Determining the energy efficiency of different forms of lighting technology

Light – what really is it?

Lighting technology is

1. an important topic with regard to power quality as well as to energy efficiency and hence

2. a focus in the area of electrical engineering with Deutsches Kupferinstitut.

This is why this topic is granted one of the main pages here – particularly because energy efficiency is a sophisticated aspect with light.

Today, the “smart” technologies most commonly used to generate artificial light efficiently are the traditional fluorescent lamps (Figure 1) in which a gas emits light by forcing it to become electrically conductive, and the newer semiconductor-based LEDs (light-emitting diodes, Figure 2).

Figure 1: Traditional luminescent light sources: Fluorescent lamps still generate most of our artificial light
Figure 1: Traditional luminescent light sources: Fluorescent lamps still generate most of our artificial light
Figure 2: Modern luminescent light sources: LEDs are now the most common light source in a number of areas
Figure 2: Modern luminescent light sources: LEDs are now the most common light source in a number of areas
Figure 3: The classic thermal light source: The inside of an incandescent light bulb (230 V; 100 W)
Figure 3: The classic thermal light source: The inside of an incandescent light bulb (230 V; 100 W)

Compared to these “smart” methods, the original manner of generating electric light is more of a “sledge hammer” approach in which a material is heated so strongly that it glows sufficiently brightly. The typical commercial realisation of this kind of “thermal light source” is the incandescent lamp (Figure 3). It is important to remember that at the time of its invention the incandescent lamp was far more efficient than any of its precursors – candles, torches, oil lamps, etc. However, achieving another such leap in efficiency is not going to happen, as it would require lighting devices with efficiencies far greater than 100%. In fact, we are currently very close to the theoretically achievable peak energy efficiency.

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The “energy efficiency” of generating artificial light

Light is a form of energy. Whenever energy is converted from one form to another, some of that energy is lost. How much energy is lost is expressed in terms of the energy efficiency of the conversion process. Typically, the efficiency with which a technical device converts energy is expressed as the percentage ratio of the output power to the input power. But with processes that generate light, this simple definition doesn’t really work, as the brightness of light perceived by the human eye also depends on the colour (i. e. the wavelength) of the light. This is the reason why the unit used to express the light output of a lamp includes the sensitivity of a standardised “average eye”. This unit is called the “lumen”, which is simply the Latin word for light. The efficiency of an electric lamp or luminaire is therefore expressed in lumens per watt and is known as the “luminous efficacy” of the light source. This quantity, and only this quantity, is suitable for assessing which electric light source produces the greatest perceived brightness per unit of electric power.

Light, by definition, represents the visible portion of the electromagnetic spectrum. Although we occasionally talk about ultraviolet or infrared light, it’s strictly illogical and it makes about as much sense as talking about triangular and rectangular circles. The more general term – and the only correct one in this context – is “radiation”.

Table 1: Relationship between radiated power measured in watts and the light output as perceived by the human eye in lumens using a simplified model with ten wavelengths, i. e. ten colours.
Table 1: Relationship between radiated power measured in watts and the light output as perceived by the human eye in lumens using a simplified model with ten wavelengths, i. e. ten colours.

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Light quanta – two different measures

The visible spectrum makes up only a very small part of the full spectrum of electromagnetic radiation, which ranges from the radiation generated by a long-wave radio transmitter at a frequency of 155 kHz (wavelength: 1930 m) to the high-energy cosmic radiation encountered in the upper layers of the atmosphere at frequencies of 1023 Hz (wavelength: 10-15 m). Although electromagnetic oscillations are most commonly expressed in terms of their frequencies (i. e. the number of cycles per second in hertz [Hz]), it is more usual to discuss visible light in terms of its wavelength (note: the term “visible light” is, strictly speaking, tautological – a bit like talking about a round circle). But this is not a major issue, as one unit can be simply converted into the other, for example dividing the speed of propagation by the frequency gives us the wavelength. The speed of propagation used here is the speed of light, which has a constant value of approximately 300,000 km/s.

