Nyquist sampling calculator for microscopy

Wavelength, numerical aperture and pixel size (entered directly or computed from the sensor) place the sampling against the optical resolution: undersampled, adequate or oversampled image. The sampling factor is chosen: 2 for the theorem, 2.3 for the common recommendation in microscopy.

Resolution follows the chosen convention (Abbe, Rayleigh or confocal). The recommended step is the maximum pixel size.

Sampling

how finely the sensor records the optical image. It adds no resolution: it determines how much of it is kept.

Undersampling

the pixel is larger than the recommended step: details transmitted by the objective are lost.

Oversampling

the pixel is far smaller than needed: images are heavier and photobleaching higher, with no extra information.

Factor 2 vs 2.3

2 is the Nyquist-Shannon minimum for ideal sampling points. 2.3 is the common recommendation in digital microscopy: a pixel integrates light over its area, and structures have an arbitrary orientation relative to the grid.

The factor depends on the modality and on the intended image processing. Later deconvolution often justifies finer sampling; an acquisition limited by photobleaching may justify the opposite. The thresholds shown are conventions, each with its origin.

Resolution depends only on wavelength and numerical aperture; the sampling step, only on the sensor and magnification. The word "Nyquist" often refers to both.