Luminous Intensity
Luminous intensity is an SI base quantity that represents the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle. Unlike strictly physical (radiometric) quantities like radiant intensity, luminous intensity is a photometric quantity. This means it explicitly accounts for the variable sensitivity of the human visual system to different wavelengths of light.
The SI base unit for luminous intensity is the candela (cd). It is the only SI base unit that is defined around human perception, underscoring the critical importance of standardized artificial lighting in the modern world.
The Photometric Dilemma and the Luminosity Function
The human eye is not equally sensitive to all colors (wavelengths) of light. During daylight (photopic vision), the eye is most sensitive to green-yellow light at approximately 555 nanometers (nm). A 1-watt source of 555 nm green light will appear overwhelmingly brighter to a human observer than a 1-watt source of 650 nm deep red light, and a 1-watt source of infrared radiation will be completely invisible.
To create a measurement system that correlates with human perception, the International Commission on Illumination (CIE) established standard luminosity functions, denoted mathematically as $V(\lambda)$. This function is a standardized curve representing the average spectral sensitivity of human visual perception to brightness.
Therefore, luminous intensity ($I_v$) is derived from physical radiant intensity ($I_e$) by integrating across the visible spectrum, heavily weighting the physical power by the $V(\lambda)$ curve.
Historical Context: The Standard Candle
The concept of measuring light output naturally began with the most common artificial light source: the candle. In the 19th century, standard candles of specific compositions (e.g., spermaceti wax) burning at specified rates were used as the baseline for "candlepower."
However, these physical flames were notoriously unstable, flickering and changing output based on atmospheric pressure, humidity, and microscopic variations in the wick. As electric lighting emerged, the need for a rigorous, reproducible standard became critical. The standard transitioned from flames to incandescent lamps, and eventually to the freezing point of liquid platinum. However, even the platinum standard proved difficult to realize with high accuracy.
The Modern Definition of the Candela
In 1979, and reaffirmed with the 2019 SI redefinition, the candela was entirely divorced from physical artifacts and thermal blackbodies. It is now defined mathematically through a fundamental constant: the luminous efficacy of monochromatic radiation of frequency $540 \times 10^{12}$ Hz, denoted as $K_{cd}$.
The candela (cd) is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency $540 \times 10^{12}$ Hz, $K_{cd}$, to be exactly 683 when expressed in the unit lm W⁻¹, which is equal to cd sr W⁻¹, or cd sr kg⁻¹ m⁻² s³.
Note: The frequency $540 \times 10^{12} \text{ Hz}$ corresponds to a wavelength of approximately 555 nm in a vacuum, which is the exact peak of the $V(\lambda)$ photopic luminosity function.
Realization and Calibration
Because the candela is now defined directly in terms of physical power (watts), its primary realization in National Metrology Institutes is typically achieved using highly accurate cryogenic radiometers.
A cryogenic radiometer operates at temperatures near absolute zero. It measures the optical power of a stabilized laser beam (often at 555 nm or calibrated across the spectrum) by comparing the heating effect of the absorbed light to the heating effect of a precisely measured electrical current. By knowing the absolute physical power (W) and mathematically applying the $V(\lambda)$ function and the constant $K_{cd}$, the luminous intensity can be realized with extremely low uncertainty.
This primary standard is then used to calibrate secondary standards, typically highly stable incandescent or solid-state (LED) standard lamps, which are subsequently used to calibrate commercial light meters and spectroradiometers.