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I've come across this article: Fluorescent Imaging of Single Nanoparticles and Viruses on a Smart Phone.

And what is the theoretical limit for such smartphone extension? And how that limit can be computed (same as for microscope $\sim 1.22\,\lambda / D$)?

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The imaging is not being done by focusing transmitted light as would be done in an optical microscope. Instead it's detecting light emitted by the nanoparticles as they fluoresce. This means there is no lower limit to the size of the particle detected, except that when the particles get very small they emit too little light, i.e. they are too faint, for the phone camera to distinguish them from background noise.

There still remains a limit to detecting structure in the particles. For large particles you'd expect to resolve differences in the fluorescence across the particle, while for small particles they will just appear to be a featureless blob.

It's a bit like seeing stars with the naked eye. A star is far too small for your eye to resolve but you can still see the light coming from it. The only limitation is that the star appears as a fuzzy blob rather than a disk.

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