Improving diameter measurement from Fraunhofer diffraction with fringe segment splicing

Fraunhofer diffraction is an easy but powerful method for measuring the diameter of a thin filament. In practice, however, the diffraction pattern attainable is always subject to limits imposed by various imperfections in real systems, such as small angle approximation and sensor threshold, thus degrading the measurement resolution. In this Letter, we propose a method of fringe segment splicing for improving the diameter measurement from Fraunhofer diffraction. The fringe segment is chosen from a real diffraction pattern and is used to reproduce an ideal diffraction fringe, where the theoretical estimates give the best approximation to the observations. The problem of diameter measurement is solved in the spatial frequency-domain with an ideal diffraction fringe. Our results show that the relative error in this method is less than 0.1% and is far superior to that of previous methods.