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Innovations like these will happen a lot more often once there's a proper hardware platform for this, like ARA is.
What's ARA? Sounds like it might be interesting.
This reminds me of this Kickstarter project that I backed a while back: https://www.kickstarter.com/projects/968523355/micro-phone-l...

This one just sticks to your phone rather than requiring an enclosure, but only has a max zoom of 60x (or 15x without phone zoom).

'Phone zoom' is all software, so it wouldn't be true 60x.
That depends on the phone.

Some Nokia devices (for one example I know of: no doubt there exist other cameras and camera phones that do something similar) have a higher resolution CCD than they need for unzoomed images and use the extra resolution for noise reduction and such when scaling the image down to the final size - so with zoom you genuinely get more detail but possibly at the expense of extra signal noise.

We saw this on AOL On on ROKU last week-end, pretty cool.
Digging these new cheap microscope concepts (this is and the as-of-yet unbuyable paper microscope). Just reading about them moved me to build this contraption someone linked to in the paper microscope thread comments:

http://www.instructables.com/id/10-Smartphone-to-digital-mic...

It's pretty cool, but if you build one, definitely use caution and wear eye protection when drilling through the Plexiglas.

Seconded on the eye protection. Also, drill slow (without too much pressure) and drill a pilot hole so you stay centered.

There are special plexiglass drills, those make life a bit easier, a glass bit works as well (even better, actually).

Looks like the similar Foldscope is more powerful because it can do up to 2000x magnification: http://en.wikipedia.org/wiki/Foldscope
In terms of magnification, yes, but there are also many other variables that can be relevant, so I guess it's good to have multiple cheap designs to choose from, depending on the goal and circumstances. For example Foldscope seems to be using ball lens, which indeed gives higher magnification, but probably also suffers more from aberration, may be trickier to fix firmly and precisely into the microscope housing compared to the lens that are already created on a flat plate, etc., so for those tasks where lower magnification is sufficient or preferred the droplet lens might sometimes be more suitable.
This is awesome work. I just want to point out that it's pretty much a marketing lie to say that the lens gives you 160x magnification. Sort of like saying how digital zoom gives you magnification on a camera.

A non-linkbait title would also report the numerical aperture of their microscope. From their paper, it looks like the new lens performs comparably to a research grade 10x 0.25NA objective.

OK, kind of cool, but would you not be better with a real camera on the end rather than a half arsed phone camera?

I am aware that the lens is usually what makes camera phones poor in comparison to regular cameras, but I still find my phone camera barley usable, and the quality crap compared to my point and shoot camera. I am sure it isn't only down to the lens.