I was hoping somebody would get it right, if I read down far enough! Cheers for Alpha-bob-boo!!! Only about 20% of HID light spectrum is usful for plants (that's PAR light, Photosynthecally Active Radiation). That 20% is, mostly, made up of two narrow parts of the blue spectrum and two narrow parts of the red spectrum. These correspond to the four "spikes" you see in the light spectrum absorbtion graphs for Chlorophyll-A and Chlorophyll-B. To make a long story short - 80% of the watts you pump into your HID's result in wasted money! You are paying $100 to get $20 worth of useful light.
In the second place, the "Inverse Square Law" has nothing to do with LED's. The Inverse Square Law is only applicable to "point" light sources like a normal light bulb or a candle flame (where the light radiates in a 360 degree radius, in all directions). The nature of LED's, on the other hand, is that they are focused into a concentrated beam; like a spotlight. When you buy LED's, one of the specifications you look for is the "projection angle". The narrower the beam, the less light photons get "lost". That's why LASAR beams are so powerful - they don't spread out! There is a formula for figuring out light loss/distance for LED's but it is pretty complicated and it takes into consideration the "angle" of projection.
Third, and last. I'd just like to give my $.02 worth about watts, and lumens. The plant couldn't care less how many watts or lumens you are throwing at it! The plant only cares about how many photons of PAR light actually land in it's light receptors. Sorry if this is a little deep, but it's important! The actual amount of photons that are available to the plant is measured in micro-einstiens, not lumens.
Lumens are just a measurement of how bright a light appears to the human eye. Remember that 80% of HID light is wasted on plants? That's the same 80% that produces the highest ratio of lumens per watt. The human eye is more sensetive to green, so x amount of green light appears brighter than x amount of red light (or blue). In other words - green light, which is useless to plants, produces more lumens.
LED's produce light in a very narrow slice of the color spectrum, so by using just the right combination of colored LED's (measured by wavelength), virtually 100% of the light output is useful to the plant (PAR light) - as opposed to 20% for an HID. The bottom line is that LED grow lights look like puny little weaklings because red and blue light is not strong in the "Lumens Dept.". But the truth of the matter is that LED's produce concentrated PAR light.
Don't get me wrong, using lumens is very useful when dealing with "Wide Spectrum" lights like HID's or Flourescents. For example: all 400 watt Metal Halide bulbs put out "about" the same amount of lumens - that's how we come up with the "50 watts per square foot" rule of thumb. Once the "wrinckles" are all worked out of LED grow lights, I'm sure they will become more widely used and better understood. My interest in LED grow lights has been rekindled - I get really jazzed when I read a thread like this!