Most recent advances in fluorescence microscopy have focused on achieving spatial resolutions below the diffraction limit. However, the inherent capability of fluorescence microscopy to non-invasively resolve different biochemical or physical environments in biological samples has not yet been formally described, because an adequate and general theoretical framework is lacking. Here, we develop a mathematical characterization of the biochemical resolution in fluorescence detection with Fisher information analysis. To improve the precision and the resolution of quantitative imaging methods, we demonstrate strategies for the optimization of fluorescence lifetime, fluorescence anisotropy and hyperspectral detection, as well as different multi-dimensional techniques. We describe optimized imaging protocols, provide optimization algorithms and describe precision and resolving power in biochemical imaging thanks to the analysis of the general properties of Fisher information in fluorescence detection. These strategies enable the optimal use of the information content available within the limited photon-budget typically available in fluorescence microscopy. This theoretical foundation leads to a generalized strategy for the optimization of multi-dimensional optical detection, and demonstrates how the parallel detection of all properties of fluorescence can maximize the biochemical resolving power of fluorescence microscopy, an approach we term Hyper Dimensional Imaging Microscopy (HDIM). Our work provides a theoretical framework for the description of the biochemical resolution in fluorescence microscopy, irrespective of spatial resolution, and for the development of a new class of microscopes that exploit multi-parametric detection systems.