Spectral Measurement of Light (Photometry)

One of the central problems of optical measurements is the quantification of light sources and lighting conditions in numbers directly related to the perception of the human eye. This discipline is called “photometry” and its significance leads to the use of separate physical quantities that differ from the respective radiometric quantities in only one respect: Whereas radiometric quantities simply represent a total sum of radiation power at various wavelengths and do not account for the fact that the human eye’s sensitivity to optical radiation depends on wavelength, the photometric quantities represent a weighted sum with the weighting factor being defined by either the photopic or scotopic spectral luminous efficiency function. Thus, the numerical value of photometric quantities directly relates to the impression of “brightness”. Photometric quantities are distinguished from radiometric quantities by the index “v” for “visual”. Furthermore, photometric quantities relating to scotopic vision are denoted by an additional prime, for example Φv’. The following explanations are given for the case of photopic vision, which describes the eye’s sensitivity under daylight conditions and are therefore very significant for the vast majority of lighting situations (photopic vision takes place when the eye is ad /en-us/service-and-support/knowledge-base/basics-light-measurement/appendix/?stage=Stage ted to luminance levels of at least several candelas per square meters, scotopic vision takes place when the eye is adapted to luminance levels below some hundredths of a candela per square meter. For mesopic vision, which is between the photopic and scotopic range, no spectral luminous efficiency function has been defined yet). However, the respective relations for scotopic vision can be easily derived by replacing V(λ) with V'(λ) and K_m (= 683 lm/W) with K’_m (= 1700 lm/W).

Since the definition of photometric quantities closely follows the corresponding definitions of radiometric quantities, the corresponding equations hold true – the index “e” only has to be replaced by the index “v”. Thus, not all relations are repeated. Instead, a more general formulation of all relevant relations is given in the Appendix.

Measuring instruments for these applications are often called photometers or in the case of illuminance measurement luxmeters as well as spectral photometers or respectively spectral luxmeters.

Definitions

Luminous flux Φv is the basic photometric quantity and describes the total amount of electromagnetic radiation emitted by a source, spectrally weighted with the human eye’s spectral luminous efficiency function V(λ). Luminous flux is the photometric counterpart to radiant power. The luminous flux is given in lumen (lm). At 555 nm where the human eye has its maximum sensitivity, a radiant power of 1 W corresponds to a luminous flux of 683 lm. In other words, a monochromatic source emitting 1 W at 555 nm has a luminous flux of exactly 683 lm. The value of 683 lm/W is abbreviated as Km (the value of Km = 683 lm/W is given for photopic vision. For scotopic vision, K_m’ = 1700 lm/W has to be used). However, a monochromatic light source emitting the same radiant power at 650 nm, where the human eye is far less sensitive and V(λ) = 0.107, has a luminous flux of 0.107 × 683 lm = 73.1 lm. For a more detailed explanation of the conversion of radiometric to photometric quantities, see paragraph Conversion between radiometric and photometric quantities.

Luminous intensity Iv quantifies the luminous flux emitted by a source in a certain direction. It is therefore the photometric counterpart of the “radiant intensity (I_e)”, which is a radiometric quantity.

Luminance L_v describes the measurable photometric brightness of a certain location on a reflecting or emitting surface when viewed from a certain direction. It describes the luminous flux emitted or reflected from a certain location on an emitting or reflecting surface in a particular direction (the CIE definition of luminance is more general. This tutorial discusses the most relevant application of luminance describing the spatial emission characteristics of a source is discussed).

with Θ denoting the angle between the direction of the solid angle element dΩ and the normal of the emitting or reflecting surface element dA.

Illuminance E_v describes the luminous flux per area impinging upon a certain location of an irradiated surface.

Generally, the surface element can be oriented at any angle towards the direction of the beam. Similar to the respective relation for irradiance,

Luminous exitance M_v quantifies the luminous flux emitted or reflected from a certain location on a surface per area.

The unit of luminous exitance is 1 lm m^-2, which is the same as the unit for illuminance. However, the abbreviation lux is not used for luminous exitance.

Monochromatic radiation

In the case of monochromatic radiation at a certain wavelength λ, a radiometric quantity X_e is simply transformed to its photometric counterpart X_v by multiplication with the respective spectral luminous efficiency V(λ) and by the factor K_m = 683 lm/W.

Example: An LED (light emitting diode) emitsnearly monochromatic radiation at λ = 670 nm, where V(λ) = 0.032. Its radiant power amounts to 5 mW.

Since V(λ) changes very rapidly in this spectral region (by a factor of 2 within a wavelength interval of 10 nm), LED light output should not be considered monochromatic in order to ensure accurate results. However, using the relations for monochromatic sources still results in an approximate value for the LED’s luminous flux which might be sufficient in many cases.

