Facts of light. Sanjay Joshi. PDF version by Baldasso, L. F.

Transcription

1 Facts of light Sanjay Joshi PDF version by Baldasso, L. F.

2 Introduction: Part I: What is Light? The choice of lighting is one the most important decisions to make when setting up a reef tank. The light fixtures and related equipment are some of the more expensive pieces of equipment both at initial setup up as well as in their contribution to daily operating costs. In addition to being necessary for the photosynthetic organisms we keep in our aquariums, light also provides the visual element of color. From talking to aquarists and perusing the various reef-related bulletin boards, it has been my experience that lighting and color are often a very misunderstood aspect of aquarium keeping. Given that lighting and color are important in the functional and aesthetic elements of reefkeeping, I feel it is important that hobbyists have a good understanding of light and color. The purpose of this series of articles is to provide beginning and intermediate reef aquarists with a comprehensive understanding of lighting concepts and terminology, and the ability to understand and comprehend lighting related discussions and data. The information will be presented in a series of short columns focusing on a few concepts at a time and build to a comprehensive understanding of light, especially as it relates to reef aquariums. according to the amount of energy contained in the radiation. Visible light is a part of this electromagnetic spectrum that creates the sensation of light when it falls on the human eye. The properties of all electromagnetic radiation can be described by three inter-related terms. These are wavelength, frequency and energy. Since light is a part of this spectrum, it too can be described by these terms. Hence, it is important to understand these terms as a first step towards understanding light. Wavelength Simplistically, we can think of light traveling as a wave. A typical wave form (e.g., ripples on the surface of water) has crests (or peaks) and troughs (or valleys). The distance between two consecutive peaks (or troughs) is called the wavelength, and is denoted by the Greek letter λ (lambda). Because the wavelength is a measure of distance, it is measured in units of length (meters). Since these wavelengths of visible light can be quite small, they are measured in nanometers (nm) where 1 nm = 1 billionth of a meter (10-9 meters). The wavelength of visible light is between nm. Incidentally, these also happen to be the majority of wavelengths of light that are relevant to photosynthesis. The combined effect of the complete range of radiation between nm appears as white light to the human eye. Radiation with a wavelength of 400 nm generates a response in the human eye that makes it perceived as violet, while radiation Figure 1:The electromagnetic spectrum covers a wide range of wavelengths and photon energies. Light used to "see" an object must have a wavelength about the same size as or smaller than the object. The ALS generates light in the far ultraviolet and soft x-ray regions, which span the wavelengths suited to studying molecules and atoms. Light is a form of energy, and to understand light we begin with the electromagnetic spectrum (figure 1) which is basically a grouping of all electromagnetic radiation arranged with a wavelength of 700nm appears red. The different colors of the rainbow (ROYGBV - red, orange, yellow, green, blue and violet) are arranged in descending order of their wave-

