Fundamentals of Illumination Engineering

2

Fundamentals of Illumination Engineering

Learning Outcomes: ■

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Is light a wave or a stream of quantum particles? How is the light spectrum related to the radio spectrum? What is the difference between additive and subtractive color mixing? What are primary and secondary colors? What is a color space? Which information is contained in a CIE 1931 chromaticity diagram? What is special about white light? Which properties have an impact on color quality? Are the spectral characteristics of commonly used illuminants similar? What is the difference between radiometric and photometric values? What is the commonality between candela, lumen, and lux? Why should dimming and flicker be considered jointly? Why is human centric lighting relevant for human beings? What is the challenge of VLC in the context of human centric lighting?

2.1

Light Spectrum

According to the wave-particle duality, light can be either interpreted as a radio wave or as quantum-scale objects, called photons. Classical waves spatially propagate through a medium. At a certain time instant, a classical wave is at different locations. Depending on the location, the superposition of waves is either constructive or destructive. Classical particles, however, cannot be at different locations at the same time. A classical particle is located at a certain position and all of its energy is there. Although it is difficult or even impossible to provide an intuitive description of the wave-particle duality, in several key experiments it has been proven that both behaviors apply for quantic entities. As Albert Einstein and Leopold Infeld have remarked [Ein38]: “It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are

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faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do!”

10−12 γ-rays

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EUV NUV NIR MIR FIR EHF SHF UHF VHF HF

X-rays

Visible Light Spectrum

4 · 10−7

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102 MF

104 LF

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VLF ULF

All wavelengths in m

7 · 10−7

Figure 2.1 Electromagnetic spectrum.

The part of the electromagnetic spectrum which is visible by human eyes stretches from about 390 nm (770 THz) to about 720 nm (420 THz), see Fig. 2.1 [Lin97]. (This visible wavelength range is taken from the CIE 1978 eye sensitivity function, assuming a threshold of V (λ) = 10−3 . Below this threshold, the sensitivity of the human eye is very low at daylight. Sometimes other values are reported, e.g. 380-780 nm or 380-825 nm.) The relationship between the wavelength λ (in m) and the frequency f (in Hz) is given as f = c/λ,

(2.1)

where c is the speed of light (c ≈ 3 · 108 m/s in vacuum). Correspondingly, the useful bandwidth is approximately 350 THz – much wider compared to traditional radio bands. Additionally, the ultraviolet (UV) spectrum and the infrared (IR) spectrum can be partly used for data transfer. Consequently, the channel capacity (which is defined as the maximum data rate at which information can be transmitted virtually error free) and hence the theoretical throughput is extremely large. In OWC systems, nowadays usually solid-state light sources including LEDs and lasers are used. LEDs are available between about 200 nm (UV-C) and several thousands of nano meters (MIR range), lasers for an even larger wavelength range. Albeit ultra-wideband signaling is possible, practical data rates in OWC systems currently are much smaller than promised by channel capacity. This serves as a strong motivation for future research, both in photonics and communications. The perceptual light spectrum is, for example, visible in a rainbow, or when white light hits a prism, see Fig. 2.2.

2.2

Color Mixing

There are two possibilities of color mixing [Fal86]: additive mixing and subtractive mixing, respectively. Additive mixing is when two or more light beams superimpose. Red, green and blue (RGB) are called the three primary colors in additive mixing. When all three primary colors are superimposed in equal amount, the result is white. When none of these

2.2 Color Mixing

Figure 2.2 Decomposition of the light spectrum by means of a prism.

colors superimpose, the result is black. Neutral gray is a mixture of white and black. Pure colors are those of a rainbow, they are monochromatic. A tint/tone/shade is a mixture of pure colors with only white/gray/black added – the color is unchanged but lighter/less vibrant/darker than the original color. Secondary colors are obtained, when two primary colors are superimposed in equal amount: red plus green results in yellow, green plus blue assembles cyan, and blue plus red gives magenta, cf. Fig. 2.3. Therefore, yellow, cyan, and magenta (YCM) are the three secondary colors in additive mixing.

Figure 2.3 Subtractive mixing (left) vs. additive mixing (right).

Physically, the original wavelengths are preserved in additive mixing. This fact needs to be taken into account when choosing a proper light source. For example, let us assume that cyan light offers best propagation conditions for underwater communications. In this case, cyan light should not be obtained by mixing light generated by monochromatic green and

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blue light sources, because two spectral lines are preserved in this case (which are subject to attenuation in seawater), as opposed to a single spectral line in the cyan regime. Because white light is a mixture of colors (for example red, green, and blue), white light cannot be expressed by a single wavelength. It is common to define the color of white light by means of the color temperature [Sch18]. The color temperature of a light source is the temperature (in K) of a black-body radiator that radiates light of comparable chromaticity to that of the light source under investigation. According to DIN 5035, temperatures below 3300 K are called warm colors, temperatures between 3300-5000 K are neutral white, whereas temperatures above 5000 K are considered to be cool colors. (In the next section, the so-called chromaticity diagram according to CIE 1931 will be introduced. It is illustrative to assign the color temperature in the chromaticity diagram, as done in Fig. 2.6, or in similar diagrams. Strictly speaking, the definition of color temperature only holds for thermal radiators. A generalization which includes solid-state white light sources is provided in Section 2.4.) An ideal black-body radiator does not exist. The blackest artificial substance known today is dubbed vantablack [The12]. This substance made of vertically aligned nanotube array (VANTA) coatings is claimed to absorb up to 99.965 % of radiation in the visible spectrum. A spray-on version marketed as Vantablack S-VIS [May16] is said to have a reflectance of typically 0.2 % in the visible spectrum. For some people, additive mixing is counter-intuitive, because yellow plus blue does not result in green, as we are used to in painting. This problem is solved by the definition of subtractive mixing. Subtractive mixing refers to the mixing of substances (like paint), rather than the mixing of light. In subtractive mixing, the three primary colors are yellow, cyan, and magenta (entitled YCM primaries). When all three primary colors are superimposed in equal amount, the result is black. When none of these colors superimpose, the result is white. The secondary colors are obtained, when two primary colors are superimposed in equal amount: yellow plus cyan results in green, cyan plus magenta results in blue, and magenta plus yellow gives red, cf. Fig. 2.3. Therefore, red, green, and blue are the three secondary colors in subtractive mixing. The notion “subtractive” can be explained by the following example: cyan light is obtained by an additive mixing of green and blue light. A cyan substance, paint for example, absorbs all colors except for green and blue. Green paint absorbs particularly blue color. Hence, it can be said that the green paint subtracts the blue from the cyan paint. Complementary colors are pairs of color which cancel out in additive mixing, like red plus cyan, green plus magenta, and blue plus yellow. In the chromatic circle (“color wheel”), complementary colors are antipodal, see Fig. 2.4. Colors with opposite characteristics are said to have a large color contrast. Contrariwise, the tone contrast is defined as the difference in tones, from white to black. It is interesting to note that magenta is not included in the natural light spectrum. Magenta is an additive mixture of blue and red color, as mentioned before. Magenta completes the chromatic circle in the sense that it connects the red with the blue region. Furthermore, it is worth mentioning that additive mixing is used in LED technology: the principle of additive mixing is used in RGB LEDs in order to obtain white light. The same statement holds for blue LEDs with yellow phosphor coating made of yttrium aluminum garnet (YAG), sometimes referred to as converted LEDs.

