# 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 from the unstable hand of a photographer. Jitter is typically differentiated from smear, which has a lower frequency relative to the integration time.[1] 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

${\displaystyle MTF_{jitter}(k)=e^{-{\frac {1}{2}}k^{2}\sigma ^{2}}}$

where k is the spatial frequency and ${\displaystyle \sigma }$ is the amplitude of the jitter.[2] Note that this frequency is in radians of phase per cycle. The equivalent expression in Hz is

${\displaystyle MTF_{jitter}(u)=e^{-2\pi ^{2}u^{2}\sigma ^{2}}}$

where u is the spatial frequency and ${\displaystyle \sigma }$ 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.

## References

1. ^ Encyclopedia of optical engineering, p. 2380, at Google Books
2. ^ Johnson, Jerris F. (10 November 1993). "Modeling imager deterministic and statistical modulation transfer functions". Applied Optics. 32 (32): 6503–13. doi:10.1364/AO.32.006503. PMID 20856491.