Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit

The intensity distribution in Fresnel diffraction through a slit includes numerous small fluctuations referred to as ripples. These ripples make the modelling of the intensity distribution complicated. In this study, we examine the characteristics of the Fresnel diffraction intensity distribution to deduce the rule for the peak position and then propose two types of quantum-mathematical models to obtain the distance between the edge and the peak point. The analysis and simulation indicate that the error in the models is below 0.50 μm. The models can also be used to detect the edges of a diffraction object, and we conduct several experiments to measure the slit width. The experimental results reveal that the repetition accuracy of the method can reach 0.23 μm.