This is what I first saw.
Lรกszlรณ Kovรกcs used deep focus photography in Paper moon. The technique brought everything into the same focus, background and foreground. It was like The Arnolifini Portrait.
We see a scene in ways that human beings are incapable of seeing. We see reflections, crisp shadows, we see detail that our normal ocular faculty cannot give us.
In the diner scene in Paper Moon, I noticed this for the first time today:
A woman's reflection, in perfect profile, captured in the background in a mirrored center panel of a jukebox sitting behind Addie.
I went back and watched the movie through that scene and up to that point. We first see the woman as a gauzy shadow through the front windows from outside the diner. The store lettering across the street is a reflection and so reversed. She though is not a reflection.
We then see her inside the restaurant, with the reflecting glass storefront window no longer rendering her gauzy, but still in the background. That's Addie's Nehi soda bottle in the foreground. Addie is seated to the viewer's left, Moze to the right.
The hat is distinctive and is captured in the jukebox reflection but I had to view the jukebox reflection a few times and compare with other diners pictured to be sure that it was the same woman. I wasn't sure if her dress pattern was the same at first. But it was. In sequence then: