Not sure the subject says what I need it to — but here is the situation:

Setup:
- I have a node with a PDF file attached
- The whole site is setup for "Private Downloads"
- I have a Custom Formatter, that creates a JPG preview of a PDF when the node is displayed
- The JPG preview is saved in the /sites/default/files/private/pdf_preview directory

Problem:
- I am trying to display the programmatically created JPG preview file, but authenticated site visitors can't "see" the image, because it's in the "private" directory.

How can I show this image for authenticated users, but keep it hidden for public users. Right now no one can see it.

Any ideas?