Nyquist sampling calculator for microscopy
recommended step = resolution / sampling factor
Enter wavelength, numerical aperture and pixel size (entered directly or computed from the sensor): the tool compares recording fineness with optical resolution and tells you whether you are undersampled, adequate or oversampled. The sampling factor is an explicit parameter, 2 for the theorem, 2.3 for the common recommendation in microscopy.
Verdict: Undersampled, the pixel is too large. Optically available information is lost.
Lateral resolution: 226.6 nm · Sampling factor achieved: 2.09
Required optical magnification: 65.98× · Total magnification that would be needed, with the same sensor, to reach exactly the recommended step.
Notes
- Undersampling: the pixel is larger than the recommended step, so part of the optically available information is lost.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasrecommended step = resolution / sampling factor
recommended step = resolution / sampling factor
factor = 2 (theorem) or 2.3 (microscopy recommendation)
Resolution is that of the chosen convention (Abbe, Rayleigh or confocal). The recommended step is the maximum pixel size: a larger pixel loses information.
- Sampling
- · how finely the sensor records the optical image. It never creates resolution: it only decides what is kept.
- Undersampling
- · the pixel is larger than the recommended step: details genuinely transmitted by the objective are permanently 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, valid for ideal sampling points. 2.3 is the common recommendation in digital microscopy: a pixel integrates light over its area, and structure orientation relative to the grid is arbitrary.
Validity domain"Nyquist" is not a single universal value: the factor depends on the modality and on the intended image processing.
"Nyquist" is not a single universal value: 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. No threshold shown here is a physical law, each carries its convention and its origin.
Resolution and sampling step are not the same thingResolution is what the optics transmits: it depends only on wavelength and numerical aperture.
Resolution is what the optics transmits: it depends only on wavelength and numerical aperture. Sampling step is recording fineness: it depends only on the sensor and magnification. The word "Nyquist" constantly conflates the two. This tool shows them separately, precisely to keep the distinction readable.