Calculate Total Solid Angle from Perpendicular Divergences in a Laser Beam?

[sachi]

we have radiation contained within a spectral band of width delta lambbda such tha (delta lambda)/lambda = (10^-4) the laser beam has a diameter of 50 micrometers and it has a divergence in both the horizontal and vertical directions of 10 millirads. we need to calculate the spectral brightness of the beam - i.e the power per unit area per unit solid angle per 0.01 percent bandwith. I can calculate the power, the area (this is the original area of the beam before it diverges) okay, but I'm a bit confused about the total solid angle. how do you convert a divergence is two perpendicular directions into a total solid angle (I have a feeling it has something to do with multiplying them together). thanks very much for your help.

Sachi

 

[Gokul43201]

...but I'm a bit confused about the total solid angle. how do you convert a divergence is two perpendicular directions into a total solid angle

Because the divergences are equal in both directions, the shape of the window formed on a distant plane will be a circle. If the total divergence angle is \theta and this plane is at a distance R from the source, which is large compared to the width of the beam, then the area of the circle formed on the plane is \pi R^2 tan^2(\theta/2) \approx \pi R^2 \theta^2/4. Dividing by R^2 gives you the total solid angle.