2.3 CIE, RGB, and HSV Color Spaces

Figure 2.4 Chromatic circle. Complementary colors are antipodal.

2.3

CIE, RGB, and HSV Color Spaces

A color model is a mathematical description of colors as numbers. A color space is a multi-dimensional representation of all colors which can be generated by the chosen color model. Color models and spaces are used in many applications/devices, including photography, video processing, displays, printers, and graphics software, etc. Theoretically, the number of color spaces is infinite. Some thirty different color spaces are currently used in technical use cases. In order to focus on the main principles, we will concentrate on three important examples [Fal86, Kuc03]: ■

CIE 1931 XYZ color space,

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RGB color space, and

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HSV color space.

Many modifications exist, a few are mentioned subsequently.

2.3.1

CIE 1931 XYZ Color Space

The first colorimetric standard dates back to the year 1931, established by the International Commission on Illumination (Commission Internationale de l’Eclairage, CIE). The CIE 1931 XYZ color space (or CIE 1931 color space for short) is the first color space based on measurements of the human color perception. It is the basis of all other color spaces, because it considers all colors visible by the human eye, although with modern equipment and methods slightly different perception curves and additional insights have been gained. ¯ ¯ In the CIE 1931 standard, three standard colorimetric observer functions x(λ), y(λ), and ¯ z(λ), also known as color-matching functions, have been specified [Sch07]. These observer functions, plotted in Fig. 2.5, have been determined by subjective experiments with test candidates, and subsequently tabulated in 5 nm steps. Colorimetric sensitivity is diverse from person to person. For example, some individuals have four different cone cells, rather than three (RGB) as most people. Other people have an impaired color vision. The three

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standard colorimetric observer functions represent the spectral responsivity of the photoreceptors in the human retina averaged over the set of test candidates. Data is based on the equipment and methods available in 1931. 2 x(λ) y(λ) z(λ) 1.5 Observer functions

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Figure 2.5 CIE 1931 standard colorimetric observer functions.

Given a light source of a certain color characterized by the radiance L(λ) (to be defined in Section 2.5), so-called tristimulus values X , Y , and Z can be obtained by computing the inner products Z 780 nm ¯ X = L(λ) · x(λ) dλ 380 nm 780 nm

Z Y Z

= =

380 nm Z 780 nm 380 nm

¯ L(λ) · y(λ) dλ ¯ L(λ) · z(λ) d λ.

(2.2)

The values X and Z represent the chrominance (with emphasize on Z in the blue regime), whereas Y represents the luminance (= brightness). The reason for the latter fact is the ¯ observation that y(λ) is identical with the eye sensitivity curve V (λ). Therefore, the X − Z plane contains all possible chromaticities at a given luminance Y . The tristimulus values X Y Z are device independent. The tristimulus values X Y Z can be normalized as [Sch07] x=

X , X +Y + Z

y=

Y , X +Y + Z

z=

Z . X +Y + Z

(2.3)

The scaled coefficients x y z are called chromaticity coordinates. Note that x + y + z = 1, therefore z can be expressed by x and y as z = 1 − x − y. Accordingly, all three chromaticity coordinates x y z can completely be represented by the two-dimensional chromaticity diagram drawn in Fig. 2.6. In this two-dimensional projection of the tristimulus values X Y Z , y is plotted versus x. The convex hull (i.e., the curved border) of the visible range is ∩-shaped. The set of visible colors is named visible color gamut. Colors outside the

2.3 CIE, RGB, and HSV Color Spaces

visible range are virtual. Points on the convex hull are pure spectral colors. The spectrum locus is sometimes called laser locus, because laser light ideally is monochromatic. The corresponding wavelengths are pointed out in the figure. With the exception of the magenta region at the bottom, these are the colors of the rainbow. The dashed line in Fig. 2.6 connecting violet and far red is known as the purple line. Any straight line between two arbitrary coordinates inside or on the convex hull resolves all colors that can be produced by mixing the colors specified by the two points. Consequently, any color can be obtained in different ways by means of additive color mixing.

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Figure 2.6 CIE 1931 xy chromaticity diagram.

In the chromaticity diagram depicted in Fig. 2.6, the so-called Planckian locus is included, displayed by the bended line crossing the center of the visible color gamut. Any (white) light source whose chromaticity coordinates lie directly on the Planckian locus has a color temperature equal to the black-body temperature of the Planckian radiator [Are07]. In simple words, the Planckian locus is the color temperature curve of a black-body radiator. In the figure, the Planckian locus is labeled by selected color temperatures. In color science, the spectral power distribution (SPD) of a light source is a measure of the power per unit area contributed per unit wavelength. For a given illuminant (characterized by a certain SPD), the white point is the chromaticity of a white object. Hence, the white point depends on the chosen illuminant. Numerous standard radiators have been defined. For an equal-energy illuminant with flat SPD, called illuminant E, the white point is defined by the coordinates [x, y] = [1/3, 1/3]. These CIE 1931 coordinates are in agreement with a temperature of 5454 K. For the CIE D-series standard illuminant D65, the white point has coordinates [x, y] = [0.3127, 0.3290]. Standard illuminant D65 resembles overcast-sky daylight, which has a spectrum similar to that of a black body with a temperature of 6504 K. CIE

