Numerical aperture unit

Clemex is a distributor of Nikon metrology microscopes as part of our turnkey image analysis soultions in North America, South America and Europe.

Numerical aperture, or N.A., is a value that indicates the resolving power of a lens and is defined by the equation below.

n: refractive index of observation medium [e.g. n(air) = 1]θ: angle between the optical axis and the light at the outermost of the effective diameter of the lens

Na of a lensformula

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Numerical Aperture calculator

Numerical apertureofmicroscope

The value from this formula is resolution. According to this equation, the larger the numerical aperture (N.A.), the smaller the radius of the Airy disk. Therefore, a lens with a larger N.A. will be able to resolve smaller features, resulting in a sharper image.

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Although N.A. determines the resolution of a lens, diffraction also plays a role in what can be resolved. Diffraction is a phenomenon that causes light to spread out like a wave. This property prevents even the most high-resolution lens from being able to gather focus to a single point source, making the focal point more of a disk. The smallest-size light disk that can be resolved is known as an Airy disk, and its radius is expressed by the formula below.

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Numerical aperture formula

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