## What is the Resolution of the Microscope?

In microscopy, the term ‘resolution’ is used to describe the ability of a microscope to distinguish detail. In other words, Resolution refers to the ability to see two items as separate and discrete units rather than as a fuzzy, overlapped single image.

The resolution of a microscope is intrinsically linked to the numerical aperture (NA) of the optical components as well as the wavelength of light that is used to examine a specimen. We can magnify objects, but if the objects cannot be resolved, the magnification is useless.

Microscope resolution is the amount of detail that can be resolved from the light being refracted through a specimen and presented to the observer through a microscope.

For example, imagine you had a specimen on your slide under your microscope for examination and when you look at two cells side by side unresolved they just look like a blurry mass but when you focus the microscope they now become clear and you can clearly distinguish one cell from another.

When I first started microscopy, this was a little ambiguous to me and really did not add much to my understanding of the concept of resolution and what it means. So I dug a little deeper and it turns out there is much more to the story.

In this article, we will look at some of the fundamentals that will help you understand the concept of resolution in the context of microscopy and hopefully present it to you in a concise digestible manner.

## Microscope Resolution and Wavelength of Light

Light has a number of properties that affect our ability to visualize objects, both with the unaided eye and with the microscope. Understanding these properties will allow you to improve your practice of microscopy.

One of the most important properties of light is its wavelength or the length of a light ray. Represented by the Greek letter lambda (λ).

The sun produces a continuous spectrum of electromagnetic radiation with waves of various lengths. Visible light rays, as well as ultraviolet and infrared rays, constitute particular parts of this spectrum.

White light is the combination of all colors of visible light. The wavelength used for observation is crucially related to the resolution that can be obtained.

the wavelength of light is an important factor in the resolution of a microscope. Shorter wavelengths yield higher resolution and vice versa.

For example, imagine a target with a foot-high letter E hanging in front of a white background. Suppose that you throw at the target ink-covered objects with diameters corresponding to various wavelengths.

If one object has a diameter smaller than the distance between the “arms” of the letter E, the object will pass between the arms, and the arms will be distinguishable as separate structures.

First, imagine tossing basketballs. Because they cannot fit between the arms, light rays of that size would give poor resolution. Next, toss tennis balls at the target. The resolution will improve. Then try jelly beans and, finally, tiny beads.

With each decrease in the diameter of the object thrown, the number of such objects that can pass between the arms increases. Resolution improves, and the shape of the letter is revealed with greater and greater precision.

Microscopists use shorter and shorter wavelengths of electromagnetic radiation to improve resolution. Visible light, which has an average wavelength of 550 nm, cannot resolve objects separated by less than 220 nm.

Ultraviolet light, which has a wavelength of 100 to 400 nm, can resolve separations as small as 110 nm. Thus, microscopes that used ultraviolet light instead of visible light allowed researchers to find out more about the details of cellular structures.

But the invention of the electron microscope, which uses electrons rather than light, was the major step in increasing the ability to resolve objects. Electrons behave both as particles and as waves. Their wavelength is about 0.005 nm, which allows the resolution of separations as small as 0.2 nm.

## Microscope Resolution and Numerical Aperture

Microscope resolution is affected by several elements. An optical microscope set on a high magnification may produce an image that is blurred and yet is still at the maximum resolution of the objective lens.

The numerical aperture of the objective lens affects the resolution. This number indicates the ability of the lens to gather light and resolve a point at a fixed distance from the lens.

The smallest point that can be resolved by an objective is in proportion to the wavelength of the light being gathered, divided by the numerical aperture number. Consequently, a higher number corresponds to a greater ability of a lens to define a distinct point in the view field.

The numerical aperture of an objective lens also depends on the amount of optical aberration correction.

## What is the Resolving Power of Microscope?

Resolving power denotes the smallest detail that a microscope can resolve when imaging a specimen; it is a function of the design of the instrument and the properties of the light used in image formation. The smaller the distance between the two points that can be distinguished, the higher the resolving power.

