As you can see in the below image and, as I'm sure most TNG watchers would have noticed, there are a series of orange 'plates' on Picard's desk. Does anyone know what these are? (Does Picard ever use them or talk about what they are?)
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I asked Michael and Denise Okuda (TNG production and art designers) this question ten minutes ago at the Star Trek 50th Anniversary Celebration in Las Vegas.
MICHAEL: That's a darn good question.
He then explained that, out-of-universe, these orange plates are props left over from The Motion Picture. Circuit designs were painted on them for TNG.
In-universe, he said that no specific function had ever been assigned to the plates. There was talk at one point amongst production personnel and/or set designers that they might serve as PADD-style devices (data display devices or readers, but smaller and thinner than PADDs). But he insisted that no official purpose had ever been assigned to them by any designers or writers. He did say that, in retrospect, they should probably be data storage devices.
DENISE: They were just something for Picard to play with!
They look like giant isolinear chips or circuit boards.
I can't find any documentation on those exact ones, but these pretty-similar-looking ones from ST VI and ST VII are referred to as isolinear chips in a plexiglass isolinear chip holder:
The ones on Picard's desk in TNG have more rounded corners, but they have roughly the same design.
You can see some slightly smaller and more conventional-looking isolinear chips on Troi's desk here:
Here are some more from Picard's Enterprise-E ready room that are used in First Contact, Nemesis and Generations:
Picard is seen holding a stylus or circuit-diagnostic/repair device to one of these plates in one episode. So they might be more like circuit boards or interactive e-readers than simply storage devices.