Luminance and Brightness

Luminance Definition

Luminance is a measure of light weighted by the human visual system’s sensitivity:

$L_v = \int L(\lambda) \cdot V(\lambda) \, d\lambda$

where:

• $L(\lambda)$ is the spectral radiance
• $V(\lambda)$ is the luminous efficiency function (photopic)

Luminous Efficiency Function

$V(\lambda)$ represents the eye’s sensitivity at each wavelength for daylight (photopic) vision:

• Peaks at 555 nm (green)
• Determined by L and M cone sensitivities
• Normalised to 1.0 at peak

Units

Unit	Symbol	Description
Candela per square metre	cd/m²	Luminance (also called “nit”)
Lumen per watt	lm/W	Conversion factor
Conversion constant	$k = 683.002$	Converts radiometric to photometric

Why 555 nm?

The peak at 555 nm arises from the sum of L and M cone sensitivities:

$V(\lambda) \approx L(\lambda) + M(\lambda)$

This reflects the evolutionary importance of detecting green light in natural environments.

Luminance vs Brightness

Luminance ≠ Brightness

Concept	Nature
Luminance	Physical measurement weighted by spectral sensitivity
Brightness	Subjective perceptual experience

The relationship is non-linear and context-dependent.

The Electromagnetic Spectrum

Visible Light Range

The visible spectrum spans approximately 380 nm to 730 nm:

Wavelength Range	Colour
380-450 nm	Violet, blue
450-495 nm	Blue
495-570 nm	Green
570-590 nm	Yellow
590-620 nm	Orange
620-730 nm	Red

Why This Range?

• Earth’s atmosphere transmits light in this range
• Higher energy than thermal infrared (heat doesn’t interfere)
• Below UV threshold (tissue damage avoided)

The Helmholtz-Kohlrausch Effect

This effect demonstrates luminance ≠ brightness:

• Highly saturated colours (pure red, blue) appear brighter than desaturated colours (grey) of the same physical luminance
• Physical luminance calculations alone do not predict perceived brightness
• Colourfulness contributes to brightness perception

Visual Acuity

Foveal Vision

• Highest cone density
• Each cone connects to separate nerve fibre
• Maximum acuity: ~1 arc minute

Peripheral Vision

• Lower resolution
• Larger receptive fields
• Better motion detection
• Better low-light sensitivity (rods)

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Summary

• Luminance measures light weighted by human spectral sensitivity
• The luminous efficiency function peaks at 555 nm
• Luminance is physical; brightness is perceptual
• The Helmholtz-Kohlrausch effect shows colour saturation affects brightness perception

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Past Paper Questions

2024 Paper 3 Question 3: What is the luminous efficiency function? How does it relate to cone sensitivity?

2023 Paper 3 Question 3: Explain the difference between luminance and brightness. Give an example where they differ.

2022 Paper 3 Question 4: What is the Helmholtz-Kohlrausch effect and what does it demonstrate?