Equation 6 · Part 4 · How Scientific Instruments and Metrology Actually Work
Symbol α
What this part means
the numerical aperture of the imaging system.
Its job in the formula
α occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Full expression→Symbol α→Article meaning
Where the article explains it
where is the wavelength of the illuminating radiation, and n is the numerical aperture of the imaging system.
The passage around this formula
An electron microscope is a useful worked example precisely because almost the entire modern instrument exists to correct for a limitation baked into its own optics. The achievable resolution of any imaging system with a circular aperture is bounded, in the simplest diffraction-limited approximation, by a form of the Rayleigh criterion: . where is the wavelength of the illuminating radiation, and n is the numerical aperture of the imaging system. For visible light this caps optical microscopy at roughly 200 nanometres — far too coarse to resolve individual atoms, whose spacing in a solid is typically a few tenths of a nanometre. Electron microscopy…
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
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Sources cited in the article section
- [8] Imaging single atoms using secondary electrons with an aberration-corrected electron microscope ↗
- [7] Electron ptychography of 2D materials to deep sub-ångström resolution ↗
These citations provide research context; check each source for the exact claim it supports.