3 length. Roughly, we can break down the various colors into wavelength bands as follows: Color Wavelength (λ) Violet 400 to 440nm Blue 440 to 490nm Green 490 to 540nm Yellow 540 to 590nm Orange Red Radiation below 400 nm wavelength is called ultraviolet (UV) radiation, and is typically divided into three segments: UV-A ( nm), UV-B ( nm) and UV-C ( nm). UV radiation is not visible to the human eye, but it can have a damaging impact on humans (as well as corals). The UV-A segment, the most common in sunlight, overlaps slightly with the shortest wavelengths in the visible portion of the spectrum. UV-B is effectively the most destructive UV radiation from the sun, because it penetrates the atmosphere and can injure biological tissues. UV-C radiation from the sun would cause even more injury, but it is absorbed by the atmosphere, so it almost never reaches the Earth s surface. Infrared (IR) radiation has slightly longer wavelengths than visible light. The IR region of the electromagnetic spectrum is also divided into three segments: IR-A ( nm), IR-B ( nm) and IR-C ( nm). Infrared radiation is thermal and is felt as heat. Frequency 600 to 650nm 650 to 700nm The number of waves that pass a given point in space during a specified time interval is the light s frequency; consequently, frequency is a time based unit. Frequency carries the units per second, but we use a special term for the unit called - Hertz (Hz), where 1 Hz corresponds to 1 wave/second, so 50 Hz would mean 50 waves/second. imply that the frequency will be higher. Thus wavelength and frequency are inversely related: the shorter the wavelength of the wave, the higher the frequency of the wave. Since all the waves travel at the same speed - the speed of light - the relationship between wavelength and frequency is determined by the following formula: Wavelength = speed of light / frequency In the typical notation that you will see in most articles and books: where: λ = c/ν λ = wavelength ν = frequency c = speed of light The speed of light is 299,792,458 meters per second (approximately meters/second). To be precise, what we usually call the speed of light is really the speed of light in a vacuum (the absence of matter). In reality, the speed of light typically varies depending on the particular medium that it travels through. Light moves more slowly in glass than in air, and in both cases the speed is less than in a vacuum. If we look at the colors of the rainbow from blue to red, we can now understand that the blue light (400nm wavelength) will have a higher frequency than red light at 700nm, with the other colors of the rainbow falling in between. In fact, the frequency of blue light will be 75% (700/ = 75.14%) higher than the frequency of red light. Energy As mentioned earlier, light is a form of energy. According to the quantum theory, all energy is transmitted and absorbed in discrete particles called quanta or photons. Thus, the smallest amount of radiation energy that can exist is one photon. As seen in the figure above, the wavelength and frequency are related to each other. If we take any two points on the waveform labeled start and end, and count the number of waves in between, we can easily see that we will have more waves if the wavelength is smaller. More waves If one thinks of the photon as a small packet or ball of energy, it is most useful in understanding light, especially for our purpose of reefkeeping. For our purposes, let us take a simplified, unified description that says that light travels as discrete photons along a wave. Visible light is a mixture of many photons with different wavelengths. The photons are

4 reflected and absorbed by various surfaces, and when they reach the eyes, they create the sensation of sight and resultant perceptions of color and brightness. These photons are also directly responsible for photosynthesis in plants and corals. The energy from the photons is used during photosynthesis to convert CO2 into sugar, which is a primary energy source for the photosynthetic endosymbiotic zooxanthellae living within corals. As discussed earlier, the energy carried by electromagnetic radiation is contained in the photons that travel as a wave. According to quantum theory, the energy in a photon varies with its frequency, according to the equation: Where: Energy = Plank s constant Frequency E = hν = hc/λ h = Plank s constant is joules per second Energy is measured in units called joules. As the frequency of the radiation increases (wavelength gets shorter), the amount of energy in each photon increases. Now we can begin to understand why the red light gets absorbed quickly in water as a function of depth. we can measure the number of photons in moles where: 1 mole = Avagadro s number So photons would correspond to moles. Now, this number is too small, so instead we will measure in micromoles, where: 1 micromole (denoted as µmol) is 10-6 mole, giving us micromoles of photons. What about watts? Energy is measured in joules, and the watt is the unit used as a measure of power. Power is defined as the rate of flow of energy. By definition: 1 watt = 1 joule/second So, one watt of power from light at 500nm would need to provide photons per second or micromoles/sec. The figure below shows the relationship between watts and micromoles of photons to generate 1 watt of power. These basic equations provide us with the relationship between wavelength, frequency, energy and photons, and can be used to go back and forth as seen in the following examples. Example 1: What is the energy in a single photon of light at 500nm? E = /( ) E = J Example 2: How many photons per joule exist for light at wavelength λ = 500nm? E = Energy/photon, so to create 1 J of energy we will need N photons. N E = 1 joule, hence N = 1/E N = λ/hc = photons As seen above, to produce 1 Joule of energy by light at a wavelength of 500nm requires a very large number of photons. To avoid having to deal with such large numbers, Summary This column has focused on providing the basic terminology required to understand light. Light is a form of energy, and can be simply described as a stream of photons traveling along a wave. Photons are discrete particles of energy. The characteristics of light and the photons are specified by three terms: wavelength, frequency and energy, which are mathematically related. Photons with wavelengths of 400 nm carry more energy than those with larger wavelengths and will appear violet to the human eye, and photons with wavelengths of 700nm carry less energy and will appear red. White light is a mixture of photons in the wavelength range nm. This range is what the eye can see and is also useful for photosynthesis. The photons carry the energy and the number of photons is measured in units of micromoles.

