Photometry is based on the fact that the human visual system does not respond equally to all wavelengths of visible light.
A radiometric measurement simply sums radiant power across the spectrum, treating one watt of deep red radiation the same as one watt of green radiation, even though the eye responds to them very differently.
Photometric quantities account for this by weighting the spectrum according to the spectral sensitivity of the human eye, using the photopic luminous efficiency function V(λ) for daylight vision (or V′(λ) for dark-adapted, scotopic vision).
The result is a set of photometric quantities—commonly denoted by the subscript v (“visual”)—that correlate with perceived brightness rather than physical radiant energy.
Why photometry is more than radiometry with a filter.
Two overlapping curves on one wavelength axis (380–780 nm): a flat spectral power distribution (“equal spectral radiant power”) and the bell-shaped photopic luminous efficiency function V(λ), peaking at 555 nm.
Core photometric quantities
Luminous flux (Φv), measured in lumens (lm), is the photometric counterpart of radiant flux and represents the total visually weighted light output of a source. At 555 nm, where the human eye reaches its maximum photopic sensitivity, 1 W of radiant flux corresponds to exactly 683 lm (the maximum luminous efficacy, Km). At other wavelengths, the photopic weighting decreases rapidly. For example, radiation at 670 nm contributes only about 3% of the maximum luminous efficacy, even if its radiant power is identical.
Luminous intensity (Iv), measured in candela (cd), describes the luminous flux emitted per unit solid angle in a given direction:
1 cd = 1 lm/sr
It is particularly useful for characterizing directional light sources such as LEDs, lamps, and optical projectors.
Luminance (Lv), measured in cd/m², is the photometric quantity describing luminous intensity per unit projected area in a specified viewing direction. It is the quantity directly measured by luminance meters and imaging photometers and correlates strongly with the perceived brightness of surfaces such as displays, illuminated panels, or light-emitting devices.
Illuminance (Ev), measured in lux (lx), is the luminous flux incident on a surface per unit area. It is the standard quantity used to specify how much visible light reaches a working surface, roadway, sensor, or other illuminated object.
Luminous exitance (Mv), measured in lm/m² (numerically equal to lux), describes the luminous flux leaving a surface per unit area through emission, reflection, or transmission.
A simple measurement geometry showing a point source, a solid angle Ω subtended toward a small surface element dA, with arrows labeled Φv, Iv, and Ev illustrating the relationship between luminous flux, luminous intensity, and illuminance.
From monochromatic to broadband sources
For monochromatic radiation, converting a radiometric quantity into its photometric equivalent simply requires multiplication by the photopic luminous efficiency function V(λ) and the constant 683 lm/W. Real light sources, however, are rarely monochromatic. Even narrowband LEDs possess sufficient spectral width that the steep slopes of V(λ), particularly in the blue and red regions, make the single-wavelength approximation inaccurate.
For broadband or structured spectra, the correct procedure is to integrate the spectral power distribution multiplied by V(λ) over the visible wavelength range and then apply the 683 lm/W scaling factor. This calculation is performed automatically by a spectroradiometer, which measures the complete spectral distribution rather than only an integrated photometric quantity.
Interaction of light with materials: reflection, transmission, and absorption
When light reaches a material, it may be reflected, transmitted, or absorbed within the material, where the absorbed energy is typically converted into heat or other forms of energy. Reflection and transmission each consist of two components:
- regular (specular), following the laws of geometric optics;
- diffuse, resulting from scattering into many directions.
Left: a smooth surface producing one reflected beam and one transmitted beam (specular case). Right: a rough or turbid material scattering the reflected and transmitted light into many directions (diffuse case).
Quantitatively:
- Reflectance (ρ) = reflected radiant flux ÷ incident radiant flux, with total reflectance given by ρ = ρr + ρd.
- Transmittance (τ) = transmitted radiant flux ÷ incident radiant flux, with τ = τr + τd.
- Absorptance (α) = absorbed radiant flux ÷ incident radiant flux.
All three are dimensionless quantities satisfying
ρ + τ + α = 1
provided all reflected and transmitted components are included.
These quantities generally depend on wavelength, sample thickness, surface finish, angle of incidence, temperature, and polarization. Consequently, a single reflectance value is meaningful only when the measurement conditions are fully specified, often with respect to a standard illuminant such as CIE Standard Illuminant D65.
Total reflectance and transmittance are commonly measured using an integrating sphere, which collects light over nearly the entire hemisphere. With appropriate measurement geometries, integrating-sphere systems also allow reliable separation of diffuse and specular components.
Describing directional reflection: BRDF
For many engineering materials—including brushed metals, painted surfaces, plastics, and road pavements—a single reflectance value is insufficient because the reflected light depends strongly on direction.
The Bidirectional Reflectance Distribution Function (BRDF) describes how reflected radiance at a given wavelength depends on both the incident illumination direction and the observation direction. BRDF measurements make it possible to predict a material’s appearance under arbitrary lighting and viewing geometries rather than under a single measurement condition.
Suggested sketch 4: A hemisphere positioned above a flat sample surface, with one incident ray defined by angles θi and φi, and multiple reflected rays distributed over the hemisphere at various θr and φr. Highlight one reflected direction to indicate the specific BRDF measurement geometry.
Practical instrumentation
Different photometric instruments measure different quantities:
- Luxmeters measure illuminance (Ev).
- Luminance meters measure luminance (Lv).
- Photometers measure various photometric quantities depending on their optical configuration.
- Imaging photometers provide spatially resolved luminance measurements for applications such as display characterization and automotive lighting.
- Spectroradiometers are required whenever the spectral power distribution must be measured directly, such as for LED characterization, color-critical lighting, display calibration, or whenever accurate photometric quantities cannot be obtained using a single-wavelength approximation.
