Optical resolution

Optical resolution describes the ability of an imaging system to resolve detail, in the object that is being imaged. An imaging system may have many individual components, including one or more lenses, and/or recording and display components. Each of these contributes (given suitable design, and adequate alignment) to the optical resolution of the system; the environment in which the imaging is done often is a further important factor.

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 ${\displaystyle r}$ 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 the 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:

$${\displaystyle r={\frac {1.22\lambda }{2n\sin {\theta }}}={\frac {0.61\lambda }{\mathrm {NA} }}}$$ where

This formula is suitable for confocal microscopy, but is also used in traditional microscopy. In confocal laser-scanned microscopes, the full-width 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 to the Rayleigh-based formula given above. $${\displaystyle r={\frac {0.4\lambda }{\mathrm {NA} }}}$$

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. $${\displaystyle r={\frac {\lambda }{2n\sin {\theta }}}={\frac {\lambda }{2\mathrm {NA} }}}$$

When a condenser is used to illuminate the sample, the shape of the pencil of light emanating from the condenser must also be included. $${\displaystyle r={\frac {1.22\lambda }{\mathrm {NA} _{\text{obj}}+\mathrm {NA} _{\text{cond}}}}}$$

In a properly configured microscope, ${\displaystyle \mathrm {NA} _{\text{obj}}+\mathrm {NA} _{\text{cond}}=2\mathrm {NA} _{\text{obj}}}$.