= Solution
For a weak phase object, the <contrast transfer function> gives the signed transfer of an object's spatial Fourier components into intensity contrast. In a common convention,
$$
H(u)=E(u)\sin\chi(u),\qquad
\chi(u)=\pi\left(\frac12 C_S\lambda^3u^4+\Delta f\lambda u^2\right),
$$
where $u$ is a cyclic <spatial frequency>, $\Delta f$ the defocus, $C_S$ the <spherical aberration> coefficient, and $E(u)$ a coherence envelope. A zero suppresses that <frequency>; crossing a zero reverses contrast. The overall sign depends on the image convention, but the zeros do not. Single-image division by $H$ cannot recover information exactly at its zeros. The microscope manufacturer's discussion explicitly connects the first zero with interpretable resolution and the higher-frequency sign changes.<Phase-contrast transfer function, PCTF by JEOL>[glossary, first-zero and envelope-function discussion]{ref}
The plotted first nontrivial zero is at approximately $u_0=4.0\ \mathrm{nm^{-1}}$. Hence \b[the smallest spacing in the first uninterrupted contrast band is about $d_0=1/u_0=0.25\ \mathrm{nm}$]. This axis is cycles per <length>, not an angular wave number requiring a factor of $2\pi$. Smaller spacings can contribute in later bands, but their contrast has reversed and requires appropriate interpretation or multiple-defocus reconstruction.
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