# Lens numerical aperture

1. Jan 12, 2014

### u0362565

Hi,

I have a question about resolution as defined by rayleigh's equation r = 0.61 x lambda/numerical aperture

The maximum half angle of acceptance of a lens is 90 degrees and the sine of this is 1. At this point the only thing that can increase the value of the denominator in the equation is to increase the refractive index of the imaging medium e.g. Immersion oil. So if you could find a medium with a higher refractive index than immersion oil (1.515) then according to the equation this would make the minimum resolvable distance between two points smaller. This would also mean tho that any other medium between the object and lens would need to have the same refractive index or at least close to minimise spherical aberration. So I'm guessing immersion oil is as good as we can do? But why is that?

Many thanks.

2. Jan 12, 2014

### Andy Resnick

For far-field linear imaging, the limiting factor for resolution is indeed the refractive index- but immersion oil does not have the highest possible refractive index. Besides other fluids, solid immersion lenses can go up to n = 3.5 or so.

There is a great deal of work demonstrating imaging with resolution exceeding the Abbe limit using alternate methods (so-called super-resolution or non-diffraction-limited imaging), typically applied to fluorescence methods (RESOLFT, STORM, FPALM, etc.) but structured illumination and near-field scanning methods can be used more generally.

3. Jan 13, 2014

### u0362565

Thanks andy, i haven't heard of solid immersion lenses before, i'll look into that.

4. Jan 17, 2014

### Claude Bile

Keep in mind that the "immersion" material needs to be transparent at whatever wavelength you want to image at. Semiconductors with n > 3.5 are opaque in the visible. Diamond has the highest refractive index that is transparent in the visible at around ~2.

Honestly, the amount of effort required is not worth the marginal improvement in resolution. Much better to investigate schemes such as structured illumination mentioned by Andy.

Claude.