Orion: First a bit of nit picking: fluorescent tubes, whether T5, T8 or T12, all emit light from the inside surface of the tube, not its centerline. The centerline of the bulb contains the mercury arc which emits UV, which strikes phosphors on the inner surface of the bulb, which absorb the UV and re-radiate the energy as visible light. So, Tony's chart you showed isn't at all accurate, and there is no optimal reflector for a fluorescent bulb.

Yes, I understand your theory about diffuse or imperfect reflection vs near perfect reflection. You may be correct, but I don't know any way that I have available to verify that. One could do an experiment with a light source that approaches being a point source, with a simple flat reflector, but the sensor would have to be very small for the experiment to work. (I think.)

The mylar I am using is, I think, aluminized on both the front and back surfaces. Neither surface is 100% metalized, but the combination comes close. (Some light goes through the metalizing through the gaps.) That is one source of inefficiency. Another source is the anti-oxidation coating on the aluminum coating, and I don't know what that is or how thick it is.

Mylar looks so "perfect" only because it gives a very nearly true reflection, so it works reasonably well as a mirror for shaving, for example. But, our eyes are extremely capable of using a wide variation in light intensity and ignoring the variatiions. So, if only 80% of the incident light is reflected the mirror effect will still seem to be perfect.

Aluminum foil, not having nearly as perfect a surface, looks like a poor reflector - it gives a distorted image. But, our eyes concentrate on that aspect and ignore the higher percentage of incident light being reflected. That is my opinion.

White paint gives pure diffuse reflection, but appears blindingly white only because such a high percentage of incident light is reflected. That reflected light is reflected at small angles off of perfect reflection, making it useless as a mirror, but the small angles are not great enough ot greatly reduce the total amount of light being usefully reflected. Again, this is my opinion.

Others have been posting that mylar isn't really very good as a reflector, and that white paint is very good. I couldn't accept that since it was so counter intuitive. Those "others" also have said that aluminum foil isn't a good reflector. I intuitively accepted that. What I think we have here is a failure of intuition.