ChrisR wrote:there's nothing telecentric about the setup used here
Correct.
thin glass would only serve to bring any images from reflections in the glass closer to the original
No, thin is important mostly to avoid introducing aberrations. There would be no problem if the beam-splitter were in an infinity portion of the optical train, where the image-forming light is organized into pencils of parallel rays. But located in front of the lens like this where the light is focusing in a cone, even glass that's perpendicular to the optical axis will introduce spherical aberration. (Think of cover glass thickness under a high-NA microscope objective.) Glass that's not perpendicular to the optical axis is even worse, since the path length through the glass not only increases but becomes different on opposite sides of the aperture.
To illustrate, here are three images that I shot just now. These are actual pixels from a Canon T1i and Canon 100 mm f/2.8 L IS USM macro lens at very close to 1:1, same as the original stacks were shot. However these were shot at f/2.8 to maximize the effect of the glass. As you can see, the thin glass has only a small effect on image formation, but the thick glass really messes things up.
Left = no glass; middle = 1.15 mm at 45 degrees; right = 3.1 mm at 45 degrees.
but you avoided them by careful positioning of the lights
I didn't worry about reflections of the subject. Those are formed by a double-bounce from the two glass surfaces, so their intensity will be under 1%, too small to matter here.
However, anything on the side opposite the light will reflect in a single bounce, which basically means it's just as important as the subject. Of course that's exactly the direction light is shining toward, so it's easy for things over there to be bright. I could have stuck a big piece of Protostar over there, but it was simpler to just orient things so that what was being reflected was a far-away wall, and turn off the room lights. Then inverse square applies, the wall becomes relatively dark, and that's what the beam splitter reflects.
The most ideal setup would be a thin piece of optical glass with no coating on the side facing the subject and multi-coating on the side facing the lens. This would give the maximum light on the subject with the minimum amount of contrast loss.
Sounds good at first thought, but I don't think that holds up under careful analysis. Check me out here...
Suppose the two surfaces of the beam splitter reflect fractions f1 and f2 of the light that hits them, and for simplicity let's assume that f1 and f2 are both much less than 1 so that we can leave second-order effects out of the algebra. Let the wasted illumination that gets through the beam splitter hit a surface with net reflectivity W, while the reflectivity of the subject is S. Let the brightness of the illumination be I.
Then the illumination reflected onto subject is I*(f1+f2), and (1-(f1+f2)) of whatever reflects from the subject is what gets through the beam splitter and back to the camera to form the desired image. Overall product for the subject is I*(f1+f2)*S*(1-(f1+f2)).
On the other side, wasted illumination getting through the beam splitter is I*(1-(f1+f2)), and of whatever reflects back toward the beam splitter, the fraction reflecting into the camera is (f1+f2). Overall product for the waste light is I*(1-(f1+f2))*W*(f1+f2).
Take the ratio between subject image and waste light, and everything cancels except S/W. S is fixed, so all you really get to play with is W.
In other words, what you really need is to avoid reflecting waste light back toward the beam splitter. The reflectivity of the beam splitter, and how that's divided across the two surfaces, does not matter for minimizing the effect of waste light that becomes flare. It's kind of a surprising result, but on the other hand it implies you don't need to hunt up clever glass to make a beam splitter. Just figure out how to deal with the waste light.
--Rik
Edit: typo
