This is an electro-optical question.
I'd like to make my own large 7-segment-type displays using discrete LED devices.
What's a method to get an clean, even illumination of the segment from the LEDs (one or more)?
Ideally, there's a good general approach that will work making any shape illuminated item, not just 7-segment displays. Segment sizes would range from 1" to 1' or more.
You would be looking for LED driver ICs with "dot correction" or "grayscale correction", for making such a panel / 7-segment / matrix / whatever LED display.
The idea behind such ICs is that each LED channel can be programmatically configured to adjust its current to even out against the actual output of each LED. Some such devices store the configuration in non-volatile memory within the IC, so they can be set up once and for all after putting together the LED panel / matrix. Others require the dot correction data to be transmitted to them each time the board is powered up.
Perhaps the most well-known such driver in the DIY community is the TLC5940, a 16 channel, per-channel dimmable, serially controlled, constant current LED driver. It is an expensive IC ($3.78 apiece), as has been pointed out, but has great support on common DIY microcontroller communities such as the Arduino and MSP430 LaunchPad. One reason for its popularity is that it is available as a through-hole DIP IC, unlike the various 24, 32 or even 48-channel ICs with similar functionality.
Footnote:
Dot correction is actually required for even commercially manufactured multi-LED displays, not just DIY ones. The consistency of illumination between LEDs varies across batches, and even within a batch. Though manufacturers go through a "binning" exercise to sort LEDs by illumination per current, some variation still sneaks through.
