Shoot the scene in 48 or 96 fps. Sync the set lighting to odd frames. Every odd frame, the set lights are on. Every even frame, set lights are off.
For the backing screen, do the reverse. Even frames, the backing screen is on. Odd frames, backing screen is off.
There you go. Mask / normal shot / Mask normal shot / Mask ... you get the idea.
Of course, motion will cause normal image and mask go out of sync, but I bet that can be remedied by interpolating a new frame between every mask frame. Plus, when you mix it down to 24fps you can introduce as much motion blur and shutter angle "emulation" as you want.
- It'll bleed on fast motion. Hair in the wind would just not work.
- Incandescent lights are out.
You could solve both by having two ghost frames shot very close to the real frame (no need to evenly space the frames, after-all) and using strobing a high powered laser.
You'd need very fast sensor or another one optically on the same position.
The calculation isn't too hard though. The width of a pixel divided by the velocity of the subject on the sensor is the maximum delta(T) between real and ghost frames.
But, again, you dont have to shoot faster. You just have to drop the 180-180 degree phase between a real and ghost frame to be 10-350 degrees. Then your 24 fps is capturing the background as if it were 870 fps
In any case, if you actually have a scene bright for 1/24th of a second and then dark for 1/24th of a second, repeating, you're well within photosensitive epilepsy range. Don't do that to your actors unless you've discussed it with them and with your insurance company first.
Artifacts?
I bet that can be remedied by interpolating a new frame between every mask frame. Plus, when you mix it down to 24fps you can introduce as much motion blur and shutter angle "emulation" as you want.
Motion blur can also be very forgiving. You are more likely to notice artifacts in still or slow moving scenes and then the problem goes away.
Incandescent lights flicker at twice your AC power frequency -- to a decent approximation, their power is proportional to V^2. But this is input power -- the cooling of the filament is slowish and the modulation depth is low. Most people aren't bothered by this.
Fluorescent lights with old or very crappy "magnetic" ballasts flicker at twice the mains frequency, with deep modulation. The effect on people varies from moderate to extremely unpleasant, and it's extra bad if anything is moving quickly (gyms, etc). There are even studies showing that office workers perform worse under such lighting even if they don't experience personally perceptible symptoms. The effect is so severe that people invented the "electronic ballast", which flickers at much, much higher frequency and avoids low-frequency components. Phew. (The light might still be a nasty color, but the temporal output is okay.)
"Driverless LEDs" are deeply modulated at twice the mains frequency. These are very nasty.
If you actually have a light that flickers at the AC power frequency (certain LED sources in a two-brightness diode-dimmed kitchen appliance fixture will do this, as will driverless LEDs with certain types of failures), then it's extra nasty.
There are plenty of people around who find (depending on the actual waveform) 60Hz flicker intolerable and 120Hz flicker extremely unpleasant. And there are plenty of people who can often perceive flicker under appropriate circumstances up to at least several hundred Hz and even into the low kHz with certain shapes of light sources. You can read up on IEEE 1789 to find a standard based on actual research on what lighting waveforms should look like.
The effect of 120 Hz flicker is bad enough that energy codes in some places (e.g. California) have started to require that LED sources minimize this flicker, but, sadly, it's poorly enforced.
Anyway, an old HN submission I still use when buying light bulbs: https://news.ycombinator.com/item?id=14023196
There were a large number of lights around it and each one was blinked on for an instant while the camera shot at an insanely high frame rate - something like 288 frames per second with twelve lights.
This meant that after the fact you could pick any one of the twelve frames for that 1/24th of a second, to choose the angle the light was hitting at.
