We present a method to find the optimum distribution of scatterers in an edge-lit lightguide plate (LGP) for rendering a uniform distribution of the outcoupled light. We propose a simple mathematical model describing the light propagation in a waveguide with a distribution of scattering elements located on the lower surface of the waveguide. We have found a differential equation giving the distribution of scattering elements leading to a uniform irradiance along the LGP, and we propose a method to determine the value of the outcoupling coefficient of an individual scattering element from the irradiance (or radiance) measurements. We have verified the validity of this model by performing ray tracing simulations on an LGP with the scattering elements distributed according to the solution of the proposed differential equation, and we have found a quantitative agreement between the analytical results and the simulated ones. Also this model has been used to directly calculate the output power of a given embossed LGP.