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illuminant A models an incandescent light source, corresponding to a Planckian radiator at 2856 K. The equivalent coordinates are [x, y] = [0.4476, 0.4074]. The relative SPD of these selected standard illuminants is plotted in Fig. 2.7. A relative SPD is normalized so that at a reference wavelength (usually 555 nm or 560 nm) the power ratio is one. This simplifies a comparison of diverse light sources. For single-color light sources or illuminants with line spectrum, alternatively the peak wavelength frequently is taken as a reference. Illuminants based on thermal radiation naturally lie on the Planckian locus, whereas non-thermal processes like solid-state lighting normally have coordinates outside the Planckian locus. 3 CIE Illuminant A CIE Illuminant D65 CIE Illuminant E

2.5 Relative spectral power distribution

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Figure 2.7 Relative spectral power distribution of CIE standard illuminants A, D65, and E.

Note again that the CIE 1931 xy chromaticity diagram is a two-dimensional projection rather than a complete color space. This diagram splits hue and saturation (to be defined in Section 2.3.3) from brightness. If the luminance Y is considered additionally, the CIE 1931 XYZ color space is retrieved. The color space determined by x, y, and Y is entitled CIE xyY color space. Given x, y and Y , the tristimulus values X and Z can be recovered by X = x · Y /y and Z = (1 − x − y) · Y /y. The CIE 1976 L*, u*, v* (CIELUV) color space is a transformation of the 1931 CIE XYZ color space with improved perceptual uniformity.

2.3.2

RGB Color Space

Motivated by the principle of additive color mixing, the RGB color space is based on the primary colors red, green, and blue in order to generate a variety of other colors. The RGB color space is a linear color space that can be represented as a cube, see Fig. 2.8. The edges of the cube are either labeled by float numbers defined over the interval [0, 1], where 0 corresponds to 0 % and 1 means 100 %, or by integer numbers defined for instance over the set [0, 255], corresponding to an 8-bit tuple. The three primary colors, determined by their wavelength, form a (color) triangle in the chromaticity diagram. Only colors within or on the border of this triangle can be generated by additive color mixing. This subset of

2.3 CIE, RGB, and HSV Color Spaces

colors is the primary color space and is dubbed color gamut of the primaries or simply gamut. R R+ R

Black

G

B+ +

G

B-

B

White

G R-

B

G

Figure 2.8 RGB color space.

In the year 1931, the following monochromatic primary colors (called primaries for short) have been used: ■

Red: 700 nm,

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Green: 546.1 nm,

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Blue/violet: 435.8 nm.

The exact wavelength for red is not critical. The green and blue monochromatic colors are easily reproducible lines of a mercury vapor discharge. The CIE 1931 primaries span a large triangle in the chromaticity diagram with coordinates ■

Red: [x, y] = [0.73, 0.27],

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Green: [x, y] = [0.27, 0.72],

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Blue: [x, y] = [0.17, 0.01].

In the meantime, other primaries have been proposed. For example, in the so-called standard RGB (sRGB) color space, the following chromaticity coordinates have been specified: ■

Red: [x, y] = [0.64, 0.33],

■

Green: [x, y] = [0.30, 0.60],

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Blue: [x, y] = [0.15, 0.06].

The corresponding gamut is much smaller, particularly some colors in the green regime cannot be generated, cf. Fig. 2.9. On the other hand, sRGB is simple to implement in printers, displays, and other technical devices.

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Figure 2.9 Gamut of the sRGB color space within the CIE 1931 xy chromaticity diagram.

Concerning the transform from RGB coordinates to CIE XYZ values (and vice versa), for each specific RGB color space a unique matrix exists. For the sRGB color space the transform is   X 0.4124  Y  =  0.2126 Z 0.0193 

0.3576 0.7152 0.1192

   0.1805 R 0.0722  ·  G  , 0.9505 B

(2.4)

and   R +3.2406  G  =  −0.9689 B +0.0557 

−1.5372 +1.8758 −0.2040

   −0.4986 X +0.0415  ·  Y  +1.0570 Z

(2.5)

is the inverse transform. After the linear transformation, occasionally some nonlinear (“gamma”) correction is applied.

2.3.3

HSV Color Space

In the HSV color space, color is defined by hue, saturation, and value as follows: ■

The hue H is an angle on the chromatic circle (0◦ corresponds to red, 120◦ corresponds to green, and 240◦ corresponds to blue), as illustrated on the left-hand side in Fig. 2.10. Hue and chromaticity coincide.

2.3 CIE, RGB, and HSV Color Spaces

■

■

The saturation S is measured in percent (0 % corresponds to neutral gray, 50 % to a medium saturation, and 100 % to a pure color) or defined over the interval [0, 1]. The value V is measured in percent (0 % corresponds to “off”, 50 % to medium brightness, and 100 % to full brightness) or defined over the interval [0, 1]. Value and luminance are the same.

The HSV color space applies cylindrical coordinates, which can be represented by the cone shown on the right-hand side in Fig. 2.10.

(a) Chromatic circle

(b) HSV cone

Figure 2.10 Chromatic circle (left) and HSV cone (right).

Prominent alternatives of the HSV color space are the HSL color space (L stands for luminance/brightness) and the HSI color space (I stands for intensity). The transform from the RGB color space to the HSV color space is as follows. Let us define R,G, B ∈ [0, 1], M AX := max(R,G, B ), and M I N := min(R,G, B ). Neglecting pathological cases like M AX = M I N , the transform is ¡ ¢  G−B ◦ if M AX = R  60 · ¡0 + M AX −M I N ¢ 60◦ · 2 + M AXB −R if M AX = G H = −M I N ¢ ¡  R−G if M AX = B 60◦ · 4 + M AX −M I N S

=

V

=

M AX − M I N M AX M AX .

