Fresnel Fringes Research Articles

Quasi/non-equilibrium state in nanobubble growth trajectory revealed by in-situ transmission electron microscopy

Nanobubbles have attracted significant attention in recent years for their potential applications in various fields, including engineering, environmental, biological, and medical. Furthermore, different types of nanobubbles are used for different fields due to their distinct properties. Yet, the challenge remains to understand the growth kinetics of both interfacial and bulk nanobubbles at the nanoscale to meet the requirements of different applications. Using liquid cell transmission electron microscopy, we revealed a quasi-equilibrium state in the growth trajectory of nanobubbles induced by the electron beam in the aqueous solution in real-time. Specifically, we successfully distinguished between interfacial and bulk nanobubbles by combining the analysis of growth kinetics and the Fresnel fringe method. Furthermore, the non-equilibrium growth of some nanobubbles from solution to the interface was revealed by the above method. These insights on the nanoscale growth kinetics of nanobubbles can help better engineer tailored nanobubbles with specific kinetic behaviors for different applications.

Talbot photolithography optimization with engineered hybrid metal-dielectric mask: High-contrast and highly-uniform Talbot stripes

Conventional projection Talbot lithography usually employs opaque (amplitude) or transparent (phase) masks for creating a periodic array of Fresnel diffraction fringes in the photosensitive substrate. For particular mask design the longitudinal periodicity of Talbot carpet can be avoided producing quasi uniform striped pattern (Talbot stripes). We propose a novel hybrid amplitude-phase mask which is engineered for obtaining extremely smooth Talbot stripes and simultaneously high lateral optical contrast and extreme spatial resolution better than a third of laser wavelength. By means of the numerical simulations, we demonstrate the robustness of produced striped diffraction patterns against mask design deviation and light incidence angle variations. The reproducibility of the Talbot stripes is reported also for 1D and 2D metal-dielectric projection masks.

Visualization of different carrier concentrations in n-type-GaN semiconductors by phase-shifting electron holography with multiple electron biprisms.

Phase-shifting electron holography (PS-EH) using a transmission electron microscope (TEM) was applied to visualize layers with different concentrations of carriers activated by Si (at dopant levels of 1019, 1018, 1017 and 1016 atomscm-3) in n-type GaN semiconductors. To precisely measure the reconstructed phase profiles in the GaN sample, three electron biprisms were used to obtain a series of high-contrast holograms without Fresnel fringes generated by a biprism filament, and a cryo-focused-ion-beam (cryo-FIB) was used to prepare a uniform TEM sample with less distortion in the wide field of view. All layers in a 350-nm-thick TEM sample were distinguished with 1.8-nm spatial resolution and 0.02-rad phase-resolution, and variations of step width in the phase profile (corresponding to depletion width) at the interfaces between the layers were also measured. Thicknesses of the active and inactive layers at each dopant level were estimated from the observed phase profile and the simulation of theoretical band structure. Ratio of active-layer thickness to total thickness of the TEM sample significantly decreased as dopant concentration decreased; thus, a thicker TEM sample is necessary to visualize lower carrier concentrations; for example, to distinguish layers with dopant concentrations of 1016 and 1015 atomscm-3. It was estimated that sample thickness must be more than 700nm to make it be possible to detect sub-layers by the combination of PS-EH and cryo-FIB.

Measurement of thickness of thin film by fitting to the intensity profile of Fresnel diffraction from a nanophase step.

Diffraction of light beams from the phase steps due to abrupt/sharp changes in the boundary of the steps leads to Fresnel fringes whose visibility and intensity profile depend on the change of the step height or light incident angle. The visibility has been utilized in measurements of different physical quantities. In this paper, for the first time to our knowledge, by introducing the fitting method as a fast method, we show that by fitting the theoretical intensity distributions on the experimental intensity profiles of the light diffracted from a step at different incident angles, one can specify the step height with precision of a few nanometers. In addition, we show that this approach provides accurate film thickness in a broad range of thicknesses using modest instrumentation. Furthermore, based on Fresnel diffraction from the phase step, we have manufactured and trademarked an optical device for measuring the thickness of thin films.

Illumination semiangle of 10-9 rad achieved in a 1.2-MV atomic resolution holography transmission electron microscope.

