Punch out area of shape using another—with translucent edges

I have a ellipse-ish shape with a ragged, translucent edge. I'd like to use this to punch out the same shape (with the same ragged, translucent edge) from a photo, so that I end up with a photo in the ellipse-ish shape.

In Illustrator, I could use the Pathfinder "crop" tool, though not sure how I'd approach the translucent edges. Is this possible in Photoshop? Thanks for reading.