(2.6)

The back-transform from the HSV color space to the RGB color space is as follows. Let ¥H ¦ and us specify H ∈ [0◦ , 360◦ ), S ∈ [0, 1], and V ∈ [0, 1]. We calculate the interval i := 60 ◦ H the value h := 60 ◦ − i within the interval i , where h ∈ [0, 1]. Moreover, we calculate three auxiliary variables v 1 := V · (1 − S), v 2 := V · (1 − S · h), and v 3 := V · (1 − S · (1 − h)). The back-transform is  if i = 0   [V, v 3 , v 1 ]    [v 2 ,V, v 1 ] if i = 1    [v ,V, v ] if i = 2 1 3 [R,G, B ] = (2.7)  [v 1 , v 2 ,V ] if i = 3     [v 3 , v 1 ,V ] if i = 4    [V, v 1 , v 2 ] if i = 5.

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2.4

Color Quality

In illumination engineering, color quality is of primary interest. As mentioned above, combining light with different intensities (“additive color mixing”) can produce light that appears to be white to the human eye. Distinct wavelength combinations exist so that the light emitted by various light sources appears to have the identical color (in terms of the color temperature). But the effects of these light sources on objects may be quite different. For this reason, it is meaningful to have a closer look at color temperature, spectral power distribution, and additional measures like color rendering. Recall that the color temperature of a white light source is the temperature of a black-body radiator whose hue best matches with that of the light source under investigation, subject to the constraint that the chromaticity coordinates of the light source lie exactly on the Planckian locus. Incandescent and halogen light bulbs are thermal radiators. Thermal radiators fit well to the definition. Solid-state lighting sources, however, emit light essentially by non-thermal processes. For white light sources having chromaticity coordinates near the Planckian locus, the so-called correlated color temperature (CCT) is more appropriate. The CCT is defined as the temperature (in K) of a black-body radiator which is, in the CIE chromaticity diagram, closest to the chromaticity of the light source under investigation [Are07]. Trajectories with constant CCT are straight lines crossing the Planckian locus, as plotted in Fig. 2.6. The CCT provides a reasonable indication of the appearance of artificial white light, between cool and warm as defined above (2700-6500 K). However, the CCT does not provide information about the spectral power distribution. The spectral power distribution (SPD) of an illuminant is a graphical representation of the emitted power vs. wavelength, per unit area and unit wavelength, radiated by the light source. SPDs can be measured by spectrophotometers. Typical spectral resolutions of handheld spectrometers are 1-10 nm. Additionally, micro-spectrometers are available. They have a worse spectral resolution, for example 15 nm, but are as compact as a fingertip and cheap, and therefore suitable as sensor nodes in smart lighting applications. In Fig. 2.11, the relative SPD is depicted for eight different light sources, normalized at 555 nm. All measurements have been performed with a Gigahertz-Optik BTS256-EF spectral light meter achieving a resolution of 1 nm. (a) The SPD of an RGB LED light source is characterized by three distinct spectral peaks. Here, no attempt is made to tune the peak intensities of the three colors. (b) In the SPD of an off-the-shelf high-quality warm white LED light bulb, a narrow peak in the blue range is visible caused by the blue LED. The main peak is shifted to the green and yellow region by means of YAG coating. (c,d) The SPD of incandescent, halogen and xenon light sources is characterized by thermal radiation – the spectral distribution is a monotonically increasing function of wavelength. The spectral distribution well matches with that of CIE standard illuminant A shown in Fig. 2.7. (e) Candle light is based on thermal radiation as well, but red is even more prevailing. Note the characteristic spectral peak at about 770 nm. (f ) The spectral distribution of a smartphone homescreen is similar to an RGB LED, the blue portion is dominant. For this reason, extensive smartphone use at nighttimes is problematic, unless a blue light filter is activated. (g) The SPD of overcast-sky daylight is pretty flat in the visible wavelength range, it is well modeled by CIE standard illuminant D65. (h) Contrarily, the SPD of a fluorescent light source has noticeable peaks. Mercury vapor lamps (not illustrated here) are characterized

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Relative spectral power distribution

Relative spectral power distribution

2.4 Color Quality

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Figure 2.11 Measured relative spectral power distributions of different light sources.

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by narrow spectral lines as well. Although the SPD provides a detailed picture of the spectral components of light sources, it does not disclose all effects of light on objects. Besides CCT and SPD, the color quality depends on color rendering. According to the CIE, color rendering is the “effect of an illuminant on the color appearance of objects by conscious or subconscious comparison with their color appearance under a reference illuminant” [Sch07]. The color rendering index (CRI) and related indices (like the television lighting consistency index (TLCI) or the gamut area index (GAI)) are quantitative measures of the aptitude of a light source to display the colors of manifold objects authentic in comparison with a black-body radiator or daylight, respectively. The CRI represents the ability of a light source to render the colors of an object realistically. A high CRI is desirable, preferably between 80-100. Natural daylight has a CRI of 100. In white LEDs, the CRI as well as the CCT are adjusted during fabrication by the YAG concentration. The motivation for defining the CRI and related indices is that the spectrum of natural light is homogeneous and wideband, whereas artificial light sources frequently produce a line spectrum, rather than generating the entire visible color gamut. Therefore, the colors of objects spotted by an observer typically appear different when illuminated with artificial light sources. In order to suppress the influence of spectral lines, some RGB LEDs are supplemented by a white LED. Still, the light spectrum is incomplete. The future is wideband illumination.

2.5

Candela vs. Lumen vs. Lux

The task of an electric light source is to convert electrical power into photons. The radiated optical power can be measured as ■

radiometric value in Watt (W), or as

■

photometric value in lumen (lm).

It is interesting to mention that the radiometric value typically is documented for violet/royal-blue LEDs and for deep-red/far-red LEDs only. For colors in-between the photometric value is often mentioned in datasheets. Correspondingly, a conversion between these two measures is necessary. The conversion depends on the ■

photometric eye sensitivity, and on the

■

luminous efficacy.

Four essential photometric quantities measured in SI units are defined in the following way [Sch18, Kos13]:

The luminous intensity I V is defined as follows: a monochromatic light source emitting an optical power of 1/683 W at a wavelength of 555 nm into a solid angle of one steradian (sr) has a luminous intensity of 1 candela (cd).

2.5 Candela vs. Lumen vs. Lux

It is helpful to imagine that a standard plumber’s candle causes a luminous intensity of 1 cd, although this former definition of the luminous intensity is obsolete.

