1. A method for recording and displaying an image of a sample, the method comprising the steps of: generating an electron beam; scanning a surface of the sample with the electron beam; detecting electrons emanating from the sample while scanning the sample with the electron beam; generating an image of the surface of the sample based on the detected electrons and displaying the generated image as a gray value image; generating a binary edge image from said gray value image so that edges present in said gray value image are determined as line areas around said edges; applying a sharpness algorithm in the gray value image within regions which correspond to said line areas; carrying out a smoothing process in the gray value image within regions which lie outside of said line areas so that an additional smoothed, sharpened gray value image is generated; and, displaying the smoothed, sharpened gray value image.