5 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 nm. 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? 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. 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. 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 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 nm (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 nm falling on a 1 meter square area per second. PPFD is a Figure 4: How stuff works figure helps explain the process measure of Photosynthetically of the photons generations in atoms. Available Radiation abbreviated as PAR. Recall from Part 1 that to generate 1 watt of power we would need 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 = , hence 1 micromole = ). Hence the units of

6 PPFD are micromoles/m 2 /sec, so, a PPFD of 1 corresponds to 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 nm 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/m 2 ) 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 5 below. This is the most important piece of information about a light source, and all relevant light measures can be derived from it. Figure 6:Photon Distribution (measured as PPFD) for a 400 W Ushio lamp on a Magnetek (M59) ballast - 18 from the lamp. Adding all the photons over the range of nm 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 6. 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. Figure 5:Spectral Power Distribution for a 400-W Ushio Lamp on Magnetek (M59) ballast - 18 from de lamp. Note that for each wavelength the spectroradiometer measures the power density in watts/m 2. 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/m 2 /second of energy. Using the relationship between energy and wavelength, it can be determined how many photons/m 2 /sec at 420nm will be required to generate 0.4 joules of energy micromoles. Thus, we can easily convert from watts/m 2 to micromoles/m 2 /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. In 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/m 2 ) 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 nm 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

7 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. Figure 7:Comparison of the spectral distribution of two lamps with similar PFD values. 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 7 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. 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/m 2 /sec. Using just the PPFD number gives us information only about the number of photons in the nm 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. According to the Inverse Square Law: PPFD1/PPFD2 = (D2/D1) 2 D1 and D2 = distance at which PPFD1 and PPFD2 are measured.

8 Part III: Making Sense of Light Measures A large amount of confusion about light measurements comes from the fact that there are several different ways of measuring light. Many terms are used to measure aspects of lighting, and a simple cruise on the Internet will take you through a plethora of terms such as: lumens, lux, candlepower, foot-candles, lamberts, phot, nit, irradiance, illuminance, Color Rendition Index (CRI), Kelvin and Photosynthetic Photon Flux Density (PPFD), among others. Why are there so many measures to describe light? This article will sort through this abundance of lighting measures. There are basically three categories of light measures based on the particular application and interpretation, each with its own set of terminology. 1. Recall that light is a form of radiation, and hence can be measured as radiant energy using energy based measures. These units of light measurement are termed radiometric measures of light. 2. Light is also used to illuminate for visual purposes, hence light can also be measured for this application based on how the human eye perceives light. Measures of light based on visual perception are called photometric measures, and are by far the most commonly used and available metrics because they are used by the large lighting industry. The quantity of light at the source is termed flux, and is measured as quantity per unit of time. This is very similar to measuring the flow of a pump in gallons/hr or liters/min. We can think of a light source as a pump emitting radiation and measure this pumping capacity over time. It represents the total light output from the source per unit of time. What this measured quantity is depends on whether the light is interpreted using radiometric, photometric or photosynthetic standards. The light radiating from the source ultimately falls onto an object, and we can measure the amount of light falling onto a given area of the object. This quantity is measured per unit area, and measures the light s density on a unit area. The light emanates in several directions and we can either measure this without regard to the direction from which it comes, or measure it in a given direction. When measuring light in a given direction, it s helpful to visualize the light as radiating from all directions in a sphere. This sphere can be broken down into cones whose apex is at the center of the sphere with the cone specified by the solid angle at the apex. Thus the light can be measured as the amount of flux contained in such a cone and measured per unit angle. The unit angle used is called a steradian (similar to a radian in three dimensions). A complete sphere has 4π steradians. The different quantities used in light measurements and their units of measure are summarized in the table below, and will be discussed in further detail. 3. The form of measurement that we, as reefkeepers, are concerned about is the Photosynthetically Available Radiation (PAR), which measures the number of photosynthetically useful photons, and has been discussed in detail in Part II. 1) at the source, There are two main ways light can be measured: 2) at the surface of the object being illuminated. Radiometric Measurement of Light Because light is radiant energy, the energy is measured in typical units of energy - joules (J). Radiant Flux, also called radiant power, is the flow rate of radiant energy. It is measured in terms of power units called watts, which are basically a measure of energy per unit time.

