Microscope Pixel Size and Nyquist Sampling Calculator (Resolution Depends on Pixels, Not Magnification)

“I’m using a 60× oil objective” — that tells you nothing about whether your image actually has resolution.

If the two points an objective can resolve both land on the same camera pixel, that resolution never makes it into the image. What determines imaging detail is not the magnification; it is how many pixels sample one resolvable distance.

Three steps

Effective pixel size at sample = camera pixel size × binning ÷ (objective magnification × intermediate magnification)
Resolution d (Rayleigh) = 0.61 × λ ÷ NA
Sampling ratio = d ÷ effective pixel size, must be ≥ 2.3

Note that effective pixel size is in “micrometres at the sample”, not on the sensor — the magnification maps the sample onto the sensor, so it goes in the denominator.

Why 2.3, not 2

The classic Nyquist criterion says the sampling interval must be less than half the minimum resolvable distance, i.e. a factor of 2. That conclusion holds only when the structure is aligned exactly along the horizontal or vertical axes of the pixel grid. Biological samples do not cooperate: a structure running diagonally sees a pixel grid spacing √2 larger in that direction, so the factor must be raised to 2.3 (some references use 2.8).

Verification

Check against a published parameter set: λ = 550 nm, NA = 1.25, 100× objective, 12 µm pixel.

d               = 0.61 × 550 ÷ 1.25 = 268.4 nm
Effective pixel = 12 ÷ 100          = 0.12 µm = 120 nm

The published values are exactly “resolution ≈ 268 nm” and “effective pixel 120 nm”. This tool uses those two equations; you can verify with your own system parameters.

A note on what this parameter set implies: 268.4 ÷ 120 = 2.24, just barely short of 2.3. A 100× objective with 12 µm pixels sounds generous, but it sits right on the boundary.

The most common setup is also right on the boundary

A 60×/NA 1.40 oil objective with a 6.5 µm sCMOS sensor is the standard fluorescence imaging configuration today:

d               = 0.61 × 520 ÷ 1.40 = 226.6 nm
Effective pixel = 6.5 ÷ 60          = 108.3 nm
d ÷ effective pixel = 2.09

Meets the classical 2× criterion, does not meet the diagonal-corrected 2.3× criterion. Adding a 1.5× intermediate magnifier brings the total to 90× effective magnification, reducing the effective pixel to 72.2 nm and the ratio to 3.14 — at the cost of shrinking the field of view to 2/3 and cutting photons per pixel by more than half. There is no universal right answer to that trade-off, but it should be calculated, not assumed.

Over-sampling also has a cost

A ratio far above 2.3 is not better and better: the field of view shrinks, photons per pixel decrease, and maintaining the same SNR requires longer exposures or stronger excitation — which translates directly into photobleaching and phototoxicity. This tool flags both extremes.

The difference between the two criteria

The Abbe criterion d = λ / (2·NA) gives the smallest periodic structure the optical system can transfer. The Rayleigh criterion d = 0.61 λ / NA gives the minimum separation at which two point sources can just be distinguished — a larger value, and more directly relevant to the question “can I tell these are two separate points?” For sampling decisions, Rayleigh is the conventional choice. This tool reports both; the sampling verdict uses Rayleigh.

Use the emission wavelength

λ should be the emission wavelength, not the excitation wavelength — you are imaging the light that comes out. GFP ≈ 510 nm, mCherry ≈ 610 nm, DAPI ≈ 460 nm. Resolution scales with wavelength, so the same objective is more likely to be under-sampled in the red channel — worth calculating separately for each imaging channel.

Limitations

• This calculation covers lateral resolution and sampling only. Axial (z) resolution has a separate formula and is typically 2–3× worse.
• NA cannot exceed the refractive index of the immersion medium (air 1.0, water 1.33, oil ≈ 1.515).
• Actual confocal resolution also depends on pinhole size; the values here are the diffraction limit of the objective.
• Super-resolution methods (structured illumination, STED, single-molecule localization) break this limit and are not covered by these equations.

Related tools

For pixel-to-physical-size conversion of publication figures, see Figure Resolution and DPI; for concentration calculation from microscope counts, see Hemocytometer Cell Counting.