How to multiplex several light sources into one optical path? I'd like to design a device that takes 4 channels of light from sets of LEDs and multiplexes them into one optical path, which finally creates a rectangle pattern of light that is approximately 30mm tall and 1mm wide. This is to be used with a line scan camera. In practice, only one of the 4 channels would be illuminated at any given time.
Here's a rough drawing of what I'm imagining:

I've thought about doing it with mirrors as shown below, but obviously my LEDs are not perfectly collimated sources of light so this would not work. Perhaps this can be solved with a pair of convex cylindrical lenses facing each other to roughly collimate the light, but that would require a lot of lenses and money.

I've also seen a lab setup in this paper, but once again my light sources are not collimated and I suspect a lot of light would be lost to the beam splitters. The LEDs I'm using are in the 100s of lumens.

I would appreciate if anyone could point me in the right direction on this design problem. I'm familiar with the basics of optics, but clearly I'm not an expert. Thank you.
 A: This is going to be really hard to do with LEDs since they're not collimated. If they were instead lasers then you would have some options at your disposal.

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*If you have control over the polarization then you can combine the beams using polarizing beam splitters with lower power loss (but you would have differently polarized light at the output, may or may not be a problem)

*You can use non-polarizing beamsplitters as you've shown. You would lose 50% of the power of each beam

*You can use an acousto optic modulator or deflector. This is a device designed for spatial multiplexing of light. I'll leave it up to you to look it up. However, I'm not sure it will work over such a wide range of optical wavelengths.

*Probably the optimal way to do this would be dichroics. These are optics that reflect light above (or below) a certain wavelength and transmit light below (or above) a certain wavelength.

A: To do this efficiently, you want an optical device known as an X-cube. This is a cube that has three input faces: for red, green, blue. The output face combines all of those.  Look up "X-cube optics" on the web, (so you don't get X-cube toys).
Since you also want a fourth channel, that is a complication. People would typically add a dichroic plate beamsplitter in the beam path. The fourth wavelength is injected into this beamsplitter. (The main beam passes straight through).
It is unusual to combine more than 3 colors. It may require specialized coatings that will cost money.
Your output beam will never be perfectly collimated. The LEDs have a finite spatial width at the source. When you use a lens to collimate light from a finite size object, the output beam can never be perfectly focused. (This is true even ignoring diffraction, which is another source of beam spreading).
A: It sounds like you want a projector. Normally you use it to project a multicolored image on a screen. You want to project 4 different uniformly colored images on a small screen, one at a time.
Or perhaps you just want to put 4 different LEDs some distance from the screen and turn on one at a time.
