I'm trying to design a device that produces visible light with a somewhat controllable spectrum. My goal is to measure the human eye cone cell responses by switching between two different spectra and finding spectra that are hard to distinguish by eye, so an RGB led won't be sufficient for this purpose.
My first draft PCB has 13 LEDs in different wavelengths set in a circle with a diameter of 20 mm, but I can change this arrangement in whatever way is desirable. The LEDs I plan to use come in 2 mm x 2 mm packages, so they could also be fit more tightly if that's useful for the mixing (see image below). Their "typical viewing angle" is between 145° and 170°. (LED datasheet)
What kind of optics could I use to produce a well mixed light out of these? I would not need more than a (say) 2 cm x 2 cm diffuse surface with well mixed light. The output power need not be large—ideally it would be comfortable to look at from a distance of tens of centimeters—and it is not a huge problem if a fair amount of the light is absorbed.
I have looked into light pipes in the Digikey catalog, and while I have a feeling they might be part of the solution, they generally seem to be designed for leading the light from a single led to a panel. I think a light pipe should mix light shot into it from a sufficient angle. I also have explored all kinds of weird ideas like installing LED reflectors upside down and having diffuse lenses in the other end. Another idea is to put the LEDs in a separate, smaller board that fits inside a reflector. In the end, it's clear to me that I don't know enough about optics to understand how to best approach this problem.
Here's a very early draft design of a Raspberry Pi hat (65 mm x 56 mm) with the 13 LEDs in a d=20 mm circle.