Testing scalar diffraction theory: Gaussian beam on a slit

We recorded diffraction patterns using a commercially available slit and sensor over a wide range of experimental circumstances, including near- and far-field regimes and oblique incidence at large angles. We then compared the measured patterns with theoretical intensity curves calculated via the numerical integration of formulas derived within the framework of scalar diffraction theory. Experiment and theory show particularly good agreement when the first Rayleigh-Sommerfeld (R-S) formula is used. The Kirchhoff formula, though problematic in the context of mathematical consistency, agrees with the first R-S formula, even for large incidence angles, whereas the second R-S formula differs visibly. To obtain such a good agreement, we replaced the assumption of an incident plane wave with that of a Gaussian beam and implemented geometric corrections to account for slit imperfections. These results reveal how the scope of scalar diffraction theory can be extended with a small set of auxiliary assumptions.