Bokeh describes the rendition of out-of-focus points of light.
Bokeh is different from sharpness. Sharpness is what happens at the point of best focus. Bokeh is what happens away from the point of best focus.
Bokeh describes the appearance or "feel" of out-of-focus backgrounds and foregrounds.
Unfortunately the good bokeh doesn't happen automatically in lens design. Perfect lenses render out-of-focus points of light as circles with sharp edges. Ideal bokeh would render each of these points as blurs, not hard-edged circles. Mathematicians would say the intensity distribution of the blur circles are rectangular in perfect lenses, and good bokeh would prefer a Gaussian distribution. This is one area in which physics doesn't mirror what we want artistically.
Differing amounts of spherical aberration alter how lenses render out-of-focus points of light, and thus their bokeh. The word "bokeh" comes from the Japanese word "boke" (pronounced bo-keh) which literally means fuzziness or dizziness.
A technically perfect lens has no spherical aberration. Therefore a perfect lens focuses all points of light as cones of light behind the lens. The image is in focus if the film is exactly where the cone reaches its finest point. The better the lens, the tinier this point gets.
If the film is not exactly where that cone of light reaches its smallest point, then that point of the image is not in focus. Then that point is rendered on film as a disk of light, instead instead of as a point. This disc is also called the "blur circle," or "circle of confusion" by people calculating depth-of-field charts. In a lens with no spherical aberration this blur circle is an evenly illuminated disc. Out of focus points all look like perfect discs with sharp edges. (OK, at smaller apertures where the image is in pretty good focus you may see additional "Airy" rings around the circle, but that's a diffraction pattern we're not discussing here.) This isn't optimal for bokeh, since as you can imagine the sharp edge of these discs can start to give definition to things intended to be out-of-focus.
There are no perfect lenses, so one usually does not see these perfect discs.
Real lenses have some degree of spherical aberration. This means that in practice, even though all the light coming through the lens from a point on the subject may meet at a nice, tiny point on the film, that the light distribution within the cone itself may be uneven. Yes, we are getting abstract here, which is why some denser photographers refuse to try understand bokeh.
Spherical aberration means that the discs made by out-of-focus points on the subject will not be evenly illuminated. Instead they tend to have more of the light collect in the middle of the disc or towards the edges. Here are some illustrations:
1. Poor Bokeh. This is a greatly magnified blur circle showing very poor bokeh. A blur circle is how an out-of-focus point of light is rendered. Note how the edge is sharply defined and even emphasized for a point that is supposed to be out-of-focus, and that the center is dim.
2. Neutral Bokeh. This is a a technically perfect and evenly illuminated blur circle. This isn't good either for bokeh, because the edge is still well defined. Out-of-focus objects, either points of light or lines, can effectively create reasonably sharp lines in the image due to the edges of the sharp blur circle. This is the blur circle from most modern lenses designed to be "perfect."
3. Good Bokeh. Here is what we want. This is great for bokeh since the edge is completely undefined. This also is the result of the same spherical aberration, but in the opposite direction, of the poor example seen in Fig. 1. This is where art and engineering start to diverge, since the better looking image is the result of an imperfection. Perfect bokeh demands a Gaussian blur circle distribution, and lenses are designed for the neutral.
As you may have gathered, if the light tends to collect towards the middle of the out-of-focus discs on one side of the cone, then it will collect on the outsides of the discs on the other side of the cone. Under-corrected spherical aberration causes the light to collect in one way, overcorrected spherical aberration causes it to collect in the other. Therefore, a lens with great bokeh for backgrounds has awful bokeh for foregrounds, and vice-versa.
Things get weirder from here. Another big factor is how sharply the outside of the blur circle is rendered. Even if we have a poor signature, if the outer edge of this is rendered softly, as it is in the AF-S Nikkor 80-200 f/2.8, we have good bokeh.
Artistically most people tend to prefer sharper foregrounds and softer backgrounds. Fuzzy foregrounds tend to make people crazy, and fuzzy backgrounds are fine. Therefore I classify lenses with good bokeh as those with good background bokeh. Personally I avoid anything fuzzy in my foregrounds by moving the camera or the foreground object.
The reason bokeh is discussed in photography is because we prefer soft out-of-focus areas to hard ones that seem to take on texture, even though everything is out-of-focus. Because of this, it is preferable to those who want soft out-of-focus areas to have the distribution of the light within each blur circle to be concentrated more towards the center of the blur circle. That way each blur circle tends to be a bright spot that gets dimmer gradually towards the edges. This way all the blur circles blend nicely.
On the other hand, if one is trying to keep everything as sharp as possible, these bokeh effects will work differently where your image is close to being in focus. If in doubt, try it out. Lens design very quickly gets very weird.
There is no measurement for bokeh, since scientists aim for the mediocre as their "perfect" lens. Like everything else in art, you gauge bokeh by looking at the image.
Nikon's Defocus Control, or DC, Lenses
Nikon's Defocus Control, or DC, lenses for their popular 35mm SLR cameras actually allow one to manipulate the nature of the spherical aberration correction to allow one to locate the region of good bokeh to be either in the foreground or background. It also allows one to change the amount of spherical aberration for total control.
Reflex and Mirror Lenses
Mirror, or reflex lenses, have awful bokeh. This is because they have a relay mirror in the front of the lens that blocks the central part of the lens' aperture. Therefore all the out-of-focus highlights are represented as doughnuts, which looks unnatural and awful.
Leitz 90 mm f/2.2 Thambar
This was a 1940s soft-focus lens with a twist. Spherical aberration was deliberately left uncorrected at the sides. The softening is most obvious at full aperture. The lens becomes sharp as you stop it down. Leitz pulled a clever trick and included a removable front filter with an opaque central circle. The central stop eliminates the contribution from the lens' highly corrected central portion and let you get a soft central image as desired.
Diaphragm Blades
The shape and number of a lens' diaphragm blades has little to do with bokeh. They define the shape of the blur circle, but they don't define how the light is distributed within that circle. These circles are no longer circles, but shapes with as many sides as there are blades. For instance, with five blades as most Hasselblad and Mamiya lenses one gets five-sided pentagons as the shapes of out-of-focus highlights instead of circles. This isn't too great. With six blades, most common in discount lenses for 35mm SLRs, one gets hexagons. With seven blades (most Nikkor SLR lenses) things really start to improve, since the seven-sided heptagons start looking like circles instead of recognizable shapes. Nine blades (common on Nikkor telephotos) are great, and lately they are being designed with curved blades to give a close approximation of a circle.
Odd numbers of blades will give diffraction and reflection stars around very bright points of light that have double the number of points as the number of blades. For instance, a seven-blade diaphragm will give a lovely 14-pointed star. Even numbers of blades will give stars with the same number of points as you have blades. An eight-bladed diaphragm will give a boring eight pointed star.
Again, how well one approximates a circle is only a small part of the equation. The important part is how the light is distributed. Obviously at full aperture where most people worry about this the diaphragm plays no part.
The reason some manufacturers attempt to draw a correlation between bokeh and numbers of diaphragm blades is because it's easy to see how many blades there are at the sales counter, but almost impossible to see bokeh.
p/s: review taken from the internet