Subpixel edge localization with reduced uncertainty by violating the Nyquist criterion

Abstract

In this contribution, the extent to which the Nyquist criterion can be violated in optical imaging systems with a digital sensor, e.g., a digital microscope, is investigated. In detail, we analyze the subpixel uncertainty of the detected position of a step edge, the edge of a stripe with a varying width, and that of a periodic rectangular pattern for varying pixel pitches of the sensor, thus also in aliased conditions. The analysis includes the investigation of different algorithms of edge localization based on direct fitting or based on the derivative of the edge profile, such as the common centroid method. In addition to the systematic error of these algorithms, the influence of the photon noise (PN) is included in the investigation. A simplified closed form solution for the uncertainty of the edge position caused by the PN is derived. The presented results show that, in the vast majority of cases, the pixel pitch can exceed the Nyquist sampling distance by about 50% without an increase of the uncertainty of edge localization. This allows one to increase the field-of-view without increasing the resolution of the sensor and to decrease the size of the setup by reducing the magnification. Experimental results confirm the simulation results.