Luminous Efficacy in Photometry

Overview

Luminous efficacy is a core concept in photometry and lighting engineering, serving as the definitive benchmark for evaluating how efficiently a light source converts electrical power into visible light. It is mathematically defined as:

[ \text{Luminous efficacy} (\eta) = \frac{\text{Luminous flux (lm)}}{\text{Electrical power (W)}} ]

The unit is lumens per watt (lm/W). This metric allows direct comparison between light sources—such as LEDs, fluorescent lamps, and incandescent bulbs—by quantifying the amount of visible light produced per unit of energy consumed.

Luminous efficacy considers both the physical properties of the light source and the human eye’s varying sensitivity to different wavelengths, as described by the CIE photopic luminosity function V(λ). The theoretical upper limit is 683 lm/W at the wavelength where the human eye is most sensitive (555 nm), but practical light sources achieve lower values due to spectral distribution, non-visible emissions, and energy losses.

Luminous Flux

Luminous flux (Φ) represents the total quantity of visible light emitted by a source, adjusted for the eye’s sensitivity. Its SI unit is the lumen (lm). The calculation integrates the source’s spectral power distribution (SPD) with the CIE V(λ) function:

[ \Phi = 683 \int_{380,\mathrm{nm}}^{780,\mathrm{nm}} V(\lambda) \cdot P_{\lambda} , d\lambda ]

• 683 lm/W is the peak sensitivity at 555 nm.
• V(λ) is the normalized photopic luminosity function.
• Pλ is the spectral radiant power at wavelength λ.

Luminous flux is crucial for specifying lamp outputs and designing lighting systems to meet required illumination levels.

Electrical Power in Lighting

Electrical power is the rate at which a light source consumes energy, measured in watts (W). It includes all losses from drivers, ballasts, and power conversion. Accurate measurement is vital, especially for modern sources like LEDs with complex drivers.

• System efficacy: Accounts for all optical and electrical losses.
• Source efficacy: Considers only the device power input.

Electrical power input helps determine operational costs, carbon footprint, and compliance with efficiency regulations.

The CIE Photopic Luminosity Function V(λ)

The CIE V(λ) function models the average human eye’s sensitivity to visible light under well-lit (photopic) conditions. It peaks at 555 nm (green), decreasing toward violet and red wavelengths.

[ \Phi = 683 \int V(\lambda) \cdot P_{\lambda} , d\lambda ]

V(λ) is foundational for converting radiometric quantities (all electromagnetic energy) to photometric quantities (visible light as perceived by humans), forming the basis for international lighting standards and specifications.

SI Units in Photometry

These SI units are codified by international standards bodies (BIPM, CIE, IEC) and are essential for consistent measurement and specification.

Luminous Intensity

Luminous intensity measures the luminous flux emitted in a particular direction, per unit solid angle, with the SI unit candela (cd):

[ 1 \ \text{cd} = 1 \ \text{lm/sr} ]

Luminous intensity is critical for directional lighting applications, including runway edge lights, vehicle headlights, and signal lamps.

Illuminance

Illuminance quantifies the amount of luminous flux incident per unit area, measured in lux (lx):

[ 1 \ \text{lx} = 1 \ \text{lm/m}^2 ]

It is a fundamental metric in lighting design for visual comfort, safety, and compliance with standards such as EN 12464-1 or ICAO Annex 14 for aviation.

Luminance

Luminance describes the perceived brightness of a surface from a particular direction:

[ L = \frac{dI}{dA \cdot \cos\theta} ]

• L: Luminance (cd/m²)
• dI: Differential luminous intensity
• dA: Differential area
• θ: Angle between surface normal and observation direction

Luminance is crucial for display screens, signage, and safety-critical lighting.

Luminous Efficiency

Luminous efficiency is the ratio of actual luminous efficacy to the theoretical maximum (683 lm/W), expressed as a percentage:

[ \text{Luminous efficiency} = \frac{\text{Actual luminous efficacy}}{683 \ \text{lm/W}} \times 100% ]

This figure provides a benchmark for comparing different lighting technologies.

Radiometric vs. Photometric Quantities

Radiometric measurements include all electromagnetic energy, while photometric measurements account only for visible light as perceived by humans.

Calculation of Luminous Efficacy

1. Measure Luminous Flux:
   Use an integrating sphere or goniophotometer to capture all emitted light and determine total luminous flux (lm).

2. Measure Electrical Power:
   Record input power (W) at the lamp or fixture terminals, including all driver or ballast losses.

3. Calculate Efficacy:
   [ \eta = \frac{\text{Luminous flux (lm)}}{\text{Electrical power (W)}} ]

Theoretical Maximum Luminous Efficacy

The upper limit for luminous efficacy is 683 lm/W at 555 nm. Real-world sources emit across a range of wavelengths, so their efficacy is always lower. For instance, the best available white LEDs achieve 90–220+ lm/W, while monochromatic sources like low-pressure sodium lamps can attain ~200 lm/W.

Factors Affecting Luminous Efficacy

• Source Technology:
  Incandescent (6–19 lm/W), fluorescent (40–85 lm/W), LEDs (90–220+ lm/W)

• Spectral Distribution:
  The closer the emission spectrum aligns with V(λ), the higher the efficacy.

• Power Supply Efficiency:
  Losses in drivers/ballasts reduce system efficacy.

• Optical Losses:
  Reflectors, diffusers, and lenses can absorb or scatter light.

• Thermal Management:
  High operating temperatures reduce efficacy, especially for LEDs.

• Aging and Dimming:
  Light output often decreases over time, impacting efficacy.

Applications and Use Cases

• Aviation:
  High-efficacy lighting for runways and taxiways, meeting ICAO and FAA standards.

• General Lighting:
  LEDs now dominate due to their high efficacy and longevity.

• Automotive:
  Energy-efficient headlights and signals improve safety and efficiency.

• Emergency/Signal Lighting:
  High-efficacy LEDs ensure visibility with minimal power.

• Portable Devices:
  Maximized battery life in flashlights and mobile displays.

Comparative Efficacy of Common Light Sources

Luminous Efficacy in Standards and Regulations

International bodies such as the CIE, IEC, ISO, and ICAO specify luminous efficacy requirements for lighting products in public infrastructure, aviation, workplaces, and consumer markets. Compliance ensures safety, efficiency, and environmental responsibility.

Summary

Luminous efficacy is a powerful tool for comparing and optimizing lighting solutions, driving energy savings, improved visibility, and compliance with global standards. Whether in aviation, commercial buildings, or portable devices, understanding and applying this metric is essential for modern lighting design.