Part II: Photons

As discussed in Part I, we need to think of light in terms of photons. A photon is the smallest discrete particle of energy that travels along a wave defined by its wavelength, and the amount of energy contained in the photon can be mathematically determined. For the purposes of reefkeeping and human vision, we are interested in photons that have a wavelength in the range 400-700nm. In this article, we will look at how photons are generated by light sources, determine how they are distributed according to wavelength, how this distribution is represented as a spectral plot, and the correct terminology used to characterize photons.

How are Photons Generated?

Any source of light is basically a source of photons. Atoms emit light as a release of energy, in the form of photons. Atoms under normal conditions are in a ground state, with their electrons (the negatively charged particles) moving around the atom's nucleus (which has a net positive charge). An atom's electrons have different levels of energy, depending on several factors, including their speed and distance from the nucleus. Electrons with different energy levels occupy different positions within the atom. Electrons with greater energy move in an orbit farther from the nucleus. When the atoms are excited (by the addition of energy) the electrons jump to a higher energy level. This is an unstable state, and the electron quickly returns to a lower energy state by releasing this energy as a photon. Because the jump from one energy level to another is discrete, the photons carry a discrete amount of energy. If this released photon has a wavelength that is within the visible range of the electromagnetic spectrum it appears as light. The light's wavelength depends on how much energy was released which, in turn, depends on the electron's position. Atoms of different materials have electrons at different energy levels and hence release different 'colored' photons. This is the basic mechanism for the generation of all light.

The following picture (Figure 1), taken from How Stuff Works, helps explain the process.

What differs in the various light sources is the mechanism by which the electrons are excited and the composition of materials used to provide the atoms. In an incandescent lamp, atoms are excited by heat created by a filament's electrical resistance. In a fluorescent lamp free electrons are created between a cathode and anode, and these free electrons are used to energize atoms of mercury, which give off photons in the UV range. These UV photons then strike the lamp's phosphor coating, pushing its electrons to a higher energy level and emitting visible light in different wavelengths, depending on the mix of phosphors used. Metal halide lamps use a different approach, in which atoms of metal halide gas are used along with mercury, and are energized by a plasmal arc between electrodes.

What is important to note here is that a photon is a photon is a photon… no matter what source is used to generate it. In other words, a yellow photon from a candle's light is the same as the yellow photon from the metal halide lamp. The only difference is that the metal halide lamp generates a lot more photons/second than the candle light.

Characterizing the Photons

A light source is basically a continuous source of photons, in our case converting electrical energy into visible photons. So when we characterize a light source, we are interested in determining how many photons it generates per unit of time. This is called its photon flux. These photons are generated and spread in all directions, and ultimately land on some object of interest (often in our case, the corals). A light source generates photons at a constant rate, and as we move away from the source, the photons will spread over a larger area, hence fewer photons land on the target area the further we move from the light source. We are interested in how many photons land on a given area, usually 1 meter square, and this number is called the photon density. Additionally, we are interested in the photons that are available for photosynthesis, which happen to be photons in the range 400-700nm (the same as visible light). These are called photosynthetic photons. These three entities of interest combine to comprise the Photosynthetic Photon Flux Density (PPFD), which is a measure of the number of photons in the range of 400-700nm falling on a 1 meter square area per second. PPFD is a measure of Photosynthetically Available Radiation abbreviated as PAR. Recall from Part 1 that to generate 1 watt of power we would need 25.15 × 10¹⁷ photons/sec at 500nm. This is a lot of photons!!! Since we are dealing with a large number of photons, the number of photons are measured in units called micromoles (1 mole = Avogadro's number = 6.022 × 10²³, hence 1 micromole = 6.022 × 10¹⁷). Hence the units of PPFD are micromoles/m²/sec, so, a PPFD of 1 corresponds to 6.022 × 10¹⁷ photons falling on a 1 meter square per second. In the aquarium hobby we often refer to light output in terms of PAR. Technically, this is incorrect. PAR is typically measured as PPFD.

Different light sources have different distributions of photons in the 400-700nm range. The light source can be characterized by determining this distribution of the photons, and this is done using an instrument called a spectroradiometer. A spectroradiometer simply is an instrument that has a sensor and associated hardware and software to determine the distribution of energy (measured as power density in Watts/m²) at different wavelengths of the electromagnetic spectrum. This is usually displayed as a graph with the wavelength on the X-axis and the power density on the Y-axis, and is called the Spectral Power Distribution (SPD) plot. One such SPD plot is shown in Figure 2 below. This is the most important piece of information about a light source, and all relevant light measures can be derived from it.

