When I apply to a PhD program, may I ask a postdoc who closely supervised me to write a recommendation letter? My supervisor also has written one for me, but I believe the postdoc can comment on my research skills in a more detailed and precise way. Does a postdoc have enough authority to convince admission committee?
While it's possible that a postdoc letter (in the absence of further context) might carry less weight, there are good reasons to ask them anyway:
the letter is a testimonial about your ability to do research. A postdoc who's worked with you is in a much better position to say something nontrivial about this. Lines like "I closely worked with so and so" carry weight.
the postdoc might know faculty at the university you're applying to. In that case the letter carries even more weight (I'm likely to pay more attention to letters from people that I know)