Numerical Aperture (NA): Why It Matters in Microscope?

When choosing a microscope objective, one of the most important specifications you should take into account is the Numerical Aperture (NA). But what does it really signify, and why is it so important?

What is NA?

Numerical Aperture is a dimensionless number. Its value describes the capacity of objectives lens to collect the light. Mathematically, NA is defined as the product of the refractive index n of the medium between the lens and the sample and the sine value of the half-angle θ of the collected light cone.

In simple terms, the higher the NA, the more light is captured, and the more signals you can get.

Why it matters?

The fundamental reason why NA is so important is that NA determines how much light signal the objective lens can collect.

Firstly, NA affects the resolution of your imaging systems.

Resolution improves as NA increases. In microscope, we define resolution as the distance by which two objectives must be separated in order to be distinguished. According to the Rayleigh criterion, that distance is equal to a constant 0.61 times the wavelength of the illumination light and divided by NA.

The higher the NA is, the smaller distance becomes, and the higher the resolution is.

Secondly, NA decides the brightness of the final generated image.

It’s quite intelligible because more light collection means brighter images. It should be noticed that this property is critical for fluorescence microscope, where signals can be very weak.

Thirdly, the depth of field (DOF) is also relative to NA.

Depth of Field (DOF) is defined as the longitudinal range within which a sample can maintain clear imaging when it moves back and forth along the optical axis. Higher NA gives shallower depth of field, which is because the larger the NA is, the greater the angle of the collected light cone becomes. Therefore, the focus is more sensitive to the deviation from the optical axis direction and the depth of field becomes shallower.

Additionally, NA also determines the field of view of the microscope.

This can be explained by Lagrange invariant. The Lagrange invariant, also known as the Smith-Helmholtz invariant, is a fundamental conservation law in geometric optics. Its physical meaning indicates that the information and energy carried by light are always conserved. If you want to get a wide field of view, then the angular aperture that each point can collect must be very small. This corresponds to a low numerical aperture, meaning the image is darker (with less light flux) and the theoretical resolution is lower. This is the typical feature of a wide-angle lens. If you want to achieve high resolution and high brightness (that is, a high numerical aperture), then the field of view you can see will necessarily be very small. This is the typical feature of a microscope objective lens.

Lastly, NA is also related to the working distance.

This is because if NA is high, the light cone angle is large and the light beam is very steep. To receive these light beams with large angles, the front end of the objective lens must be very close to the sample. The operation of researchers is relatively restricted in this case.