2\right)\) the NL phase shift extends (compresses) beyond the incident intensity distribution, while for \(m=2\) the NL response of the medium is considered as local43. It is worth mentioning that the \({n}_{2}\) values measured in this work for \(m\ne 2\) are related to the thermo-optic coefficients that tend to induce self-defocusing effects in an equivalent way to the third-order NL refractive indices for the Kerr effect./p>2.0\right)\). Conversely, large illumination diffuser areas lead to the construction of a pattern with a large number of speckles, with smaller sizes, resulting in a more homogeneous intensity distribution, i.e., lower intensity contrast \(\left({g}_{self, max}^{\left(2\right)}<2.0\right)\). For this reason, the IC-scan curves present a peak-to-valley structure opposite to those of D4σ, which directly measure the beam size in the detection plane./p> 1.0 kW/cm2) are high enough to excite both linear and NL effects. Therefore, the cross-correlation function allows to analyze the statistical properties of the speckle patterns that were modified only by NL refraction effects./p> 15 kW/cm2, it is observed that for the colloid with f = 4.1 × 10–2, \(\Delta {g}_{cross, max}^{\left(2\right)}\) also deviates significantly from the values found for pure ethanol, indicating the contribution of some new NL phenomenon that influences the characterization of the NL refractive behavior. To understand the origin of the change in the slope of the \(\Delta {g}_{cross, max}^{\left(2\right)}\) versus I curve, experiments to characterize the behavior of the scattered light intensity with the increase of the laser intensity were performed. In these experiments, a cell with 1.0 mm thickness, containing SiO2 colloids, was located in the focus of a 10 cm lens, identical to that used in the Z-scan, D4σ and IC-scan experiments. The scattered light was collected in a direction nearly perpendicular to the propagation direction of the incident laser beam by using a microscope objective, a plano-convex lens and a photodetector, as schematized in Fig. 5i./p> 15 kW/cm2. This NL scattering contributions can be understood from the Rayleigh-Gans model60, by expressing the scattering coefficient as: \({\alpha }_{scat}={g}_{s}{\left(\Delta n\right)}^{2}\), where \(\Delta n\) represents the difference between the effective refractive indices of the NP and the host medium, and \({g}_{s}\) is an intensity-independent parameter, but depends on the size, shape and concentration of the NPs and the optical wavelength. By considering the NL refractive behavior of the colloids \(\left(\Delta n=\Delta {n}^{L}+\Delta {n}_{2}^{eff}I\right)\), it is possible to find expressions for the linear \(\left({\alpha }_{scat}^{L}={g}_{s}{\left[{\Delta n}_{L}\right]}^{2}\right)\) and NL \(\left({\alpha }_{scat}^{NL}=2{g}_{s}{\Delta n}_{L}{\Delta n}_{2}\right)\) scattering coefficients, with \({\alpha }_{scat}={\alpha }_{scat}^{L}+{\alpha }_{scat}^{NL}I\). Since the NL contribution of the SiO2 NPs was considered small compared to the solvent, \({\Delta n}_{2}\) corresponds mainly to the NL refractive index of ethanol, which became significant for higher intensities. Thus, as shown in Table 1, \({\alpha }_{scat}^{NL}<0\), decreasing the linear scattering coefficient for high intensities and corroborating the results of Fig. 5h,j. Therefore, in addition to the IC-scan technique allowing scattering-free NL refraction measurements, it also has the ability to distinguish linear and NL scattering contributions./p>