Physics: Fixtures as Lighting Source


In this contributor article, Edward LaVilla of Specteros explains the physics and mathematics behind how lighting sources work as fixtures.

Edward LaVilla

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Physics: Fixtures as Lighting Sources


Introduction

Whether you are using supplemental lighting in a greenhouse or horticultural lighting in a warehouse, there are a myriad of lighting options that you can choose. There are many tools and measurements you can use to determine the value of a light source, such as Spectrum, PPF, and PPFD light maps, but you can easily be overwhelmed at the amount of information available when trying to select a fixture. In order to differentiate one fixture from another, this article will explore some fundamental optical principles of fixtures as lighting sources.


Lighting fixtures can be divided into two categories:

  1. Bare emitting fixtures
  2. Secondary optic fixtures

Fixtures with sources that are completely exposed to the ambient conditions of the grow space are called bare emitters. Bare emitters have a projected light footprint that is determined by the source geometry. For example, a fluorescent bulb emits radially where as an LED has a more concentrated footprint.

Secondary optic fixtures couple a light source with some form of condenser. The condenser alters the projected footprint of the source, modifying it for a specific application. Traditional HPS fixtures are secondary optic fixtures. They use a back reflector to redirect light emitted from the top of the bulb back towards the plant canopy. LED fixtures, on the other hand, use large transmission optics (lenses) to shape the light for a desired footprint.

Figure 1: Bare emitter (top) vs. secondary optics or directional lighting (bottom)


Intensity and irradiance (PPFD) are two widely interchanged lighting topics that are actually different subjects:

  1. Intensity is the amount of light contained in a unit solid angle in a given direction from the source.
  2. Irradiance is the amount of light incident on a surface.

I’ll provide an example of the difference in definitions below:

  1. Intensity: If we assume a canopy of fan leaves and main cola branches that are all the same height, our colas will be directly underneath the lighting fixture. We will see lower intensity values around the fan leaves than what the sugar leaves would see around the cola.
  2. Irradiance: To understand irradiance, we use a common metric called Photosynthetic Photon Flux Density (PPFD). If our grow light puts out 1000 μmols, the PPFD tells us how that light gets stretched over the canopy.

If we change our distance away from the fixture, the values for intensity and irradiance will change:

Figure 2: Intensity distribution at incremental distances away from a spherical source

If we move far enough away from the lighting fixture, we enter a region referred to as the “far-field”. The far-field criterion allows us to use the inverse-square law, which states that the irradiance on a detector varies as a function of intensity of a light source and is inversely proportional to the distance squared. This is shown in the equation below. The inverse-square law is only valid when considering a point source, and the far-field criterion allows us to approximate a large source as a point source.

E= I/r2

So when is your canopy in the far-field? Below is a table that demonstrates when we can assume that you are in the far-field based on your fixture shape and size. This table also demonstrates the “5 times away” rule of thumb. We can see that for a given light source’s geometry and size, the rule of thumb value changes. This tells us where we need to hang our fixture to enter the far-field.

Figure 3: Source geometry and size and far-field condition. The distance between the fixture and directly down to the canopy is defined as r_min. [1]

Lighting patterns from most commercial fixtures have a similar light distribution. There is a high amount of light in the center which falls off as we expand outwards.

With this knowledge of optical principles, it is now possible to read specifications and estimate if a given fixture will perform well enough inside the grow room. Anyone can master lighting in their grow space, and understanding fixtures as light sources is an important step.

References

  1. [1] Moreno, I. and Sun, C. (2017). Citeseerx.ist.psu.edu. Available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.700.3934&rep=rep1&type=pdf


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Resources:

  1. Want to get in touch with Specteros? They can be reached via the following methods:
    1. Website: http://www.specteros.com/
    2. Email: [email protected]

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About the Author

Edward is a Ph.D candidate in optical engineering and has worked on design concepts for visual science, infrared materials, and ranging optics.