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
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