We report preliminary results of a study for investigating the spatial homogeneity of induced and spontaneous oscillations in the concentration of oxyhemoglobin on the scalp/skull layer of two human subjects. Hemodynamic oscillations were induced by modulation of arterial blood pressure, which triggers the cerebral autoregulation mechanism. Induced hemodynamic oscillations are used in coherent hemodynamics spectroscopy to derive physiological parameters of interest for medical diagnostics. For example, our dedicated mathematical model translates typical near-infrared spectroscopy observables, like the amplitude and phase relationship of the oscillations of oxy- and deoxyhemoglobin concentrations into capillary and venous blood transit times, cutoff frequency of the autoregulation process, and other parameters related to microvascular blood volume. In this study, we focused on the phase relationship between the oscillations of oxyhemoglobin concentrations in three optical channels, two of which feature a short (5 mm) source-detector separation (sampling the scalp/skull only) and the third one features a long (30 mm) source-detector separation (sampling both extracerebral and cerebral tissues). The two main goals of the study were: a) to compare the coherence of induced and spontaneous oscillations; b) to assess if induced and spontaneous oscillations may be assumed to be uniform in the extracerebral layer. This was assessed by studying the phase relationship of oscillations in oxyhemoglobin concentration at the two short source-detector separations. About point a) we verified that induced oscillations have a higher incidence of coherence than spontaneous oscillations: 74% for induced oscillations, and 30% for spontaneous oscillations. About point b) the results show an overall trend for both spontaneous and induced oscillations to be homogeneous or “quasi-homogeneous” in the extracerebral tissue; however, we observed cases where a significant non-zero phase difference was measured, indicating spatial heterogeneity. We propose a method for taking into account the possible inhomogeneous behavior of the oscillations in the scalp/skull in order to increase the accuracy of measurements of cerebral hemodynamic oscillations.