# Smallest object resolvable by optical microscopy

I am wondering what is the smallest object you can resolve with an optical microscope. I am aware of the equation

$\delta=\frac{\lambda}{2\textrm{NA}}$

that basically gives you the resolution. $\delta$ would then be the minimum distance between two objects which will allow you to say that there are indeed two separate objects. But what if I do not care about how many objects are actually there, but instead of if an object is there in the first place?

Let's assume that I am using an optical microscope with an oil immersion objective. The oil has a refraction index of 1.5, so for a wavelength of let's say 500 nm the $\delta$ is ~166 nm. But what if my particle is smaller than this? 100 nm? 50 nm? Let's assume that this is a perfectly reflective metallic particle embedded in transparent glass. Can I still observe it?

This question is related, however does not address my question directly: Resolving power of a microscope?

Yes you are correct if you only want to detect if a single object is there the object can be below the diffraction limit. In this case your ability to detect the object is related to the amount of reflected light compared to the noise. As the object becomes smaller it becomes more difficult to distinguish its signal from random noise - although this point will be dependent on the optical properties of the object as well as your measurement setup.

In any case it is important to note that you cannot easily determine the size of such an object as it will still appear blurred to approximately the same size by diffraction effects.

Only techniques of microscopy which measure the far-field and are diffraction-limited. This limit is beaten routinely using near-field microscopy in which one measures the evanescent waves which usually decay off within a distance of a few tens of micrometers from the object.

However, since you say that you only care if the object is there, then that means that you just need to observe some scattering of photons. In that case, I believe you can reach even below atomic length-scales and will only be limited by quantum-mechanical (Heisenberg-type) limits.

Not exactly. The formula you provided is the Abbe limit, and emitters are only resolvable when they are separated by a distance greater than this.

The Rayleigh criterion, 0.61*lambda/NA is a better measure of minimally resolvable objects. This corresponds to the zero order maxima of one point spread function (PSF) coinciding with the first minima of the nearby PSF.

There also exists a Sparrow limit, which is the largest separation at which the sum of two nearby PSFs yields an approximately flat-topped profile. Emitters at this distance are not resolvable.

I worked many years in the semiconductor industry. The company I worked for was identifying differences in chips in the 12nM range using optical imaging. This was back in 2018.