In Blender, the OSA option (over-sampling) will render per pixel multiple samples, this to achieve anti-aliased images. By default, we use in Blender a fixed "Distributed Jitter" table. The samples within a pixel are distributed and jittered in a way that guarantees two characteristics;
1) each sample has equal distances to its neighbour samples
2) horizontally and vertically the samples cover equally all sub-pixel positions
The images below show Blender sample patterns for 5, 8, 11 and 16 samples. To show that the distribution is equalized over multiple pixels, the neighbour pixel patterns were drawn as well. Note that each pixel has an identical pattern.




When the samples have been rendered, we've got color and alpha information available per sample. It then is important to define how much each sample contributes to a pixel.
The simplest method is to average all samples and make that the pixel color. This is called using a "Box Filter". The disadvantage of this method is that it doesn't take into account that some samples are very close to the edge of a pixel, and therefore could influence the color of the neighbour pixel(s) as well.
Blender's renderer allows to distribute colors over 3x3 pixels, or calculated from the center of a pixel, over a distance of -1.5 to +1.5. A large amount of formulas have been developed for what distribution factor would give the most pleasant results.
Blender now supports the following filter types:







The horizontal range of these diagrams go from -1.5 to 1.5.
For the Box Filter, you can see that only the samples within the pixel itself are added to the pixel's color.
For the other filters, the formula ensures that a certain amount of the sample color gets distributed over the other pixels as well.
In Blender, next to the filter choice menu (Display Buttons, Render Panel), you can also adjust the filter size. Making the filter size value smaller will squeeze the samples more into the center, and blurring the image more. A larger filter size make the result sharper.
Notice that the last two filters also have a negative part, this will give an extra sharpening result.
The images below are all rendered with 8 sampes.
The lines and dots show the sampling process for polygons, the center part shows the sampling process for textures (here the Material option "Full OSA" was used).







While antialiasing pixels, the value halfway between white (1.0) and black (0.0) usually becomes 0.5. Whether or this is the actual halfway intensity depends on the display device and the human vision system.
It reallly matters if you print graphics, display it on a regular TV or a LCD monitor, or transfer images to film for projection.
The typical solution is to gamma-correct images. Unfortunately that gives too dark images or too washed out colors as well.
Instead of gamma-correcting the output result, Blender can gamma correct the addition of colors. Each sample then gets gamma correcting first, then get added/averaged, and then the result is inverse-gamma corrected back.
To illustrate this effect, two images were added below which were rendered using the "Gamma" option. Compare these to the first images... it will really depend on your monitor type and gamma setting how things look.

