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)
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,You just treat the two polarizations independently and add up the photocurrents when you're done.
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)
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
On Thu, 10 Feb 2022 11:35:31 -0500, Phil Hobbs wrote:
Rhydian wrote:
Hi,You just treat the two polarizations independently and add up the
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)
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.
Building a refractometer?
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.
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