Figure 4: The visible range is only a very small part of the known electromagnetic spectrum
Figure 4: The visible range is only a very small part of the known electromagnetic spectrum

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The visible region of the electromagnetic spectrum begins with red at a frequency of around 384 THz (terahertz; 1012 cycles per second) or a wavelength of 780 nm (1 nanometre = 10-9 m) and ends with violet at a frequency of 789 THz or a wavelength of 380 nm. Across the visible region of the spectrum, the frequency ratio is barely more than 1:2 (see Figure 4). In comparison, audible acoustic oscillations (i. e. sound perceptible to humans) ranges from about 50 Hz to approximately 20 kHz, which corresponds to a ratio of 1:400. But the range of visible radiation is centred more or less around the point where the sun’s radiation is at its most intense, which from an evolutionary perspective is probably not just a coincidence. Of course it would be nice if we were able to see infrared radiation at night. But for us to be able to see what an infrared camera can, the visible range would need to extend quite far into the long-wavelength infrared region. After all, the human body radiates with a “colour temperature” of precisely 310 K (see Section 7 for more information about colour temperature).

Another difference between the ways we treat light and sound is that we use a logarithmic scale for sound pressure levels, as our perception of noise levels is logarithmic. While humans also perceive brightness logarithmically, we measure light intensities in the linear units of lumens [lm] or lux [lx]. This logarithmic scale becomes apparent when we consider the fact that office spaces typically require an illuminance of 500 lx [lm/m²] but direct sunshine provides us with no less than 100,000 lx, while at full moon, with only 0.2 lx available, we can still find our way around, and we are still just able to perceive something at an illuminance level of a mere 0.0001 lx. So light from a full moon is only 2 ppm (parts per million) of that on a bright, sunny day. On an overcast winter’s day, which we typically associate with November but which can actually be found throughout most of the winter season, the illuminance level is no more than 1000 lx, which is just 1% of that from direct sunshine. But an overcast November day still doesn’t appear that dark to us. In fact, the range of perceptible brightness covers nine orders of magnitude, which is almost as large as the audible frequency range. Once this has been understood, the struggle to squeeze out another lumen per watt, which is so characteristic of the energy efficiency debate, loses some of its significance. Potentially far greater energy savings could be made by identifying those applications in which half the brightness (strictly, illuminance) would still suffice.

Table 2: The higher the frequency of a light quantum (photon), the shorter its wavelength and the higher its energy
Table 2: The higher the frequency of a light quantum (photon), the shorter its wavelength and the higher its energy
Figure 5: The “quantum leap” from Table 2
Figure 5: The “quantum leap” from Table 2

Depending on the experiment being carried out, light can act like a wave or a particle. While physicists are still debating how best to describe the nature of light, technicians find they can work perfectly well with the existing models. These models are able to explain all observations of practical relevance for lighting technicians – and are therefore the tools of choice. One important aspect of electromagnetic radiation (and, hence, of light) is that its energy is quantised. The energy of a light quantum, which the physicists call a photon, is equal to the frequency of the radiation multiplied by a natural constant, called Planck’s constant h (Table 2). As red light has a lower frequency than violet light, a photon of red light has less energy than a photon of violet light.

Modern lighting technology makes use of a number of physical processes in which a higher energy photon can be converted into a lower energy one, i. e. into one with a lower frequency or longer wavelength. The difference in energy is “lost” as heat. This type of conversion process takes place, for example, in fluorescent lamps. The actual gas discharge yields UV radiation, which excites the luminescent material (the phosphor coating) causing it to emit lower energy light photons. A UV photon that strikes the phosphor coating in the lamp generates a lower energy photon, which if the coating has been chosen correctly, will lie in the visible part of the spectrum. Not all of the UV radiation is converted, however. One advantage of this technology is that the colour of the light produced can be controlled by carefully choosing the composition of the luminescent material.

It is also of interest to note that the white LEDs currently available are also essentially fluorescent light sources. Since it uses blue light rather than UV radiation as the exciting radiation, the LED has the advantages that some of the blue light can be used directly and that less energy is lost overall, as the conversion is from a lower energy blue (rather than a UV) source.

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Quantity: How much light am I getting?

The maximum possible luminous efficacy of a light source, i. e. the maximum efficiency with which energy in one form can be converted into energy in the form of light, is 683 lumens per watt [lm/W]. However, this value only applies in the case of monochromatic green light with a wavelength of 555 nm, where the human eye is at its most sensitive and where sunlight “coincidentally” exhibits its peak radiant power. So it turns out that our most efficient lamp – our “greenest” lamp so to speak – really is green. Efficient they may be, but not even the politically greenest of our legislators are going to suggest using monochromatic green radiation to light our streets, buildings or homes

Table 3: Relationship between radiated power measured in watts and luminous flux (i. e. the light output as perceived by the human eye) in lumens using a full model with 400 measurements at 400 wavelengths, i. e. 400 colours (only sample values shown here).
Table 3: Relationship between radiated power measured in watts and luminous flux (i. e. the light output as perceived by the human eye) in lumens using a full model with 400 measurements at 400 wavelengths, i. e. 400 colours (only sample values shown here).

