= Solution
The <optical pupil> mapped onto the <deformable mirror> has actuator pitch approximately $s=D/N$. A sinusoidal <wavefront error> must have at least two actuator intervals per period to avoid aliasing, by the <Nyquist–Shannon sampling theorem>. Thus
$$
\boxed{\Lambda_{\min}\simeq2s=\frac{2D}{N}.}
$$
If the $N$ actuator centres include both endpoints of the <optical pupil> <diameter>, the literal pitch is $D/(N-1)$ and the corresponding expression is $2D/(N-1)$; the paper uses the customary large-$N$ pitch convention. At the exact Nyquist boundary one quadrature can be poorly sampled, and real influence functions and actuator coupling reduce useful correction near the cutoff. The result is an ideal sampling bound, not a guarantee of arbitrary correction at its endpoint.
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