9 1 watt = 1 joule/sec. Radiant Intensity is the radiant flux per unit solid angle and is measured in watts/steradian. The radiant intensity is independent of the distance because it measures only the amount of radiant flux contained in the cone with an angle at the apex equal to one steradian. As we move further from the source, the cone s spread increases so the radiant intensity falls onto a larger surface. Thus, the density of light falling onto the surface decreases as the area increases (following the inverse square law for a point source), even when the angle at the cone s apex does not change. This is measured as radiance. Radiance is the radiant flux density per unit solid angle and is measured in watts/m 2 /steradian. If we do not care about the light s direction and want to measure the light falling onto a source from all directions, then we measure this as irradiance. Irradiance, also known as radiant flux density, is the radiant flux per unit area at a point on the surface. Hence, its units are expressed in watts/m 2 or joules/sec/m 2. It is denoted as E. Spectral Irradiance is the irradiance per unit wavelength interval at wavelength λ. This is denoted as Eλ and its units are expressed in watt/m 2 /nm. Recall that the spectral power distribution plot discussed in Part II is plotted using spectral irradiance values. Photometric Measurements Photometric measurements are geared toward how the human eye perceives light. The sensitivity of human eyes is different for different wavelengths. In the late 1920s the Commission Internationale de L Eclairage (CIE), based on experimentation using human subjects, established how the human eye responds to light at different wavelengths. The human eye is more sensitive to light at 555 nm (green) and less sensitive to blues and reds. This characteristic of human vision established the standard observer response curve known as the luminous efficiency function to represent how the human eye responds to light at different wavelengths. Per this standard, detectors in the eye respond differently to different regions of the spectrum, and the response is scaled with respect to the peak values. The change in the eye s spectral response can be explained by the presence of two types of receptors, rods and cones, in the retina. Cones are active at high light levels and are most densely situated in the central part of the field of view. The cones spectral response corresponds to the photopic sensitivity curve. The rods are responsible for human vision at low light levels and are prevalent in the peripheral field of view, away from our direct line of sight. As light levels are reduced, cones become less active and rods become active with established spectral sensitivity gradually switching toward the scotopic response curve. The peak spectral sensitivity for photopic vision is 555 nm, and 507 nm for scotopic vision. From this it is quite clear that the human eye finds light at 555 nm to be the brightest, with the blues and reds tending to be less bright. The luminous efficiency functions are shown in Figure above. All photometric light measurements evaluate light in terms of this standard visual response described by the luminous efficiency function and, hence, all are weighted measures. Not all of the wavelengths are treated equally. The wavelength at 555 nm is assigned a weight of 1, and the others are scaled according to this function. According to this function, light at a wavelength of 450 nm is given a weight of This explains why a light source with large amounts of radiation in the blue region will have a low reading when using photometric units. The quantities used for photometric measurements correspond to those used for radiometric measurements, with the main difference being that the measurements are evaluated with respect to the human eye s response. Luminous Flux is the amount of radiation coming from a source per unit time, evaluated in terms of a standard visual response. Unit: lumen (lm). You will see most data from lighting companies refer to light output in terms of lumens. Think of this as the amount of light produced by the lamp as perceived by the human eye. Luminous Intensity is the luminous flux per unit solid angle in a given direction. Unit: candela (cd). One candela is 1 lumen/steradian. Illuminance is the luminous flux per unit area. It is measured in lux (lumen/m 2 ) or footcandles (lumen/ft 2 ). The light emanating from a lamp is used to illuminate objects

