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We introduce the basic elements of a spatio-angular theory of fluorescencemicroscopy, providing a unified framework for analyzing systems that imagesingle fluorescent dipoles and ensembles of overlapping dipoles that labelbiological molecules. We model an aplanatic microscope imaging an ensemble ofin-focus fluorescent dipoles as a linear Hilbert-space operator, and we showthat the operator takes a particularly convenient form when expressed in abasis of complex exponentials and spherical harmonics$-$a form we call thedipole spatio-angular transfer function. We discuss the implications of ouranalysis for all quantitative fluorescence microscopy studies and lay out apath towards a complete theory.

Spatio-angular fluorescence microscopy I. Basic theory