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. 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

$MTF_{smear}(u)={\frac {sin(\pi \alpha u)}{\pi \alpha u}}$

where u is the spatial frequency and $\alpha$ is the amplitude of the smear in pixels.