Radiant energy, spectral absorption and solid angles

[mikeph]

Hi
I'm trying to follow a derivation, I don't think I'm allowed to post the content (copyright) but the paper is here: http://www.sciencedirect.com/science/article/pii/002240739290117M. Does anyone have access to this and know a little bit about integrating over solid angles?

I've spend half a day pondering over the logic linking equations 20-23.

It seems they're defining a unit sphere and taking the intensity change over the surface to equal the change in number of photons inside the sphere. What I don't understand is:
1. where the log goes between eq. 20 and 21
2. where dL is relative to this sphere?

Thanks for any help. Very stuck.

 

[eljose79]

Hello, I understand your confusion with the derivation. I do have access to the paper and I am familiar with integrating over solid angles. The log in equation 21 comes from applying the definition of the natural logarithm to the equation. As for the position of dL, it is the distance from the center of the sphere to the point on the surface over which the intensity is being measured. I hope this helps clarify things for you. Let me know if you have any other questions.