On Babinet's principle and a diffraction-interferometric technique to determine the diameter of cylindrical wires

Abstract

Laser diffraction is a robust and precise technique for measuring wire diameters. However, classical Fraunhofer diffraction formulas are inappropriate for determining the size of three-dimensional objects. Babinet's principle (from classical diffraction theory) allows the use of such formulas only for angles of diffraction tending to zero. In practice diffraction measurements require a finite angular range (about 10°) for good resolution. We show that use of the classical slit-diffraction formula for this extended angular interval introduces significant error. We develop a simple diffraction model valid for cylindrical shapes and a formula to obtain the diameter of cylindrical wires. To validate the diffraction formula we calibrate the diameter of the wires using an independent interferometric technique, which to our knowledge is original for this particular task. We have verified our diffraction formula to within about 0.2 µm for various wire materials and diameters (30 µm to 300 µm) and a wide angular range (±25°). Two different experimental set-ups were implemented to increase the reliability of the results. The calibration procedure revealed a systematic disagreement with Babinet's principle, in particular a systematic overestimation of the diameter by about 0.6 µm, almost independent of the material and the diameter itself. This is particularly relevant to metrological applications involving diffraction phenomena and based on classical diffraction theory.