# Re: Optics question (Fresnel equations)

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### Phil Hobbs

Feb 10, 2022, 11:35:36 AM2/10/22
to
Rhydian wrote:
> 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

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

### Rhydian

Feb 10, 2022, 6:13:31 PM2/10/22
to
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.

### Phil Hobbs

Feb 10, 2022, 6:57:25 PM2/10/22
to
> 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.
>

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.