XPost: sci.electronics.design   
   From: pcdhSpamMeSenseless@electrooptical.net   
      
   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   
      
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