The Edge Sharpen adjustment in Aperture is a professional tool that's used to sharpen photos. Unlike some sharpeners, Edge Sharpen has four special characteristics:
It has often been mentioned on professional photography sites that typical sharpening algorithms can be improved by using several small sharpening steps with lower intensity. Usually the visual improvement is a decrease in the "ringing" around hard edges. These three sharpening passes are accomplished at different pixel radii (you can think of them as 1, 2, and 4 pixels, although their exact radii, actually standard deviations, are slightly different). Also, each sharpening pass uses a lowered intensity to purposefully avoid excessive "ringing" around edges. The relative contributions of each sharpening pass can be controlled using the Falloff slider.
Note: The 1, 2, and 4 scales were chosen specifically because they straddle the typical sharpening radius for a digital camera image (2.2 pixels).
You can control Edge Sharpen to get professional results.
Intensity
The Intensity slider controls the overall amount of sharpening applied. Drag the Intensity slider to the right to increase the amount of sharpening applied to the image, and drag the Intensity slider back to the left to reduce it.
Edges
The Edges slider controls which pixels are edges and which are not. Drag the Edges slider to the right to increase the number of pixels that qualify as edges, and drag the Edges slider back to the left to restrict sharpening further. If you see noise increasing in a flat area of the image, like the sky, decrease the Edges parameter value.
Falloff
The Falloff slider controls how much sharpening is applied during the three sharpening passes at 1, 2, and 4 pixels respectively. Usually, the most sharpening happens in the 1-pixel pass, less in the 2-pixel pass, and less still in the 4-pixel pass. Drag the Falloff slider to the right to equalize the amount of sharpening power between the three sharpening radii, and drag the Falloff slider back to the left to increase the total sharpening power proportionately at the smallest features. Typically you should set the falloff parameter to a value between 0.4 and 0.7; a value of 0.7 means that, proportionately, only 70 percent of the sharpening power applied at the 1-pixel scale is applied at the 2-pixel scale, and only 49 percent of the 1-pixel scale sharpening is applied at the 4-pixel scale. Note that total intensity (between the three passes) always adds up to the indicated value of the Intensity slider.
You can control the amount of sharpening applied in the RAW demosaic process as well. It is controlled by the Intensity and Edges sliders in the RAW Fine Tuning adjustment. This sharpening is generally applied to all your RAW files, so you might want to turn it down (or off) and apply sharpening as an adjustment later. If you want sharpening applied automatically as part of your RAW workflow, leave the settings at the default values. They are intended to "undo" the effect of the camera's internal anti-aliasing filter and provide a suitably sharp image right out of RAW conversion.