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In this paper, we show that optical inverse tone-mapping (OITM) in light microscopy can improve the visibility of specimens, both when observed directly through the oculars and when imaged with a camera. In contrast to previous microscopy techniques, we premodulate the illumination based on the local modulation properties of the specimen itself. We explain how the modulation of uniform white light by a specimen can be estimated in real time, even though the specimen is continuously but not uniformly illuminated. This information is processed and back-projected constantly, allowing the illumination to be adjusted on the fly if the specimen is moved or the focus or magnification of the microscope is changed. The contrast of the specimen's optical image can be enhanced, and high-intensity highlights can be suppressed. A formal pilot study with users indicates that this optimizes the visibility of spatial structures when observed through the oculars. We also demonstrate that the signal-to-noise (S/N) ratio in digital images of the specimen is higher if captured under an optimized rather than a uniform illumination. In contrast to advanced scanning techniques that maximize the S/N ratio using multiple measurements, our approach is fast because it requires only two images. This can improve image analysis in digital microscopy applications with real-time capturing requirements.