16

Human eye sensitivity and photometric quantities

The recipient of the light emitted by most visible-spectrum LEDs is the human eye. In this
chapter, the characteristics of human vision and of the human eye and are summarized, in
particular as these characteristics relate to human eye sensitivity and photometric quantities.

16.1 Light receptors of the human eye

Figure 16.1 (a) shows a schematic illustration of the human eye (Encyclopedia Britannica, 1994).
The inside of the eyeball is clad by the retina, which is the light-sensitive part of the eye. The
illustration also shows the fovea, a cone-rich central region of the retina which affords the high
acuteness of central vision. Figure 16.1 (b) shows the cell structure of the retina including the
light-sensitive rod cells and cone cells. Also shown are the ganglion cells and nerve fibers that
transmit the visual information to the brain. Rod cells are more abundant and more light sensitive
than cone cells. Rods are sensitive over the entire visible spectrum. There are three types of cone

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cells, namely cone cells sensitive in the red, green, and blue spectral range. The cone cells are
therefore denoted as the red-sensitive, green-sensitive, and blue-sensitive cones, or simply as the
red, green, and blue cones.

Three different vision regimes are shown in Fig. 16.2 along with the receptors relevant to
each of the regimes (Osram Sylvania, 2000). Photopic vision relates to human vision at high
ambient light levels (e.g. during daylight conditions) when vision is mediated by the cones. The
photopic vision regime applies to luminance levels > 3 cd/m2. Scotopic vision relates to human
vision at low ambient light levels (e.g. at night) when vision is mediated by rods. Rods have a
much higher sensitivity than the cones. However, the sense of color is essentially lost in the
scotopic vision regime. At low light levels such as in a moonless night, objects lose their colors
and only appear to have different gray levels. The scotopic vision regime applies to luminance
levels < 0.003 cd/m2. Mesopic vision relates to light levels between the photopic and scotopic
vision regime (0.003 cd/m2 < mesopic luminance < 3 cd/m2).

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 16.2 Basic radiometric and photometric units

The approximate spectral sensitivity functions of the rods and three types or cones are shown
in Fig. 16.3 (Dowling, 1987). Inspection of the figure reveals that night-time vision (scotopic
vision) is weaker in the red spectral range and thus stronger in the blue spectral range as
compared to day-time vision (photopic vision). The following discussion mostly relates to the
photopic vision regime.

16.2 Basic radiometric and photometric units

The physical properties of electromagnetic radiation are characterized by radiometric units.
Using radiometric units, we can characterize light in terms of physical quantities; for example,
the number of photons, photon energy, and optical power (in the lighting community frequently
called the radiant flux). However, the radiometric units are irrelevant when it comes to light
perception by a human being. For example, infrared radiation causes no luminous sensation in
the eye. To characterize the light and color sensation by the human eye, different types of units
are needed. These units are called photometric units.
The luminous intensity, which is a photometric quantity, represents the light intensity of an
optical source, as perceived by the human eye. The luminous intensity is measured in units of
candela (cd), which is a base unit of the International System of Units (SI unit). The present
definition of luminous intensity is as follows: a monochromatic light source emitting an optical
power of (1/683) watt at 555 nm into the solid angle of 1 steradian (sr) has a luminous intensity
of 1 candela (cd).
The unit candela has great historical significance. All light intensity measurements can be
traced back to the candela. It evolved from an older unit, the candlepower, or simply, the candle.
The original, now obsolete, definition of one candela was the light intensity emitted by a
plumber’s candle, as shown in Fig. 16.4, which had a specified construction and dimensions:

one standardized candle emits a luminous intensity of 1.0 cd .

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16 Human eye sensitivity and photometric quantities 16.2 Basic radiometric and photometric units

The luminous intensity of a light source can thus be characterized by giving the number of
standardized candles that, when combined, would emit the same luminous intensity. Note that
candlepower and candle are non-SI units that are no longer current and rarely used at the present
time.
The luminous flux, which is also a photometric quantity, represents the light power of a
source as perceived by the human eye. The unit of luminous flux is the lumen (lm). It is defined
as follows: a monochromatic light source emitting an optical power of (1/683) watt at 555 nm
has a luminous flux of 1 lumen (lm). The lumen is an SI unit.
A comparison of the definitions for the candela and lumen reveals that 1 candela equals
1 lumen per steradian or cd = lm/sr. Thus, an isotropically emitting light source with luminous
intensity of 1 cd has a luminous flux of 4S lm = 12.57 lm.
The illuminance is the luminous flux incident per unit area. The illuminance measured in lux
(lux = lm/m2). It is an SI unit used when characterizing illumination conditions. Table 16.1 gives
typical values of the illuminance in different environments.

