In pulsed-laser micromachining, incubation refers to the chemical and structural change of a surface due to irradiation from a single pulse and the effect of this change on the absorption of the subsequent pulse. This ability to account for change in absorption properties of a surface – which is done through fitting of a single, material-dependent parameter – allows for prediction of the damage that will occur with irradiation and provides a pathway to uncover the complicated processes that govern incubation. However, the model as it currently stands only accounts for laser pulses irradiating a single spot on a surface. We develop, as a first step towards implementing incubation models for fabrication of surfaces with real-world applications, a mathematical description of the manner in which fluence accumulates during irradiation of surfaces moving with constant velocity relative to a beam. Within this description, we define the criteria for the accumulated fluence profile to be both fully-developed and flat and show that, when these criteria are met, the incubation models can be extended to moving surfaces. We demonstrate the necessity of such a framework with proof-of-concept experiments on three surfaces with distinct incubation behavior: glass, Titanium, and PET. Additionally, when the conditions of flat and fully-developed profile are relaxed, the cumulative and accumulated fluence profiles can differ continuously in the scanning direction. Comparison of real surfaces lased in this manner with their energy profiles can provide a new tool to further our understanding of the processes governing incubation.