Final answer:
Kirchhoff's scalar diffraction theory has inconsistencies related to its boundary conditions, with issues arising in the treatment of wavefronts and secondary waves. Remedies include more rigorous solutions such as the Helmholtz equation and the Fresnel-Kirchhoff diffraction formula, as well as quantum mechanical approaches for submicroscopic scales.
Step-by-step explanation:
Kirchhoff's scalar diffraction theory is a fundamental concept used to describe how light waves propagate and interact with objects, particularly in the context of diffraction. However, it is known to have mathematical inconsistencies related to the imposed boundary conditions. The theory assumes light waves propagate in a homogeneous medium and that under certain conditions, the waves can be approximated as rays. One inconsistency arises since it treats points on a wavefront as secondary point sources, but does not correctly account for the obliqueness of the secondary waves - a necessary condition for there to be wave propagation in the direction normal to the wavefront. These inconsistencies can lead to incorrect predictions when they are not insignificant compared to the wavelength of light, for example in near-field diffraction.
More rigorous solutions to the wave equation, such as those based on the Helmholtz equation, can be used to remedy the inconsistencies of Kirchhoff's theory. Alternatively, the Fresnel-Kirchhoff diffraction formula tries to fix these problems with a better approximation of the boundary conditions. Quantum mechanics can also address some of the deficiencies of classical diffraction theories by providing a more accurate description at submicroscopic scales, as is the case in the analysis of crystal structures using X-ray diffraction and Bragg's law.