What is the maximum refractive index for lens numerical aperture?

[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.

 

[Andy Resnick]

<snip>So I'm guessing immersion oil is as good as we can do?

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.

 

[u0362565]

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

 

[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.

 

[sardar]

The maximum refractive index for lens numerical aperture is determined by the material properties of the lens and the surrounding medium. In theory, the maximum refractive index for lens numerical aperture is infinite, as long as the surrounding medium has a higher refractive index than the lens material. This would result in a numerical aperture of 1, which is the maximum possible value. However, in practical applications, the maximum refractive index for lens numerical aperture is limited by the availability of materials with high refractive indices and their compatibility with the lens material. Immersion oil, with a refractive index of 1.515, is currently the highest available medium that is compatible with most lens materials. Therefore, it is currently the best choice for achieving the highest possible numerical aperture and resolution. However, research and advancements in material science may lead to the development of new materials with even higher refractive indices in the future.