Optical silica micro and nanofibers are the subject of intense research due to the diversity of their potential uses, such as sensors and active components. Although these fibers are easy to produce, their full characterization is cumbersome. These objects are indeed a few hundred nanometers in diameter for lengths exceeding a few centimeters. Electron microscopy may provide the required full profile of these fibers but at the expense of an excessive cost and of the destruction of the component. To bring a solution of this problem, we propose a simple technique to improve the precision of classical optical microscopes beyond the diffraction limit. It relies on the a priori knowledge of the object, and on a computer simulation of the images acquired by the microscope. Experimentally, we use a bright field illumination microscope in the blue range. The nanofiber which is freely suspended in the air is set perpendicular to the illumination axis. A scanning stage moves the microscope objective upstream and downstream the nanofiber, perpendicularly to its axis. For long nanofibers, the nanofiber itself is also moved along its axis. We thus acquire the full optical field diffracted by the nanofiber. This diffracted pattern is compared to a bank of diffracted patterns simulated based on Maxwell equations with the only assumption that the nanofiber is a perfect silica rod. There is one such simulated pattern for each radius of a full series of possible nanofiber radii, with a 1 nm spacing between two successive radii. A comparison between the acquired pattern and the simulated ones allows determining the profile of the nanofiber with an accuracy better than 50 nm on its radius at each point along its axis. Suggestions for further resolution improvement will be presented.