# Lambert Cosine Emission¶

A **Lambertian emitter** has the same brightness (i.e. current per area per
solid angle) when observed from all angles.
A Lambertian emitter therefore follows **Lambert’s cosine law**,
which is to say that the angular current density
(i.e. current per solid angle) observed from
an angle (relative to the surface normal) is
proportional to .
That is because the emission surface appears to have a size proportional
to
from a vantage point of that angle.
The angular current density is independent of the angle
of rotation around the surface normal.

**FLY2:**
See SIMION Example: particles (lambert_cosine.fly2) (added in 2015-07-15) for an
example of generating a Lambert Cosine distribution of emission in a
Monte Carlo Method fashion in a FLY2 file.

**Sampling:**
If all rays traced in a beam represent the same current, we can sample a
random ray from a Lambert cosine distribution in Monte Carlo fashion as follows.
The probability of a ray with angle is for
.
This gives a random variable
, where is a uniformly
distributed random variable between 0 and 1.
The probability of a sampling a ray with angle is
proportional not to but to
since
the solid angle covered by *all* observers (at *any* ) with
angle is proportional to .
Inverting this distribution,
, implies
.
So, we have the random variable .