Table 16.1. Typical illuminance in different environments.

Illumination condition Illuminance

Full moon 1 lux
Street lighting 10 lux
Home lighting 30 to 300 lux
Office desk lighting 100 to 1 000 lux
Surgery lighting 10 000 lux
Direct sunlight 100 000 lux

The luminance of a surface source (i.e. a source with a non-zero light-emitting surface area
such as a display or an LED) 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). The
luminance is measured in units of cd/m2. In most cases, the direction of interest is normal to the
chip surface. In this case, the luminance is the luminous intensity emitted along the chip-normal
direction divided by the chip area.
The projected surface area mentioned above follows a cosine law, i.e. the projected area is
given by Aprojected = Asurface cos 4 , where 4 is the angle between the direction considered and the
surface normal. The light-emitting surface area and the projected area are shown in Fig. 16.5.
The luminous intensity of LEDs with lambertian emission pattern also depends on the angle 4

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according to a cosine law. Thus the luminance of lambertian LEDs is a constant, independent of
angle.

For LEDs, it is desirable to maximize luminous intensity and luminous flux while keeping
the LED chip area minimal. Thus the luminance is a measure of how efficiently the valuable
semiconductor wafer area is used to attain, at a given injection current, a certain luminous
intensity.
There are several units that are used to characterize the luminance of a source. The names of
these common units are given in Table 16.2.
Typical luminances of displays, organic LEDs, and inorganic LEDs are given in Table 16.3.
The table reveals that displays require a comparatively low luminance because the observer
directly views the display from a close distance. This is not the case for high-power inorganic
LEDs used for example in traffic light and illumination applications.
Photometric and the corresponding radiometric units are summarized in Table 16.4.

Table 16.2. Conversion between common SI and non-SI units for luminance.

Unit Common name Unit Common name

1 cd/cm2 1 stilb (1/S) cd/m2 1 apostilb
(1/S) cd/cm2 1 lambert (1/S) cd/ft2 1 foot-lambert
1 cd/m2 1 nit

Table 16.3. Typical values for the luminance of displays, LEDs fabricated from organic
materials, and inorganic LEDs.

Device Luminance (cd/m2) Device Luminance (cd/m2)

Display 100 (operation) Organic LED 100–10 000
Display 250–750 (max. value) III–V LED 1 000 000–10 000 000

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Table 16.4. Photometric and corresponding radiometric units.

Photometric unit Dimension Radiometric unit Dimension

Luminous flux lm Radiant flux (optical power) W
Luminous intensity lm / sr = cd Radiant intensity W / sr
2
Illuminance lm / m = lux Irradiance (power density) W / m2
Luminance lm / (sr m2) = cd / m2 Radiance W / (sr m2)

Exercise: Photometric units. A 60 W incandescent light bulb has a luminous flux of 1000 lm. Assume
that light is emitted isotropically from the bulb.
(a) What is the luminous efficiency (i.e. the number of lumens emitted per watt of electrical input power)
of the light bulb?
(b) What number of standardized candles emit the same luminous intensity?
(c) What is the illuminance, Elum, in units of lux, on a desk located 1.5 m below the bulb?
(d) Is the illuminance level obtained under (c) sufficiently high for reading?
(e) What is the luminous intensity, Ilum, in units of candela, of the light bulb?
(f) Derive the relationship between the illuminance at a distance r from the light bulb, measured in lux,
and the luminous intensity, measured in candela.
(g) Derive the relationship between the illuminance at a distance r from the light bulb, measured in lux,
and the luminous flux, measured in lumen.
(h) The definition of the cd involves the optical power of (1/683) W. What, do you suppose, is the origin
of this particular power level?
Solution: (a) 16.7 lm/W. (b) 80 candles. (c) Elum = 35.4 lm/m2 = 35.4 lux. (d) Yes.
(e) 79.6 lm/sr = 79.6 cd. (f) Elum r2 = Ilum. (g) Elum 4Sr2 = )lum.
(h) Originally, the unit of luminous intensity had been defined as the intensity emitted by a
real candle. Subsequently the unit was defined as the intensity of a light source with specified
wavelength and optical power. When the power of that light source is (1/683) W, it has the
same intensity as the candle. Thus this particular power level has a historical origin and
results from the effort to maintain continuity.

