The concept of photon acceleration is revisited. It is shown here than it can be described as an inelastic scattering process. This new approach is applied to the study of relativistic plasma bubbles or wakefields, as those created by an intense laser pulse or by a particle beam moving in a background plasma. Scattering of an incident probe photon beam by a relativistic plasma density perturbation is considered. The angular dependence of frequency and intensity of the scattered signal are discussed in detail. The case of relativistic electron beams propagating in vacuum is also considered for comparison. Such a scattering process could be used as a diagnostic of the space-time structures created by laser driven bubbles and wakefields, for particle acceleration studies.