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The extraction of "Level 2" detail -- ridge terminations, ridge bifurcations, bridges etc. -- from digitised images of fingerprints requires an accurate segmentation of the image into ridges and valleys. Small breaks and irregularities in the ridge pattern occur as a result of imperfections in the print capture process that, if not rectified, give rise to many false level 2 features at later stages of the analysis. We propose a method for enhancing the ridge pattern by applying a process of oriented diffusion, which is an adaptation of anisotropic diffusion. This acts to smooth the image only in the direction parallel to the ridge flow. The result is an image in which intensity varies smoothly as one traverses along the ridges or valleys, with most of the small irregularities and breaks removed, but with the identity of the individual ridges and valleys preserved. The method offers the advantage of requiring no prior estimate of the ridge frequency. Results show improved performance by comparison with the method of enhancement using frequency-tuned filters, which sometimes performs well but may produce erroneous results if the filter is tuned to a frequency that does not match the actual ridge frequency.