Robert D Feinman

Some scanners use "oversampling" to improve the quality of the image. This seems to violate the laws of information theory, but can actually improve the image when done right.
Here is an oversimplified explanation of one way it might work.
This is an ideal scan of a bar chart. The height of the bars represents the density with the bars reaching the top having 100% density and those in between with 0.

In a real image there is some bleeding of the image from one sensor to the next so the contrast will not be 100% or 0.
For the example we assume the max density is 90% and the minimum 10%.
This is represented by the tall bars not reaching the top and the short ones having a finite height. The image would be somewhat lower in contrast than "ideal".

We now oversample or overscan by inserting a value half way between each "real" sample. The density is the average of the two adjacent real samples. So in the ideal image we get steps at about 50% density between the 100% and the 0 steps. In a scanner this is usually done by advancing the stage at 1/2 the pitch of the sensors.

Ideal Image Oversampled

Here is the real image under the same conditions. With our simplified example the intermediate steps are also at 50%. If this was the final result delivered by the scanner the image would not only be lower in contrast, but would appear fuzzier than if the oversampling had not been used. Instead the scanner software must process the image before it is done. Here is an example of how.

Real Image Oversampled

The scanner "knows" that it has inserted an artificial value between the real ones and can use that value to modify the real values on either side. For each pixel we take the values on either side and average them we then subtract the value from the intermediate value if has 50% density or below or add if it is above 50%.

So for the ideal image:

We then remove the artificial steps giving real steps of 0 and 100%. Note we can't have more that 100% or less than 0 density.

50%+50%/2 = 25% subtracted from 0 = 0. (real step)

0%+100%/2 = 50% subtracted from 50% = 0.

50%+50%/2 = 25% add to 100% = 100%. (real step)

One For the real image the steps are the same, but the values being used are 90% and 10%.
But look what happens when we apply the sharpening logic. The dark steps are brought up to 100% and the light steps are back at 0. These are the "real" values that the scanner could not capture without adjustment.
The image is not "sharper", but has improved contrast and thus appears sharper. We have not violated the rules of information theory.
Note this is a very simplified explanation, but the general steps are similar to what the sharpening algorithms do.

90%+10%/2 = 50% subtracted from 50% = 0.

50%+50%/2 = 25% subtracted from 10% = 0.(real step)

10%+90%/2 = 50% subtracted from 50% = 0.