Strobe Diffusers

[Interceptor121]

Last November I was trying a new fisheye set up for my camera and in order to check field of coverage I took a few shots against the pool wall. I realised that I could cover pretty much the whole frame except extreme corners with my officially 100 degrees diffuser.
This week I went to the pool again before it got shut for covid and this time I had a rectilinear lens with 107 degree field of view. I took a number of test shots with one and two strobes and run the through false color to see how the light was falling off. Those are the shots sorry for the false color it is on my field monitor so took some pictures with my phone
You can see here a shot without diffuser the respective false colour a shot with diffuser at increased power and false color

The light grey is 50% the blue is 20% the lens horizontal field of view is 95% and vertical is 75%.
What I can see is that the drop from center to vertical is 50% (1 stop) and at sides is a bit more 1.3 Ev and in the corners is 2 stops
Without the diffuser the coverage is around 75 degrees so looks like the strobe is loosing coverage from the 80 degrees on land however with the diffuser it follows pretty much the inverse square law as if it were an ideal radiant
When the diffuser is declared 100 degrees it means that at 50 degrees it would drop 1 stop however an additional stop is lost on a flat surface because the edges are further away so this is consistent with the specifications however it looks like water is not affecting the coverage of the diffuser at all
I understand light is made of particles and waves and water is a fluid much more dense than air so something must be happening when light particles are hitting the water that is different to what traditional thinking suggests
To be clear you would think that the 100 degrees would drop to 84 but this is clearly not the case here the 100 degrees are mantained
This is rather interesting for me as I always thought I needed to get some dome shaped strobes to fight the loss of coverage however it looks that a strong opal diffuser (0.8 Ev) works as good as
Interested to understand if anyone has observed similar behaviour
Of course when you are in the ocean is not possible to check all of those things as flat surfaces do not exist

 

[Chris Ross]

I wouldn't expect water to change coverage of the diffuser. With a clear dome light it is traveling as rays and bends when it passes from dome to water due to change in refractive index. With the diffuser the light hits the surface and transmits the light but it acts like a new light source with light rays coming from more less random directions on the surface of the diffuser. The coverage is set by the surface brightness of the diffuser which will vary somewhat with the amount of light hitting each square cm of the diffuser surface, so there would be multiple point sources spread out over the surface of the diffuser. I don't know if I have explained that properly, but I don't believe the change in refractive index really applies in this situation.

 

[Interceptor121]

I think the diffuser is not anymore a light source that you can approximate with optics but a lambertian radiator Lambert's cosine law - Wikipedia
So it scatters light depending on the energy acculumated and replaces the strobe bulb as you said
However I also think that this scattering in water is only affecting absorption and not angle
So if at the end the strobe with the diffuser is the same as a perfect light following inverse square law why bother making strobes with dome shapes or dome diffusers?
The shape of the light source behind the diffuse no longer matters once the diffuser is loaded of energy and you will gain nothing with the dome shape that you don't already have