One-quarter Power:  you can still see the rise to full power, followed by the quenching of the flash at about 350 microseconds after peak light output.

For 1/4 power:       t-0.5       501 microseconds   or   1/1995 seconds
                              t-0.1       578 microseconds   or   1/1730 seconds
                              P50        250 microseconds   or    1/4000 seconds
                              P90        468 microseconds   or    1/2140 seconds

One-eighth power: the top frame shows the properly-measured flash output.  It still rises to full power, but is quenched shortly thereafter.  The bottom frame (note the change in vertical scale) shows what happens if the peak flash output light is not reduced enough before it falls on the phototransistor, with the result being that the detector is saturated: the light curve is "flat-topped" at almost the power supply voltage (minus a few tenths of a volt for the phototransistor emitter-collector junction voltage).  The base appears to be much broader than it should be - imagine the upper frame to be greatly expanded in the vertical direction but you can observe only the bottom portion.  Measurements made from this data would be wildly incorrect!

For 1/8 power:       t-0.5       251 microseconds   or   1/3980 seconds 
                              t-0.1       325 microseconds   or   1/3080 seconds
                              P50        128 microseconds   or   1/7810 seconds
                              P90        252 microseconds    or   1/3970 seconds

One-sixteenth power: the flash output never reaches the peak value for longer durations; it is now quenched before it has fully turned on.

For 1/16 power:       t-0.5      116 microseconds   or   1/8620 seconds
                                t-0.1      185 microseconds   or   1/5400 seconds
                                P50         66 microseconds    or   1/15000 seconds
                                P90       146 microseconds    or   1/6850 seconds

Because the rise time of the light putput now determines a significant portion of the light curve, the different timing levels are rather different.

This is beginning to be in the ballpark for stopping falling water drops.