In-line Electron Holography
- Practical Electron Microscopy and Database -
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Based on fundamental in-line holography theory, in the in-line electron holography, the incident (reference) wave and scattered (diffraction) wave can be given by,
         incident (reference) wave ----------------------- [2609a]
         scattered (diffraction) wave ----------------------- [2609b]

Figure 2609 shows an in-line electron holographic setup with a point source. Note that the general in-line holography concepts are still applicable to the in-line electron holography.

In-line point source electron holographic setup

Figure 2609. In-line point source electron holographic setup. Electron waves generated by a point electron source (O) scatter on an object at a distance d and interfere with the reference wave on a screen at a distance L. The distance vectors (r, s, p) are also shown. [1]

According to Huygens–Fresnel principle, the wave at p is given by,

         scattered (diffraction) wave ----------------------- [2609c]

Here, the wave functions can be modeled by different theories.

Therefore, the interference intensity recorded at the hologram plane is given by,

         scattered (diffraction) wave ----------------------- [2609d]

         scattered (diffraction) wave --- [2609e]

The first term in Equation 2609e is only a background (i.e. no scattering object), while the second term represents the intensity of the scattered wave. The last term is the holographic term, originating from the interference between the reference and scattered waves and recording both the amplitude and the phase of the object wave in the hologram. The second term is negligible if the object scatters only a small fraction of the incident wave. Furthermore, by subtracting the background (the first term) from the total intensity, the contrast hologram, Iholo(s), can be obtained. Note that the contrast hologram is used as input for digital reconstruction.

Even though the original electron holography work described the reconstruction of an image by illuminating an ‘in-line’ electron hologram with a parallel beam, the reconstructed image is disturbed by a ‘ghost’ or ‘conjugate’ twin image. The method of electron holography that is most often used for solving problems in materials science is the off-axis, or ‘sideband’, mode.

 

 

 

[1] Lucian Livadaru, Josh Mutus, Robert A. Wolkow, In-line holographic electron microscopy in the presence of external magnetic fields, Ultramicroscopy 108 (2008) 472–480.

 

 

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