Rayleigh Criterion
- Practical Electron Microscopy and Database -
- An Online Book -


This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.


The resolution for light microscope is defined by Rayleigh criterion,

              δ = 0.61λ/μ sinβ ------------------------- [1982a]

where λ -- Wavelength of the light;
          μ -- Refractive index of the viewing medium;
          β -- Semiangle of collection of the magnifying lens.

Based on the Rayleigh criteria, the ability (spatial resolution) of the microscope to resolve two spots as two essentially relates to how sharply the Airy disks are defined. As the disks get closer, the intensity dip between the two spots becomes smaller. For instance, the two spots can be resolved in Figure 1982 (a) and (b), while they cannot be resolved in Figure 1982 (c).

Rayleigh’s criteria - Airy disk

Figure 1982. The two resolvable spots in (a) and (b) and the two irresolvable spots in (c). Adapted from [1]

In electron microscopes, the aperture-induced diffraction effect on the size of the electron beam is given by,

         Diffraction effect on beam diameter ------------------------- [1982b]

         α -- The convergence half-angle of the electron beam due to the aperture.

The beam diameter due to diffraction effect (dd) is the Rayleigh criterion mentioned above and refers to a spacing between two overlapping images of the beam.





[1] Methods in Cell Biology, Vol. 81, DOI: 10.1016/S0091-679X(06)81002-2, David E. Wolf, The Optics of Microscope Image Formation, (2007).




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