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I've seen this in a lot of animations of spaceships, as well as the intro sequence to The Expanse which I've attached a screenshot of. https://vimeo.com/734114243 is also an example.

The above screenshot again, but with the contrast boosted: enter image description here

While in both cases this overlay has been added in post, what kind of camera setup are they trying to emulate?

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It’s called a Résau plate:

…a transparent sheet of glass or plastic engraved with a grid of crosshatches called fiducial markers. It was commonly used in film cameras (before the advent of digital cameras) for scientific and technical photography.

These were used on several of the cameras on the Apollo missions, which is probably where this pattern entered public awareness. From the NASA article linked above:

The crosses are recorded on every exposed frame and provided a means of determining angular distances between objects in the field-of-view.

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