Diffracted Beam Interferometry Research Articles

Diffracted beam interferometry – Differential phase contrast image of an amorphous thin film material

Differential phase contrast based on diffracted beam interferometry is used to explain the good phase contrast found of an amorphous thin film material deposited on the surface of a gold (Au) crystal substrate. An electron biprism is used to interfere two symmetrically diffracted beams generated by the Au crystal substrate that carried the phase of the amorphous material specimen. Bragg diffraction from the Au crystal substrate is used to explain why the phase of the amorphous thin film material is so well phase imaged. The phase of the amorphous material that was deposited on the specimen’s upper surface of the Au crystal substrate is canceled and thus not revealed in the phase image whereas the phase due to the amorphous material deposited on the bottom surface of the Au crystal substrate does not cancel due to having a lateral phase shift in the amorphous material specimen plane proportional to the substrate thickness and Bragg angle of the diffracted beams. The lateral phase shift enabled differential phase contrast of the amorphous material specimen.

Phase imaging dislocations using diffracted beam interferometry.

A phase imaging method that measures the phase shift existing at a dislocation's core is described. The method uses the interference of two symmetrically diffracted beams on the optic axis by means of an electron biprism. Each diffracted beam carries half the phase of the dislocation core. When combined, the entire phase shift of the dislocation core is obtained.

Lattice Vibration Measurements of Atomic Planes Using the Interference of Thermal Diffuse Scattered Electrons

Lattice vibrations of the atomic planes have been measured using the self-interference of its thermal diffuse scattered (TDS) electron intensity on the diffraction plane by means of diffracted beam interferometry. Reconstruction of the fringes in the TDS intensity using the 222 Bragg diffracted beam of aluminum as the carrier frequency has found a wide range of vibrational frequencies existing between the atomic planes, as expected, but also some lateral vibrational components that likely represent vibrations which are parallel to the atomic planes.

Electron interference from an amorphous thin film on a crystal transmission electron microscopy specimen

The electron intensity of a beam from an amorphous surface layer on a crystal transmission electron microscopy (TEM) specimen has been found to have sufficient coherence to produce fringes in interferograms, created by interfering two electron diffracted beams from the crystal, using a method of electron interference referred to as diffracted beam interferometry. This interference method involves amplitude splitting of the electron beam by means of a crystal with a thin amorphous layer on its surface. The amorphous intensity is transferred along with the crystal's Bragg diffracted beams and is then self-interfered when the crystal's Bragg diffracted beams are interfered by an electron biprism. The interference fringes in the interferograms exist in low to high electron scattering angles. The spatial frequency of the amorphous intensity fringes depends on the Bragg angle of the crystal's interfered diffracted beams. It is shown that the absolute phase of the amorphous intensity is possibly obtained using a Cs-corrected TEM and two interfering diffracted beams having equal but opposite phases. This method of interference is a good step towards measuring the phase of amorphous materials that is useful in determining their complex atomic structures.

Amplitude and phase characterization by diffracted beam interferometry: blind dbi

Diffracted beam interferometry is a self referenced method characterization technique whose operation principle is based on the reconstruction of the phase of a beam starting from the interference data between the beam and its diffracted copy. The phase is recovered indirectly by means of an iterative algorithm that relates the irradiances of the interfering beams and its phase difference. The first experimental demonstration of DBI was implemented on a Mach-Zenhder interferometer which incorporated an afocal imaging system in each arm, in order to form an image of a common object in different planes at the output of the interferometer. The irradiance data as well as the phase difference data were picked up from one of the image planes and they were introduced in the iterative algorithm. In this work we discuss a modification of the algorithm that allows to reconstruct simultaneously the amplitude and phase of the wavefront starting from, exclusively, the phase difference between the two waves that interfere in one of the image planes. This new algorithm improves the reconstruction process because the data acquisition process is faster and consequently the method is less influenced by environment disturbances. The method has been applied successfully to the characterization of phase plates and laser beams as well as to the local characterization of ophthalmic lenses.

Coherent electron interference from amorphous TEM specimens

For the first time, the electron intensity on the diffraction plane from amorphous transmission electron microscope (TEM) specimens has been found to have sufficient coherence to produce fringes in interferograms that were created using a wavefront splitting method of diffracted beam interferometry. The fringes were found to exist from low to high electron-scattering angles. Their spatial frequency depended on the angular overlap of the interfering beams, which was controlled by an electron biprism. From these interferograms, phase information of amorphous materials, which is information now lacking and required for determining their atomic structures, was obtained. An immediate application of this interference is a new method to determine the spatial resolution of the TEM that occurs at the shear angle for fringe disappearance.

Single-shot amplitude and phase reconstruction by diffracted-beam interferometry

We use diffracted-beam interferometry and spatial frequency modulation to reconstruct both amplitude and phase of a signal beam in a single measurement. We describe the numerical algorithm that performs the beam reconstruction and we present some experimental examples.

Wavefront sensing by diffracted beam interferometry

We consider the reconstruction of an optical wavefront by means of the interference of a light beam with a diffracted copy of itself. We present the basis of the method and a numerical algorithm for phase retrieval from the experimental data.

Diffracted beam interferometry for EM and materials research

Diffracted beam interferometry, DBI, is a practical method of interferometry which removes the strict requirement for a bright, coherent source and extends the availability of holography to a wider community of electron microscopists. The only alteration to the microscope is the installation of an electron biprism into a post-objective lens position. DBI is very flexible as the interferogram can be produced from the conditions of the infocus diffraction (Fraunhofer plane), through the Fresnel (de)focus region to the infocus specimen plane by varying the strength of the post-objective lenses, Fig. 1. As well the convergence of the interfering beams can vary from highly convergent (Fig. 1) to pseudoparallel (Fig. 2). Although the phase in the interferogram due to beam tilt and the contrast transfer function of the prefield objective lens cancel out when the interfering beams are exactly overlaid, the phase due to the spatial frequency of the biprism, KB, the contrast transfer function, uL,R, of the postfield objective lens for each beam, L,R, and the inherent material phase, FL,R, remain.

Reflection diffracted beam interferometry (RDBI) applied to the study of surfaces

Diffracted beam interferometry, DBI, (previously referred to as Convergent Beam Electron Diffraction + Electron Biprism Interferometry, CBED+EBI) which uses an electron biprism to deflect diffracted beams (convergent or parallel) can produce an interferogram between any two beams within the information envelope of the microscope such that the beam's amplitude and phase can be measured and studied. As well, the electron source need not be highly coherent. So far, DBI has been applied only to transmission electron diffraction, although there is no reason why it shouldn't be applicable to all electron diffraction methods including reflection high (low) energy electron diffraction, RH(L)EED and, possibly, back-scattered electron diffraction, BSED, in the SEM for the study of surfaces. DBI has already shown that substantial phase information, such as strain at interfaces and dislocations, compositional gradients and small defect clusters which are on the size scale of the unit cell, are retrievable from its holograms.