For “white” light – or what we perceive as white when equal amounts of physically radiated power are mixed for all the colours in the range 380 nm to 780 nm – the theoretical maximum falls to a mere 182 lm/W (see Table 3; or just 161 lm/W using the simplified model shown in Table 1). A spectrum comprising a radiated power of 2.5 mW at each of the 400 wavelengths between 380 nm and 780 nm generates 400 * 2.5 mW = 1 W of overall radiated power. This would then be perceived by a standard human eye as a luminous flux of 182 lm. If there was an electric light source available that could produce this spectrum with an efficiency of 100%, then the source would consume a mere 1 W of electric power. Although modern light sources do not operate without losses, they are in fact closer to the 100% limit than the most advanced and most efficient of today’s diesel engines. The good old incandescent lamp, in contrast, is barely as efficient as a steam locomotive.

If, rather than assuming a theoretical source of white light, we take a real one, such as the sun, which is a thermal light source with a surface temperature of around 5800°C (approximately 6000 K), then the colours either side of the green region are a little weaker, while the 555 nm spectral line itself and those closely adjacent to it are somewhat stronger. Obviously, we still perceive this spectrum as “white”, but the theoretical upper limit – corresponding to an energy efficiency of 100% – increases to 198 lm/W. As the correlation between energy efficiency and the ratio of luminous flux to power is so “flexible”, it is established practice to talk about the “luminous efficacy” [lm/W] of a light source rather than its energy efficiency [%]. Independent experts place the theoretical maximum efficacy of a white light source at around 320 lm/W. The resulting white light from such a source would probably be “white” enough for many applications, if only the efficiency of physically converting electricity into visible radiation was close to 100%.

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Directionality: Where’s the light going?

If the value of the luminous efficacy of a lamp is too small for marketing purposes, there are a whole range of other metrics that technical marketing departments like to use (and misuse) to impress the unsuspecting public. The first such quantity is the “luminous intensity” I, which is measured in candelas [cd].

The ratio of luminous flux to luminous intensity indicates whether the lamp is focussed strongly, weakly or not at all. A light source that radiates equally in all directions would distributes its light evenly over the inner surface of an imaginary sphere centred at the lamp. The surface area of the sphere is given by:Asphere = 4πr².

With a radius of 1 (i. e. a diameter of 2), its surface area is about 12.6 – irrespective of the unit of length used. Clearly, if the radius is measured in metres, the surface area will be expressed in square metres.

The solid angle Ω, measured in steradians [sr], is the (three-dimensional) angle at the apex of a light cone that illuminates a circular section on the inner surface of the sphere. It is called a solid angle because a cone is a three-dimensional solid body. The solid angle is defined as being equal to one steradian (Ω = 1 sr) when the base surface of the cone is A = 4πr² where r is the height of the cone, which is also the radius of the sphere – see Figure 6. Interestingly, the relationship between the solid angle Ω and the plane angle ε is neither directly proportional (linear) nor inversely proportional (reciprocal), but looks like a shifted cosine curve (Figure 7). This becomes clearer, when (after a little geometry) one realises that the solid angle can be expressed by the formula:

Figure 6: A graphical representation of 1 steradian
Figure 6: A graphical representation of 1 steradian

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Table 4: Relationship between solid angle Ω and the plane angle ε and the dependence of the ratio of luminous intensity I to luminous flux Φ as a function of ε
Table 4: Relationship between solid angle Ω and the plane angle ε and the dependence of the ratio of luminous intensity I to luminous flux Φ as a function of ε

where ε is the planar angle of the cone of light whose apex is located at the centre of the sphere. The relationship between the “normal” two-dimensional angle ε and the three-dimensional angle Ω is shown numerically in Table 4 and graphically in Figure 7. A convenient conversion tool is available on the internet. The tool is a useful means of seeing the effects of different parameters, and it can be readily shown that:

  • If ε = 65.54°, the solid angle Ω = 1 sr.
  • A luminous flux of Φ = 1 lm illuminates a surface of 1 m² if the distance is 1 m (at a distance of 2 m, the area illuminated would increase to 4 m²).
  • This would yield an illuminance of EV = 1 lm/m² = 1 lx (at a distance of 2 m, the illuminance would be reduced to only 0.25 lx).
  • The luminous intensity of the light source is I = 1 cd (at a distance of 2 m, it remains unchanged).

