Radiometry Foundations

What this lecture covers

Why radiometry is the right language for light transport.
The relationship between flux, irradiance, and radiance (see eq.irradiance and eq.radiance).
How these quantities appear in rendering equations.

Understanding the geometry of light transport is essential. As shown in fig.radiometry-diagram, we measure light from different perspectives depending on what question we’re asking.

Derivation

Starting from flux $\Phi$ , irradiance over a differential area is defined by eq.irradiance.

E = \frac{d\Phi}{dA}

eq.1.1

For directional dependence, we introduce radiance (eq.radiance):

L = \frac{d^2\Phi}{dA \, d\omega \, \cos\theta}

eq.1.2

These two fundamental quantities form the basis of all light transport calculations.

Basic math test

what

The irradiance equation (eq.irradiance) describes how flux spreads over an area. When we need directional information, we use the radiance formulation from eq.radiance.

Inline math: $E = dΦ / dA$

Block math:

L = d²Φ / (dA · dω · cosθ)

eq.1.2

If equations render correctly, KaTeX/MathJax is configured. Hover over any equation reference above to see a preview!

Code block test

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struct Ray {
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    vec3 origin;
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    vec3 direction;
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};
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vec3 trace(const Ray& ray) {
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    return vec3(0.0f);
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}

Image component examples

The radiometry diagram below (fig.radiometry-diagram) illustrates the key geometric relationships we need to understand for light transport.

Radiometry diagram (single image block) — **Figure 1.1**: Geometric relationships in radiometry, showing how light interacts with surfaces at different angles

Radiometry diagram A — **Figure 1.2**: at different angles

Radiometry diagram B — **Figure 1.2**: at different angles

Try hovering over the figure reference fig.lol above to see a preview! When you’re studying light transport, you’ll frequently refer back to fig.radiometry-diagram to understand the geometric setup. what??