The luminous flux ΦV is defined as follows: a monochromatic light source radiating an optical power of 1/683 W at a wavelength of 555 nm has a luminous flux of 1 lumen (lm). Note that 1 cd = 1 lm/sr.

An isotropic light source with luminous intensity of 1 cd has a luminous flux of 4π lm.

The illuminance E V (measured in lux) is the luminous flux per unit area, i.e., 1 lux = 1 lm/m2 .

Typical values of the illuminance are summarized in Table 2.1. It should be recognized that the difference between moonlight and sunlight differs by five orders of magnitude. The human eye has a logarithmic characteristic and is able to adjust to this wide range of variation. Photodetectors, however, have problems to resolve artificial light when observed in bright sunlight. Table 2.1 Typical values of illuminance for selected environments [Sch18]. Environment

Illuminance

Full moon

1 lux

Street lighting

10 lux

Home lighting

30-300 lux

Office desk lighting

102 -103 lux

Surgery lighting

104 lux

Direct sunlight

105 lux

The luminance L V (in cd/m2 ) of a surface source (like a display or a flat LED chip) is the ratio of the luminous intensity emitted in a certain direction (measured in cd) divided by the projected surface area in that direction (measured in m2 ). Often, the direction of interest is perpendicular to the display or chip surface. For so-called Lambertian sources the luminance is angle-independent.

Typical values of the luminance are summarized in Table 2.2. Table 2.2 Typical values of luminance for selected devices [Sch18]. Device

Luminance

Display

102 -103 cd/m2

OLED

102 -104 cd/m2

III-V LED

106 -107 cd/m2

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In the illumination engineering community, photometric quantities are most relevant: a bright light source emitting in the IR or the UV range simply is useless for lighting, because the emitted photons cannot be detected by the human eye. In the area of OWC, the opposite is true: the received optical and hence also the electrical power (measured in W) is of primary interest. Table 2.3 highlights the relationship between photometric quantities and corresponding radiometric quantities. Table 2.3 Relation between photometric quantities and corresponding radiometric quantities. The suffix “v” stands for “visual”. Photometric quant.

Unit

Radiometric quantities

Unit

Luminous flux ΦV

lm

Radiant flux Φe (radiated opt. power)

W

Luminous intensity I V

lm/sr=cd

Radiant intensity I

W/sr

Illuminance E V

lm/m2 =lux

Irradiance E (power density)

W/m2

Luminance L V

lm/(sr m2 )=cd/m2

Radiance L

W/(sr m2 )

Radiometric values can be converted into photometric values given the so-called eye sensitivity function V (λ), 0 ≤ V (λ) ≤ 1, also named luminosity function or luminous efficiency function. The eye sensitivity function can only be determined by subjective experiments with test candidates. For point-like light sources and a viewer angle of 2◦ , in 1924 the CIE has released a reference curve, nowadays called CIE 1931 eye sensitivity function, V (λ) [Sch07]. This function is valid for daylight (> 3 cd/m2 ), known as photopic vision regime, and has its maximum at 555 nm. In 1978, modified data have been published, because the CIE 1931 data underestimates the sensitivity at wavelengths below 460 nm. The modified reference curve is known as the CIE 1978 eye sensitivity function [Sch07]. Although this modified function is more accurate in the violet regime, the CIE 1931 standard is still in use. At low ambient light (< 3 · 10−3 cd/m2 ), called scotopic regime, the eye sensitivity shifts to lower wavelengths. This is due to the fact that in the retina, rod light receptors are more light-sensitive than cone cells. At nightlight, the eye sensitivity has its maximum at 507 nm. The corresponding function V ′ (λ) has been released in the CIE 1951 standard. In Fig. 2.12, all three eye sensitivity functions are plotted. Besides rod cells and cone cells, the human retina hosts a third type of photoreceptor: socalled melanopsin-containing retinal ganglion cells. These trigger sleep promoting hormones (melatonin) as well as stress hormones (cortisol), and hence affect our circadian rhythm. The conversion of radiometric values to photometric values is as follows [Sch18]:

For arbitrary sources, the luminous flux (in lm) is obtained as ΦV = 683

lm W

Z

825 380

nm

nm

V (λ) Φ(λ) d λ,

(2.8)

where Φ(λ) is the spectral power distribution (SPD), i.e., the radiated light power per unit wavelength, and P T, opt is the radiated optical power: Z P T, opt =

825 380

nm

nm

Φ(λ) d λ.

(2.9)

2.5 Candela vs. Lumen vs. Lux

0

Eye sensitivity function V(λ)

10

CIE 1931 (photopic vision) CIE 1978 (photopic vision) CIE 1951 (scotopic vision)

-1

10

-2

10

-3

10

300

350

400

450

500

550 600 650 Wavelength λ in nm

700

750

800

850

900

Figure 2.12 Eye sensitivity functions according to CIE 1931, CIE 1978, and CIE 1951.

Below 380 nm and above 825 nm all CIE data is zero. For monochromatic sources, the conversion simplifies and becomes bidirectional: ΦV = 683

lm V (λ) P T, opt W

⇔

P T, opt =

ΦV . lm 683 V (λ) W

(2.10)

The luminous efficacy of optical radiation (in lm/W) is defined by the CIE as K := ΦV /Φe .

(2.11)

It is a measure of how well a light source produces visible light.

For monochromatic light sources, the luminous efficacy is equal to the eye sensitivity function V (λ) multiplied by 683 lm/W. Consequently, for monochromatic light sources the maximum is 683 lm/W, obtained for an ideal monochromatic 555 nm source. For nonmonochromatic light sources, the theoretical maximum is less. For a black-body radiator, for example, the theoretical maximum is 348 lm/W at 5800 K color temperature. The dimensionless luminous efficiency of a source is frequently defined as K /(683 lm/W).

In the lighting community, the luminous efficacy of a source (in lm/W) is defined as η V := ΦV /P T, el .

(2.12)

It is a measure of the perceived power of light normalized by the electrical power P T, el consuming the light source.

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The wall-plug efficiency (also called radiant efficiency) is often defined as η el := Φe /P T, el .

(2.13)

It is a measure of the overall efficiency. Sometimes, η el includes the efficiency of the driver (plus cooling, if applicable) and the loss caused by the optics (lenses, filters).

