= Lateral position jitter
<Lateral position jitter> is the fluctuating in-plane displacement of successive acquired images relative to a chosen reference. In <serial block-face scanning electron microscopy>, it can displace corresponding features between block faces even when the cutting increment is perfectly regular. A simple <image registration> model is
$$
I_k(x,y)\simeq S_k(x-\delta x_k,y-\delta y_k),
$$
where $S_k$ is the ideal image of the current face and $(\delta x_k,\delta y_k)$ is its lateral shift. The specimen itself changes between faces, so not every apparent shift is instrumental motion.
A primary apparatus study estimated inter-image displacement from <cross-correlation> peaks in several subregions. Its Figure4 central cluster had <standard deviations> of $10.9\,\mathrm{nm}$ and $11.8\,\mathrm{nm}$ along the two axes; outliers and changing specimen patterns required interpretation.<Serial Block-Face Scanning Electron Microscopy to Reconstruct Three-Dimensional Tissue Nanostructure by Winfried Denk and Heinz Horstmann>[Results, registration paragraph; Figure4 and caption; Materials and Methods, Data analysis]{ref}
For an original one-axis example, take measured frame offsets $0,1,-1,0$ pixels at <pixel pitch> $p=4\,\mathrm{nm}$. The offsets are $0,4,-4,0\,\mathrm{nm}$ and their <root mean square> about zero is
$$
\sigma_{\rm frame}=\sqrt{\frac{0^2+4^2+(-4)^2+0^2}{4}}=\sqrt8\,\mathrm{nm}\simeq2.83\,\mathrm{nm}.
$$
The successive differences are $4,-8,4\,\mathrm{nm}$, whose <root mean square> is $\sqrt{32}\,\mathrm{nm}\simeq5.66\,\mathrm{nm}$. These are different statistics. For independent equal-variance frame offsets, the theoretical difference variance is $2\sigma^2$; correlation or drift changes that relation. Specify the reference, detrending and normalization when reporting jitter. <Image registration> can estimate a correction but does not prove that all residual motion or specimen deformation has been removed.
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