10 and the amount of light (measured in lumens) falling onto a specific area of the object, usually one square meter, is termed lux. When we measure this same area in square feet, the unit is footcandles. These units are often used in photography, where we are interested in how much light is falling onto the subject. Conversion from Radiometric Units to Photometric Units The following method is used to convert between photometric units and radiometric units. As defined, 1 watt = 683 lumens at 555 nm (peak photopic response), and it is scaled for other wavelengths based on the Luminous Efficiency Function V (λ). To determine a lamp s lux values, the spectral irradiance at each wavelength (taken from the spectral power distribution) in the spectral range ( nm) is multiplied by the luminous efficiency function at the equivalent wavelengths. Then, all of these multiplied values are summed and multiplied by 683 to find the total lux output. As you can see, the conversion requires knowledge of the spectral power distribution and cannot be done without it. So far we have been dealing with metric units. To convert to English units, or to other measurement systems, appropriate conversions need to be made. These converted units are often given different names (thereby adding to the confusion)! As an example we can look at the different terms and units used for measuring luminance. LUMINANCE: 1 lm/m2/sr (lumens per sq. meter per steradian) = 1 candela/m2 (cd/m2) = 1 nit = 10-4 stilb (sb) (or 1 candela/cm2) = x 10-2 cd/ft2 = π apostilbs (asb) = π x 10-4 lamberts (L) = x 10-1 foot-lamberts (fl) Units for Photosynthesis Measurements In keeping corals and plants we should not be concerned about light as humans see it, but rather as the plants and corals see it. For the purpose of photosynthesis, light is termed Photosynthetically Available Radiation (PAR). This radiation s range is identical to what humans can see in the nm range, but each photon is treated uniformly in this measurement (unlike the photometric measurement, which weights the photons according to how the human eye sees them). The reason for expressing PAR as a number of photons instead of energy units is that the photosynthetic reaction takes place when a plant absorbs the photon, regardless of the photon s wavelength (provided it lies in the range between 400 and 700 nm). That is, if a plant absorbs a given number of blue photons, the amount of photosynthesis that takes place is exactly the same as when the same number of red photons is absorbed. Note, however, that the plant or coral may have an absorption response that preferentially absorbs more photons of certain wavelengths (more on this later). Recall from Part II, PAR is measured as PPFD, which are Einstein/m 2 /s or µmoles/m 2 /s. One Einstein = 1 mole of photons = photons 1 µeinstein = photons. Conversion from Radiometric Units to PPFD If we know the spectral irradiance at any given wavelength (we can get this from the spectral power distribution), then we can determine the PPFD for the given wavelength by multiplying the spectral irradiance (watts/m 2 ) by the watts to Einstein conversion factor for each wavelength (recall from Part I how to convert energy at a given wavelength into the number of photons). To compute the total PPFD over the range of nm, compute the PPFD for each wavelength and sum over the range of nm. Summary There are three basic forms of light measurement - radiometric, photometric and photosynthetic - and these can be measured at the source or at the object onto which the light falls. Photometric measurements are derived from the radiometric measurements by factoring in the human eye s response, and do not treat

