Measurement methods | ParticleBio
Particle size, defined
A size distribution starts with a clear measurement definition and a calibrated image.
Calibrate the image
Use the scale bar or the original image calibration to establish the physical length represented by each pixel. Preserve that calibration when cropping or resizing an image. Select an analysis area that excludes labels and the scale bar.
Equivalent circular diameter
For projected area \(A\), the equivalent circular diameter is:
\[d_{ECD}=2\sqrt{A/\pi}\]
The example uses circular synthetic objects and a calibration of 0.5 nm per pixel. Each object’s area, diameter, table entry, and histogram bin come from the same geometry.
Review included objects
Inspect boundaries before accepting an object. Record decisions about touching objects, image-edge objects, and ambiguous outlines. Treat an unresolved cluster as one segmented object unless its individual boundaries have been established.
Read the distribution
The example shows a number-based distribution: each included object contributes one observation. Histogram intervals are 5–10, 10–15, 15–20, 20–25, and 25–30 nm. Intervals include the lower endpoint; the final interval also includes its upper endpoint. The median is recalculated whenever inclusion changes.
TEM measurements describe projected geometry. DLS hydrodynamic diameter and XRD crystallite size use different measurement definitions and should be reported separately.