What is Nyquist sampling in microscopy?

Nyquist sampling states that you must sample at least 2× the highest spatial frequency in your image to faithfully reconstruct it. In practice this means your pixel size should be $\leq$ half the optical resolution (often divided by 2.3 for safety margin).

What is the Point Spread Function (PSF)?

The PSF describes how a single point source of light is blurred by the optical system. Its full-width at half-maximum (FWHM) in the lateral and axial directions defines the practical resolution limit of the microscope.

What happens if I oversample?

Oversampling (pixel size much smaller than Nyquist) increases file sizes and acquisition time without improving real resolution. It can also reduce signal-to-noise ratio by spreading photons across more pixels.

How does confocal pinhole size affect resolution?

A pinhole smaller than 1 Airy unit (AU) improves lateral resolution beyond widefield limits — down to 0.37×λ/NA at ≤0.5 AU. However, closing the pinhole also reduces signal, so there is a trade-off between resolution and brightness.

Why does STED achieve super-resolution?

STED uses a depletion beam to shrink the effective excitation volume. The resolution scales as r_confocal / √(1 + I/I_sat), where I/I_sat is the saturation factor. Higher depletion power yields finer resolution, limited by photodamage.

ToolsConductScience tool

MicroscopyFree in-browser calculator

Nyquist Sampling & PSF Calculator.

Compute optimal pixel size, z-step, and PSF dimensions for widefield, confocal, STED, two-photon, and light sheet microscopy. Enter your objective NA and wavelength to get Nyquist-compliant sampling intervals.

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Validated2026-04-08

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Microscope Settings

ModalityNumerical ApertureExcitation λ (nm)Emission λ (nm)Immersion Medium

Sampling Check (Optional)

Enter your actual acquisition settings to check Nyquist compliance.

Actual Pixel Size (nm)Actual Z-Step (nm)

Results

Parameter	Value
Lateral Resolution	228.8 nm
Axial Resolution	811.6 nm
Nyquist Pixel Size	99.5 nm
Nyquist Z-Step	352.9 nm
PSF FWHM Lateral	191.3 nm
PSF FWHM Axial	493.6 nm

Resolution & PSF Comparison

When to use

Setting up a new microscope acquisition to determine correct pixel size and z-step
Checking whether your current settings satisfy Nyquist sampling
Comparing resolution across modalities for a given objective and wavelength
Estimating PSF dimensions for deconvolution setup

Do not use for

As a substitute for measuring the actual PSF with sub-resolution beads
For aberrated or misaligned optical systems (formulas assume ideal optics)
When using non-standard beam shaping (e.g., Bessel beams, lattice light sheet)

NA matters more than magnification

Resolution depends on numerical aperture, not magnification. A 60×/1.4 oil objective resolves the same as a 100×/1.4 oil objective.

Match immersion medium to the objective design

Using oil immersion objective in water produces spherical aberration that degrades real resolution far below the theoretical values.

Axial resolution is always worse

Axial resolution is typically 2-3× worse than lateral. Budget z-step accordingly — it will be much larger than pixel size.

Confocal pinhole trade-off

Closing the pinhole below 1 AU improves resolution but reduces signal. For dim specimens, 1 AU is often the practical compromise.

Method

Rayleigh criterion (0.61λ/NA) for widefield; confocal formula with pinhole interpolation; STED saturation model; two-photon effective wavelength λ/√2; light sheet min(detection, sheet). PSF FWHM via Born & Wolf. Nyquist factor = 2.3.

Validated

Last validated 2026-04-08. Calculations are designed for planning and documentation support; verify procurement decisions against manufacturer specifications or institutional SOPs.

How to cite

How to Cite

ConductScience Nyquist Sampling & PSF Calculator (v1.0). ConductScience, Inc. 2026. https://conductscience.com/tools/nyquist-sampling-psf-calculator

Pawley JB. Handbook of Biological Confocal Microscopy. Springer, 2006.

Born M, Wolf E. Principles of Optics, 7th Ed. Cambridge University Press, 1999.

Nyquist-Shannon Sampling in Optical Microscopy

The Nyquist-Shannon theorem requires sampling at ≥2× the highest spatial frequency to avoid aliasing. In microscopy the diffraction limit sets the highest frequency, so the required pixel size depends on the optical resolution.

Practical rule: divide the resolution by 2.3 (rather than exactly 2) to provide a small safety margin. This applies independently in X/Y (lateral) and Z (axial) dimensions.

Under-sampling causes aliasing artifacts and lost information. Over-sampling wastes acquisition time, disk space, and signal-to-noise without improving real resolution.

Modality Resolution Comparison

Different microscopy techniques achieve different resolution limits:

Widefield: Rayleigh limit 0.61×λ/NA lateral; axial limited by depth of field
Confocal: Pinhole rejects out-of-focus light; can reach 0.37×λ/NA lateral with small pinhole
Spinning disk: Fixed pinhole array — widefield-like lateral, confocal-like axial
STED: Super-resolution via stimulated emission depletion — below 50 nm possible
Two-photon: Uses IR excitation; effective wavelength = λ_ex/√2
Light sheet: Axial resolution set by min(detection axial, sheet thickness)

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