Physically-Based Lighting

Flux

how much energy flows from/to/through a surface per unit of time.
Symbol: Φ
Units = Watt

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Irradiance

energy density = flux per area
$E=\frac{d\varphi }{dA}$

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Lambert's law

$E_1=\frac{d\varphi }{d{A}^{\perp }}{E}_2=\frac{d\varphi }{dA}=\frac{d\varphi cos\theta }{d{A}^{\perp }}=E_{1}cos\theta$
since: $A^{\perp }=Acos\theta$

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Exitance

same thing as Irradiance, except for light leaving a surface

$M_1=\frac{d\varphi }{d{A}^{\perp }}=\frac{d\varphi }{cos\theta dA}=\frac{E_2}{cos\theta }$

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Intensity
Radiance

The BRDF