When a condenser is used to illuminate the sample, the shape of the pencil of light eminating from the condenser must also be included.

In a properly configured microscope, .

The above estimates of resolution are specific to the case in which two identical very small samples that radiate incoherently in all directions. Other considerations must be taken into account if the sources radiate at different levels of intensity, are coherent, large, or radiate in non-uniform patterns.