Q:

Optical refocusing efficiency

What is the material for optical focusing that produces the less diffraction losses?
Suppose one have a sequence of serial optical elements $R$ that keep refocusing a beam of collimated light, each a distance $D$. Now suppose that the wavelength $\lambda$, the optical element and the distance are such that the $\epsilon$ is the amount of radiation that falls outside the next optical element, which i'll take to be small. 
I'm concerned with other losses in this system, for instance, the optical material can have some intrinsic diffusion, or it absorbs a portion of the radiation
What are the main losses that an optical element can have of this kind, and which are the best refocusing optical elements that minimise those losses?

A:

If you use lenses to refocus a beam, with high quality optics, the limiting factor will   most likely be the quality of the anti-reflection coatings of your lenses and not the absorption or scattering from their optical material (at least for visible/NIR light). It's not easy to lose less than 0.1% per surface from Fresnel reflections.
If you are desperate to get the smallest losses possible, then you may want to use a refocusing system that involves mirrors. Losses while reflecting of a dielectric mirror can be less than 0.01%, taking into account scattering, absorption and transmission. 