The resolving power (RP) of a lens is a numerical measure of the resolution that can be obtained with that lens. The smaller the distance between objects that can be distinguished, the greater the resolving power of the lens.

## Airy Disk

As we have seen, light passes up through a specimen and gets transformed into an image. The points of the specimen are seen as small patterns. These patterns are called Airy patterns and the central maximum of the Airy patterns is called an Airy disk. The disks visually look like concentric light and dark circles.

This is where we get back to our original definition of resolution being the minimum distance between two distinct points that can be distinguished between two points; the points being the Airy disks.

The Airy Disk idea is credited to George Biddell Airy who lived from 1801 to 1892. Airy was an English astronomer and mathematician. Airy’s paper ‘On the Diffraction of an Object-Glass with Circular Aperture’ is where Airy expounded on these ideas.

## Rayleigh Criterion

I’ll spare you the math, but the Rayleigh criterion builds on the Airy disk concept and is basically a mathematical criterion for when two points are distinguishable from one another.

Now that you understand Airy disks, the Raleigh criterion, and the numerical aperture, you can probably guess that if we can get smaller Airy disks, we can discern more detail or achieve more resolution.

It turns out that there is an inverse relationship between numerical aperture and Airy disks such that as the numerical aperture increases and more light information is collected the Airy disks are smaller.

## How to calculate the resolution of a microscope

Taking all of the above theories into consideration, it is clear that there are a number of factors to consider when calculating the theoretical limits of resolution. Resolution is also dependent on the nature of the sample.

Let’s look at calculating resolution using Abbe’s diffraction limit and also using the Rayleigh Criterion.

Firstly, it should be remembered that:

**NA= n x sin α**

Where n is the refractive index of the imaging medium and α is half of the angular aperture of the objective. The maximum angular aperture of an objective is around 144º. The sine of half of this angle is 0.95.

If using an immersion objective with oil that has a refractive index of 1.52, the maximum NA of the objective will be 1.45. If using a ‘dry’ (non-immersion) objective the maximum NA of the objective will be 0.95 (as air has a refractive index of 1.0).

Abbe’s diffraction formula for lateral (i.e. XY) resolution is:

**d= λ/2 NA**

Where λ is the wavelength of light used to image a specimen. If using a green light of 514 nm and an oil immersion objective with an NA of 1.45, then the (theoretical) limit of resolution will be 177 nm.

Abbe’s diffraction formula for axial (i.e. Z) resolution is:

**d= 2 λ/NA2**

Again, if we assume a wavelength of 514 nm to observe a specimen with an objective NA value of 1.45, then the axial resolution will be 488 nm.

The Rayleigh Criterion is a slightly refined formula based on Abbe’s diffraction limits:

**R= 1.22 λ/NA obj + NA cond**

Where λ is the wavelength of light used to image a specimen. NA obj is the NA of the objective. NA cond is the NA of the condenser. The figure of ‘1.22’ is a constant. This is derived from Rayleigh’s work on Bessel Functions. These are used for calculating problems in systems such as wave propagation.

Taking the NA of the condenser into consideration, air (with a refractive index of 1.0) is generally the imaging medium between the condenser and the slide. Assuming the condenser has an angular aperture of 144º then the NA cond value will equal 0.95.

If using a green light of 514 nm, an oil immersion objective with an NA of 1.45, condenser with an NA of 0.95, then the (theoretical) limit of resolution will be 261 nm.

As stated above, the shorter the wavelength of light used to image a specimen, then the more detail will be resolved. So, if using the shortest visible wavelength of light of 400 nm, with an oil immersion objective with an NA of 1.45 and a condenser with an NA of 0.95, then R would equal 203 nm.

To achieve the maximum (theoretical) resolution in a microscope system, each of the optical components should be of the highest NA available (taking into consideration the angular aperture).

In addition, using a shorter wavelength of light to view the specimen will increase the resolution. Finally, the whole microscope system should be correctly aligned.