We study how a liquid-based inferior mirage, obtained by layering distilled water and ethanol, transforms the phase structure of a light beam possessing a helical wave front. An inferior mirage amounts for one total internal reflection, which effectively reverses the handedness of the wave front. We show that this transformation is accompanied by smooth unidirectional astigmatic changes and variations of the non-canonical strength of the phase singularity nested in the beam. A skew in the beam

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... ntensity distribution is observed where the phase singularity is inverted and allows the direct measurement of the topological charge of the beam. Freely propagating, partially inverted beams possessing spatially varying orbital fluxes can be obtained at the exit plane of the solution by adjusting the incidence conditions of the beam. This work lays the foundations for phase engineering of light beams in liquid-based optical mirages. Supplementary material for this article is available online