optics isn;t my strong point, but...
I'd start here:
https://en.wikipedia.org/wiki/Infrared#page=5 which gives you an idea of a quartz tungsten-halogen light source spectra. It also goes into alignment procedures that needed to be followed.
In our research we needed a cheap stable light source which turned out to 120 VAC ELH lamps until we could afford a $40,000 light source. It turne dout that we HAD to use GE branded bulbs. Sylvania did not have the same spectra, These lamps have a dichroic reflector that puts the IR out the back of the bulb. We were not interested din IR.
The specra above is for quartz-Halogen. Quurtz has better IR and UV transmission. The halogen lamps may not have been invented. At least it give you an IDEA of what your getting. The emission of the actual bulbs would be ideal.
Microscope illuminators use a low voltage flange based lamp. In one application we had to change to a 12 V EYC because of vibrations. Momochometer bulbs are the same way. Those you have a reflector behind and have to image the filament so it fills the gaps and the light is more uniform.
next, take the research here
https://en.wikipedia.org/wiki/Infrared and look at the best wavelength for a given purpose.
if your looking for something to replace the lamps with lamps, I;d look at microscope bulbs, e.g.
https://www.specialtyoptical.com/product/lighting/77z-15w-microscope-light-bulb/ I don;t have the catalogs I used to have, but it may be an option.
We put an ELH lamp in a fiber illuminator with a Y light pipe for a custom instrument too.
For about a 70 W/m light source we had to run four 300 W ELH bulbs to get about a 5% uniformity over 4 inches. You had alignment issues and diffuser issues (frosted glass) and distance and the thermal issues. As they age, they loose output in the blue.