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Luminous Efficacy
1. Definition
Luminous efficacy is a metric that measures the efficiency of a light source in converting energy into visible light. It is defined as the ratio of luminous flux ($\Phi_V$) to input power, with the SI unit of lumens per watt (${lm·W}^{-1}$). It serves as a crucial bridge connecting radiometry and photometry, converting physical radiant flux into luminous flux perceivable by the human eye through the luminous efficiency function $K(\lambda)$:
$$K = \frac{\Phi_V}{\Phi_e} = \frac{\int_0^\infty K(\lambda)\Phi_{e,\lambda}\mathrm{d}\lambda}{\int_0^\infty \Phi_{e,\lambda}\mathrm{d}\lambda}$$
- Radiometry: Measures total physical energy in terms of radiant flux ($\Phi_e$, unit: Watt W);
- Photometry: Measures light energy perceivable by the human eye in terms of luminous flux ($\Phi_V$, unit: lumen lm).
The “input power” here can refer to two scenarios:
1. The radiant flux output by the light source
Its luminous efficacy is referred to as the luminous efficacy of radiation. The result depends solely on the spectral shape of the light source and the luminous efficiency function, which measures the standard human eye's sensitivity to different wavelengths of light.
2. The total power consumed by the light source
Its luminous efficacy is then referred to as the luminous efficacy of a light source or overall luminous efficacy, which is a more commonly used metric in engineering.
Example: The luminous efficacy of LED lamps is much higher than that of incandescent lamps, requiring less power to produce the same luminous flux.
2. Maximum Luminous Efficacy
The maximum luminous efficacy \(K_\text{m}\) represents the maximum luminous flux (in lumens) that can be produced per unit of radiant power (in watts) at the wavelength where the human eye is most sensitive.
This graph shows the luminous efficiency function for photopic vision, reflecting the relative sensitivity of the human eye to different wavelengths of visible light. Its peak directly determines the value of the maximum luminous efficacy. The horizontal axis is the wavelength of light (unit: nanometer nm), and the vertical axis is the relative sensitivity, with a maximum value of 1.0.
The peak of the curve occurs at 555 nm (yellow-green light), where the visual sensitivity of the human eye is highest ($V(\lambda)=1$). The maximum luminous efficacy can be found through CIE standard data tables. The further the wavelength deviates from 555 nm (such as violet light near 400 nm or red light near 700 nm), the lower the sensitivity, and the curve drops accordingly. Therefore, for white light sources, which include wavelengths such as red and blue where the luminous efficiency function values are less than 1.0, the overall luminous efficacy is reduced.
According to the International Commission on Illumination (CIE) standards, the maximum luminous efficacy under different conditions corresponds to different symbols and values:
| Visual Condition | Symbol | Reference Value |
|---|---|---|
| Photopic vision (default) | $K_m$ | $683\ \text{lm·W}^{-1}$ |
| Scotopic vision | $K'_m$ | $1700\ \text{lm·W}^{-1}$ |
| Mesopic vision | $K_{m,\text{mes}}$ | Varies dynamically with ambient luminance |
| Photopic vision 10° field | $K_{m,10}$ | — |
| Photopic vision 2° field | $K_{m,M}$ | — |
Note: If the photometric condition is not specified, it defaults to \(K_\text{m}\) for photopic vision.
The $K_\text{m} \approx 683\ \text{lm·W}^{-1}$ for photopic vision is not an experimentally measured value, but a defined value in the International System of Units (SI). Its formula is:
$$K_\text{m} = \frac{683}{V(\lambda_{\text{cd}})}\ \text{cd·sr·W}^{-1}$$
where:
\(683\) is a constant directly specified in the definition of the candela; \(V(\lambda_{\text{cd}})\) is the value of the photopic spectral luminous efficiency function at the reference wavelength \(\lambda_{\text{cd}}\), which corresponds to a frequency of \(540 \times 10^{12}\ \text{Hz}\), exactly the 555 nm wavelength where the human eye is most sensitive (the peak wavelength of the CIE 1924 photopic function). Therefore, \(V(\lambda_{\text{cd}}) = 1\), resulting in \(K_\text{m} = 683\ \text{lm·W}^{-1}\).
Difference Between Luminous Efficacy and Luminous Efficiency?
Luminous efficacy is an absolute performance metric, with the unit of lumens per watt (${lm·W}^{-1}$), directly reflecting the actual efficiency of a light source in converting input power into visible light. A higher value indicates that the light source produces more visible light per unit of power.
Luminous efficiency is a relative dimensionless value (usually expressed as a percentage), which is the ratio of the actual luminous efficacy to the theoretical maximum luminous efficacy ($K_\text{m} \approx 683\ \text{lm·W}^{-1}$). It reflects how close the efficacy of an actual light source is to the theoretical limit.
Effect of Dimming on the Luminous Efficacy of Different Light Sources
Dimming incandescent lamps significantly reduces their luminous efficacy because the filament cools down. In contrast, light-emitting diodes (LEDs) and fluorescent lamps can typically be dimmed while maintaining high efficacy.
See Also
Luminous Flux