What is the difference between radiance and irradiance in BRDF Currently I am reading the BRDF section from Real Time Rendering and I am having a hard time to visually understand the definition of this function. BRDF is the ratio between the radiance in outgoing direction and irradiance of incoming direction. I can't visually understand what does irradiance of a certain direction means? And what is the difference with radiance of certain direction? They both represents the power of light. What does irradiance of a certain direction means? Doesn't we associate a direction with radiance? Isn't radiance defined as irradiance in a single direction? I feel like i misunderstand something here. Is E(v) &lt;= L(v) where v is direction?
First of all, irradiance at a certain point of a surface is the density of radiant flux (power) per unit of surface area, while radiance at a certain point of a surface in a certain direction is the density of radiant flux per unit of surface area and unit of solid angle. Vaguely speaking, irradiance is the amount of light incoming to a certain point from possibly all directions, while radiance is the amount of light incoming to a point from a single direction. Why on Earth do we talk about irradiance from a direction then?
The thing is that the BRDF definition assumes that there is radiance $L_i\left(\omega_i\right)$ incoming to point $x$ through an infinitesimal cone $\mathrm{d}\omega_{i}$ around the direction $\omega_i$ with solid angle size denoted $\mathrm{d}\sigma\left(\omega_{i}\right)$, which then generates some irradiance on the surface. This &quot;partial&quot; irradiance is then denoted $\mathrm{d}E\left(\omega_{i}\right)$. This incident light can be partially absorbed by the surface and partially scattered in all directions. The out-scattered contribution of $\mathrm{d}E\left(\omega_{i}\right)$ to radiance outgoing in direction $\omega_o$ is denoted as $\mathrm{d}L_{o}\left(\omega_{o}\right)$.
It can be shown experimentally that the amount of outgoing radiance $\mathrm{d}L_{o}\left(\omega_{o}\right)$ is proportional to the incoming irradiance $\mathrm{d}E\left(\omega_{i}\right)$ and the BRDF is then defined simply as the ratio between the two:
$$
f_{r}\left(\omega_{i}\rightarrow\omega_{o}\right) = \frac{\mathrm{d}L_{o}\left(\omega_{o}\right)}{\mathrm{d}E\left(\omega_{i}\right)}
$$