Such a sensor (used to) exist, Foveon X3. It is very interesting as it also uses the differential absorption of different wavelengths of light at different depths in silicon to distinguish colours: https://en.m.wikipedia.org/wiki/Foveon_X3_sensor It had various advantages, and some disadvantages related to distinguishing colours, but ultimately wasn’t very successful in the market despite getting shipped in some DSLRs, possibly due to the marketing challenges (Bayer array sensor manufacturers count each R/G/B sub pixel as part of their “megapixel” count, so the Foveon sensor appeared low resolution by that metric).

My Sigma SD1M still produces mind-blowing images I can't do with high-end Nikons and Canons. Foveon can truly make magical images, though there were so many issues with DSLRs it shipped on, e.g. they were almost always awfully slow and had very bad (but film-like) low-light performance. Also, original research suggested that to get realistic colors, up to 7 layers are needed. Bayers OTOH just interpolate and cook colors, but with the increase of resolution might at some point perform similarly, when lens limit is hit. Foveon was also always manufactured by a far worse process than e.g. Sony top-end sensors, and its quantum efficiency was orders of magnitude worse.

Bayers don't cook colors when they interpolate, they cook edges.

I don't follow, Sigma hasn't stopped using Foveon sensors, they still use the Foveon Quattro stuff afaik. Now they use a 1:1:4 ratio for R/G/B layer resolution, where the blue layer also records luminance.

They decided they wanted to confuse people more when they tried to compare it to a Bayer sensor.

Actually I didn't realise they still made them... Nice to know. I remembered the Foveon sensors from when they were first introduced, but didn't see any reference to them still being made when I did a quick search to refresh my memory, so they may have a bit of a marketing issue ;)

Higher resolution - no. Resolution is limited due to diffraction, so adding more pixels doesn't necessarily add more details.

Better images in the dark - possibly.

More important than the diffraction limit is probably the fact you put an image sensor in front of your image sensor, and it will distort the wavefront for the sensor behind it.

Plastic bags are also quite transparent, but you never get a better picture by putting them in front of your camera.

Isn't it possible to computationally counter the effects of diffraction and distortion?

Generally speaking yes! That's what companies do that create masks for lithography so that the structures the manufacturers can create are smaller than the wavelength they use in the process. (See https://en.m.wikipedia.org/wiki/Computational_lithography). The article states that generally this is rather computationally expensive and I would wager that an analogous concept would be too. Perhaps a Neural Network could be trained to infer corrections and maybe that would be feasible then but maybe someone else with more experience in the field can elaborate on that.

Neural networks suffer from provability issues, you don't want to make a multi million dollar mask set only to find out your ConvNets were hallucinating. There are more standard computational lithography techniques such as OPC, RET and inverse lithography.

With that being said, there's been some work done:

https://ieeexplore.ieee.org/document/5726499/

https://www.spiedigitallibrary.org/conference-proceedings-of...

http://iopscience.iop.org/article/10.1088/2040-8978/12/4/045...

https://www.google.com/url?sa=t&source=web&rct=j&url=http://...

Non-mobline link:

https://en.wikipedia.org/wiki/Computational_lithography

Especially when you have a predistortion image from the frontmost sensor, and I would imagine that the diffraction would remain constant between photos - manufacture differences would presumably mean each sensor would need to be calibrated, but with the multiple sensors, it seems quite possible that could be done by the consumer.

They say the answer is "yes". It's even nominally offered as a feature in, e.g. Canon's RAW processing tool (called "DLO")

Unfortunately, in practice it seems to behave more like smart sharpening than a discrete reverse convolution math op.

Already on the market. Interview with Foveon cofounder Richard Lyon : https://www.youtube.com/watch?v=pIZp0qPZySw

Fun fact - Carver Mead was one of cofounders, of the Conway-Mead fame (founder of modern VLSI revolution). Another was Faggin, father of Intel 4004. Whole company was loaded by hardcore semiconductor process design engineers.