BOX I: Metrics of optical radiation and (bio-)effectiveness

Here follows a concise representation of the physical and bio-effective metrics of optical radiation as discussed in and in mathematical formulae with physical dimensions given in square brackets,”[ ]”. Given the spectral irradiance E(λ) in [W/m2 /nm] at the wavelength λ in [nm], we find the total irradiance, E, in [W/m2] by integration over the wavelengths:

E = ∫ E(λ) dλ,

If the spectral irradiance varies with time, we find the spectral exposure, H(λ) in [J/ m2 /nm] at wavelength λ by integration over time, t in [s]:

H(λ) = ∫ E(λ,t) dt

and the exposure, H, by integration over λ:

H = ∫ ∫ E(λ,t) dλdt = ∫ H(λ) dλ.

which simplifies to:

H = ε ∫ E(λ) dλ = ε.E

if E(λ) is constant over the exposure time ε in [s]. To ascertain the bio-effectiveness of the radiation we define a dimensionless action spectrum S(λ) to weight the spectral exposure. S(λ) is inversely proportional to the exposure Hr(λ) required at a certain wavelength λ for a certain level of biological response (level), and normalized to equal “1” at λmax, the most effective wavelength to induce this response with smallest Hr(λ), i.e.

S(λ) = Hr(λmax)/Hr(λ).

The effectiveness spectrum is then defined as:

Ee(λ) = S(λ).E(λ),

The (bio-) effective irradiance as:

Ee = ∫ S(λ) E(λ) dλ,

and the (bio-) effective exposure or photobiologic “dose” as:

He = ∫ S(λ) H(λ) dλ,

where Ee(λ), Ee and He are then given in equivalents of [W/m2 nm], [W/m2] and [J/m2], respectively, at wavelength λmax. Note that this procedure of spectral weighting requires “additivity” to hold, i.e. that separate effective doses from different wavelengths can be added up to a total effective dose. The irradiance at the retina of the eye from a radiant source is strongly dependent on the imaging, i.e. focusing, of the source onto the retina which can cause up to a 200,000-fold increase in irradiance from the surface of the eye to the retina3. When we consider a source (a lamp or a reflecting surface), its spectral radiant power in [W/nm] emitted per radiant surface area in [m2] into a solid angle in steradian [sr], i.e. the spectral radiance,

L(λ), in [W/sr m2 nm], towards the pupil of the eye is crucial to the retinal irradiance Eret in [W/m2]:

Eret = (π/4) (dp/f)2 ∫ L(λ) τ(λ) dλ,

where τ(λ) is the transmittance from the source to the retina at wavelength λ, dp denotes the pupil diameter in [m] and f is the focal length of the eye in [m]. Note that the distance of the source from the eye drops from the equation (as the source is moved away from the eye the image spot on the retina becomes smaller but the irradiance remains constant if the radiance is constant over the surface of the source). L is also referred to as the source’s “intensity”. The eye tremor (around 80 Hz with amplitudes of 0.2 to 2.5 μm) spreads a point source over a larger image area on the retina (about 25 μm in diameter in 1 sec and 190 μm in 100 s, subtending about 11 mrad). It should also be noted that in a realistic assessment, for example of a human who is reading, the source is a page at a certain distance from a lamp, i.e. not the lamp itself. The eyes rarely focus on a primary light source, a lamp, and strongly evade looking into bright ones (eyes closing and causing the face to turn away from the source).

To ascertain the bio-effectiveness on the retina Eret (λ) and L(λ) can be weighted by an action spectrum S(λ). For example, taking S(λ) as the photopic* luminous efficiency function, V(λ), (normalized to 1 at λmax = 555 nm) one converts a physical radiant power spectrum, or spectral flux Φ(λ) in [W/nm], into a luminous flux, Φv, in lumens [lm] representing the visual effectiveness:

Φv = 683.002 [lm/W] ∫ V(λ) Φ(λ) dλ.

Illuminance (the photometric equivalent of irradiance) equals the luminous flux per surface area in lux, [lx] = [lm/m2]. The photopically weighted radiance, luminance Lph, of a source is given in candela per surface area [cd/m2] = [lm/sr m2]. Luminance is also loosely referred to as the “brightness” of a radiant source, i.e. the visual intensity.

* Photopic refers to daylight vision, i.e. with a light-adapted eye; scotopic, on the other hand, refers to night vision, i.e. with a dark-adapted eye.


Source: SCENIHR, Health effects of artificial light, 19 March 2012,
 3.4.1 Optical radiation and 3.4.2 Radiant energy absorption, pp. 22-31.

Related publication:
Artificial Light homeHealth Effects of Artificial Light
Other Figures & Tables on this publication:

Figure 1. Electrical lighting sources technologies

Figure 2. Wavelength regions in optical radiation

Figure 3. Chromophores and their absorption bands (adapted from Jagger 1967)

Figure 4a. Interaction of UV radiation with the human eye at all ages (adapted from Sliney 2002).

Figure 4b. Specificity of optical radiation interaction with the eye of children below 9 years of age (adapted from Sliney 2002).

Figure 4c. Optical radiation interaction with the young human eye (10 years old up to young adulthood) (adapted from Sliney 2002)

Figure 4d. Optical radiation interaction with the eye of an aging human (adapted from Sliney 2002)

Figure 5. Light penetration in the skin

Table 1. Lamp parameters supplied by the European Lamp Companies Federation

Table 2. Overview of the classes of photodamage to the retina

Table 3. Interaction of light with eye tissues and chromophores

Table 4. "Light related" skin diseases

Table 5. Wavelength dependency in photosensitive diseases

Table 6. Examples of exposure situations from artificial light for the general population

Table 7. Percent increase in SCC incidence and risk at 80 years of age due to certain added UV doses

Table 8. Estimates of SCC risk

BOX I: Metrics of optical radiation and (bio-)effectiveness

Figure 6. shows the typical adverse effects of light on eye tissues as a function of wavelength.

Figure 7. Production of reactive oxygen species (ROS) by rod photoreceptors exposed to blue light in vitro (adapted from Yang et al. 2003)

Figure 8. Photosynthesis of vitamin D3 and further metabolism (adapted from Dutch Cancer Society 2010)