11 all radiation equally. Photosynthetic measures, on the other hand, treat all radiation equally. The starting point for all these measures is the spectral power distribution, from which all other entities can be derived. Conversion from one set of units to the others is simply not possible unless the spectral power distribution is known. In addition to these lighting measures, additional measures such as Color Rendition Index (CRI) and Correlated Color Temperature (CCT) are used to describe light. These will be covered in the next part of this series. Part IV: Color Temperature One the most abused and misunderstood terms in reef aquarium lighting is color temperature. Lamps, both fluorescent and metal halide, are being sold in the hobby based on color temperature ratings ranging from 5000K to 50000K, with a wide range of values in between. It is not uncommon to find lamps rated as 6500K, 10000K, 11000K, 12000K, 12500K, 13000K, 14000K, 15000K, 18000K, 20000K and 50000K being sold in the hobby. As interpreted by reef aquarists, these numbers tend to convey the apparent blueness of the light emitted by the lamps. The aquarium lighting industry has used this color temperature interpretation as a way to label their lamps, and use it to signify how their lamps would appear in comparison to other lamps and as a selling point for their lamps. It has been my experience, however, that these numbers often seem to be rather arbitrarily created and often there is very little correlation between the scientifically defined term of color temperature and the label on the lamp, thereby making it more difficult for the aquarist to make choices based on color temperature ratings. In this article I will explain the concept of color temperature, its relationship to spectral power distribution, and the color temperature nuances of light sources. Understanding color temperature starts with understanding black body radiation and the Kelvin temperature scale. A theoretical black body is an object that has no color and is black because it absorbs all radiation incident on its surface and emits no radiation at 0 Kelvin. In the Kelvin temperature scale, 0 Kelvin (abbreviated by K) corresponds to C and is the temperature where all molecular motion has ceased. This is called absolute zero. Recall that for radiation to be generated, the electrons have to be jumping to higher energy levels and releasing the energy as photons. At absolute zero all motion ceases and there is no energy being emitted. Hence, at 0K the black body emits no radiation. As the black body is heated above 0 K it starts to emit radiation that lies within the electromagnetic spectrum. The radiation s spectral distribution depends on the black body s temperature. At low temperatures (e.g. room temperature) the black body is emitting radiation, but it is not in the range that is part of the visible spectrum. For visible radiation the back body must be quite hot. At about 1000K it looks red, yellow at about 1500K, white at 5500K, bluish-white at 6500K and more bluish at 10000K. The spectral irradiance of the radiation and color changes with temperatures have been well studied by physicists, and the relationships are given by the well-known black body radiation laws. Plank s law gives the spectral irradiance at different wavelengths, Wien s law provides the wavelength at which the peak irradiance occurs, and Stephan Boltzman s law relates the total amount of energy to the temperature of the black body. Details of these can be found in any physics textbook and will not be covered here. How does this relate to the light sources we use - fluorescent and metal halide lamps? Does this mean that a lamp being sold as a color temperature of 20000K is a black body radiator and has an actual physical temperature of 20000K? No, since the lamps are not black body radiators! To be able to assign a color temperature to a light source there must be Figure 7:below show the radiation of the black body at different temperatures and the peak of the radiation. It also shows the visible portion of the radiation as colored bands. This is how a perfect black body radiator behaves, and the radiation is a function of the temperature to which it is heated.source:

