Fluorescence microscopy is used to look at small samples that can't be seen clearly with a traditional light microscope. Transparent or very small materials like DNA strands can be tagged with fluorophores - fluorescent proteins that emit bright visible light when illuminated with ultraviolet light. They can be specially designed to stick to certain kinds of materials so we can selectively look at only the parts of a sample we're interested in. The light emitted is typically collected by a CCD to form an image. In this paper, Backer and Moerner make an improvement on fluorescent microscopy by showing theoretically that they can infer additional information about the fluorophores by the patterns of light each one makes on the CCD.

Each fluorophore points a particular direction in space, and the amount of light we detect from the molecule depends on this orientation as well as the direction of the electric field we apply and detect, called the polarization of the light. It is useful to be able to measure the fluorophore's orientation, since it allows us to track movement in samples. By measuring the intensity emitted by the fluorophore at different polarizations, scientists have been able to determine physical properties of DNA, and study the movement of motor proteins. These directional measurements are not completely reliable, though. In particular, the authors show how typical measurements can't tell the difference between a fluorophore that is completely fixed in space, and one that is allowed to wiggle around about a fixed axis.

The authors begin by asking what patterns we expect to see in the image from a fluorophore for each possible combination of orientation and rotational mobility. They find that each pattern can be characterized by three numbers, which are in turn related to the fluorophore's characteristics. They then "invert" the problem, instead using the patterns in the image to estimate the orientation and mobility of a molecule. They show that the method works even in noisy experimental conditions, and outline the technical challenges that need to be overcome before this kind of measurement can be performed. In particular, the position of each fluorophore affects the pattern it produces on the CCD. Since we don't know the positions of the fluorophores, they need to be estimated for this analysis to work. If our estimate is wrong, it may affect the accuracy of the results.

It is common in physics not to be able to measure certain quantities directly, but instead to infer them from related measurements. The presence of planets can be inferred by their gravitational effects on stars, and the charge of an electron can be inferred from the electric force on oil drops. But in order to make these inferences, we need physical models. We need a way to map between the measurements and the physical quantities of interest. This paper is an example of such a problem. The CCD image produced by the microscope contains information at every pixel - far more than would be produced by a single intensity measurement. But this information is effectively useless unless we have enough of an understanding of the physics of the problem to relate the patterns to the direction and rotational mobility of the fluorophores.

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