Event cameras, an innovative bio-inspired sensor, differ from traditional cameras by sensing changes in intensity rather than directly perceiving intensity and recording these variations as a continuous stream of "events". The intensity reconstruction from these sparse events has long been a challenging problem. Previous approaches mainly focused on transforming motion-induced events into videos or achieving intensity imaging for static scenes by integrating modulation devices at the event camera acquisition end. In this paper, for the first time, we achieve event-to-intensity conversion using a static event camera for both static and dynamic scenes in fluorescence microscopy. Unlike conventional methods that primarily rely on event integration, the proposed Inter-event Interval Microscopy (IEIM) quantifies the time interval between consecutive events at each pixel. With a fixed threshold in the event camera, the time interval can precisely represent the intensity. At the hardware level, the proposed IEIM integrates a pulse light modulation device within a microscope equipped with an event camera, termed Pulse Modulation-based Event-driven Fluorescence Microscopy. Additionally, we have collected IEIMat dataset under various scenes including high dynamic range and high-speed scenarios. Experimental results on the IEIMat dataset demonstrate that the proposed IEIM achieves superior spatial and temporal resolution, as well as a higher dynamic range, with lower bandwidth compared to other methods. The code and the IEIMat dataset will be made publicly available.