Can a Sphere's Irradiance Be Modeled Using a Disk Emitter?

[mnb96]

Hello,
I consider a Lambertian spherical emitter with radius R and placed at the point (0,0,h).
I would like to compute the irradiance received by the infinitesimal surface patch at (0,0,0) whose normal is the vector (0,0,1).

- My question is: is it possible to convert this calculation into calculating the irradiance received from an "equivalent" disk-shaped emitter placed at (0,0,h) ?
- Is it correct to compute the flux received by each patch of the disk and then using it to compute the irradiance at (0,0,0)?

(I know all this this might sound useless, but I am trying to re-cast the original problem because I will later need to compute the irradiance received from portions of the sphere, and it is easier to handle portions of a two dimensional disk instead).

Thanks.

 

[Valerie Park]

Yes, it is possible to convert the calculation into calculating the irradiance received from an "equivalent" disk-shaped emitter placed at (0,0,h). To do this, you can use the cosine law to calculate the flux received by each patch of the disk and then use it to compute the irradiance at (0,0,0). The cosine law states that the irradiance at a point on a surface is equal to the cosine of the angle between the normal vector at that point and the vector pointing from the source to the point, multiplied by the flux emitted by the source. Using this law, you can calculate the irradiance received by the infinitesimal surface patch at (0,0,0) by first calculating the flux received by each patch of the equivalent disk-shaped emitter.