The luminous intensity IV of the light source indicates the power of the light passing through the cone. An electrician might see certain similarities with an electrical conductor in which the current is the same at the beginning and at the end, despite the fact that the conductor cross-section changes along its length. Obviously, electricians don’t install conical conductors, but this rather unusual idea may help in understanding the difference between luminance LV and illuminance EV.

Strictly speaking, the solid angle Ω = A/r² is a dimensionless quantity, as it has units like [m²/m²], and is measured in steradians – analogous to the two-dimensional (planar) angle measured in radians. A is the illuminated portion of the surface of the sphere that has the light source at its centre, and r² is the square of the radius of that same sphere. Because the size of the illuminated area A increases with the square of the distance r, the illuminance is inversely proportional to r². In this article we will be following common practice and will express the solid angle in units of steradians [sr].

Figure 7: Plots of the solid angle Ω and the ratio of luminous intensity I to luminous flux Φ as a function of the plane angle ε
Figure 7: Plots of the solid angle Ω and the ratio of luminous intensity I to luminous flux Φ as a function of the plane angle ε

The models introduced above are based on idealised representations that assume that the illuminated segment of the sphere’s surface is indeed circular and that the illuminance measured at that surface is completely homogeneous. In practice this is, at best, no more than an approximation. In practical applications, there is no sharp boundary between the illuminated area and the unilluminated dark area. Despite such inaccuracies, the metrics discussed offer a convenient means of estimating how much light is to be expected in a particular spatial direction.

And the application of these models is not restricted to circular “spots” of light. A value for the luminous intensity or the illuminance can be assigned to any other surface patch within which these quantities are distributed more or less evenly. Instead of a light cone, one can in these cases imagine either a square pyramid or can assume that the patch of surface is illuminated by a large number of extremely thin, pointed, “unit cones”.

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An example application

Forming a plastic imagination of this configuration may be somewhat difficult, among others, because the planar base surface of our light cone is not equal in size with the warped illuminated part of the (interior) surface of the sphere. Moreover, the luminous intensity would be inhomogeneous, for the brim of the circular ground surface is further away from the light source than the centre is, and on top of this the radiation does not hit vertically at the brim. The warped piece of surface on the inner side of the sphere is a bit larger, but the luminous density is always homogeneous – for any angle. This non-linear dependence depicted in Figure 7 and Table 4 increases ever more as the angle increases. Considering e. g. the a. m. lighting angle of 65.54°, then 1 m² of surface area will always be illuminated from a distance of 1 m. The interior surface of the unity sphere with a radius of 1 m, however, always comprises 12.6 m² (4π m², to be quite precise). The light from a light source radiating uniformly in all directions will be distributed evenly over this inner surface. So if the radius r of the sphere is 1 m, a luminous flux of 1 lm is distributed over an area of 12.6 m². This would result in an illuminance EV of

For a sphere of radius 1 cm, the illuminance would be

However, the luminous intensity would be the same in both cases, as luminous intensity merely describes the quantity of light emitted by a point light source in a particular direction – irrespective of the distance travelled. The practical utility of this metric is therefore rather limited.

If the light source does not radiate uniformly in all directions, then the luminous intensity will naturally be greater the smaller the solid angle subtended by the light source. At planar angles of up to 65.54° the value of the three-dimensional solid angle is less than one steradian; as the planar angle increases, however, the solid angle grows much more rapidly. But a larger solid angle also means that the same amount of light is spread over a larger area, so at large solid angles the values of the illuminance in lux and those of the luminous intensity in candelas are smaller than those of the luminous flux in lumens.

This is why in the past lamp manufacturers preferred to specify luminous intensity at lighting angles below about 65° – and to keep silent about the luminous flux, because the figure printed on the package would then be greater. And the more well-known the manufacturer, the more likely you were to see this practice. At wider angles, it was always considered more advantageous to indicate the lamp’s luminous flux. Nowadays, the EU regulations governing lamps used for general lighting applications clearly set out what information the manufacturer needs to provide. In niche sectors, such as bicycle lighting, manufacturers specify “the” illuminance (which one?), but fail to mention the distance at which the illuminance is to be measured.

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Luminance: How much light do I get back?

The luminous intensity can also be used to derive a quantity called “luminance” LV [cd/m²], which is a measure of a surface’s apparent brightness and describes how much light is coming from a unit of surface area. Luminance is used, for example, to quantify how much light is reflected by a passive surface such as a cinema screen, or how much light is radiated by an active surface such as a TV or PC screen.

