It is presented a criteria for selecting the optimum aperture radius for the one beam Z-scan technique (OBZT), based on the analysis of the transmittance of the aperture. It is also presented a modification to the OBZT by directly measuring the beam radius in the far field with a rotating disk, which allows to determine simultaneously the non-linear absorptive coefficient and non-linear refractive index, much less sensitive to wave front distortions caused by inhomogeneities of the sample with a negligible loss of signal to noise ratio. It is demonstrated its equivalence to the OBZT.

Monte Carlo method (MCM) is a useful tool to simulate and understand random process in the nature. Many of this process are difficult to solve by means of analytic expressions, due we do not know many of its variables involved in the process. The core of MCM is to generate random variables, which represent physical variables, through of its probability distribution function (PDF). Every random physical variable has a law of probability to obtain a certain value, within a specific interval. Specially, in the data obtained by lidar returns, we got information of the type of scatterer from the radiation backscatter to receiver. This portion of backscatter radiation is a little part of the function that describes the total scattering in radians. This function is called "phase function" and has a particular way depending on size, refractive index, shape, etc. of the scatterer. In this work we present the numerical results to consider different phase functions in the simulation of lidar returns, through of MCM.

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