Numerical Aperture is a dimensionless value describing the Light Gathering Power and Resolution capability of a microscope objective lens.

NA was described by Ernst Abbe in 1873 and is defined:

where:

n = the lowest refractive index between the condenser and objective;

a = the angular aperture, or collection angle, of the objective.

The common element is that resolution in a microscope system is a function of the NA of the objective and the wavelength of light used for observation. Rayleigh "improved" on Abbe's definition by accounting for the diffraction of light around a small object. He described resolution as the minimum distance between two (light diffracting) points.

Rayleigh's definition of resolution (d) may be described in the following two ways depending on whether light is transmitted through the sample or light is reflected off the sample.

Brightfield microscopy
(transmitted light)
Fluorescence microscopy
(self-luminous object)
Objectives with different Angular Apertures (a) and Working Distances (WD). Objective A will have a higher NA due to the increased aperture size.
Abbe described a microscope system by defining resolution in terms of wavelength, where d, or the smallest measurable object, is a function of wavelength and objective NA.