Radiance (L)- light carried by a ray from a light source.

1 Watt(W) = 1 Joule per second.

A radian(r) is a measure of an angle, a steradian/ square radian^[(sr) is a measure of a solid angle.

e.g. In a cone it’s the amount of the radian area of the cone.

Irradiance (E)- light arriving at the surface.

Formulas per unit area:

L = W*Meter(m)¯²sr¯¹ = Radiance

E= W*m¯² = L *cos(dω)

BRDF – bidirectional reflectance distribution function

$f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})\,=\,{\frac {\operatorname {d} L_{\text{r}}(\omega _{\text{r}})}{\operatorname {d} E_{\text{i}}(\omega _{\text{i}})}}\,=\,{\frac {\operatorname {d} L_{\text{r}}(\omega _{\text{r}})}{L_{\text{i}}(\omega _{\text{i}})\cos \theta _{\text{i}}\,\operatorname {d} \omega _{\text{i}}}}$

where ωi is the incoming light direction and ωr is the outgoing light direction.

where i = incident light and r = reflected light.

Reflected Light(Outgoing light):

Specular/regular reflection:

Is the mirror-like reflection of waves, such as light, from a surface.
In this process, each incident ray is reflected at the same angle to the surface normal as the incident ray, but on the opposing side of the surface normal in the plane formed by incident and reflected rays.
For each incident ray the angle of incidence equals the angle of reflection, and the incident, normal, and reflected directions are coplanar.

Diffuse reflection:

Light is scattered away from the surface in a range of directions rather than just one.

Ideal diffuse reflection surface- Lambert’s cosine law:

Such a surface has the equal radiance/brightness /luminance when viewed from any angle/direction lying in the half-space adjacent to the surface.
Although the emitted power from a given area element is reduced by the cosine of the emission angle, the solid angle, subtended by surface visible to the viewer, is reduced by the same very amount.
Because the ratio between power and solid angle is constant, radiance (power per unit solid angle per unit projected source area) stays the same.

BRDF – bidirectional reflectance distribution function

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