Z-Stack Step Size Calculator (Axial Resolution & Nyquist Sampling)
When acquiring a z-stack, setting the wrong step size (z-step) does not just make the image blurry — the geometry of the 3D reconstruction is wrong: too large a step and a spherical nucleus appears flattened in orthogonal views; too small a step doubles the slice count and photobleaching with no gain in information.
The correct step size is not “I always use 0.5 µm” — it is determined by how many samples span the axial resolution.
Two steps
Axial resolution r_z = F × λ_em × n ÷ NA² F: widefield 2.0, confocal 1.4
Step size Δz = r_z ÷ 2.3
n is the refractive index of the immersion medium (air 1.00, water 1.33, glycerol 1.47, silicone oil 1.405, immersion oil 1.515), not the sample. λ_em is the emission wavelength, not the excitation wavelength.
Note that NA appears squared in the denominator: raising NA from 1.0 to 1.4 improves axial resolution twofold, while lateral resolution improves only 1.4-fold. Axial resolution is always the worst of the three dimensions — with a 1.4 NA oil objective at 550 nm emission, lateral is ~0.24 µm and axial is ~0.60 µm, a 2.5× difference.
Why F = 1.4 for confocal and 2.0 for widefield
The confocal pinhole rejects out-of-focus light, shortening the axial PSF. 1.4 ÷ 2.0 = 0.70, a 30% reduction — consistent with Evident’s statement that “the confocal axial PSF is ~30% shorter than widefield,” so the two coefficients cross-validate each other.
Note that 30% is smaller than most people expect. The real advantage of confocal is rejecting out-of-focus scatter (contrast), not multiplying the axial resolution several times over.
Why divide by 2.3, not 2
The classical Nyquist criterion sets the sampling interval at half the smallest resolvable distance. That result assumes the structure is aligned with the sampling grid; oblique structures require denser sampling along the diagonal direction, so 2.3 is used in practice. The lateral pixel size tool on this site uses the same factor of 2.3.
Verification
| Conditions | Axial resolution | Step size (÷2.3) |
|---|---|---|
| Confocal λ550 NA1.4 oil n1.515 | 595.2 nm | 258.8 nm |
| Widefield λ550 NA1.4 oil n1.515 | 850.3 nm | 369.7 nm |
| Confocal λ520 NA1.0 water n1.33 | 968.2 nm | 421.0 nm |
| Confocal λ520 NA0.45 air n1.0 | 3.595 µm | 1.563 µm |
The first row matches the frequently cited benchmark of “~0.2 µm lateral, ~0.6 µm axial” for confocal (PMC6961134), and can serve as a sanity check for this tool’s output. The fourth row shows that a dry objective gives only micron-scale axial resolution — debating nanometer-level step adjustments in that regime is pointless.
Limitations
- There is a stricter criterion, used for deconvolution. Huygens/SVI applies strict band-limiting based on the OTF cutoff frequency: widefield Δz = λ ÷ (4n(1−cos α)), α = arcsin(NA/n), with confocal requiring half that. For the same 1.4 NA oil objective at λ550, this gives 147 nm versus this tool’s 370 nm — a 2.5× difference. Neither is wrong; they measure different things (bandwidth versus PSF half-width). Use the band-limiting criterion for deconvolution (roughly doubling the slice count); this tool’s step size is sufficient for presentation or morphological measurements.
- NA cannot exceed the refractive index of the immersion medium; the tool will report an error if this is violated. A common mistake is selecting “water” while entering an oil-objective NA of 1.4.
- The formula gives the diffraction-limited theoretical value, which is an upper bound. Spherical aberration, refractive-index mismatch, and low signal-to-noise will all degrade performance; real axial resolution is always worse than the calculated value by an amount that depends on the specific system.
- Refractive-index mismatch distorts the z-axis scale itself: when using an oil objective (n 1.515) on an aqueous sample (n ≈ 1.33), 1 µm of stage travel does not correspond to 1 µm inside the sample, and the error grows with depth. This is a source of shape distortion independent of step size; it cannot be corrected post hoc — only a matched objective or axial calibration can address it.
- Does not apply to two-photon, light-sheet, or super-resolution modalities. Axial behavior in those systems is governed by different mechanisms.
FAQ
What step size is actually correct?
Divide the axial resolution by 2.3. For a 1.4 NA oil objective at 550 nm emission with confocal, axial resolution is ~0.60 µm, giving a step of ~259 nm — the "~0.25 µm" figure commonly cited. **Do not fix on a single number for all experiments**: with a 0.45 NA dry objective at the same wavelength, axial resolution is 3.6 µm and the correct step is ~1.56 µm; using 0.25 µm would waste more than 6× as many slices.
Why does confocal improve axial resolution by only 30%? I thought confocal sectioning was much better.
What improves is **contrast**, not resolution. The pinhole rejects out-of-focus light, making individual confocal slices look far cleaner; but the axial PSF FWHM is only shortened to 0.70× that of widefield (factor 1.4 vs. 2.0). Equating "looks sharper" with "several times better axial resolution" is a common misconception — genuinely improving axial resolution requires higher NA or a switch to 4Pi, light-sheet, or super-resolution methods.
Should I use the excitation wavelength or the emission wavelength?
Use the **emission wavelength** for fluorescence imaging, because the image is formed by the emitted light. The two typically differ by a few tens of nanometers; using the excitation wavelength (e.g., 488 instead of 520) overestimates resolution by ~6% — not catastrophic, but unnecessary. For multi-channel acquisitions, set the step size using **the longest emission wavelength** so every channel is adequately sampled.
My deconvolution software asks for a smaller step size. Is it wrong?
No, it uses a different criterion. Huygens/SVI applies strict band-limiting based on the OTF cutoff: widefield Δz = λ ÷ (4n(1−cos α)), with confocal requiring half that; for the same 1.4 NA oil objective at λ550, this gives 147 nm versus this tool's 370 nm — a 2.5× difference. The two criteria answer different questions: one measures bandwidth, the other measures PSF half-width. **If you are running deconvolution, follow your deconvolution software**; it needs to capture all information within the cutoff frequency. For presentation or morphological measurements, this tool's step size is sufficient and saves more than half the photobleaching.
The calculated resolution does not match what I measure experimentally.
That is expected. The theoretical value is the diffraction-limited upper bound; measured values can only be worse. Common causes: spherical aberration (wrong coverslip thickness or immersion oil grade), refractive-index mismatch, insufficient signal-to-noise (PSF tails undetectable in weak-signal samples), and objectives that do not reach their rated NA in practice. In addition, **refractive-index mismatch distorts the z-axis scale itself**: when an oil objective images an aqueous sample, 1 µm of stage travel does not equal 1 µm inside the sample, and the error accumulates with depth, directly distorting the reconstructed geometry.
How do I set the lateral (xy) sampling?
That is a separate question governed by camera pixel size and magnification. This site has a dedicated tool: [Microscope Pixel Size & Nyquist Sampling](../microscope-pixel-size/). Both tools use the same 2.3 sampling factor, so they can be used together consistently.
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