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Math question

Gomer

Gomer

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There was a time when I could probably easily answer the question...but that time has long passed.

The simple illustration first:

Suppose you had a uniform laser beam that is 1mm in diameter that is measured on a detector. If you have a small disc that is say 1% the size of the laser and you levitated it through the middle of the beam, you could calculate and measure the signal basically as the overlap of areas. With the exception of the very beginning and end of the traverse, the signal on traverse is area-of-disc/area-of laser. Easy.

Now lets make it much harder: The laser profile is Gaussian

Anyone care to derive the formula for the intensity profile where the diameter of the laser (FWHM) is "D" and the diameter of the disk is "d"
Assume the disc traverses the middle of the profile through the maximum intensity. (bonus points for formalization that to include an offset from center)

:-D
 
No.
Although I did just fire for the first time a brand spanking new Nd:YAG a few minutes ago.
Next up alignment through the optical system, and let's make some plasma!!
 
lol. well, if I can pull off this proposal (the OP question is just a minor point but illustratively useful), then I'll be using a YAG to make a plasma too :-D
 
Hmm it's been a while you'll want to integrate your gaussian function over the diameter.

Basically integrate from d/2 to -d/2 e^(-r^2) dr however IIRC that doesn't have a closed form solution, so you'll need to tackle that bad boy numerically. I've been teacher elementary level stuff WAY too long to remember much beyond that though :D
 
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