K , η V , and η el (and related measures like the quantum efficiency) are key parameters in judging how well a light source converts electrical power into light. Note that η V = K · η el . Modulating an LED/laser for the purpose of OWC degrades the luminous efficacy [Len17].

2.6

Dimming

In order to control the illumination, commonly referred to as dimming, naturally one would adjust the current and/or the voltage of the electric light source. This, however, comes at additional hardware cost. Both for LEDs and lasers, it is simpler to control the so-called duty cycle δ. Let us assume for simplicity that the light is periodically switched “on” and “off”. Then, the duty cycle refers to the “on” period divided by the “on-plus-off” period. For example if δ = 0.9, the light is on for 90 % of the time. The relationship between the measured light intensity (controlled for instance by the duty cycle) and the light intensity perceived by human eyes is nonlinear. It is given as [Rea00] s Perceived light in % = 100 ·

Measured light in % . 100

(2.14)

For example if δ = 0.5 (50 % duty cycle), the perceived intensity is about 71 %. For δ = 0.01 (1 % duty cycle), the perceived intensity is still 10 %. This relation is depicted in Fig. 2.13 on the left-hand side. It needs to be taken into account in any dimming design. 100

100

90

Mod% = 0.08 f/Hz 80

Modulation depth in %

Perceived intensity in %

34

70 60 50 40 30

10

Recommended operating area

1

Mod% = 0.025 f/Hz

20 10 0

0

10

20

30

40

50

60

70

Measured intensity in %

(a) Dimming

80

90

100

0.1 1

10

100

1000

10000

Frequency in Hz

(b) Flicker

Figure 2.13 Relation between perceived intensity and measured intensity (left). Recommended operating area for avoiding harmful flicker [IEEE1789] (right).

2.7 Flicker

In practice, it is not relevant whether the light is switched “on” and “off” truly periodically or not. In effect, any flicker should be avoided. We will come back to dimming when introducing modulation techniques in Chapter 4 and the IEEE 802.15.7 standard in Chapter 6.

2.7

Flicker

In OWC, any harmful impact on the human eye/brain ought to be avoided. This refers to eye safety, particularly when using IR, UV, or collimated laser beams, but also to flicker as well as to psychological and biological effects. Flicker, occasionally called flutter or shimmer, are “variations of luminance in time” [IEEE1789]. The reasons of flicker is manifold: sometimes flicker is caused by the AC supply, sometimes by the construction of the light source, sometimes by the driver circuit. Often, flicker is periodic. In OWC, an additional source of flicker is the digital modulation of the light source. Fluctuations in light intensity due to data transmission should be minimized. This is possible by means of sophisticated modulations schemes, like metameric modulation. Flicker can cause serious health problems. Flicker may lead to headache, fatigue, and reduced visual performance, in extreme cases even nausea or epilepsy. Most people probably have experienced flicker. An illustrative example is the stroboscopic effect of an oscillating light source. In office and home environments flicker is serious, because exposure time is typically long. In industrial workspaces, flicker may be even fatal, because the stroboscopic effect can give workers the wrong impression that fast moving machinery appears to be slow or even still. (Note the analogy between the stroboscopic light and sampling: according to the sampling theorem, a low sampling rate causes aliasing.) Flicker is also subject in TV sets. By choosing frame rates of 200 Hz and beyond, most problems can be avoided, however. Flicker caused by digital modulation may be severe for two reasons. One reason is the flicker amplitude, the other the flicker frequency. These are two important parameters that have impact on the human brain. In digital modulation, the amplitude fluctuations are normally much larger than for classic sources of flicker, like the AC power supply. Secondly, in the digital modulation long runs of zeros or ones may happen, causing lowfrequency flicker. Low-frequency flicker is particularly harmful. For flicker avoidance, the “on/off” period must be shorter than the so-called maximum flickering time period (MFTP) [Ber91]. For example, a frequency of 200 Hz corresponds to an MFTP of 5 ms. Concerning the impact of flicker on the brain numerous experiments have been conducted, see [Her01] for instance. As a result, recommended practices for modulating current in high-brightness LEDs have been proposed by IEEE in order to mitigate health risks to viewers [IEEE1789]. The recommended practices summary is illustrated in Fig. 2.13 on the right-hand side, where the modulation depth (in %) as a measure for the flicker amplitude is plotted versus the flicker frequency (in Hz). Modulation depth is defined as the difference between maximum and minimum luminance divided by the sum of maximum and minimum luminance (multiplied by 100). Frequency is the repetition rate of period patterns. The recommended operating area is shown on the right-hand side. For frequencies above 1250 Hz, i.e. MFTPs ≤ 0.8 ms, flicker is harmless for most people, independent of its amplitude.

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2.8

Human Centric Lighting

Supplementary to visual effects, light quality and light fluctuations are reported to provoke psychological and biological effects [Pop16]. Psychological effects have an impact on mood, feelings, motivation, and emotions. Biological effects are generated by stress hormones (cortisol) and sleep promoting hormones (melatonin). The circadian rhythm that regulates the cortisol and melatonin levels is affected by (mostly blue) light: “Circadian disruptions, including decrease of melatonin levels, have been suggested to play an important role in development of chronic diseases and conditions such as: cancer, cardiovascular diseases, reproduction, endometriosis, gastrointestinal and digestive problems, diabetes, obesity, depression, sleep deprivation, and cognitive impairments” [Pop16]. As a consequence, any impact of data modulation on the light quality should be avoided. Human centric lighting (HCL) is the framework of considering health, productivity, and emotional comfort of people by a personalized control of light sources [Wal14]. Light quality (including spectral contents, intensity, and timing of light exposure) is an essential recipe of HCL, and should be matched to our circadian rhythm. Working hours should be supported by cool light (> 5000 K, > 1000 lux), working breaks and lunch time by reduced color temperature, and evening hours by warm light (< 3000 K, < 1000 lux) avoiding blue portions. Concerning the light sources, a consideration of the SPD over the entire VIS range is important in the context of HCL, rather than just looking at the CCT (since the same CCT can be obtained by mixing light in different ways). But also the positioning of the light sources (i.e., the directivities of the light waves) play an important role, as melanopsincontaining retinal ganglion cells are said to be concentrated in the lower half of the human retina. Hence, downlight is preferable. Besides health/productivity/emotional comfort, HCL has an often ignored impact on safety at work [Lan18] and at home. The combination of HCL and VLC has not yet been studied in detail [Che17, Hig18], but it is believed that VLC is an enabling technique towards personalizing light quality, coined human centric Li-Fi (HCLiFi) in [Hoe19]. HCLiFi employs intensity-modulated multi-channel wideband light sources for the objective of simultaneous illumination and data transfer. The spectral components of the light must be controllable individually. This can be achieved by using a sufficient number of narrowband colored LEDs per light source covering the entire VIS range. Supplementary IR/UV LEDs are optional, as well as white LEDs. Although being intensity modulated by the data, highest color quality constraints must be fulfilled – for example by means of metameric modulation (to be introduced in Chapter 4). The SPD emitted by the modulated light sources, together with daylight and other light sources, is measured preferably near a target person. The differences between the measured SPD and the target SPD (sampled at the peak wavelengths of the LEDs) are used in order to adapt the spectral intensities of the light sources. The measured SPD is should be sufficiently smoothed. The slowly time-varying target SPD is matched to the circadian rhythm of the target person, both with respect to brightness and spectral distribution. The technology of the uplink is arbitrary, IR and RF radio are just two examples. HCLiFi inherently includes personalized daylight harvesting. If the daylight is strong enough, emission in the VIS range is stopped automatically, and data transfer may be via the supplementary IR/UV LEDs.