Note that for each wavelength the spectroradiometer measures the power density in watts/m². This is termed the Spectral Irradiance. You may recall from Part 1 that there is a direct relationship between power/energy at each wavelength and the number of photons. For example, as seen in the graph above, at 420nm the lamp produces 0.4 watts/m² of power or 0.4 joules/m²/second of energy. Using the relationship between energy and wavelength, it can be determined how many photons/m²/sec at 420nm will be required to generate 0.4 joules of energy - 1.46 micromoles. Thus, we can easily convert from watts/m² to micromoles/m²/sec. If this is done for all wavelengths, we would get a plot that shows the distribution of the number of photons at each wavelength per meter squared per second.

Adding all the photons over the range of 400-700nm will provide the measure of the photosynthetically available radiation (PAR) measured in terms of PPFD. Technically, the photosynthetically available radiation would be the area under the curve shown in Figure 3. These computations are often performed by software that is available with the spectroradiometers. Since the power distribution and the photon distribution are mathematically interchangeable, either of them can be used as the basis for comparison of light output from different light sources.

On my website, www.reeflightinginfo.arvixe.com, which catalogs the light output from various metal halide lamps and ballast combinations, I have been using the spectral power distribution to show the light output. By using the data available, comparisons can easily be made between different metal halide lamps based on their spectral distribution. The plots depicted show the spectral irradiance at each wavelength. The values indicate the amount of power density (Watts/m²) at each wavelength. So, a lamp with higher power at a given wavelength will also have a larger number of photons at that wavelength.

What is important to note is the following:

1) Because each photon's energy is different at different wavelengths, a different number of photons will be required to produce the same amount of energy at different wavelengths. To produce the same amount of total energy at 400nm would require 57% less photons than at 700nm, because the photons at 400nm have higher energy.

2) Because the PPFD is a summation of all photons in the 400-700nm range, two very different spectral distributions can have the same PPFD. What this means is that there is not a one-to-one relationship between PPFD and spectral distribution, so knowing a light source's PPFD does not tell us anything about how its photons are distributed. Different light sources with similar PPFD values can have very different spectral distributions. As seen in Figure 4 below, the two lamps have very similar PPFD values, but their spectral distributions are very different. The independence of PPFD and spectral distribution is one reason that we must consider spectral distribution data as well as PPFD when comparing light sources.

3) Also note that PPFD measures photons falling on a given area; the number of photons falling on this area changes as its distance from the light source increases. Hence, when comparing lamps' PPFDs it is very important to know the distance at which the measurements were taken, and only PPFD values at the same distance can be compared.

The spectral distribution of the lamps is quite different when compared to sunlight. Figure 4 also shows the spectral plot of sunlight at the surface of the water in the tropics at noon time during summer. For a more detailed comparison of the underwater light field to natural light underwater, the reader is referred to "Underwater Light Field and its Comparison to Metal Halide Lighting."

Inverse Square Law of Light

The relationship between PPFD and distance from the light source follows what is called the Inverse Square Law, as long as the source is a point source of light.

According to the Inverse Square Law:

PPFD₁/PPFD₂ = (D₂/D₁)²

D₁ and D₂ = distance at which PPFD₁ and PPFD₂ are measured.

This rule basically says that if you know the PPFD at a given distance from the lamp, then you can compute the PPFD at any other distance. It will vary as an inverse function of the square of the distance.

For example, if the PPFD is 100 at 1 meter, then at 2 meters it is 25. If the distance is doubled, the irradiance is reduced to ¼ of the value at the original distance. This effect can be easily visualized by shining a flashlight on the wall. Stepping away from the wall increases the size of the light spot and decreases its intensity.

This rule is applicable only to point sources of light (or lights whose source can be approximated by a point). The "five times rule" is often used as the rule of thumb. As long as the distance from the source is five times the size of the emitting source, we can consider it to be a point source of light. For a clear metal halide lamp, the size of the point source can be considered to be the inside envelope that contains the gases. If we wanted to consider a 4' fluorescent lamp to be a point source, it would have to be at least 20' away! Similarly, a 2' reflector would have to be at least 10' away to be approximated as a point source.

Summary:

In this article, I have described how the light from a source can be characterized by the distribution of the photons that emanate from it. Two mathematically equivalent plots - one using the power density distribution at each wavelength and the other using numbers of photons - can be used to show the distribution as a spectral plot. The light available for photosynthesis is termed PAR, and is typically measured as PPFD (photosynthetic photon flux density) with units of micromoles/m²/sec. Using just the PPFD number gives us information only about the number of photons in the 400-700nm range but does not tell us anything about their spectral distribution. Two lamps with the same PPFD can have very different spectral distributions. Additionally, the PPFD measurements can be compared only if the distances at which the measurements are taken are the same. However, given that light follows the Inverse Square Law, we can compute PPFD at different distances if we know it at one particular distance.

The next article in the series will discuss other measurements of light that you may have seen such as Lux and Lumens and how they relate to measurements of light for photosynthesis.