Physical Principles of Electron Microscopy: An Introduction to TEM ...

Recent Developments 185
Besides having the same wavelength, the reference wave must have a
fixed phase relationship with the wave that travels through the specimen.
One means of achieving this is to have both waves originate from a small
(ideally point) source, a distance �z from the specimen; see Fig 7-5. This
source can be produced by using a strong electron lens L1 to focus an
electron beam into a small probe, as first proposed by Gabor (1948). If the
specimen is very thin, some electrons are transmitted straight through the
specimen and interfere with those that are scattered within it. Interference
between transmitted and scattered waves produces a hologram on a nearby
screen or photographic plate.
This hologram has some of the features of a shadow image, a projection
of the specimen with magnification M � z/�z. However, each scattering point
S in the specimen emits spherical waves (similar to those centered on S in
Fig. 7-5) that interfere with the spherical waves coming from the point
source, so the hologram is also an interference pattern. For example, bright
fringes are formed when there is constructive interference (where wavefronts
of maximum amplitude coincide at the hologram plane). In the case of a
three-dimensional specimen, scattering points S occur at different zcoordinates,
and their relative displacements (along the z-axis) have an effect
on the interference pattern. As a result, the hologram can record threedimensional
information, as its name is meant to suggest (holo = entire).
Reconstruction can be accomplished by using visible light of wavelength
M�, which reaches the hologram through the glass lens L2 in Fig. 7-5. The
interference fringes recorded in the hologram act rather like a zone plate (or
a diffraction grating), directing the light into a magnified image of the
specimen at S, as indicated by the dashed rays in Fig. 7-5. Because M may
be large (e.g., 10 5 ), this reconstruction is best done in a separate apparatus. If
the defects (aberrations, astigmatism) of the glass lens L2 match those of the
electron lens L1, the electron-lens defects are compensated, and so the
resolution in the reconstructed image is not limited by those aberrations.
At the time when Gabor made his proposal, no suitable electron source
was available; he demonstrated the holographic principle using only visible
light. Nowadays, light-optical holography has been made into a practical
technique by the development of laser sources of highly monochromatic
radiation (small spread in wavelength, also described as high longitudinal
coherence). In electron optics, a monochromatic source is one that emits
electrons of closely the same kinetic energy (low energy spread �E). In
addition, the electron source should have a very small diameter (giving high
lateral coherence). As a result, the widespread use of electron holography
had to await the commercial availability of the field-emission TEM.