Candela (cd): The SI Unit of Luminous Intensity

The candela (symbol: cd) is the SI base unit for luminous intensity, quantifying the perceived brightness of visible light emitted by a source in a particular direction. Unlike other SI units grounded solely in invariant physical constants, the candela uniquely incorporates a physiological aspect—human photopic vision—making it the only SI base unit fundamentally linked to human perception.

Definition and Foundation

The candela is officially defined as follows:

“The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² hertz, Kcd, to be 683 when expressed in the unit lm·W⁻¹, which is equal to cd·sr·W⁻¹.”

This means that one candela is the luminous intensity, in a given direction, of a source emitting monochromatic radiation at 540 × 10¹² Hz (corresponding to a wavelength of 555 nm in air—green light, where human eye sensitivity peaks) with a radiant intensity of 1/683 watt per steradian in that direction.

The CIE photopic luminosity function (V(λ)) shows the human eye’s sensitivity to visible wavelengths. The candela’s definition uses the maximum at 555 nm.

The candela is directional and perceptual:

• Directional: It measures intensity in a specific direction, not the total light output.
• Perceptual: It is weighted by the human eye’s response, described by the CIE photopic luminosity function (V(λ)), not just by physical energy.

Scope and Limitations

What does the candela measure?

• Luminous intensity (cd): the visible light power emitted per unit solid angle in a specific direction, as perceived by the average human eye.
• It does not measure total light output (lumen), incident light on a surface (lux), or non-visible radiation (infrared/ultraviolet).

Where is it used?

• Lighting design (spotlights, vehicle headlights, display screens)
• Aviation, automotive, maritime, and railway signaling
• Safety regulation and compliance (e.g., emergency exit signs, obstruction lights)
• Display and visual technology
• Ergonomics and visual comfort studies

What are its limitations?

• Only applies to visible light, as defined by the standard observer response (V(λ)).
• Unsuitable for non-human perception applications (e.g., machine vision, IR/UV systems).
• Not indicative of total source output—directional, not integral.

Historical Development

The candela evolved from early attempts to standardize light using candles and lamps:

• 19th century: “Standard candles” (e.g., English sperm candle, French Carcel lamp) defined light output, but were highly variable.
• 1909: International candle defined via carbon filament lamp.
• 1933: Shift to physical reference—black body at platinum freezing point.
• 1948: SI system formalizes this as the base unit.
• 1979: Modern definition based on monochromatic radiation at 555 nm (540 × 10¹² Hz), aligning with peak human eye sensitivity.
• 2019: Current SI revision ties the candela to fundamental constants and the fixed luminous efficacy of 683 lm/W at 555 nm.

This progression reflects a move from empirical reference standards to reproducible, physics- and physiology-based definitions.

Photometric Quantities: The Family of Light Measurement

The candela is central to photometry, which quantifies light in terms meaningful to human vision. Related quantities include:

• Luminous Intensity (cd): I = Φ/Ω
• Luminous Flux (lm): Φ = I × Ω
• Illuminance (lx): E = Φ/A or E = I/r² (perpendicular surface)
• Luminance (cd/m²): L = I/A (projected area)

Example Calculation

A point source emits 1 candela uniformly in all directions. Since a sphere has 4π steradians, total luminous flux:

[ \Phi = 1,\text{cd} \times 4\pi,\text{sr} \approx 12.57,\text{lm} ]

The Human Eye and CIE Photopic Curve

Human eyes are not equally sensitive to all visible wavelengths. The CIE photopic luminosity function V(λ) models this, peaking at 555 nm (green-yellow). The candela’s definition uses this peak for maximum luminous efficacy:

• 1 watt at 555 nm = 683 lumens
• For other wavelengths, efficacy is lower (e.g., ~73 lm/W at 435 nm blue)

Photometric instruments and calculations always weight light by V(λ), differentiating photometry from radiometry (which treats all photons equally).

Realizing the Candela in the Laboratory

Realizing the candela involves:

1. Photodetector Calibration: Use precision silicon photodiodes with filters matching the V(λ) curve.
2. Reference Sources: Employ monochromatic sources at 555 nm for primary standards.
3. Radiant Power Measurement: Precisely measure source power and geometry (solid angle).
4. Calculation: Use radiant power, solid angle, V(λ) weighting, and the fixed value of 683 lm/W.
5. Traceability: National metrology institutes (e.g., NIST, BIPM) disseminate standards through calibrations.
6. Secondary Standards: Use calibrated lamps, LEDs, or integrating spheres for routine measurements.

Integrating spheres are used to measure total luminous flux and calibrate sources relative to the candela.

Applications: Aviation, Lighting Design, and Beyond

Aviation

• Runway and taxiway lights: Minimum candela values specified by ICAO and FAA for visibility and safety.
• Aircraft anti-collision beacons: Required to emit specific candela levels horizontally and vertically.
• Obstruction lights: Tall structures must have lights visible for miles, specified in candela.

Lighting Product Specification

• Spotlights, headlamps, luminaires: Datasheets specify “peak candela” and candela distribution curves for beam control.
• Emergency lighting: Building codes require minimum candela in escape path directions.

Environmental and Health Impacts

• Light pollution: Regulations may restrict maximum candela above the horizontal to protect night skies and wildlife.
• Glare and circadian impact: Lighting standards use candela to ensure comfort and minimize biological disruption.

Mathematical Relationships

• Luminous Intensity: ( I = \Phi / \Omega )
• Luminous Flux: ( \Phi = I \cdot \Omega )
• Illuminance: ( E = I / r^2 ) (perpendicular surface)
• Luminance: ( L = I / A )
• Solid Angle: ( \Omega = A / r^2 )

Example:
A lamp emits 500 cd into a 2π sr hemisphere:
( \Phi = 500,\text{cd} \times 2\pi,\text{sr} \approx 3142,\text{lm} )

Everyday Examples

• Candle flame: ≈ 1 candela in all directions
• Traffic signal: 200–300 candela for visibility in daylight
• Theatrical spotlight: 10,000+ candela in a focused beam
• Aviation beacon: 400+ candela for anti-collision visibility

Why Reference 555 nm (Green)?

The eye is most sensitive (under bright conditions) at 555 nm. The candela’s definition uses this for maximum reproducibility and physiological relevance, ensuring that photometric units reflect how humans actually see.

Laboratory Realization: Practical Tools

• Integrating spheres: Capture all emitted light for total flux calibration.
• Goniophotometers: Map angular distribution of intensity (cd) from a source.
• Calibrated photodiodes: Provide traceable electrical signal matching V(λ).

Summary

The candela unites physics and human perception, providing a reproducible, universally accepted standard for specifying visible light intensity. From aviation to architecture, display screens to environmental protection, the candela ensures that light is measured, regulated, and optimized for human vision.

For further technical or regulatory details, consult the SI Brochure, CIE standards, or your national metrology institute.

Candela distribution curves are essential for lighting design, showing intensity as a function of angle.

References

• SI Brochure (BIPM): https://www.bipm.org/en/measurement-units
• CIE Photometric Standards: https://cie.co.at/
• NIST Photometry: https://www.nist.gov/pml/weights-and-measures/si-units-candela
• ICAO Annex 14 – Aerodromes
• FAA Advisory Circular 150/5345-43

If you have more questions about the candela or photometric measurement, feel free to contact our experts .