Divergence question

Anybody care to translate this for me- maths are not my thing.


assume nothing please.

arctan?? wtf


this equation may as well be in chinese to me.


Laser Beam Divergence = 2 arctan ( (D(f) - D(i)) / 2 L


this ^^^ came from here
Laser Pointer - How to Measure Beam Divergence

so I get the paper and distance part but not much more than that.

Please do not post if you are not willing to give me the version for Dummies. I am not fluent in algebra.

TY Len

Divergence Calculator - Safe Lasers - Laser safety information, tools, and free warning labels.

That might help.

-Trevor

I'm not sure if Trevors link already helped - I'll try to explain:

Look at the attached image: green is the laser beam.

The divergence is the full angle between the two green lines.
You measure the diameter of the beam at two positions D(initial) and D(final).
To calculate the divergence, you look at the red triangle: the long side is the distance L between your measurements, the very short side is the difference between the measured radii: D(f)/2 - D(i)/2. The sharp angle of the red triangle is half of the divergence.
There is the formula: tangens(Angle) = Short Side / Long Side, so here we have:

tan (Divergence/2) = ( D(f)/2 - D(i)/2 ) / L = ( D(f)-D(i) )/2L

To get the angle there is the inverse function to tangens: arctan
We do on both sides the same:

arctan ( tan (Divergence/2) ) = arctan ( ( D(f)-D(i) )/2L )

You can skip arctan(tan), so:

Divergence/2 = arctan ( ( D(f)-D(i) )/2L )

Divergence = 2 * arctan ( ( D(f)-D(i) )/2L ) :beer:

On your pocket calculator, you'll find arctan as 'tan^-1' and you normally can select it by pressing 'INV' followed by 'tan'.

If I look at my post:thinking: - probably Trevors help was much more useful:crackup:

I'll try to help you out, hak...

First, you will need some known values.

• Beam diameter at the point of beam termination in meters (call this d2)
• Beam diameter at the aperture in meters (call this d1)
• The distance at which you are measuring in meters (call this m)

Note that 1mm is equivalent to 0.001 meters, 2mm is 0.002m, 10mm is 0.01m, etc.
We will call divergence, the answer we are looking for, "D."
Now, to calculate divergence, use this formula:

D = [1000 (d2-d1)] / m

That is, Divergence is equal to (d2 minus d1) multiplied by 1000 and then divided by m.
This will give you approximately the divergence of your laser in mRad.

Does that make sense?

The same formula can be used to calculate the beam diameter at any given distance if you isolate "d2" on one side of the equation.
The algebra is really not that difficult to derive the formula. I'm not great with numbers either, but I managed!
Hope it helps.

For small angles that would work, for larger angles the arctan is needed and for precision you'd need the gaussian beam propagation (assuming the beam is gaussian) because the beam diameter around the beam waist is not a nice straight line.

Let the beam diverge far bigger then the initial spot. The divergence is then:
D = 1000 * d/m
With D the divergence in milliradians, d the diameter of the spot and m the distance. This would actually work better then subtracting the initial beam diameter because that is where the beam waist lies not on the cone made by the beam.