Measurement of distance with the nanoscale precise imaging by rapid beam oscillation method

We discuss here the principles of a novel optical method in which the scanning of a laser spot around a fluorescent object is used to determine its shape, orientation, and fluorophore distribution. The scanning pattern is adapted to the shape of the object according to a feedback principle based on intensity modulation measurements. The modulation of the intensity with respect to the angular coordinate is used to keep the orbit centered on the object. The modulation induced by rapid oscillations of the orbit radius is used to measure the local distance from the surface with nanometer precision. We provide a model to describe the fundamental relationship between modulation and distance and discuss the range of validity of several approximate expressions. According to this model, the distance can be measured with a precision dependent on the steepness of the point spread function and the total number of detected photons. To test our findings, we performed experiments with one or two channels on fluorescent spheres of known size and characterized the modulation function of our microscope setup. We conclude that the method can be used to measure distances in the range 10-200 nm between two surfaces labeled with two different probes.