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While doing an experiment to measure the angular spread (or say divergence) of a beam of laser (which in my case was an inexpensive diode laser), what is the most accurate way of measuring the diameter of the beam?

Angular spread, $θ$ = $d'/l$ where $d'$ is diameter of the spread laser beam and $l$ is the distance of laser from screen

spreading of a laser beam

The problems are

  • as the distance $l$ increases, the spread becomes more non-uniform (it spreads more in one direction)
  • the the maximum intensity center's diameter ($d$) which also changes with increase in $l$, is not easy to measure as it depends on observer's eyes

Any easier ideas?

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  • $\begingroup$ I wonder if you could use some device with lens... or a concave mirror. $\endgroup$ – TZDZ Nov 18 '14 at 12:21
  • $\begingroup$ how? can you explain a bit more? $\endgroup$ – Sudhanshu 'Sid' Vishnoi Nov 18 '14 at 12:22
  • $\begingroup$ Well, that was just an idea for better experimental operators than me. I was thinking about moving a couple of lens/mirror (with known focal length) until the image would be the smallest... Maybe that's stupid. $\endgroup$ – TZDZ Nov 18 '14 at 12:28
  • $\begingroup$ (thinking of the infamous "barometer and height of building" question) - how about using the manufacturer's datasheet? $\endgroup$ – Carl Witthoft Nov 18 '14 at 13:25
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If you have a powermeter and a translation stage available, you can do the following:

Get a knife edge and put it onto the translation stage. Move the knife edge into the beam and measure the intensity for different positions. From this you can derive the beam width, however you may define it (1/e, FWHM, ...).

Do this for different positions along the beam axis (at least 2), and then you can calculate the divergence by trigonometry.

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  • $\begingroup$ um.. easier way? what about photographing on a graph paper? $\endgroup$ – Sudhanshu 'Sid' Vishnoi Nov 18 '14 at 11:59
  • $\begingroup$ Of course you could measure the beam width by photographing the beam and then create a 1D-intensity profile on a pc. This might be a good technique if you do not have special equipment available, however, the accuracy might not be that good. $\endgroup$ – Timitry Nov 18 '14 at 12:01
  • $\begingroup$ You'd be better off with a pinhole, as either a knife-edge or a slit will integrate over the x- (or y-) axis. Granted, you'll need to take a lot of data in both axes with a pinhole. Been there, done that! $\endgroup$ – Carl Witthoft Nov 18 '14 at 13:26
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Another relatively simple method: get an adjustable iris and measure the total transmitted energy (use a condensing lens behind the iris, perhaps) as a function of radius. Repeat at a few distances for better accuracy :-)

Keep in mind this will be inexact for most laser diodes as their output is elliptical unless supplied by the manufacturer with a correcting lens. You'll be measuring the energy in a circular zone, but that may be sufficient for your purposes. If not, perhaps put a knife edge directly in front of the iris -- repeat for orientations in both x- and y- axes and you can estimate the ellipticity of the output.

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