Focus on Unsharp Masking 

If a traditional photograph is out of focus when the shutter snaps, you're stuck with a fuzzy image. There are no conventional means to sharpen the image beyond the limits of the original. 

Digital images, on the other hand, can often be salvaged. Because of their digital nature, it's possible to apply mathematical formulas that can create higher contrast at the edge of objects, thus creating a sharper image. This process is called unsharp masking. Most good imaging software programs, such as Adobe PhotoShop, will allow you to do this. Here's how unsharp masking works.

Pixels and algorithms: A brief review

A digital image is made up of thousands of pixels, or tiny squares, each of which is assigned its own color. Three different values combine to determine this color: the R (red) value, the G (green) value, and the B (blue) value. Varying levels of red, blue, and green produce every color in the spectrum, from yellow to purple, and black to white. 

Because the pixels have a numeric value, you can make instantaneous changes by applying a single mathematical formula that affects every pixel. For example, you could give a photo a warm, reddish cast by uniformly raising the R value of each pixel. 

That's the simplest case. The algorithm for unsharp masking, which changes the sharpness of the image rather than its color, is more complex.

Detecting and sharpening edges

An image is out of focus because one object blurs into another. For example, you've taken an out-of-focus photo of an air balloon against a blue sky. If you look closely, you'll notice there's no distinct point at which the balloon ends and the sky begins. This is because the transition occurs over three or four pixels. 

The job of an unsharp masking algorithm is to detect this blurry edge and divide it into two distinct parts. The first part--detecting the edge--is relatively easy. First, the photo is converted into a grayscale image. Then, areas that have a rapid change in brightness within just a few pixels are singled out as edges. 

So far, so good. Now the difficult part: how can you reintroduce sharpness to this edge? It's actually a three-step process. 
Edges are unsharp Edges are blurred
Original image Algorithm widens edges

First, the algorithm creates an even blurrier version of the photograph, so the blurry edges aren't just three or for pixels wide, but perhaps eight or ten.
Mask is created
Mask is created

Second, the numerical values of the pixels in the blurred copy are subtracted from the pixels of the original. The result is called a "mask." The mask is actually a series of positive and negative values. It registers the small but soon-to-be-important differences between the original and the blurred copy.

Third, the values of the mask--whether positive or negative--are added to the original image. This makes the bright half of the edge even brighter, and the dark half even darker. Thus, the original goal is achieved--higher contrast at the edge of objects, so the boundaries between objects are more distinct.
Edges are sharpened Edges are sharpened
Original edges Sharpened edges

A balancing act

As clever as an unsharp masking algorithm may be, it has its limitations, and what it detects as the edge of an object may not be an edge at all. For example, digital images often have small imperfections that are invisible to eye, such as light pixels in the middle of a shadow. If the unsharp mask function is too sensitive, it will pick up these small abnormalities and make adjustments that actually introduce more errors. And even where a real edge does exist, the unsharp mask can create edges that are too hard, giving the image a flat, unrealistic feel. 

But several solutions are possible. For example, you might use the unsharp mask function only on specific parts of the image, leaving the rest untouched. Or you could make it more or less difficult to detect edges by changing either kernel size--the width of the edge (meaning the number of pixels over which a change in contrast occurs); or the height of the edge (meaning the minimum change in contrast that defines an edge). 

As you can see, unsharp masking may require some manipulations to achieve the best results. Still, it represents a significant advance over traditional photography, since you can actually make a sharper, better image than the original.