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)

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

On 10.2.22 17.02, 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)

Building a refractometer?

--

-TV

On Thu, 10 Feb 2022 11:35:31 -0500, Phil Hobbs wrote:

> 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

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.

On Thu, 10 Feb 2022 18:52:38 +0200, Tauno Voipio wrote:

<snip>
> Building a refractometer?

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

Rhydian wrote:
> On Thu, 10 Feb 2022 11:35:31 -0500, Phil Hobbs wrote:
>
>> 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.

> 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.

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

On a sunny day (Thu, 10 Feb 2022 23:15:57 -0000 (UTC)) it happened Rhydian
<news@rblack01.plus.com> wrote in <su46bd$q1o$2@dont-email.me>:

>On Thu, 10 Feb 2022 18:52:38 +0200, Tauno Voipio wrote:
>
><snip>
>
>> Building a refractometer?
>
>Sort of, it's a non-contact fluid sensor.

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)
https://www.ebay.com/itm/255235085629

Great fun to play with:
http://panteltje.com/pub/wind_speed_by_differential_2_ebay_distance_meters_IMG_4891.JPG