Numerical aperture

The numerical aperture (symbol, NA or nA, from Latin apertus, dt open) describes the ability of an optical element to focus light. The term was introduced by the physicist Ernst Abbe. With lenses it determines the minimum size of the light spot can be generated in its focus and is therefore an important, the resolution limiting factor.

More specifically, the numerical aperture is produced from the product of the sine of the half angle of the object-side aperture ( acceptance angle), and the refractive index n of the immersion medium ( material between the lens and the focus):

Thus, the numerical aperture is a dimensionless quantity, ie a purely numerical value.

Also in optical fibers, the numerical aperture (sometimes collimating / divergence angle ) described by the sine of the acceptance angle of the fiber and corresponding to the opening of the back end face of the fiber emerging from the cone-shaped light beam.

In air ( for example, a telescope ), with the numerical aperture is always less than one. But it can take values ​​greater than one, when the space between the sample and the lens is filled with an immersion liquid having a refractive index greater than one. Frequently water (), glycerol () or oil ( ) will be used. Accordingly, the numerical aperture for the best lenses about 1.2 for water and 1.4 for oil is because the maximum acceptance angle is approximately 70 degrees.

The maximum resolution is the minimum distance between two distinguishable structures. In microscopy, the size of the focus is limited by diffraction and is proportional to the wavelength of the light used, as well as inversely proportional to the numerical aperture:

As a rule of thumb the following relationship for estimating the maximum resolution:

In vacuum or in air, and a large opening angle ( ) is given as an estimate:

The resolution can be increased beyond the diffraction limit, by exploiting non-linear responses of the molecules, for example in the analysis STORM, dSTORM, STED or (f) PALM.

An optical element such as a lens is characterized by its expansion, its numerical aperture, the optical working distance and the back image distance. Mathematically correct, the opening angle is determined by an aperture in the back focal plane of the objective, but structurally is the version of the first lens limiting. This is also approximately correct, as will be explained in the context of the Fraunhofer diffraction. It is worth noting that the object under the microscope is so small that the lens mostly just 1mm away is in the far field, as the near field extends only over the range of a few wavelengths.

Instead of the numerical aperture, the aperture ratio is often expressed in particular in the photograph. In contrast to the numerical aperture, however, the aperture ratio refers to the frame opening angle (see aperture ratio and f-number).

In optical images other effects such as aberrations or other aberrations are often so large that the theoretically possible resolution can not be reached. As a compromise, in this case the critical panel is often set at which, for a given lens in practice, the largest resolution can be achieved.