There are two factors to consider. Temperature is first; monitor the temperature at the average height of your plants. To close and you burn the tips to far away and you give up luminance penetration (PAR). Second is Luminance loss. Most experts are in agreement that light intensity diminishes exponentially fast.
For example:
A 400-watt MH from 0” to 12” is about the same luminance say 55000
Same light at 24” the luminance is now about 30000
Still good
Same light at 36” the luminance is now about 1200
Fan leafs block most of the light so nothing below sees enough of the light of day to do any good.
Lumens is a mathematical formula that measures the bulbs intensity at 1 foot. The color or type of bulb is not calculated in the formula I=L/D² Lumens received are a measured in watts-per-square foot or foot-candles. Calculating foot-candles or lux is a more accurate way to estimate the amount of light plants receive. This still only measures how much light you plants have available but not how much your plants use.
Light diminishes exponentially fast!
So how close you can place the light is really determined by the temperature at the top of your plants. 12” or less is all the same. So it’s 12” to 48” we have to balance between heat and lumens penetration and the closer to the 12” mark the better without burning the leaves and the more penetration you will get from the light. If there is too much heat coming from your light then add a glass heat shield and heat exhaust fans to either suck the heat our or inline to push the heat out. How long you vent tubs are will determine weather you push or pull the heat out. You are better off if you blow air through your hood. This will allow you to get the light as close as possible but watch the temperature!