Spectral brightness

1. Feb 18, 2006

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

2. Feb 18, 2006

Gokul43201

Staff Emeritus
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.