What is Numerical Aperture and Why it is Important?

What is the Numerical aperture in a microscope?

The numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.

By incorporating the index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface.

The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective (and hence its light-gathering ability and resolution), and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along with it.

Numerical Aperture (also termed Object-Side Aperture) is a value (often symbolized by the abbreviation NA) originally defined by Abbe for microscope objectives and condensers. It is given by the simple expression:

Numerical Aperture (NA)=n×sin(µ) or n×sin(α)

Note: Many authors use the variable µ to designate the one-half angular aperture while others employ the more common term α, and in some instances, θ.

In the numerical aperture equation, n represents the refractive index of the medium between the objective front lens and the specimen, and µ or α is the one-half angular aperture of the objective.

The numerical aperture of a microscope objective is a measure of its ability to gather light and resolve fine specimen detail at a fixed object distance.

Image-forming light waves pass through the specimen and enter the objective in an inverted cone. A longitudinal slice of this cone of light reveals the angular aperture, a value that is determined by the focal length of the objective.

In practice, it is difficult to achieve numerical aperture values above 0.95 with dry objectives. As the light cones grow larger, the angular aperture (α) increases from 7° to 60°, with a resulting increase in the numerical aperture from 0.12 to 0.87, nearing the limit when air is utilized as the imaging medium.

Higher numerical apertures can be obtained by increasing the imaging medium refractive index (n) between the specimen and the objective front lens.

Microscope objectives are now available that allow imaging in alternative media such as water (refractive index = 1.33), glycerin (refractive index = 1.47), and immersion oil (refractive index = 1.51). The numerical aperture of an objective is also dependent, to a certain degree, upon the amount of correction for optical aberration.

numerical aperture

Why you should care about the numerical aperture?

So, why should you care about the numerical aperture of a lens anyway? When you are planning your experiment, you probably think about what magnification you are going to use, after all, you need to be able to see the structure you are interested in

Magnification is nothing, however, without enough resolution to distinguish your structure of interest from everything else in the sample.

How oil and water affect the numerical aperture

What does this have to do with water and oil immersion lenses? When light leaves your sample and enters the air (or water or oil) it refracts. Refraction simply means that the angle of light changes by some degrees- it changes direction slightly. When you use a water or oil immersion lens, you change how much the light refracts when it leaves the sample. This increases the theoretical limit of the numerical aperture of your lens. How much does it change it?


  • where NA = numerical aperture
  • n = index of refraction of the medium (eg. air, water, oil, etc.)
  • α= the half-angle of the cone of light that can enter the lens.


What is a numerical aperture in the microscope?

Numerical Aperture and Resolution. The numerical aperture of a microscope objective is the measure of its ability to gather light and to resolve fine specimen detail while working at a fixed object (or specimen) distance.

What is meant by numerical aperture?

The numerical aperture (NA) is defined as being equal to n sin θ, where n is the refractive index of the medium between the objective lens and the object (n≅1 for air) and θ is half the angular aperture (or acceptance angle of image-forming rays) of the objective lens (Jenkins and White 1957).

Why is numerical aperture important?

The numerical aperture (abbreviated as ‘NA’) is an important consideration when trying to distinguish detail in a specimen viewed down the microscope. NA is a number without units and is related to the angles of light that are collected by a lens.

What does high numerical aperture mean?

Higher values of numerical aperture permit increasingly oblique rays to enter the objective front lens, which produces a more highly resolved image and allows smaller structures to be visualized with higher clarity.

Is high numerical aperture good?

The bigger a cone of light that can be brought into the lens, the higher its numerical aperture is. Therefore the higher the numerical aperture of a lens, the better the resolution of a specimen will be which can be obtained with that lens.

What is a numerical aperture in optical fiber?

The Numerical Aperture (NA) of fiber is defined as the sine of the largest angle an incident ray can have for total internal reflectance in the core. Rays launched outside the angle specified by a fiber’s NA will excite radiation modes of the fiber.

What is acceptance angle and numerical aperture?

The acceptance angle is a function of the refractive indices of the core and the cladding materials. The sine of the acceptance angle is called the numerical aperture.

What is the value of numerical aperture?

The numerical aperture is now a function of r and is maximum for a thin beam along the axis. Values of the numerical aperture vary from ≈ 0.13 for single-mode step-index fiber to ≈ 0.3 for large-core graded-index fiber.

What is the relationship between brightness and numerical aperture?

The result is that the brightness of the specimen image is directly proportional to the square of the objective numerical aperture as it reaches the eyepiece (or camera system), and also inversely proportional to the objective magnification.

Is high or low numerical aperture better?

The numerical aperture determines the resolving power of an objective, but the total resolution of a microscope system is also dependent upon the numerical aperture of the substage condenser. The higher the numerical aperture of the total system, the better the resolution.

What are the advantages of a high numerical aperture objective?

This technique can be performed inexpensively using any upright or inverted fluorescence microscope without a specialized prism. Among the benefits of using objectives for excitation are the ability to utilize standard mercury or xenon arc light sources to replace, or complement, external laser illumination.

How does numerical aperture vary with magnification?

The numerical aperture of objectives increases with the magnification up to about 40x (see Tables 1 and 2), but levels off between 1.30 and 1.40 (depending upon the degree of aberration correction) for oil immersion versions.

Does numerical aperture depend on medium?

Numerical aperture does not depend on the material outside the fiber but depends only on the indices of the core and cladding of the fiber.

What if numerical aperture is greater than 1?

It is directly related to the angle of the cone which is formed between a point on the specimen and the front lens of the objective or condenser, determined by the equation NA = n sin ∝. It can never get any larger than 1 if air is the medium between the specimen and the lens.

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