Smear (optics)

In optics, smear is used to refer to motion that has low temporal frequency relative to the integration/exposure time. This typically results from a relative rate of the image with respect to the detector (e.g., caused by movement in the scene). Smear is typically differentiated from jitter, which has a higher 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 smear is the standard sinc function associated with an extended sample

${\displaystyle \mathrm {MTF} _{\mathrm {smear} }(u)={\frac {\sin(\pi \alpha u)}{\pi \alpha u}}}$

where u is the spatial frequency and ${\displaystyle \alpha }$ is the amplitude of the smear in pixels.^[2]

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.