Numerical Aperture and Resolution - How is Resolution Determined

You may have heard the term Numerical Aperture in your hunt for microscopy lenses, but not been familiar with what it means. This is an exceedingly technical concept intended to score a lens based on the light it receives, with respect to viewing angles. There is an understood math formula for measuring this, and even ways that you can adjust the figure on your own microscope. 

In this article, you’ll get an understanding of what numerical aperture is, how to measure it, how oil immersions affect it, and how this statistic interacts with a resolution to help determine the ultimate quality of images captured through a specific lens. 

We also touch on light formations as they pass through specimens and the objective lens. Understanding light travel gives us insight into how images are captured. 

While these physics may seem daunting, this article provides a helpful base of understanding to ease yourself into dense subject matters with specific formulas. 

What is Numerical Aperture?

Numerical Aperture measures a microscope’s ability to gather light and discern detail at a specified distance. 

As the light used to form the image passes through the specimen and enters the objective in an inverted cone, it filters through the rest of the optical systems in the microscope. We measure the quality of light imagery received by the lens at proper focus with the numerical aperture as a means of understanding a lens’s quality.

Microscopy U explains that this formula is N, or the refractive index between the sample and objective lens, multiplied by the sine of one-half the angular aperture of the objective. This angular aperture is simply the angle of one-half of the beam of light that reaches the objective. 

For example, they list that a seven-degree refractive index results in a numerical aperture of just 0.12, but an index of sixty degrees extends that figure up to 0.87. So we can understand higher numerical apertures to be superior, as they offer greater quality and clarity for reviewing samples. 

Interestingly, this method is seen as not measuring the microscope itself, but the light that the microscope takes in to produce an image. 

We understand that with air as our imaging method we can increase our aperture’s angle up to 60 degrees, and achieve a numerical aperture of about 0.87. 

There are ways to exceed this, using other materials to bridge that gap. We’ll discuss that in the next section. High-quality lens makers ensure that their lenses are highly corrected and optimized at their central point to allow for the best numerical aperture possible. 

Be sure to discuss your wants and needs with your lens maker first, so they can understand what you are trying to capture, and how best to deliver that to you.

How Does Immersion Oil Impact Numerical Aperture?

Immersion oil is a special substance for microscopy that comes in two different forms, Type A and Type B, which differ only in their viscosity. 

This oil is placed on top of the coverslip and the objective lens is brought down to touch it as if to bridge the two surfaces together. The result is very little refraction of the light rays traveling through your slide, specimen, coverslip, oil, and through the glass objective lens of your microscope. 

Immersion oil is used because condenser and objective lens microscopes have a Numerical Aperture value of 1.25. But, achieving results can be somewhat different based on your microscopy level, as 100 times lenses can operate fine without oil, but 1000 times lenses differ, and 100 times lenses will see a clarity increase. 

To achieve optimal results, a material with a refractive index of 1.0 or higher is needed. As Microbus, a website operated by a retired science teacher, writes, that the best resolution for 1000 times notification at a numerical aperture of 1.25 is achieved when a drop of oil is placed between the lens and the slide.

Placing the drop of oil there works because the liquid channels the light directly, allowing it to venture between the sample and the objective lens seamlessly. At lower magnification levels this boost in clarity might not be necessary, but in situations reaching 1000 times zoom, it can help discern important details. 

Of course, before using immersion oil you should ensure your lens is designed for use with oils; it may have “oil”, “immersion” or “HI” (homogenous immersion) printed on it to let you know. 

Microscopy lenses that aren’t specifically designed for this can smudge or leak, allowing water into the lens. Even lenses made for immersion oil still require maintenance after use, so be sure to clean after use. 

Do Numerical Aperture and Resolution Relate?

Let’s introduce one more piece to the puzzle: Resolution. 

As Florida State University’s Molecular Expressions describes, we understand resolution as the smallest amount of space recognized between two entities, allowing them to distinguish from one another. 

This resolution defies conventional pixel resolution in displays, as a resolution in optical microscopes is more of a subjective concept that is altered with the introduction of elements like immersion oils. 

Numerical aperture does not have a direct correlation to the resolution of an image but is an important factor. Other factors are the substage condenser’s aperture and the sensor utilized to capture an image. 

To properly measure a microscope’s optical resolution, it needs to be properly aligned with the condenser lens distanced and angled appropriately for its own numerical aperture, so that the cone of light coming from the sample and filtering through the objective lens can reach it properly. 

Another factor to consider is the wavelength of light used within your application, as shorter wavelengths produce crisper, clearer wavelengths than longer images. 

FSU goes into detail about equations for calculating resolution in relation to the numerical aperture and wavelength of light, but these are theoretical and subjective to specific conditions. 

Airy Patterns & Discs

When light passes through a specimen, into an objective lens, and is captured, the specimen appears in the image in an airy pattern. 

This airy pattern is because the light is diffracted and scattered as it passes through the specimen and the curved aperture of an objective lens’s back. The central region of these patterns is also known as an airy disk, which is an enclosed space containing a vast majority of the luminous energy. 

As these disks lose size, the details of the specimen are easier to see, because the light is better concentrated. For that reason, there is a direct correlation between objective lenses with a higher numerical aperture and those lenses having smaller airy disks. 

Conclusion

Some uses of microscopy or day-to-day observations do not require reaching for the peak of performance from their equipment. But with specialized applications such as brightfield or fluorescence, you must think innovatively and push boundaries to achieve the best results. 

Because lenses of higher numerical aperture and magnification have such a low depth of field, scientists produce oil immersions to channel light properly and completely bridge the gap between the specimen and the objective lens. This method helps us understand the proper setting height for an objective and how to quantify a good lens in respect to that. 

A lens with a higher numerical aperture has a lower depth of field, meaning it can discern high-quality details at short distances and can produce crisper images. These lenses also enable oil immersions which filter out air and outer lighting that make samples appear blurry, thus producing a higher resolution scan. 

This technology may not be necessary for all microscopy applications, but for those where it is, it is crucial to understand the physics of light travel through optical lenses, as these will help you design your custom solution.

Visit Navitar for more information on our Custom Microscope Objectives.

Sources:

MicroscopyU - Numerical Aperture | Microscopyu.com

Microbus - Numerical Aperture (N.A.), Condenser Lens and Immersion Oil | microscope-microscope.org

Molecular Expressions - Numerical Aperture and Resolution | micro.magnet.fsu.edu