Attenuation and source positioning

[Dade Murphy]

Hello,
I've been reading about attenuation, and I wonder if there's a way to determine the distance to your source. Forgive my poor writing; I'm new to the topic.

I understand that equation for linear attenuation is

I = I₀e^-μx​

where:

I = intensity
I₀ = initial intensity
μ = attenuation coefficient
x = distance traveled through medium​

My question is this: if I have the information μ and I, is there some way to determine x, and/or I₀? It seems that I need to find either of those to find them both, so I wonder if there's some other measurements I could take that would make this possible.
For a simple-minded example, would it be possible to take measurements of intensity at a variety of perpendicular distances in order to determine the geometric spreading and work backward from that to find distance x?

Thank you kindly for your time and knowledge.

 

[BvU]

Hello Dade,

If you draw a graph of the relationship, you can see that there is no way to pinpoint the source position from a single intensity measurement: the line can be extrapolated to the left and a source of the appropriate strength can be at any position.

Your recipe should work: you get some angular distribution and clearly the width depends on the distance from the source.

Alternatively, if you know the direction the radiation comes from (because of the way the detector is built, like with a peephole or something) you can use your measurement device to do a bit of trigonometry...

 

[Dade Murphy]

BvU, thank you for the quick response!

I'm glad that the angular distribution method would work, but I'm concerned that it may take quite a few detectors to be accurate. I'm thinking purely conceptually; I've never handled this sort of data before.
Also, I'm not sure that I understand your second suggestion. Do you mean something like a cluster of sensors receiving from very specific directions, and see which one gets the signal? I suppose I could do that in two places and triangulate, is that what you meant?