12 a color match as well as a spectral match to a black body radiator. The spectral output of fluorescent lamps and metal halide lamps does not match with the black body spectral irradiance. Hence, the term color temperature, in fact, does not apply directly to these light sources. What it really means is that if we were to compare the lamp s color to a black body at 20000K, it would appear the same to a human observer. The technically correct term for this is Correlated Color Temperature (CCT) which is defined as the value of the temperature of the black body radiator when the radiator color matches that of the light source. CCT implies a color match to a black body at the specified temperature, but there is no spectral match. The table below shows CCT of various light sources: This now brings up the issues of matching lamp Temperature Light source 1500 K Candlelight 2680 K 40-watt incandescent lamp 3200 K Sunrise/sunset 3400 K One hour from dusk/dawn K Xenon lamp/light arc 5500 K Sunny daylight around noon K Electronic photo flash K Overcast sky K Blue sky color to color temperatures of the black body. Once we start talking about color, we have to remember that color is not a physical property but a physiological response created in the brain by the visible light seen by the eye. As someone adequately surmised, Color is only a pigment of your imagination. To be able to work with color mathematically, scientists have developed a mathematical means to specify color - where color is specified by numerical values called color coordinates or chromaticity. Correlated Color Temperature (CCT) can be determined by mathematical formula to find the chromaticity coordinates of the black body s color temperatures that are closest to the light source s chromaticity. (More on chromaticity and how it developed later.) Since it is a single number, CCT is simpler to communicate than chromaticity or SPD, and is used as a shorthand for reporting the color appearance of light emitted from electric light sources. Correlated Color Temperature values are being used by the reef lighting industry to give a general indication of the apparent blueness of the light emitted by the source. According to aquarium lighting industry convention, lamps with higher CCT values provide light that appears more blue. To develop a mathematical and more unambiguous definition of color and color perception, the International Lighting Commission (Commission Internationale de l Eclariage, referred to as CIE) established a colorimetry system for color matching that has, with minor changes, remained in use for the last 75 years. To understand the proper definition and meaning of CCT we need to understand color vision, how the chromaticity diagram was established, and how it is used to determine CCT of light sources. Color Vision Before understanding the CIE color diagram, it is important to understand how the human eye sees color. The human eye contains two different kinds of receptors - rods and cones. The rods are more sensitive and outnumber the cones, but the rods are not sensitive to color. Color vision is provided by the cones. There are basically three types of color sensitive cones in the human eye, corresponding roughly to red, green and blue. The response curves of these different cones have been mapped by researchers. The perception of color depends on the neural response of the three types of cones. Hence, it follows that visible color can be mapped in terms of the response functions of these three types of cones. It was shown that color samples could be matched by combinations of monochromatic colors: red (700 nm), green (546.1 nm) and blue (435.8 nm). These matching functions were determined by experiments. By simply adding various amounts of these primary colors a large range of colors could be matched, but there were still some outside this range that could not be matched by pure addition. It was found, however, that by allowing negative values of red, all colors could be matched. Allowing negative values of red is the same as adding red to the color sample being matched. CIE Chromaticity Diagram The CIE matching functions were derived from these Red, Green and Blue matching functions such that the matching functions are all positive, and any color can be considered to be a mixture of the three CIE primaries. These primary colors can be represented as mathematical functions of their wavelength, and are shown in Figure 4 below. The most commonly used CIE primaries were developed in 1931 using a two-degree field of view; since then, others have been defined using a 10-degree field of view and the functions were updated in The CIE color coordinates are derived by weighting the spectral power distribution (obtained by using a spectro-