Polychromatic radiation

If a source emits polychromatic light described by the spectral radiant power Φ_λ(λ), its luminous flux can be calculated by spectral weighting of Φ_λ(λ) with the human eye’s spectral luminous efficiency function V(λ), integration over wavelength and multiplication with K_m = 683 lm/W,

with X denoting one of the quantities Φ, I, L, or E.

Understanding Light Interaction: Reflection, Transmission, and Absorption Explained

Reflection is the process by which electromagnetic radiation is returned either at the boundary between two media (surface reflection) or at the interior of a medium (volume reflection), whereas transmission is the passage of electromagnetic radiation through a medium. Both processes can be accompanied by diffusion (also called scattering), which is the process of deflecting a unidirectional beam into many directions. In this case, we speak about diffuse reflection and diffuse transmission (Fig. 1). When no diffusion occurs, reflection or transmission of a unidirectional beam results in a unidirectional beam according to the laws of geometrical optics (Fig. 2). In this case, we speak about regular reflection (or specular reflection) and regular transmission (or direct transmission). Reflection, transmission and scattering leave the frequency of the radiation unchanged. Exception: The Doppler Effect causes a change in frequency when the reflecting material or surface is in motion.

Absorption is the transformation of radiant power to another type of energy, usually heat, by interaction with matter.

• For the optical measurement of reflection, transmission, absorption, and photoluminescence integrating sphere measuring systems are suitable.
• For the measurement of scattering samples we would like to refer to a spectrophotometer specially designed for this purpose.
• The measurement of classical transmission and reflection with a handheld device requires measuring systems with intelligent correction methods.

In general, reflection, transmission and absorption depend on the wavelength of the affected radiation. Thus, these three processes can either be quantified for monochromatic radiation (in this case, the adjective “spectral” is added to the respective quantity) or for a certain kind of polychromatic radiation. For the latter, the spectral distribution of the incident radiation has to be specified. In addition, reflectance, transmittance and absorptance might also depend on polarization and geometric distribution of the incident radiation, which therefore also have to be specified.

The reflectance ρ is defined by the ratio of reflected radiant power to incident radiant power. For a certain area element dA of the reflecting surface, the (differential) incident radiant power is given by the surface’s irradiance E_e multiplied with the size of the surface element,

Total reflectance is further subdivided in regular reflectance ρ_r and diffuse reflectance ρ_d, which are given by the ratios of regularly (or specularly) reflected radiant power and diffusely reflected radiant power to incident radiant power.

The transmittance τ of a medium is defined by the ratio of transmitted radiant power to incident radiant power. Total transmittance is further subdivided in regular transmittance τ_r and diffuse transmittance τ_d, which are given by the ratios of regularly (or directly) transmitted radiant power and diffusely transmitted radiant power to incident radiant power.

The absorptance α of a medium is defined by the ratio of absorbed radiant power to incident radiant power.

Being ratios of radiant power values, reflectance, transmittance and absorptance are dimensionless.

Quantities such as reflectance and transmittance are used to describe the optical properties of materials. The quantities can apply to complex radiation or monochromatic radiation. The optical properties of materials are not a constant since they are dependent on many parameters such as:

• thickness of the sample
• surface conditions
• angle of incidence
• temperature
• the spectral composition of the radiation (CIE standard illuminants A, B, C, D65 and other illuminants D)
• polarization effects

The measurement of optical properties of materials using integrating spheres is described in DIN 5036-3 and CIE 130-1998.

The radiance coefficient q_e characterizes the directional distribution of diffusely reflected radiation. In detail, the radiance coefficient depends on the direction of the reflected beam and is defined by the ratio of the radiance reflected in this direction to the total incident irradiance. In general, the reflected radiance is not independent from the directional distribution of the incident radiation, which therefore has to be specified.

In the USA, the concept of bidirectional reflectance distribution function BRDF is similar to the radiance coefficient. The only difference is that the BRDF is a function of the directions of the incident and the reflected beam (Fig. 3).

This BRDF depends on more arguments than the radiance coefficient. However, its advantage is the simultaneous description of the material’s reflection properties for all possible directional distributions of incident radiation, whereas the radiance coefficient is generally valid for just one specific directional distribution of incident radiation.

The unit of radiance coefficient and BRDF is 1/steradian. The BRDF is often abbreviated as the Greek letter ρ, which can easily be confused with the reflectance (see previous paragraph Reflectance ρ, Transmittance τ and Absorptance α).

Fig. 3: Geometry used to define the bidirectional reflectance distribution function (BRDF).
The BRDF depends on the directions of incident and reflected radiation.
These are given by the angles ϑ_i and ϑ_r (which are measured in relation to the reflecting surface’s normal)
and the azimuth angles φ_i and φ_r, (which are measured in the plane of the reflecting surface)

Source (valid as of 2002): http://math.nist.gov/~FHunt/appearance/brdf.html