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Just curious does anyone know why this type of shutter isn't used on modern digital cameras like DSLRs or mirrorless cameras?
They're used to photograph stuff that is a lot less bright than nuclear explosions, so properties that are desiderable for that (actually losing most of the light) aren't for general subjects.
The mirrors in SLRs are what allow you to see what you will be taking through the viewfinder, so I don't see a way to have the ability to see through the lens without the standard mechanical device. My guess is that these cameras were focused on the subject well ahead of time
The mirror moves out of the way before the shutter fires...or the shutter doesn't fire until the mirror is out of the way. There's latency or shutter delay. Accounting for it requires anticipation when shooting fast flowing scenes.
I think one of the issues would be that this requires a polarizing filter, which limits a lot of light coming in to the camera. That's going to mean that you'll loose a lot of light to the extra filtering and be much more dark than otherwise.
Really a polariser only cuts about 2 stops, so in conditions where a Kerr effect shutter makes sense, it likely doesn't matter.
Because the CCD chip (aka the sensor that reads the light) can be electronically read, discharged and reset so a shutter (mechanical or otherwise) is completely unnecessary.
These days, ordinary walk-around digital cameras use CMOS because it's less expensive. CMOS tends to be read line by line. That's why rolling shutter can be an issue when shooting video.
CCDs are always ready line-by-line, while some CMOS (global shutter) read all lines at the same time. However, in CCDs the image charges are physically shifted downwards which causes streaking instead of a rolling shutter effect. There are (very expensive) frame-transfer CCDs which have a second readout sensor that is not light sensitive. This allows quickly shifting the image into this sensor, significantly reducing streaking.
CCDs have no way to stop collecting light once the keep clean cycle has ended. A shutter is absolutely necessary for exposure times that are significantly shorter than the reasout time (typically a few ms).
A back of envelope exposure calculation using the Sunny 16 heuristic [1] and assuming that high shutter speed is the rationale for using a Kerr cell shutter [2]

Full sun bright for a "typical" scene. That's ISO 100, f16, and 1/125 seconds for "typical" exposure [3]. To make it easy, assume an f1 lens (about as fast as you can buy and assume t-stop equals f-stop and ignoring issues with acceptable depth of field). An f1 lens is 8 stops faster than f16, so it requires 1/2000 of a second exposure at ISO 100. The Raptronic shutter was 1/1,000,000 second (1 micro-second). That's nine stops faster. We're out of lens aperture so Sunny 16 says we need 9 stops of ISO. That gives ISO 102,000.

ISO 102,000 is available on consumer grade digital cameras such as the Sony A7S, the Pentax K1 and KP, etc. The Pentax KP goes to ISO 800K (for some definition of 'goes') so you could theoretically shoot at f2.8 in full sun. Theoretical if you can live with the noise and if there are not other effects from very short shutter speeds (the equivalent of solarization from short shutter speeds on analog film) [4] [5]

Most people want the ability to shoot in less than full sunlight. Most people don't want to live with a high noise baseline. Most people want the ability to achieve moderate depth of field. Most cameras are designed for a meaningful segment of most people.

So Kerr shutter digital camera is viable. It needn't be mirrorless. In a typical single lens reflex, the mirror already swings up out of the way before the shutter fires. It is also possible to mount the shutter in the lens of a single lens reflex camera. That's typical with Hasselblad, Mamiya, and some other SLR medium format cameras.

[1]: https://en.wikipedia.org/wiki/Sunny_16

[2]: https://en.wikipedia.org/wiki/Kerr_cell_shutter

[3]: e.g. snapshot conditions not Adams' Zone system or similar.

[4]: Just theorizing about the possiblity of equivalent effects. I don't know.

[5]: It would be interesting to know about the film stocks which allowed the Rapatronic to avoid solarization.

I'm not sure you're correct about solarisation. The reversal of tone found in solarisation is due to overexposure, see https://en.wikipedia.org/wiki/Solarization_(photography)

Solarisation would be a likely outcome of a too slow shutter when photographing the nuclear explosion on typical film stocks without sufficient filtering. It was at least as important to achieve sub-millisecond shutter speed as it was to properly expose the film.

One thing that does typically affect film, either with too short or too long exposures is reciprocity failure https://en.wikipedia.org/wiki/Reciprocity_(photography)#Reci... so perhaps that's what you're thinking of. It's hard to know how relevant that is to this discussion. I'm not sure it was a consideration given how energetic a nuclear explosion is, and reciprocity failure is found when there are not enough photons to convert the silver halides into a latent image.

I think you're on the right track with Sunny 16, but why not use this method to take photos of the sun itself? I've seen 16 stops recommended as the minimum for solar filtering, so that puts it in the range of standard ISO and f-stops, but without filtering, a high shutter speed like with the Kerr cell is possible.

I agree about solarization and reciprocity failure. My bad. too late to edit.

For pictures of the sun, the short shutter speed is an alternative to filters, but filters are inexpensive. I bought a pair for less than $20 to take pictures during the recent solar eclipse in the US.

TL;DR: it’s way way too fast for anything but maybe solar (and nuclear explosion) photography. (I presume the tech doesn’t scale to more down-to-earth shutter speeds.)
Is this still state of the art for ultra-fast exposures, or is there newer better technology?
Imagine the fps if it took videos
I use one of these [1] for work. The software which comes with it asks you to specify an fps when setting up an exposure. Typing in 66 Mfps always feels a bit dumb!

[1] - invisiblevision.com/products/ultra-high-speed-framing/