13 temperature is called the black body locus. The pure spectrum colors appear on the outside along the curve, and points representing non-spectral colors are inside. A straight line connects the ends and represents colors that are combinations of wavelengths of 400 nm and 700 nm (blue and red). Figure 8: 1931 CIE Color Matching Functions. radiometer) by these three functions. This gives three values, called the tristimulus values (X, Y, Z), from which the chromaticity coordinates are calculated. Without going into the mathematics of computing these values (we can let a program compute them), the Y value is a measure of luminosity, or how bright the light appears to an observer. These Y values are, in fact, defined to be the same as the photopic response of the human eye. Because perceived color depends on the relative magnitudes of X, Y and Z, the chromaticity coordinates are usually given by normalized coordinates x and y, where x = X/(X+Y+Z), y = Y/(X+Y+Z) and x+y+z = 1. The (x, y) coordinates are called the chromaticity coordinates. In the computation of the chromaticity coordinates the Y value is normalized to 100. The figure below shows the 1931 CIE chromaticity diagram. The color temperature of a true black body is also shown on this chart. The path taken by the black body color Mathematically, the Correlated Color Temperature of a light source is computed by determining the (x,y) color coordinates of the light source, and by finding the color temperature closest to the lamp (x,y) that lies on this black body locus. Details of this approach are beyond the scope of this article, but interested readers are referred to Reference 1. What is important to note is that using such an approach, two points on either side of the black body locus can have the same CCT but different color coordinates. To prevent this from creating large differences in the perceived color of light represented by the same color temperature, a small tolerance zone is typically specified near the black body locus, and if the two points are outside this tolerance, then larger color differences will be perceived. One drawback of the 1931 chromaticity diagram is the fact that equal distances on the chart do not represent equally perceived color differences because of the non linear nature of the human eye. The 1976 uniform chromaticity CIE chart (Figure 10) was developed to provide a perceptually more uniform color spacing for colors at approximately the same luminance. The coordinates used here are denoted (u,v ) and can be computed from the 1931 x,y coordinates by the following transformation: u = 4x / (-2x + 12y + 3) v = 9y / (-2x + 12y + 3) This excellent website provides the mathematical equations and a calculator to convert between the various color coordinates developed. In spite of its drawbacks, the 1931 color chart is still one of the most popular in use. Another artifact of using the CCT arises from the fact that a single number is once again being used to characterize the SPD of the lamp. It is very possible that two very different spectral power density functions can have the same CCT, as shown in the Figure 11 below taken from Light sources with different spectral distributions but with the same CCT are called metameric light sources.spectral power distribution of two metameric light sources: Figure 9: The 1931 CIE chromaticity diagram. Source: While it is too complex to represent the color appearance of a light source precisely by the color coordinates,

14 Figure 10: The 1976 CIE chromaticity diagram. it does provide a useful approximate representation of the appearance of the light source. The color theory can mathematically represent color and provide a mathematical specification of color, yet there is still a difference between color specification and humans color experience. For example, brown and orange can have the same color coordinates on a CIE chart, but both produce a very different color experience in the human eyes. This artifact of color appearance is very difficult to represent in the CIE color chart and its mathematical representation of color. This situation arises due to the normalization of the luminosity function. Color coordinates of some common blue 250-watt mogul metal halide lamps on different ballasts: Lamp Ballast Lamp Wattage x y Hamilton 14KK Icecap Hamilton 14KK M Hamilton 14KK M PFO 13KK Icecap PFO 13KK M PFO 13KK M These chromaticity coordinates are plotted on the CIE diagram, as shown in Figure 8 below. The background color for the plot is obtained by superimposing the color diagram from Figure 1. The plot is scaled to show only the relevant piece of the chart. Aquacon 14KK Icecap Aquacon 14KK M Aquacon 14KK M Aquacon 14KK ReefFan Radium - 20KK Icecap Radium - 20KK M XM 20KK Icecap XM 20KK M XM 20KK M Figure 11: The SPD on the left is that of an incandescent lamp with a CCT of 2856 K. The SPD on the right is of a red, green and blue LED mixed spectrum that is metameric with the incandescent lamp. Color Coordinates of Metal Halide Lamps As seen from the above discussion, the main input required to calculate the CIE chromaticity coordinates is the spectral distribution and the functions for the CIE primary colors. The spectral data is obtained using the Licor 1800 Spectroradiometer. Software for the spectroradiometer has built-in functions to compute the 1931 CIE color coordinates. Using this, the color coordinates of a sampling of blue 250-watt mogul metal halide lamps sold as 13000K, 14000K and 20000K are computed and shown in the table below. Figure 12: CIE (1931 2deg) Chromaticity Coordinates of 250-watt Mogul Blue Lamps: Color coordinates of some blue 250-watt mogul metal halide lamps.