Optics question (Fresnel equations)

Feb 10, 2022 Last reply: 4 years ago 6 Replies

Hi,



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.



TIA



Rhydian (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 be unpolarized.

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.

Cheers

Phil Hobbs

OK, thanks, makes sense now.

The LED is an Osram SFH4050, the top surface is slightly frosted so as you say, hopefully I can just treat it as 50:50 split between s and p polarization.

One piece of odd behaviour I did see with this LED - I assumed the output power would be roughly linear with current, and lose efficiency and tail off as the die heated up. But going up in 50 uA steps to about 5 mA (max is 100) there's a noticeable upward curve. At first I thought I'd somehow screwed up the photodiode amp, but I tested it on an Ophir Nova II and got the same results. I don't remember seeing this before with other LEDs.

So long as the output power is long-term stable to within a few dB it won't matter (there isn't space for a monitor photodiode in the design). I will put a few of them on continuously for a few months, just to check.

<snip>

Sort of, it's a non-contact fluid sensor.

Depends on the device. There's normally a bit of a toe at low currents--in the low tens of microamps for normal display LEDs--but then it's pretty linear.

If your LED is something unusual it might behave differently.

Cheers

Phil Hobbs

On a sunny day (Thu, 10 Feb 2022 23:15:57 -0000 (UTC)) it happened Rhydian snipped-for-privacy@rblack01.plus.com> wrote in <su46bd$q1o$ snipped-for-privacy@dont-email.me:

I have done that with utrasound (water height in a tank, time delay.

PS these days 3 for 9 USD on ebay (I have some)

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Great fun to play with:
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