AFM Tip Convolution Calculator
Deconvolved feature width from AFM tip radius correction.
About this calculator
Atomic force microscopy images a surface by scanning a sharp probe tip across it, but the tip itself has a finite radius -- it can't come to a true mathematical point. When that tip encounters a raised feature, it starts registering contact before it is directly above the feature's edge and keeps contact past it, so the feature reads wider in the image than it actually is. This calculator reverses that "tip convolution" effect with the geometric approximation W_real = W_apparent - 2 x sqrt(2 x tip radius x feature height), where the broadening term grows with both the tip's radius and the feature's height -- a taller feature gets convolved more by the same tip because there is more vertical distance over which the tip's curved flank makes contact before reaching the top. Apparent width is the dominant factor in the corrected real width because it is the direct measurement the broadening term is subtracted from; tip radius and feature height contribute a smaller, coupled effect through the shared square root.
Scan rate does not enter the geometric correction at all -- it affects acquisition time and tip wear, not the convolution math, so changing it never moves the corrected width. The aspect-ratio check compares your feature's height-to-width ratio against the roughly 17.5-degree half-angle of a standard silicon AFM tip, a fixed geometric limit independent of your measured dimensions: no tip, however sharp its radius, can faithfully image a feature steeper than its own sidewall angle allows. The model assumes a simple spherical-cap tip and a rectangular feature profile -- it does not account for pyramidal or worn, asymmetric tips, sample compliance, or adhesion-induced contact-area changes, all of which can shift real broadening away from this idealized estimate.
Inputs
Results
Real Width (nm)
30
Tip Broadening (nm)
20
How to Use This Calculator
- Enter the AFM tip radius (nm) from the manufacturer's specification or SEM measurement.
- Enter the apparent (measured) feature width (nm) and feature height (nm) from your scan.
- Enter the scan rate (Hz) used for the line scan.
- Review the real (tip-deconvoluted) feature width, tip broadening (nm and %), aspect ratio, and lateral resolution.
- If broadening exceeds 30%, use a sharper tip (smaller radius) or apply tip deconvolution algorithms.
How the result changes with Apparent Width (nm)
| Apparent Width (nm) | Real Width (nm) | Tip Broadening (nm) |
|---|---|---|
| 25 | 5 | 20 |
| 38 | 18 | 20 |
| 75 | 55 | 20 |
| 125 | 105 | 20 |
What each input means
- Tip Radius (nm)
- AFM probe tip radius. Standard Si: 7-10 nm, worn: 20-50 nm.
- Apparent Width (nm)
- Measured feature width from AFM image.
- Feature Height (nm)
- Measured feature height from AFM.
- Scan Rate (Hz)
- Line scan frequency.
What each result means
- Real Width (nm)
- Deconvolved true feature width.
- Tip Broadening (nm)
- Width added by tip convolution: 2√(2·R·h).
- Broadening (%)
- Broadening as percentage of apparent width.
- Feature Aspect Ratio
- Height / true width.
- Tip Can Resolve?
- Whether tip geometry allows faithful imaging.
- Lateral Resolution (nm)
- Theoretical lateral resolution limit.
- Max Resolvable AR
- Maximum aspect ratio for standard Si tip (17.5° half-angle).
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersTip Radius (nm) = 10, Apparent Width (nm) = 50, Feature Height (nm) = 5, Scan Rate (Hz) = 1 = 4 input(s) provided
- Calculate Real Width30 = 30
- Calculate Tip BroadeningTip Broadening = 2 * sqrt(2 * tipRadiusNm * featureHeightNm)20 = 20
- Calculate Broadening40 = 40
- Calculate Feature Aspect RatioFeature Aspect Ratio = featureHeightNm / max(0.01, realWidth)0.167 = 0.167
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does apparent width affect the corrected real width more than tip radius does?
Real width equals apparent width minus a broadening term of 2 x sqrt(2 x tip radius x feature height). Apparent width is a full linear term in that subtraction, while tip radius only enters inside a square root shared with feature height -- so a given percentage change in apparent width moves the result more than the same percentage change in tip radius, especially for typical AFM geometries where features are much wider than they are tall.
Does the scan rate I enter change the calculated real width?
No. Scan rate affects how fast the tip traverses the sample and can influence image quality through mechanical settling and tip wear, but the tip-convolution geometry (real width = apparent width - 2 x sqrt(2 x tip radius x feature height)) has no scan-rate term, so this calculator's width correction is unaffected by whatever cadence you enter.
What does the maximum resolvable aspect ratio depend on?
It is fixed at tan(17.5 degrees), roughly 0.315, based on the sidewall half-angle of a standard silicon AFM probe -- it does not change no matter what tip radius, feature height, or width you enter, because it represents a geometric ceiling on how steep a feature any standard-geometry tip can trace, not a value computed from your specific measurement.
Why does increasing the tip radius make the broadening effect larger?
Broadening equals 2 x sqrt(2 x tip radius x feature height), so a larger tip radius directly increases the broadening term -- a blunter, larger-radius tip contacts the sidewall of a feature farther from its true edge before reaching the top, exaggerating the apparent width more than a sharp, small-radius tip would for the same feature.
What should I do if the calculated broadening percentage is high?
A high broadening percentage, roughly over 30%, means the tip-convolution correction is a large fraction of your apparent measurement, so the deconvolved real width carries more geometric uncertainty -- consider re-imaging with a sharper tip (smaller tip radius) or applying a full blind tip-reconstruction deconvolution algorithm rather than relying on this simplified spherical-cap approximation.
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