The coherency of a 1.2-MV transmission electron microscope was evaluated through illumination semiangles calculated from lengths over which Fresnel fringes can be observed. These lengths were determined from the diameters of circular holes fully filled with Fresnel fringes, i.e. this method allows lengths to be accurately measured even if micrographs are subjected to distortions. The smallest illumination semiangle of 4.0 × 10-9 rad was obtained for a circular hole with a diameter of 191 μm. In addition, electron beam brightness was estimated to be approximately 3 × 1014 A/m2·sr from the obtained illumination semiangle values and current densities. The results provide us with essential information that can be referred to in future electron holography studies aimed at detecting weak electromagnetic fields in materials.

Correlative micro-diffraction and differential phase contrast study of mean inner potential and subtle beam-specimen interaction

We present a correlative micro-diffraction and differential phase contrast (DPC) study within scanning transmission electron microscopy (STEM) on the determination of mean inner potential (MIP) and explain the origin of subtle beam-specimen interactions at the edge of wedge-shaped crystals using both experiment and simulation. Our measurement of MIP of Si and GaAs resulted in 12.48 ± 0.22 V and 14.15 ± 0.22 V, respectively, from directly evaluating beam refraction in micro-diffraction mode. DPC-STEM measurements gave very similar values. Fresnel fringes within the diffraction disk resulting from interaction of the highly coherent electron beam with the aperture are observed and a numerical simulation scheme is implemented to reproduce the effect of the specimen on the fringe pattern. Perfect agreement between experiment and simulation has been achieved in terms of subtle displacements of the fringes upon approaching the sample edge with the electron probe. The existence of the fringes has minor effect on the DPC-STEM signal, which is well below the noise level of our setup at practically reasonable acquisition times. We suggest the possibility to perform pseudo-contactless probing of weak potential differences in beam sensitive samples by evaluating the subtle displacements of Fresnel fringes quantitatively.

Publisher’s note

We present a correlative micro-diffraction and differential phase contrast (DPC) study within scanning transmission electron microscopy (STEM) on the determination of mean inner potential (MIP) and explain the origin of subtle beam-specimen interactions at the edge of wedge-shaped crystals using both experiment and simulation. Our measurement of MIP of Si and GaAs resulted in 12.48 ± 0.22V and 14.15 ± 0.22V, respectively, from directly evaluating beam refraction in micro-diffraction mode. DPC-STEM measurements gave very similar values. Fresnel fringes within the diffraction disk resulting from interaction of the highly coherent electron beam with the aperture are observed and a numerical simulation scheme is implemented to reproduce the effect of the specimen on the fringe pattern. Perfect agreement between experiment and simulation has been achieved in terms of subtle displacements of the fringes upon approaching the sample edge with the electron probe. The existence of the fringes has minor effect on the DPC-STEM signal, which is well below the noise level of our setup at practically reasonable acquisition times. We suggest the possibility to perform pseudo-contactless probing of weak potential differences in beam sensitive samples by evaluating the subtle displacements of Fresnel fringes quantitatively.

Nanobubble nucleation studied using Fresnel fringes in liquid cell electron microscopy

Liquid cell electron microscopy is a useful technique for the observation of chemical, biological, and mechanical processes in liquids at nanometer-scale resolution. This study investigated the generation and growth of nanobubbles using the Fresnel fringe method, which enabled us to determine the location of bubble interface; the nanobubbles were induced in the 600-nm-thick water sample in the cell, by the electron beam. Nucleation occurred first at the solid–liquid interface in the upstream side of electron beam, and this was followed by second-group nucleation at the downstream-side interface; all of the stable nucleations occurred on the solid surfaces. The size of the nucleated bubbles at the moment they became visible depended on the magnification used in the electron microscope, and a higher-energy density in the electron beam induced larger bubbles. The underlying mechanism was also considered in this study.

Reconstruction Method for Phase-Shifting Electron Holography Fitted with Fresnel Diffraction Affected Fringes

Phase shifting electron holography is a transmission electron microscope technique that a number of holograms with different initial phases are acquired by changing the angle of the incident electron beam, and the intensity variation at a certain point on the holograms is fitted by sinusoidal curve to retrieve the object wave passing through a specimen. In reality, however, Fresnel fringes caused by the electrostatic biprism modulates the electron wave, limits the fitting accuracy and results in phase errors in phase reconstruction. In this study, we suggest a modified phase reconstruction method for phase shifting electron holography. The intensity variations at a certain point on each hologram are fitted not by sinusoidal curve, but by Fresnel diffraction affected curve to retrieve the object wave. This would provide better fitting accuracy, and has a potential to improve the precision of phase shifting electron holography. Simulations demonstrated the improvements of this method comparing with conventional phase shifting holography method.

