Appendix G - Light for Plants
Light for plants is different from light for humans. Light energy for humans is measured in lumens, with light falling onto a surface measured as illuminance with units of lux (lumens per square meter) or footcandles (lumens per square foot). Light energy for plants, on the other hand, is summarized as photosynthetic active radiation (PAR), with the radiant power equivilent of lumens being photosynthetic photon flux (PPF) and light falling onto a surface measured as photosynthetic photon flux density (PPFD) with units of μmol/s-m2.
| Light for Humans | Light for Plants | |
| Radiant power, 400-700 nm | Lumens | Photosynthetic Photon Flux (PPF) |
| Light falling onto a surface | Illuminance | Photosynthetic Photon Flux Density (PPFD) |
| Units | Lux, Footcandles | Micromoles per second per sq.meter (μmol/s-m2) |
The spectrum to which plants are most sensitive varies with the species, but for most plants the spectrum is very similar to the visual spectrum to which humans are sensitive, approximately 400-700 nm. This is the range that stimulates photosynthesis. Any photons within this spectrum that are absorbed by the plant will contribute to photosynthesis. However, not all wavelengths have an equal likelihood of being absorbed, as determined by the various plant pigments that might be present. As with human vision, plants are more likely to respond to (absorb) light in some wavelengths than others.
General Notes:
In ElumTools, Luminaire Manager (Horticulture tab) allows the assignment of radiant power in PPF as a light source characteristic. Alternatively, a PPF "Factor" can be entered to factor known light source lumen output. One of these entries is required to compute PPFD in Horticulture Mode.
The mathematical basis for the calculation of PPFD:
If the spectral power distribution (SPD) of a light source is known across the relevant wavelengths (400-700 nm), then the amount of photosynthetic energy available to plants can be determined. Based on its SPD, a light source will have a conversion factor that can be used to translate luminous intensity (candela) into photosynthetic photon flux per steradian (PPF/sr), in μmol/s/sr.
One watt of radiant power at 555 nm is by definition equal to 683 lumens. Given the CIE 1931 luminous efficiency function V(λ), we can calculate the spectral radiant flux Φ(λ) for plants in watts per nanometer for each lumen as:
Φ(λ)/lumen = [Wrel(λ)] / [683 * Σ(400-700) [V(λ) Wrel(λ) Δλ]]
where Wrel(λ) is the relative spectral power distribution and V(λ) is the luminous efficiency function at wavelength λ.
With this, the photosynthetic photon flux (PPF) per nanometer in micromoles per second per nanometer can be calculated:
PPF /nm = (10-3) * [λ Φ(λ)] / (Nahc),
where:
Na = Avogadro's constant, 6.022 x1023
h = Planck's constant (6.626 x 10-34 joule-seconds)
c = speed of light, 2.998 x 108 m/s
λ = wavelength in meters.
Summing over the range of 400-700 nm yields the photosynthetic photon flux (PPF) per lumen for the given light source:
PPF » 8.359 * 10-3 * Σ(400-700) [λ Φ(λ) Δλ]
Given a light source rated in lumens, we can similarly calculate the conversion factor required to translate candela (luminous intensity) into photosynthetic photon flux per steradian (PPF/sr).
SPD graphs are relatively easy to come by, but finding the same information in tabular form, needed for the above equations, is more difficult. One source is CIE 15:4, Colorimetry (2004). Adding digitized data from one LED manufacturer's white LED SPD curves, we can arrive at the following table of PPFD Conversion Factors, for converting illuminance in kilolux to PPFD in μmol/s-m2:
|
Light Source |
PPF Factor |
|
CIE A (incandescent, 2856K) |
20.3 |
|
CIE 5000K daylight (D50) |
18.1 |
|
CIE 5500K daylight (D55) |
18.1 |
|
CIE 6500K daylight (D65) |
18.3 |
|
CIE 7500K daylight (D75) |
18.6 |
|
CIE HP1 (standard HPS, 1959K) |
11.7 |
|
CIE HP2 (color-enhanced HPS, 2506K) |
19.3 |
|
CIE HP3 (metal halide, 3144K) |
14.4 |
|
CIE HP4 (metal halide, 4002K) |
15.0 |
|
CIE HP5 (metal halide, 4039K) |
16.3 |
|
2700K white light LED (Philips Luxeon Rebel LXW9-PW27) |
18.1 |
|
3000K white light LED (Philips Luxeon Rebel LXW9-PW30) |
17.1 |
|
3500K white light LED (Philips Luxeon Rebel LXW7-PW35) |
14.6 |
|
4000K white light LED (Philips Luxeon Rebel LXW8-PW40) |
14.3 |
|
5000K white light LED (Philips Luxeon Rebel LXW8-PW50) |
14.6 |
Acknowledgment: Thank you to Ian Ashdown, Lighting Analysts' Chief Scientist, for the formulas and resulting conversion table.