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.

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 Note that candlepower and candle are non-SI units that are no longer current and rarely used at the present time.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 4n 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


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

100000 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 ^projected = Asurface cos 0 , where 0 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 0

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

Basic radiometric and photometric units

Projected area: A cos 0

Fig. 16.5. Area of LED, A, and projected area, y4cos0, used for the definition of the lumi­nance of an LED.

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.


Common name

1 cd/cm2

1 stilb

(1/n) cd/cm2

1 lambert

1 cd/m2

1 nit


Common name

(1/n) cd/m2

1 apostilb

(1/я) cd/ft2

1 foot-lambert

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


Luminance (cd/m2)


100 (operation)


250-750 (max. value)


Luminance (cd/m2)

Organic LED

100-10 000


1 000 000-10 000 000

Table 16.4. Photometric and corresponding radiometric units.

Photometric unit


Radiometric unit


Luminous flux


Radiant flux (optical power)


Luminous intensity

lm / sr = cd

Radiant intensity

W / sr


lm / m2 = lux

Irradiance (power density)

W / m2


lm / (sr m2) = cd / m2


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 = I^. (g) Elum 4nr2 = Ф^.

(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.

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