Usage of comma vs. semicolon for combining two clauses in a caption

I have a short piece of text used as an image caption. Here is how it looks right now:

A picture of a painting of the Brooklyn Bridge by Aubrey Caron, reproduced here with permission from Aubrey Caron

Is this caption is grammatically and typographically correct? Is the phrase after the comma a parenthetical element? Is comma (",") the right punctuation to use here or should it be semicolon (";")?