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Nyquist Calculator

Diffraction-limited resolution and Nyquist sampling from an objective’s magnification, NA and wavelength.

Pick an objective or type your own magnification and NA, set the wavelength, and see the diffraction-limited spot pair with its minimum resolvable distance and the Nyquist–Shannon sample pitch. Everything runs in your browser.

How it works ↓

Objective

User defined

nm
380green900
Rayleigh d  0.61λ/NA
–
Abbe limit  λ/2NA
–
Nyquist pitch  d/2 at sample
–
Camera pixel  ≤ d/2 × Mag
–
Face view · two points at the Rayleigh limit
Cross profile · intensity through both peaks

Camera · does it sample at Nyquist?

How it works

A diffraction-limited objective turns a point of light into an Airy pattern. Two points are “resolved” when they sit far enough apart that your detector can still see the dip between them.

  1. 1.

    Rayleigh criterion

    The classic minimum resolvable peak-to-peak distance puts the peak of one Airy pattern on the first dark ring of the other: d = 0.61 λ / NA. At this spacing the midpoint dips to about 74% of the peaks — that is the valley in the cross profile.

  2. 2.

    Abbe limit

    The hard diffraction limit for the finest grating an objective can pass: d = λ / 2NA. It is slightly tighter than Rayleigh and is the number most deconvolution and super-resolution literature starts from.

  3. 3.

    Nyquist–Shannon sampling

    To record detail of size d without aliasing you need at least two samples across it, so the sample pitch at the specimen must be ≤ d/2. The comb under the profile shows that pitch.

  4. 4.

    Camera pixels

    The objective magnifies the image before the camera sees it, so the physical pixel may be d/2 × Mag. A 60×/1.4 objective at 520 nm resolves 227 nm, so pixels up to about 6.8 µm sample it at Nyquist.

Good to know

  • The objective list covers common Nikon, Olympus/Evident, Zeiss and Leica research objectives as a convenience. Specifications change between revisions — confirm against the maker’s catalog before you order anything.
  • Use the emission wavelength for fluorescence. Beyond ~780 nm the slider shows near-infrared, which your eye (and this pseudocolor) barely sees.
  • Rayleigh assumes an aberration-free, evenly illuminated pupil. Real systems resolve a little worse.

Matching a camera?

  • Keep the physical pixel at or below d/2 × Mag. Oversampling is safe; undersampling aliases fine detail and no software brings it back.
  • Questions about triggering or camera timing? That is what our Triggerscope is for.