Topics in Particle and Dispersion Science

Radiance, L_u, of a unidirectional light source can be defined as follows:

at z = 0, i.e. at the source itself. In the above equation, ξ is the direction unit vector, ξ₀ is the unit vector of the source beam axis, δ is the Dirac delta function, and E_u0 is the irradiance generated by the source at z = 0.

1. Why is irradiance used in Eq. 1?
2. What is the dimension of the Dirac delta function, as applicable here, and why?