# Numerical Aperture

Phaos Optic Science Educational Series

February 15, 2021
12:00 PM (GMT)

10 Minutes

## Introduction

Numerical aperture (NA) or also known as Object-side aperture is a value that measure the angular acceptance for incoming light.

It is defined based on geometrical consideration and is thus, a theoretical parameter that is calculated from the optical design. It cannot be directly measured, except in cases where there are rather large apertures and negligible diffraction effects.

## Why is NA Important?

1. It determines how bright the observed image can be for a given illumination intensity. A high-NA objective can collect more light than one with a low NA.

2. NA sets a limit to the obtained spatial resolution: the finest resolvable details have a diameter of approximately λ / (2 NA), assuming that the objective does not produce excessive image aberrations.

3. A high NA leads to a small depth of field: Only objects within a small range of distances from the objective can be seen with a sharp image.

## Formula

Numerical Aperture (NA)=n×sin(µ or α)

• n represents the refractive index of the medium between the objective front lens and the specimen
• µ or α is the one-half angular aperture (or acceptance angle of image-forming rays) of the objective lens

Its’ objective is to measure the ability to gather light and resolve fine specimen detail at a fixed object distance. As shown in the diagram above, image-forming light waves will pass through the specimen and enter the objective in an inverted cone.

A longitudinal slice of the 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. This is because as the light cones grow larger, the angular aperture (α) increases leading to an increase in the numerical aperture nearing the limit as air is utilized as the imaging medium.

## How to Get Higher NA Value?

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

Currently, there are microscope objectives that allows 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.

Overall, highly corrected objectives tend to have much larger numerical apertures for the respective magnification as illustrated in Table below.

The feature of increasing numerical aperture across an increasing optical correction factor in a series of objectives of similar magnification holds true throughout the range of magnifications.

Overall, most manufacturers strive to ensure that their objectives have the highest correction and numerical aperture that is possible for each class of objective!