For work I used to have to read and log 7-segment LCD numbers off this tiny (3cm x 1cm) screen tens of times per day. Now I have a webcam setup that reads it for me and does some OCR to automatically log the numbers. However the current setup stands out, and I want to make something more inconspicuous.

My idea is to replace the webcam with a close-up sensor that can be mounted less than a centimeter away from the LCD screen. Then I can put it all in a tiny enclosure with an LED, and make it look like a little magic matchbox.

The problem is I have no idea what this kind of component would be called. I've searched for lots of things like "low resolution photo sensor" but found nothing remotely like what I'm looking for. How can I find something like this? I am willing to do electronic component assembly, programming, pretty much anything necessary to keep me from being forced to read those damn numbers again.