Bad seeing, poor transparency, focus, & misalignment can all reduce your resolution from the theoretical diffraction limited performance of your scope. The age of digital images allows us to break through the limits of diffraction, poor seeing, and poor focus. Using measured or estimated point spread functions we can reverse diffraction and calculate a truer version of the image with increased resolution.

Deconvolution and wavelet algorithms, unlike the old sharpening techniques like unsharp mask, can recover real detail from images. Digital images can be better than the diffraction limit in real world conditions. With many factors that can decrease or increase the resolution of your final image, how can you quantify the resolution you have achieved in a final real world image?

The sampling theorem provides a way. By downscaling your image to a series of benchmark resolutions, we can artificially limit the image resolution. If we then upscale the benchmark images back to the original size we can compare them to the original image. The lowest resolution benchmark that is identical in detail to the original image was resampled at an upper bound of the original image resolution. Here's a recent example of mine - be sure to follow the link to the full size image to see the differences clearly:

You can learn more about this technique in my note Estimating image resolution by re-sampling.