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In this work, we implemented an off-axis digital holographic microscopy (DHM) setup to study the behavior of liquid drops on nanostructured porous silicon (PS) membranes. When a liquid comes into contact with the PS structure, capillary action and surface tension give rise to imbibition of the liquid into the intricate volume of the pores. At the same time, the vapor field developed around the drop enhances liquid condensation and evaporation into and from the pores. The complex interplay between these phenomena (capillary driven internal flows, condensation, and evaporation) is not yet fully understood but the methods we propose can provide new insights. We demonstrate how DHM allows determining the filling fraction of the porous membrane around drying drops of water and isobutyl alcohol. The phase information obtained from registered holograms provides quantitative information that permits to reconstruct the filling fraction along the porous membrane and its evolution during the drying process. Additionally, relevant parameters such as speed and contact angle during retraction of the drops can be measured. These methods can be further extended to other porous materials, such as porous alumina, micro- and macro-PS, to develop better fluid-dynamic models for describing fluid behavior in highly confined structures. [ABSTRACT FROM AUTHOR]