Just to clarify, by compensate you mean pay him money? Honestly, I don't think that's a good idea. I'd be worried with ethical and legal aspects of both you offering and him accepting money.
Per the American Medical Association:
"Observership programs are not intended to be organized for profit. Physicians in each specialty should volunteer their time and efforts.
Actual costs (administrative fees, immunizations, etc.) may be itemized and paid for by the observer."
How about you just ask first, without offering compensation, and see what he says?