A suitably band-limited function can be reconstructed from equally spaced samples when the sampling rate exceeds twice its largest ordinary frequency. Sampling more slowly aliases distinct frequencies in the Fourier transform. For spatial sampling, the same statement relates sample pitch to the shortest resolvable wavelength.
Samples spaced by pitch can distinguish spatial frequencies strictly below cycles per unit length. Thus the shortest limiting wavelength is ; exactly at the limit a sinusoid's phase can make all samples vanish. A practical deformable mirror has additional limits from actuator influence functions and finite pupil geometry.
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The Nyquist-Shannon sampling theorem, also known as the Nyquist theorem, is a fundamental principle in the field of signal processing and information theory. It provides a criterion for how often an analog signal must be sampled to be accurately reconstructed from its samples without losing any information.