> I'm building an optical instrument that points a 850nm LED at a boundary
> between two materials at an oblique angle, and measures the (specular)
> reflection with a photodiode at the same (opposite) angle.
> The first few prototypes are working well but I want to compare the
> performance I'm getting with the theoretical limits. My starting point
> is the Fresnel equations, but the part I'm having trouble with is that
> they give separate results for the s and p polarizations. How do I
> combine the two into a total reflected power?
> As the incident angle approaches the critical angle for total reflection,
> both the s and p numbers approach unity, so clearly I can't just sum
> them, or take the vector sum, or I would get an answer greater than 1.
> Average? Use the highest of the two?
> I'm assuming here that the photodiode detector (Osram SFH2700) has a
> response that's insensitive to polarization, but happy to be corrected on
> this point.
> I have a copy of "Building Electro-Optical Systems" but there's clearly
> something I'm missing. Google is not much help either, it finds pretty-
> much exactly the same question (but for microwaves rather than IR) from
> two years ago, and no replies.
> (who should probably have paid more attention in electromagnetics classes
> 30 years ago)
You just treat the two polarizations independently and add up the
photocurrents when you're done.
LEDs are pretty well unpolarized when you look at them from a distance.
There are polarization effects with angle, due to the Fresnel
reflections from the top surface. If the LED has a flat top facet,
p-polarized light escapes better, so there's a tendency for the light to
be somewhat radially-polarized. Textured surfaces and lensed packages
smear that out pretty well, though, so to leading order your LED should
Thus, it's a good guess to assume the LED light has equal amounts of s-
and p-polarized light. These don't interfere, so the total photocurrent
is just the sum of the s and p photocurrents.
Dr Philip C D Hobbs
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510