Normalization in computational optics

The use of computational techniques to understand the behavior of physical phenomena is well established. Nonetheless, numerical noise is still one of the most common barriers hindering the use of mathematical models to their full potential. A frequent source of issues is the mixing of scales in a given model. In this paper, we tackle this issue by presenting several normalization techniques applied to the wave equation. This allows us to bring the problem to a dimensionless form where the scales are no longer an issue. Additionally, we include a discussion on diffraction integrals, showcasing how their numerical implementation benefits from normalization techniques, particularly in the context of wave propagation and optical systems. We show how normalization can be constructed in a fashion that not only allows for better handling of the model but also provides physical intuition to the problem at hand.