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Observing deformations of 20 nm with a low-numerical-aperture light microscope

In the presented paper we show that--using appropriate image post processing--measurements with an accuracy and resolution far beyond the theoretical resolution limit of an optical sensor can be made. We demonstrate this based on the observation of tensile tests which are performed on micrometers - sized samples under a low numerical aperture microscope. Although the microscope resolves only about 4 micrometers , deformations of 20 nm can be observed. The measurement accuracy is in the same range. The algorithm achieving these results is an image matching technique combined with a diagnostic tool that automatically detects measurement errors and refines the parameter estimates applying a rigorous statistical testing framework. The paper focuses on the mathematical and physical aspects of this image processing algorithm. The use of image data from tensile experiments is motivated by the fact that we can find a ground truth--namely the linearity in the stress-strain relation in the elastic domain--even on the nanometer scale. Thus, we can test the algorithm on its performance. However, the matching technique has also the capability to estimate rigid body motion with the same accuracy and resolution. In addition, the algorithm is formulated independently of the microscope type. Therefore it is a straight forward task to transfer the procedure to other microscope types, i.e. Scanning Electron Microscopes.