Image quality is a nebulous concept with different meanings to different people. To quantify image quality a relative difference is typically calculated between a corrupted image and a ground truth image. But what metric should we use for measuring this difference? Ideally, the metric should perform well for both natural and scientific images. The structural similarity index (SSIM) is a good measure for how humans perceive image similarities, but is not sensitive to differences that are scientifically meaningful in microscopy. In electron and super-resolution microscopy, the Fourier Ring Correlation (FRC) is often used, but is little known outside of these fields. Here we show that the FRC can equally well be applied to natural images, e.g.\ the Google Open Images dataset. We then define a loss function based on the FRC, show that it is analytically differentiable, and use it to train a U-net for denoising of images. This FRC-based loss function allows the network to train faster and achieve similar or better results than when using L1- or L2-based losses. We also investigate the properties and limitations of neural network denoising with the FRC analysis.