# Question about cross-illumination and the inverse square law...



## phunkboy (May 23, 2015)

I work in horticulture with a goal of optimal illumination to the plant canopy. The industry standard is to position each light as close as possible to the top of the plant canopy directly over a limited number of plants (without burning them) in order to optimize the light intensity they receive. The inverse square law is often cited as the justification for this practice. This makes sense when you are working with one light over one fixed area.

My question has to do with how the inverse square law might apply differently when you introduce multiple light sources across a larger canopy and achieve cross-illumination. My understanding is that yes, as you move any light a further distance from a static point of measurement that you will lose intensity (total number of photons hitting that point or fixed area) due to the wider canopy of illumination that occurs as you spread the light over a larger area. However, as you raise multiple lights, evenly spaced across a large plant canopy, shouldn't the illumination at any point not also increase from the surrounding lights from which light was not previous received. And as this occurs, would not the light received at any point in the canopy begin to equalize as the lights are raised together simultaneously? 

Assuming we have highly reflective walls, my assumption is that the loss of light to heat absorption would be minimal and that the advantages gained would be lower radiant heat at the top of the plant canopy, and fewer shadows than with a single, fixed source of light. It should, thoerectically be the same number of photons hitting the plants, no? Commercial nursuries very commonly mount their lights up on the cross-beams (15ft up) and don't suspend them closer to the plants. Seems to me the indoor cultivation centers might be too obsessed with the single source light approach. So, where am I getting it wrong...?

I have linked a rough sketch of what I am describing. (Please forgive the crudeness, I am not an artist or graphic designer. But, you should get the point...)

https://app.box.com/s/5dynrxzrndei0hq79ue4fu3crz6ldpoa


Thanks for any feedback...


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## blah9 (May 23, 2015)

That makes sense to me that if you add more lights you can counteract the inverse square law even if the lights are located father away than the single original light. The number of lights depends on the brightness of each light along with its beam characteristics, etc.

Your point about minimizing shadows using multiple lights also makes sense to me, but I am certainly not even close to being an expert when it comes to lighting plants.


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## phunkboy (May 24, 2015)

agreed about the brightness and beam characteristics determining the total number of lights needed in a particular space. also, this approach only really works when you eliminate static aisles. cultivators are often switching to a floating aisle system using rolling benches (kind of like how the library stacks can be moved to create the aisle where you want it). this allows us to optimize use of floor space without the loss of canopy growth due to static aisle positioning. with static aisles, single light per space illumination makes more sense so that you don't lose light to the aisles, and hence the obsession with inverse square. 

cross illumination will result in better light penetration through the canopy, as opposed to static overhead lights only effectively illuminating the top canopy. growers will commonly run their PAR meters along the tops of growing plants, forgetting that yield comes from total light penetration to all photosynthetic plant parts, and that much of yield comes from the development you achieve in the middle and even lower canopy growth...


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## RetroTechie (May 24, 2015)

Perhaps a simpler way to look at it:

Imagine a straight line (or a surface, if you arrange light sources in a 2d matrix rather than a line) some distance below where the lights are. All light emitted sooner or later *will* cross that line. Read: all light will reach the canopy eventually. Only exception is if light was sent upwards (source emitting over a >180o​ angle).

If you have a near-infinite # of lights with walls very far to the side, virtually no light will ever hit a wall on the way down. If walls are close together & lights are relatively high, light may reflect on a wall, reflect on another wall (and so on a few times), and _then_ hit the canopy. But end result is the same. 



phunkboy said:


> Assuming we have highly reflective walls, (..)


That's the important condition which makes the above hold. If walls aren't reflective enough, any light that 'falls to the side' could be lost. With good reflective walls, all you're doing is modifying the beam pattern (mostly: making illumination more uniform, I think).

The inverse square law is an approximation for cases where you have a *single* 'point' light source, and illuminated surface relative relatively far away (as in: distance >> size of light souce). And no walls...  In that case you can regard the emitted light as covering the surface of a sphere (or more usual: a section of a sphere). If you go 2x further out, that sphere surface has a 4x larger surface. If you go 3x further out, surface area is 9x larger (so 1/9th the light per unit of surface area). If you go 10x further out, surface area is 100x larger. Etc, etc, hence the ^2 relation.


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