2.9 Chapter Summary

2.9

Chapter Summary

Illumination engineering manifests foundations of VLC with respect to light quality and related measures. This area is often overlooked in the modulation and signal processing literature. According to the wave-particle duality, light can be either described as a wave or as photons. The bandwidth of the visible light spectrum is about 350 THz – much wider than traditional radio bands. In some applications, additionally UV or IR light is applicable, extending the bandwidth even further. Concerning color mixing, it is important to distinguish between additive mixing (of light) and subtractive mixing (of substances). Additive mixing of the three primaries RGB results in white, whereas subtractive mixing of the three secondary colors YCM gives black. The color of white light is commonly defined as the temperature of a black-body radiator. Color temperatures below 3300 K/between 3300-5000 K/above 5000 K are called warm/neutral/ cool white, respectively. The chromatic circle complements the colors of the rainbow by purple. Complementary colors are antipodal in the circle. A color space is a graphical illustration of representable colors. The CIE 1931 XYZ color space is based on standard observer functions. It is common to normalize the tristimulus values X Y Z , and to depict the normalized x y coordinates in a chromaticity diagram. Human perception of color can be represented in a two-dimensional space, for instance the CIE 1931 xy chromaticity diagram, albeit three primary colors exist. Monochromatic colors shape the boundary of this chromaticity diagram, referred to as visible color gamut. Given the x y coordinates of two light sources inside or on the visible color gamut, any color along the connecting line is representable. Consequently, any color inside or on a triangle spanned by three LEDs, known as color gamut of the primaries, is producible by color mixing. The x y coordinates of a black-body radiator is called Planckian locus. Points along the Planckian locus are white points of a thermal radiator. Non-thermal illuminants, like white LEDs, are characterized by the correlated color temperature instead. Other popular color spaces are the RGB color space and the HSV color space, including modifications thereof. Color quality includes the following measures: (correlated) color temperature, spectral power distribution, and color rendering. The spectral power distribution of a light source is a graphical representation of the emitted power vs. wavelength, per unit area and unit wavelength. Different illuminants have different spectral power distribution. Color rendering is the effect of an illuminant on the color appearance of objects. Natural daylight is said to have a color rendering index of 100. For artificial light, the color rendering index should be between 80 and 100, and in museums above 90. The radiated optical power can be measured as radiometric value (in W) or as photometric value (in lm). Important photometric values include luminous flux (lm), luminous intensity (lm/sr), illuminance (lm/m2 ), and luminance (lm/(sr m2 )). The corresponding radiometric quantities are radiant flux (W), radiant intensity (W/sr), irradiance (W/m2 ), and radiance (W/(sr m2 )), respectively. The conversion between a photometric value and the corresponding radiometric quantity depends on the photometric eye sensitivity and the luminous efficacy. Besides the luminous efficacy, several other efficiency measures have been defined. Dimming is a necessary feature in sophisticated lighting systems. Often, dimming is achieved by controlling the duty cycle. It is interesting to note that the relation between

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measured light and perceived light is nonlinear. Careful dimming design is necessary in order to avoid flicker. Supplementary to visual effects, light quality and light fluctuations cause psychological and biological effects. Human centric lighting is able to match light parameters to our circadian rhythm, i.e., to personalize light with respect to health/productivity/emotional comfort/safety. A new concept combining HCL and VLC, coined HCLiFi, is proposed.

Problems 2-1 Particularly in conjunction with RF-based cellular radio, many people are concerned about electromagnetic pollution. (a) A boulevard newspaper article once claimed that “not just the frequencies are harmful, but additionally also the wavelengths”. Please comment on this. (b) Why is optical wireless communications obviously less harmful, although the wavelengths are much smaller? 2-2 Daylight harvesting is expected to reduce energy consumption and CO2 emission. (a) What is the theoretical foundation of daylight harvesting? (b) Explain the significance of considering the spectral domain rather than just intensities. (c) Is daylight harvesting compatible with human centric lighting? 2-3 Consider RGB coordinates R = 0.8, G = 0.5, B = 0.3. (a) Convert these RGB coordinates into CIE XYZ coordinates. (b) Convert the CIE XYZ coordinates into x y coordinates and plot them in a CIE 1931 xy chromaticity diagram. (c) Convert the RGB coordinates into the HSV color space. Finally, perform the backtransform to verify the HSV values. 2-4 Consider the CIE 1931 xy chromaticity diagram. (a) Mark monochromatic, multichromatic, and virtual colors. (b) Assume two LEDs are available: a blue LED at coordinates [0.1, 0.1] and a yellow one at coordinates [0.5, 0.5]. Estimate the corresponding wavelengths. Identify all colors which are representable by additive color mixing, both in terms of an equation as well as graphically. Is the [0.333, 0.333] white point included in the set of representable colors? (c) Why is the right-hand side of the diagram upper bounded by x + y = 1? (d) Due to hardware imperfections, like a fluctuating forward current and/or the lack of a temperature management, the actual coordinates of the emitters are time varying. What is the impact on the white point? (e) Now, we add a third LED. Design the third LED so that the gamut spans a triangle at right angles if hardware imperfections are neglected. Is it possible to specify the associated wavelength(s)?