16.3 Eye sensitivity function

The conversion between radiometric and photometric units is provided by the luminous
efficiency function or eye sensitivity function, V(O). In 1924, the CIE introduced the photopic
eye sensitivity function V(O) for point-like light sources where the viewer angle is 2q (CIE,
1931). This function is referred to as the CIE 1931 V(O) function. It is the current photometric
standard in the United States.
A modified V(O) function was introduced by Judd and Vos in 1978 (Vos, 1978; Wyszecki
and Stiles, 1982, 2000) and this modified function is here referred to as the CIE 1978 V(O)
function. The modification was motivated by the underestimation of the human eye sensitivity in
the blue and violet spectral region by the CIE 1931 V(O) function. The modified function V(O)
has higher values in the spectral region below 460 nm. The CIE has endorsed the CIE 1978 V(O)

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 16.3 Eye sensitivity function

function by stating “the spectral luminous efficiency function for a point source may be
adequately represented by the Judd modified V(O) function” (CIE, 1988) and “the Judd modified
V(O) function would be the preferred function in those conditions where luminance
measurements of short wavelengths consistent with color normal observers is desired” (CIE,
1990).

The CIE 1931 V(O) function and the CIE 1978 V(O) function are shown in Fig. 16.6. The
photopic eye sensitivity function has maximum sensitivity in the green spectral range at 555 nm,
where V(O) has a value of unity, i.e. V(555 nm) = 1. Inspection of the figure also reveals that the
CIE 1931 V(O) function underestimated the eye sensitivity in the blue spectral range
(O < 460 nm). Numerical values of the CIE 1931 and CIE 1978 V(O) function are tabulated in
Appendix 16.1.
Also shown in Fig. 16.6 is the scotopic eye sensitivity function V c(O). The peak sensitivity in
the scotopic vision regime occurs at 507 nm. This value is markedly shorter than the peak
sensitivity in the photopic vision regime. Numerical values of the CIE 1951 V c(O) function are
tabulated in Appendix 16.2.

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Note that even though the CIE 1978 V(O) function is preferable, it is not the standard, mostly
for practical reasons such as possible ambiguities created by changing standards. Wyszecki and
Stiles (2000) note that even though the CIE 1978 V(O) function is not a standard, it has been used
in several visual studies. The CIE 1978 V(O) function, which can be considered the most accurate
description of the eye sensitivity in the photopic vision regime, is shown in Fig. 16.7.

The eye sensitivity function has been determined by the minimum flicker method, which is
the classic method for luminance comparison and for the determination of V(O). The stimulus is a
light-emitting small circular area, alternatingly illuminated (with a frequency of 15 Hz) with the
standard color and the comparison color. Since the hue-fusion frequency is lower than 15 Hz, the
hues fuse. However, the brightness-fusion frequency is higher than 15 Hz and thus if the two
colors differ in brightness, then there will be visible flicker. The human subject’s task is to adjust
the target color until the flicker is minimal.
Any desired chromaticity can be obtained with an infinite variety of spectral power

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 16.4 Colors of near-monochromatic emitters

distributions P(O). One of these distributions has the greatest possible luminous efficacy. This
limit can be obtained in only one way, namely by the mixture of suitable intensities emitted by
two monochromatic sources (MacAdam, 1950). The maximum attainable luminous efficacy
obtained with a single monochromatic pair of emitters is shown in Fig. 16.8. The maximum
luminous efficacy of white light depends on the color temperature; it is about 420 lm/W for a
color temperature of 6500 K and can exceed 500 lm/W for lower color temperatures. The exact
value depends on the exact location within the white area of the chromaticity diagram.

16.4 Colors of near-monochromatic emitters

For wavelengths ranging from 390 to 720 nm, the eye sensitivity function V(O) is greater than
10–3. Although the human eye is sensitive to light with wavelengths < 390 nm and > 720 nm, the
sensitivity at these wavelengths is extremely low. Therefore, the wavelength range
390 nm d O d 720 nm can be considered the visible wavelength range. The relationship between
color and wavelength within the visible wavelength range is given in Table 16.5. This
relationship is valid for monochromatic or near-monochromatic light sources such as LEDs.
Note that color is, to some extent, a subjective quantity. Also note that the transition between
different colors is continuous.

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