eV (energy in electron volts) = V (the accelerating voltage). When an electron passes through a potential difference (accelerating voltage field) V, its kinetic energy with be equal to the energy of the field, i.e. The general form of the de Broglie equation is as follows: By combining some of the principles of classical physics with the quantum theory, de Broglie proposed that moving particles have wave-like properties and that their wavelength can be calculated, based on their mass and energy levels. If aberrations and distortions are present, they will determine the practical limit to resolution.ĭe Broglie equation. If all aberrations and distortions are eliminated from the optical system, this will be the limit to resolution. This is the diffraction-limited resolution of an optical system. N sin a is often expressed as NA (numerical aperture) N = index of refraction of medium between point source and lens, relative to free spaceĪ = half the angle of the cone of light from specimen plane accepted by the objective (half aperture angle in radians) Resolution in a perfect optical system can be described mathematically by Abbe's equation. If an object is just below the level of resolution, the peaks generated by the two points will make the object appear to be a single point.Ībbe's equation. Resolution is empirically described as the ability to discriminate between two points. (Of course, these continue to emanate at higher orders, but their affect on optical phenomena diminishes in importance with each higher order.) The resolution is typically described as the distance between the first order peak and the first order trough (designated "r" above). Notice the primary, secondary and tertiary wavefronts generated by the Airy disc. This is known as an Airy disc and is represented below. Instead, the image when viewed critically consists of a disc composed of concentric circles with diminishing intensity. Second, using even a "perfect" optical system, a point of light cannot be focused as a perfect dot. Notice that this causes the parallel wavefront to emerge from the aperture as a spherical wavefront.Īiry disc. Below is an example of how diffraction changes the wavefront in the presence of a small aperture. Diffraction results when a wavefront is impeded by any object, and of course the edge of the lens area constitutes an object, as does any superimposed aperture. First, it is impossible to achieve absolute focus using any optical system that uses particles with wave-like properties, because of diffraction and interference. ![]() ![]() It is desirable to understand several of the fundamental principles of light optics in order to understand the limitations of electron microscopy.ĭiffraction. Limits to Resolution in the Transmission Electron Microscope Limits to Resolution in the Electron Microscope
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