Quality: Colour, colour temperature and the colour rendering index

All bodies at the same temperature, irrespective of the material they are made of, will emit radiation of equal brightness and with the same colour composition. Light from an artificial source can therefore be described in terms of the source’s “colour temperature”. For example, when light from a lamp gives the observer the impression of “daylight white”, then the source is regarded as having a “colour temperature of 5800 K”. Colour temperature never used to be mentioned on the packaging until EU regulations demanded it. But it, too, only provides the consumer with a very rough idea of the lamp’s colour. Different colours are reflected, refracted and absorbed to different degrees within the earth’s atmosphere, so that a discontinuous spectrum arrives at the surface of the earth (Figure 8). This spectrum also shows considerable diurnal variation (i. e. variation throughout the day). As “daylight” is not the same as “sunlight”, there is a need to standardise a specific but typical daylight spectrum. In the past, colour temperature information should have been expressed as being “similar to 5800 K”. This type of phrasing is now mandatory under EU law. Only an incandescent lamp actually produces a continuous light spectrum.

Figure 8: Sunlight and daylight spectra
Figure 8: Sunlight and daylight spectra

The same applies to the colour rendering index. Deriving and defining the colour rendering index is no easy task and it would go beyond the scope of this article to attempt it. But what we do know is that when a light source has a colour rendering index of Ra = 100, it exhibits ideal colour rendering. But is that really so? Well, not necessarily. The colour rendering index is a relative metric. At colour temperatures below 5000 K, the colour rendering index relates to the actual colour temperature of the source lamp; at colour temperatures above 5000 K, the lamp’s colour rendering performance is measured against an agreed type of daylight. This approach allows light sources with different colour temperatures to be distinguished with respect to their colour rendering. A light source that is able to exactly reproduce this more or less arbitrarily defined spectrum would achieve the best colour rendering score; one with a perfectly “smooth” distribution of wavelengths (such as in the leftmost columns of Table 1 and Table 3) will not. According to expert opinion: “The index is valued within the industry, because it assigns quite respectable Ra values of around 80 even to lamps that produce a very modest, discontinuous spectral distribution. Based on our experience, a light source needs to be pretty poor with respect to perceived colour rendering before it yields significantly lower values.” (DIAL – this posting has now been withdrawn). The scale has been effectively designed to have no lower limit and can theoretically extend far further into the negative range than into the positive, while all the time creating the impression that it is a percentage scale from 0 to 100.

But there is hope that things are gradually changing: “In 2015, the North American IES attempted to put forward a “new colour rendering index”, one that was not perfect, but substantially better than the existing CRI. It remains to be seen whether the new index can become established in the industry.

Figure 9: Sensitivity of the human eye plotted against wavelength at daylight (coloured plot) and at night (when we only see black and white, shown as the blue plot)
Figure 9: Sensitivity of the human eye plotted against wavelength at daylight (coloured plot) and at night (when we only see black and white, shown as the blue plot)

It is also important to know that the maximum theoretical luminous efficacies given above refer to light perceived under (bright) daylight conditions, i. e. using what is known as photopic vision. At night, under scotopic vision, the human eye is unable to perceive colours. So under these conditions, not only are all cats grey, as the saying goes, but the eye’s maximum sensitivity shifts a little towards the blue-green portion of the spectrum (507 nm – Figure 9). So the turquoise cat will actually appear to be light grey, while red and violet cats will be practically black.

In addition, the overall sensitivity of the human eye increases considerably once we have become accustomed to the darkness. A “lamp” that operated exclusively at a wavelength of 507 nm would now achieve an efficacy of 1700 lm/W, which is great until you realise that the lamp is so dim that it could never be used to identify any other colours. So a practically useless device can still, in theory, be assigned a hugely impressive “luminous efficacy” value. Under low-light, night-time conditions, the peak of our spectral sensitivity curve and that of the available sunlight match precisely (Figure 9). This is perhaps not unexpected from an evolutionary point of view. After all, moonlight ultimately comes from the sun.

A white light source that could achieve an energy conversion efficiency of 100% would therefore have a luminous efficacy of around 200 lm/W. Achieving significantly higher values for the luminous efficacy of a light source would require not only an excellent energy conversion efficiency but would also be accompanied by a significant deterioration in colour rendering. Any such lamp would have to emit disproportionally large amounts of green light at around 555 nm and correspondingly lower amounts in the rest of the spectrum. Any claims to the contrary are likely being made by someone who claims to have invented the “perpetual light” machine – or they are selling heating devices, where the light produced is an “unfortunate” by-product.

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Summary: An overview of the quantities used in lighting technology

Table 5: Tabular summary of some important lighting metrics
Table 5: Tabular summary of some important lighting metrics