References

(f) Explain why purple colors are visible, but not part of the rainbow. 2-5 Again, consider the CIE 1931 xy chromaticity diagram. (a) Sketch the coordinates of near UV and near IR light sources in the chromaticity diagram. (b) Mark the areas of warm/neutral/cool white LEDs in the chromaticity diagram. (c) The region of gold is centered at coordinates around [0.469, 0.443], whereas silver is centered around [0.380, 0.390], i.e. near the white point. Other colors appear to be missing in the chromaticity diagram, for instance gray and brown. How can gray and brown color be generated by additive color mixing? (d) Is it possible to toggle between gold and silver by employing just two LEDs? 2-6 Eye sensitivity functions according to CIE 1931, CIE 1978, and CIE 1951 are based on the average light perception of human beings. (a) Suppose the eye sensitivity function would be flat instead, let us say from 400 nm to 800 nm, and zero outside. What would be the influence on the luminous flux? (b) Is there any difference concerning the luminous flux grading (in lumen) of a LED? (c) Comment on the impact of well-being, if the eye sensitivity function would be rectangular? (d) Try to find out about eye sensitivity functions of some animals. 2-7 Let us explore different peculiarities of red-green color blindness, also called impaired color vision or color deficiency. (a) In the case of deuteranomaly (green-weakness), the green colorimetric observer function is shifted towards red. Vice versa, in the case of protanomaly (redweakness), the red colorimetric observer function is shifted towards green, both compared to the standard colorimetric observer functions shown in Fig. 2.5. Please identify the corresponding symptoms of people concerned. (b) In the case of deuteranopia/protanopia, the green/red colorimetric observation approaches zero. Draw the corresponding xy chromaticity diagrams. 2-8 Efficiency is important both in terms of illumination (with respect to energy consumption and CO2 emission) as well as communications (regarding the signal-to-noise ratio). (a) Elaborate on the difference between “luminous efficacy of radiation” and “luminous efficacy of a source” according to the corresponding definitions. Provide the link between these two terms. (b) Explore the efficiency of off-the-shelf white LEDs.

References [Are07] A. V. Arecchi, T. Messadi, R. J. Koshel, Field Guide to Illumination. SPIE Press, 2007. [Ber91] S. M Berman, D. S. Greenhouse, I. L. Bailey, R. Clear, T. W. Raasch, “Human electroretinogram responses to video displays, fluorescent lighting and other high frequency sources,” Optometry & Vision Science, vol. 68, no. 8, pp. 645–662, Aug. 1991.

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[Che17] I. Chew, D. Karunatilaka, C. P. Tan, V. Kalavally, “Smart lighting: The way forward? Reviewing the past to shape the future,” Energy and Building, vol. 149, pp. 180–191, 2017. [Ein38] A. Einstein, L. Infeld, The Evolution of Physics. The Cambridge Library of Modern Science, 1938. [Fal86] D. Falk, D. Brill, D. Stork, Seeing the Light: Optics in Nature, Photography, Color, Vision, and Holography. John Wiley & Sons, 1986. [Her01] C. S. Herrmann, “Human EEG responses to 1-100 Hz flicker: Resonance phenomena in visual cortex and their potential correlation to cognitive phenomena,” Experimental Brain Research, vol. 137, no. 3/4, pp. 346–353, Apr. 2001. [Hig18] J. Higuera, A. Llenas, J. Carreras, “Trends in smart lighting for the Internet of Things,” arXiv:1809.00986, Aug. 2018. [Hoe19] P. A. Hoeher, J. Mietzner, “Integrative Lichtqualität – Zukünftig mit sichtbarer Lichtkommunikation kombinierbar?” in Proc. LiTG Zukunftskonferenz Licht, Hamburg, Germany, May 2019. [IEEE1789] IEEE Standard 1789-2015, “IEEE Recommended Practices for Modulating Current in High-Brightness LEDs for Mitigating Health Risks to Viewers,” IEEE Standard Association, Mar. 2015. [Kos13] R. J. Koshel (Ed.), Illumination Engineering: Design with Nonimaging Objects. IEEE Press, 2013. [Kuc03] R. G. Kuchni, Color Space and Its Divisions: Color Order from Antiquity to the Present. John Wiley & Sons, 2003. [Lan18] G. G. Langer, N. T. Launert, “Lighting future naval ships – Mission optimized and human centric,” in Proc. 14th Int. Naval Engineering Conference and Exhibition, Glasgow, UK, Oct. 2018. [Len17] R. Lenk, C. Lenk, Practical Lighting Design with LEDs. John Wiley & Sons, 2nd ed., 2017. [Lin97] J. L. Lindsey, Applied Illumination Engineering. The Fairmont Press, 2nd ed., 1997. [May16] A. D. Maynard, “Are we ready for spray-on carbon nanotubes?” Nature Nanotechnology, vol. 11, pp. 490–491, Jun. 2016. [Pop16] W. O. Popoola, “Impact of VLC on light emission quality of white LEDs,” IEEE/OSA Journal of Lightwave Technology, vol. 34, no. 10, pp. 2526–2532, May 2016. [Rea00] M. S. Rea (Ed.), Illumination Engineering Society of North America (IESNA) Lighting Handbook. Illumination Engineering, 9th ed., 2000. [Sch07] J. Schanda (Ed.), Colorimetry: Understanding the CIE System. John Wiley & Sons, 2007. [Sch18] E. F. Schubert, Light Emitting Diodes. Cambridge University Press, 3rd ed., 2018. [The12] S. P. Theocharous, E. Theocharous, J. H. Lehman, “The evaluation of the performance of two pyroelectric detectors with vertically aligned multi-walled carbon nanotube coatings,” Infrared Physics & Technology, vol. 55, no. 4, pp. 299–305, Jul. 2012. [Wal14] S. Walerczyk, Lighting and Controls: Transitioning to the Future. Fairmont Press, 2014.