alt Hacker NewsBy definition, you can't interpolate a sample. A sample is a measured value.
What you can do, if and only if you have an exactly repeating signal triggering at the same point within a cycle, is change the delay between the trigger and sample, and repeat. In other words, sample at different times within the same signal (since it's exactly repeating), to build up samples in time, of that waveform, to whatever time resolution you want.
Of course, you're limited to any noise in the trigger, variation in the signal, etc.
This is how you can record light moving through your garage [1]!
Not sure if mkeeter's comment has been ninja edited but it says between samples, it doesn't say it is interpolating to generate new samples.