Any technology that attempts to reduce the effects of vibrations in an optical system.

Vibrations at different frequencies manifest themselves as loss of resolution in photography, shake in video and severe limits in the usability of systems like binoculars and telescopes.

Optical image stabilization systems

Optical image stabilization systems, pioneered in the consumer market by Canon, introduce into the optical path some mobile component that shifts the light rays in ways that complement (and negate) the vibrations. Obviously any such system has limits both in the amplitude and in the frequency of the vibrations that it can erase. It should also be remembered that, since there is physical movement involved, all these systems consume power.

The Canon Systems

Here I am talking about Canon because that system is the one that enjoys coverage. There is an analogous Nikon system called VR, for Vibration Reduction, and it appears to perform more or less the same as the Canon system. Both makers claim that their systems will allow you to shoot handheld three stops slower than normal.

IS also known as Optical Shift Image Stabilizer: one of the lens groups inside the lens can travel in a vertical direction, according to the accleration data from a small accelerometer. Supposed to dampen oscillations in the vertical plane from 2 to 20 Hz.

IS 2: like the above, but also able to move sidewise (this would be useful for tracking shots).

Vari-Angle Prism: used in binoculars and videocameras, this is not a lens group but something trickier. In Canon's slightly ingrish description (I took the liberty of correcting bellow to bellows):

Canon's optical image stabiliser uses the Vari-Angle Prism to compensate for image shaking. The Vari-Angle Prism is composed of two pieces of flat glass joined by a flexible bellows made of a special film that can expand and contract as required. The space between the glass plates is filled with a liquid of a high refractive index. The liquid is silicon-based oil specially developed by Canon. One glass rotates for pitch movement and the other for the yaw movement. Therefore, expansion and contraction of the flexible bellows can vary the top angle.
In other words, you know that a prism (basically, a wedge of glass) will deflect lightrays at an angle depending on the prism angle. This prism can change its angle: what is even more interesting, the prism is actually two prisms, one for vertical deflection and the second for horizontal deflection. This system too gets acceleration data from two accelerometers; Canon also claims that in the rather fancy XL1S videocamera they examine the actual CCD picture to get additional camera shake data.

Is it perfect? No, Canon advised that you don't use the Optical Shift Image Stabilizer system when the camera is on a tripod (which would be SOP for long telephoto lens). In new models, apparently the electronics is smart enough to detect that the lens is on a tripod and adjust accordingly.

Additionally, some people (I do) find the effect of IS in binoculars incredibely nausea-inducing; I think that it is because the perceived movements in the eyepiece are now decoupled from the movements that one's organs of equilibrium perceive. This is analogous to what happens when reading on a car. Also, IS systems occasionally tend to "hunt" for some seconds before stabilizing, which produces a moving picture in the viewfinder. Finally, when doing panning movements there is a moment when the system decides that the pan is not a random vibration to be eliminated, and it moves rapidly to zero. This (to me) feels like I am operating the binoculars through a rubber band. Eew.

Electronic image stabilization system

Usually found in lower-end camcorders, these system attempt to remove camera vibrations in real time by executing a picture analysis and shifting while the recording is being made. It tends to degrade image quality. An analog of this idea operates after the shooting, inside a video editing suite, and it tries to remove vibration by analyzing whole segments.

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