  Microscopy is the workhorse of the physical and life sciences, producing
crisp images of everything from atoms to cells well beyond the capabilities of
the human eye. However, the analysis of these images is frequently little
better than automated manual marking. Here, we revolutionize the analysis of
microscopy images, extracting all the information theoretically contained in a
complex microscope image. Using a generic, methodological approach, we extract
the information by fitting experimental images with a detailed optical model of
the microscope, a method we call Parameter Extraction from Reconstructing
Images (PERI). As a proof of principle, we demonstrate this approach with a
confocal image of colloidal spheres, improving measurements of particle
positions and radii by 100x over current methods and attaining the maximum
possible accuracy. With this unprecedented resolution, we measure
nanometer-scale colloidal interactions in dense suspensions solely with light
microscopy, a previously impossible feat. Our approach is generic and
applicable to imaging methods from brightfield to electron microscopy, where we
expect accuracies of 1 nm and 0.1 pm, respectively.
