Gaussian Blur and Relative Edge Response

It is often convenient to use Gaussian blur in studying image quality or in data augmentation pipelines for training convoluional neural networks. Because of their convenience, Guassians are sometimes used as first order approximations of optical point spread functions. Here, we derive and evaluate closed form relationships between Gaussian blur parameters and relative edge response, finding good agreement with measured results. Additionally, we evaluate the extent to which Gaussian approximations of optical point spread functions can be used to predict relative edge response, finding that Gaussian relationships provide a reasonable approximation in limited circumstances but not across a wide range of optical parameters.