jitter (optics)

In optics, jitter is used to refer to motion that has high temporal frequency relative to the integration/exposure time. This may result from vibration in an assembly or the unstable hand of a photographer. Jitter is typically differentiated from smear, which has a lower frequency relative to the integration time.{{Google books|rcrGlrguj1YC|Encyclopedia of optical engineering|page=2380}} Whereas smear refers to a relatively constant rate during the integration/exposure time, jitter refers to a relatively sinusoidal motion during the integration/exposure time.

The equation for the optical Modulation transfer function associated with jitter is

:$MTF\_\{jitter\}(k)\; =e^\{-\backslash frac\; \{1\}\; \{2\}\; k^2\backslash sigma^2\}$

where k is the spatial frequency and $\backslash sigma$ is the amplitude of the jitter.{{cite journal|last=Johnson|first=Jerris F.|title=Modeling imager deterministic and statistical modulation transfer functions|journal=Applied Optics|date=10 November 1993|volume=32|issue=32|pages=6503–13|doi=10.1364/AO.32.006503|pmid=20856491|bibcode=1993ApOpt..32.6503J |url=http://www.opticsinfobase.org/abstract.cfm?id=40363|url-access=subscription}} Note that this frequency is in radians of phase per cycle. The equivalent expression in Hz is

:$MTF\_\{jitter\}(u)\; =e^\{-2\; \backslash pi^2\; u^2\backslash sigma^2\}$

where u is the spatial frequency and $\backslash sigma$ is again the amplitude of the jitter (note that as the jitter approaches infinity, the value of the function tends towards zero).

For spacecraft, operation in a vacuum often means low mechanical damping. Meanwhile, spacecraft are compact and rigid, to withstand high launch loads. Jitter, then, is transmitted easily and often a limiting factor for high-resolution optics.