Super-Resolution Thermometry via Computational Correction to Overcome Diffraction Limit

A computational enhancement is proposed, allowing for the realization of optical thermometry at spatial resolutions beyond the diffraction limit. Since the temperature measurement is a weighted average over the beam spot, the spot needs to be much smaller than the region of interest for accurate measurements. If it is too large, averaging creates a smoothing effect, flattening the measured profile. The simple solution is to more tightly focus the beam in order to create a smaller spot size. However, there is a limit to how much a beam of a given wavelength of light can be focused, known as the diffraction limit. For a diffraction limited system, then, there is a minimum temperature profile that is resolvable. To counter this, the relationship between the true profile, flattened profile, and beam shape can be put into the form of an integral equation, whose solution is the "true" profile. This equation takes a form that is similar in structure to problems in fields such as electromagnetism, image processing, and heat conduction. By studying how those fields approach the problem, their solutions can be used to create a set of corrective methods to undo the smoothing effect. Applying these to existing Raman systems allows for accurate measurements at scales up to 5x smaller than currently possible, improving spatial resolution without changing the underlying hardware.