We have previously introduced the Differential Laser Tracking Motion Meter (DLTMM) [Proc. SPIE 7476, 74760D (2009)] as a robust device to determine many optical parameters related to atmospheric turbulence. It consisted of two thin laser beams-whose separations can be modified-that propagate through convective air, then each random wandering was registered with position detectors, sampled at 800 Hz. The hypothesis that the analysis of differential coordinates is less affected by noise induced by mechanical vibration was tested. Although we detected a trend to the Kolmogorov's power exponent with the turbulence increasing strength, we were unable to relate it to the Rytov variance. Also, analyzing the behaviour of the multi-fractal degree estimator (calculated by means of multi-fractal detrended fluctuation analysis, MFDFA) at different laser-beam separations for these differential series resulted in the appreciation of characteristic spatial scales; nevertheless, errors induced by the technique forbid an accurate comparison with scales estimated under more standard methods. In the present work we introduce both an improved experimental setup and refined analyses techniques that eliminate many of the uncertainties found in our previous study. A new version of the DLTMM employs cross-polarized laser beams that allows us to inspect more carefully distances in the range of the inner-scale, thus even superimposed beams can be discriminated. Moreover, in this experimental setup the convective turbulence produced by electrical heaters previously used was superseded by a chamber that replicates isotropic atmospheric turbulence-anisotropic turbulence is also reproducible. Therefore, we are able to replicate the same state of the turbulent flow, specified by Rytov variance, for every separation between beams through the course of the experience. In this way, we are able to study the change in our MFDFA quantifiers with different strengths of the turbulence, and their relation with better known optical quantities. The movements of the two laser beams are recorded at 6 kHz; this apparent oversampling is crucial for detecting the turbulence's characteristics scales under improved MFDFA techniques. The estimated characteristic scales and multi-fractal nature detected by this experiment provides insight into the non-Gaussian nature of propagated light.