Google Images. There's a more detailed, explanation with very similar graphs on Wikipedia. I'll quote:
This is all well accepted stuff. Lux is weighted for human perception. Par is a flat weight across 400-700 nm. Lux is basically useless for reef tanks.
Here's a link for the luminosity function: nice, big peak at 550nm or so.
https://en.wikipedia.org/wiki/Luminosity_function
Lux is not ideal by a long shot as you say. It does have one handy use in a tank though. If your light source is homogeneous (LED is not), you can make relative comparisons. If my lux is 1500 in one spot and 1000 in another, I’m getting 2/3 the light in the second spot. Once you’ve established a baseline with a PAR meter, with older lighting, this is pretty handy.
As for the diffusers themselves, they accomplish two things. First, they scatter some of the light. This improves color mixing. It also causes some light to fire off at different angles. The absence of random scatter with LED lights can cause shaded spots and disco ball effects even with the best lights. The diffuser will help even this out. There will also be some absorption and remission going on which will reduce output and shift spectrum some. I have no idea how significant this is with the Ecotdch diffuser. My guess is the relative amount of light under a large overhang will be greater with the diffuser making it easier to grow low light species in darker areas. You would also see less dieoff lower down on larger corals.
I would also guess that the scatter issue is producing a misleadingly large drop in par. Corals are three dimensional. The meter is not. That scattered light will appear as lost light to a 2d sensor (they’re not all totally 2d, but they all miss some of the light coming from off angle sources) because the angle of attack is such that the sensor doesn’t get hit with it or because some energy is deflected, etc. For instance light coming from below is totally lost. If there is more light coming from below however, Corals can use it.
Imagine a system with 1000 par from above and 10 par reflected. In a very, very simplified sense, half the coral gets 1000 and half gets 10. Since coral can only really use 200 (again, arbitrary ballpark number), the whole coral is using 210/2 par or 105 par. If a diffuser reduces 1000 to 750 and scatters the rest, The reflected light could go up to 100 for instance. Now the whole coral is using 300/2 or 150 par. It’s also being less photoinhibited at the peaks. Net result, more better light.
Sorry, crammed in a lot of thoughts in a reply to one person. I suppose most of it is directed to the topic generally and not one poster
