Radius from AFM Image Calculator

Estimate particle radius from Atomic Force Microscopy (AFM) data based on geometric approximations used in tools like Gwyddion.

AFM Particle Radius Calculator

Visual Representation

A 2D cross-section schematic of the calculated particle, illustrating the relationship between Height (H) and Full Width at Half Maximum (W).

What is the Calculation of Radius from an AFM Image?

The calculation of a radius from an Atomic Force Microscopy (AFM) image is a method to estimate the size of nanoscale features, such as nanoparticles, quantum dots, or proteins. An AFM does not see objects directly; instead, it uses an ultra-sharp tip to scan a surface and record its topography. This process, however, introduces an artifact known as **tip convolution**, where the size and shape of the AFM tip make the measured feature appear wider than it actually is. The height measurement, however, is generally considered accurate.

Therefore, a simple geometric calculation is required to de-convolve the tip’s effect and approximate the true particle radius. This is often done in analysis software like Gwyddion by using the measured height (H) and the apparent width, typically the Full Width at Half Maximum (FWHM), of the feature. This calculator uses a common geometric model to perform this **calculation radius from afm image using gwidden**-like analysis.

Radius Calculation Formula and Explanation

Assuming a spherical particle and a much larger (or infinitely sharp) tip for simplification, the relationship between the true particle radius (R), the measured height (H), and the measured Full Width at Half Maximum (W) can be derived from the geometry of a circle. This calculator uses the following formula:

R = (H / 2) + (W² / (8 * H))

Here, the formula reconstructs the radius of a circle (the particle’s cross-section) from a chord (the FWHM) and its height. For those seeking advanced analysis, one might explore AFM tip characterization to further refine this model.

Variables Used in the Radius Calculation

Variable	Meaning	Unit (Auto-Inferred)	Typical Range
R	Calculated Particle Radius	nm or µm	1 – 1000
H	Feature Height	nm or µm	1 – 1000
W	Full Width at Half Maximum (FWHM)	nm or µm	5 – 2000

Practical Examples

Example 1: Gold Nanoparticle

A researcher images 15 nm gold nanoparticles and, after performing a profile analysis in Gwyddion, gets the following average values.

• Input (Height H): 14.8 nm
• Input (FWHM W): 40 nm
• Result (Radius R): Approximately 14.2 nm
• Result (Diameter): Approximately 28.4 nm

In this case, the calculated radius is very close to the expected value, though the measured width was significantly broadened by tip convolution.

Example 2: Polymer Micelle

A polymer micelle is imaged, showing a much broader, softer structure.

• Input (Height H): 50 nm
• Input (FWHM W): 180 nm
• Result (Radius R): 106 nm

The result suggests a much larger radius of curvature than the height alone would imply, which can be indicative of a flattened or “pancake” like structure on the surface. Understanding the output is key, and different types of image processing software offer various models.

How to Use This Calculator

Follow these steps to estimate your particle’s radius:

1. Perform AFM Analysis: First, use software like Gwyddion or another program to analyze your AFM scan. Use the profile or cross-section tool to measure the height and FWHM of an isolated, representative particle.
2. Enter Feature Height (H): Input the maximum height of the particle from the substrate baseline into the “Feature Height (H)” field.
3. Enter FWHM (W): Input the Full Width at Half Maximum into the “FWHM” field.
4. Select Units: Choose the correct units (nanometers or micrometers) that you used for your measurements.
5. Interpret Results: The calculator instantly provides the calculated Radius (R), Diameter (2R), and Aspect Ratio (H/W). Use the “Copy Results” button to save the output.

Key Factors That Affect AFM Radius Calculation

• Tip Convolution: This is the most significant factor. A dull or large AFM tip will make features appear much wider, inflating the FWHM value and affecting the calculated radius.
• Particle Shape Assumption: The formula assumes a perfectly spherical particle. If your particles are ovoid, cubic, or irregularly shaped, the calculation is only a rough approximation of the radius of curvature.
• Sample Deformation: Soft samples (like cells or polymers) can be deformed by the AFM tip, which can alter the measured height and width.
• Image Leveling: An incorrectly flattened or leveled AFM image can lead to inaccurate height and baseline measurements, directly impacting the calculation. Proper data processing is a crucial first step.
• Substrate Flatness: The calculation assumes the particle is on a perfectly flat surface. Rough or sloped substrates can skew the measurements. For detailed studies, a proper surface roughness analysis is recommended.
• Noise and Artifacts: Random noise or scanning artifacts in the image can make it difficult to get a clean profile and accurate H and W values.

Frequently Asked Questions (FAQ)

Is the calculation radius from afm image using gwidden 100% accurate?

No. It is a geometric approximation that depends heavily on the assumption of a spherical particle and the quality of the input data. It is an excellent estimation method but is not a substitute for direct, high-resolution measurement techniques if absolute precision is required. Tip convolution effects always introduce some level of inaccuracy in lateral measurements.

Why is my calculated radius so different from the particle’s height?

This often happens when tip convolution is very strong (i.e., you have a very wide FWHM compared to your height). It can also indicate that your particle is not spherical and may be flattened on the surface.

What is Gwyddion?

Gwyddion is a popular, free, and open-source software used for the analysis of data from scanning probe microscopy (SPM), including AFM. It provides tools for leveling data, measuring profiles, and analyzing particles, which are essential for getting the inputs for this calculator.

Can I use this for non-spherical particles?

You can, but the result should be interpreted as the “radius of curvature” at the apex of the feature, not necessarily its true physical radius.

My result is “NaN”. What happened?

This means “Not a Number”. It occurs if you enter non-numeric values, or if the height (H) is zero, which leads to division by zero in the formula.

How can I get more accurate measurements?

Use the sharpest AFM tip possible, ensure your sample is well-dispersed, and use multiple measurements across several particles to get a statistical average. Advanced methods involve mathematically deconvolving the tip shape, a topic related to AFM calibration standards.

Where do I find the FWHM value in Gwyddion?

After using the ‘Profile’ tool to draw a line over your feature, the resulting graph window has a ‘Measure’ button. This tool can often calculate the FWHM of peaks automatically. You can also explore options for nanoparticle size distribution within the software.

Does the unit switcher convert my inputs?

No, it assumes your inputs are already in the selected unit. The calculator uses the selection to correctly label the output. Ensure your H and W values are in the same unit system before inputting them.