…but… if we don't rely on spatial compression to achieve the density, but instead use temporal compression…
1) Consider a mirror which rotates through n angular positions.
2) At position zero it reflects off "secondary mirror #0" and onto our target at X microseconds.
3) At position one it reflects off "secondary mirror #1" and onto our target at X-k microseconds.
4) At position n it reflects off "secondary mirror #n" and onto our target at X-k * n microseconds.
5) If we turn the rotating mirror from position 0 to 1 after k microseconds, we have darkness on the target for X microseconds, then light from both secondary mirrors 0 and 1 for k microseconds.
6) If we rotate through all n positions at k microseconds/position we get n times the light at a 1/n duty cycle.
7) As n goes to infinity: PROFIT!
Mathematicians might solve for the shape of the now continuous secondary mirror. I would just write a javascript program to approximate it for segments of length epsilon. Ultimately the CNC equipment that makes the mirror will have an epsilon anyway.
You may wish to use a mirrored polygon to sweep the usable angle of your secondary mirror repeatedly.
Yes! It wasn't until lunch when it dawned on me that viewed backwards it made a time dilation device. I fear the continuous version could not be reconciled with imaging optics, but for non-imaging applications it can slow down an event for more leisurely capture.
1) Consider a mirror which rotates through n angular positions.
2) At position zero it reflects off "secondary mirror #0" and onto our target at X microseconds.
3) At position one it reflects off "secondary mirror #1" and onto our target at X-k microseconds.
4) At position n it reflects off "secondary mirror #n" and onto our target at X-k * n microseconds.
5) If we turn the rotating mirror from position 0 to 1 after k microseconds, we have darkness on the target for X microseconds, then light from both secondary mirrors 0 and 1 for k microseconds.
6) If we rotate through all n positions at k microseconds/position we get n times the light at a 1/n duty cycle.
7) As n goes to infinity: PROFIT!
Mathematicians might solve for the shape of the now continuous secondary mirror. I would just write a javascript program to approximate it for segments of length epsilon. Ultimately the CNC equipment that makes the mirror will have an epsilon anyway.
You may wish to use a mirrored polygon to sweep the usable angle of your secondary mirror repeatedly.