A Practically Simple and Easy Approach for Minimizing the Influence of Fresnel Fringes on Phase Sensitivity Measured from Electron Holography

A Practically Simple and Easy Approach for Minimizing the Influence of Fresnel Fringes on Phase Sensitivity Measured from Electron Holography

Practical procedure for retrieval of quantitative phase map for two-phase interface using the transport of intensity equation

A practical procedure for retrieving quantitative phase distribution at the interface between a thin amorphous germanium (a-Ge) film and vacuum based on the transport of intensity equation is proposed. First, small regions were selected in transmission electron microscopy (TEM) images with three different focus settings in order to avoid phase modulation due to low frequency noise. Second, the selected TEM image and its three reflected images were combined for mirror-symmetry to meet the boundary requirements. However, in this symmetrization, extra phase modulation arose due to the discontinuous nature of Fresnel fringes at the boundaries among the four parts of the combined image. Third, a corrected phase map was obtained by subtracting a linear fit to the extra phase modulation. The phase shift for a thin a-Ge film was determined to be approximately 0.5rad, indicating that the average inner potential was 18.3V. The validity of the present phase retrieval is discussed using simple simulations.

Advantages of phase retrieval for fast x-ray tomographic microscopy

In near-field imaging with partially coherent x-rays, the phase shifting properties of the sample are encoded in the diffraction fringes that appear as an additional intensity modulation in the x-ray projection images. These Fresnel fringes are often regarded as purely an enhancement of the visibility at the interfaces. We show that retrieving the phase information contained in these patterns significantly advances the developments in fast micro-tomography. Improving temporal resolution without intensifying radiation damage implies a shortening of the exposure time rather than increasing the photon flux on the sample. Phase retrieval, to a large extent, compensates the consequent photon count moderation in the images, by fully exploiting the stronger refraction effect as compared with absorption. Two single-distance phase retrieval methods are evaluated for the case of an in situ 3 Hz micro-tomography of a rapidly evolving liquid foam, and an in vivo 6 Hz micro-tomography of a blowfly. A new dual-detector setup is introduced for simultaneous acquisition of two near-field diffraction patterns. Our goal is to couple high temporal, spatial and density resolution in a single imaging system in a dose-efficient manner, opening further options for dynamic four-dimensional studies.

Advanced split-illumination electron holography without Fresnel fringes

Advanced split-illumination electron holography was developed by employing two biprisms in the illuminating system to split an electron wave into two coherent waves and two biprisms in the imaging system to overlap them. A focused image of an upper condenser-biprism filament was formed on the sample plane, and all other filaments were placed in its shadow. This developed system makes it possible to obtain precise reconstructed object waves without modulations due to Fresnel fringes, in addition to holograms of distant objects from reference waves.

Observation of the Magnetic Skyrmion Lattice in a MnSi Nanowire by Lorentz TEM

We report here the real-space observation of skyrmions and helical magnetic domains in a MnSi nanowire (NW) using Lorentz transmission electron microscopy (LTEM). The MnSi NW was thinned to a rectangular cross-section by focused-ion beam milling to reduce obstructive Fresnel fringes. Helimagnetic domains, imaged as alternating bright and dark contrast stripes with an 18 nm period, were observed to be the spontaneous magnetic ground state at 6 K, while the hexagonal skyrmion lattice (SkX) with a domain diameter of 18 nm was observed under a normal magnetic field of 210 mT. Temperature-dependent measurements reveal that the SkX is stable over a larger range in this NW system (6-35 K) compared to the narrow temperature regime of skyrmion phase in bulk MnSi (26-30 K) and thin films of MnSi (5-23 K).

Quasi 3D imaging of DNA–gold nanoparticle tetrahedral structures

Verification by imaging of the structure of 3D DNA constructs, both bare and conjugated to metal nanoparticles, is challenging. We demonstrate here two transmission electron microscopy (TEM) based methods to distinguish between fully formed tetrahedra, synthesized from DNA conjugated with gold nanoparticles (GNPs) at their vertices, and structures which are only partially formed. When deposited on a surface, fully formed tetrahedra are expected to retain their 3D pyramidal structure, while partially formed structures are expected to form a 2D structure. The first method by which 3D and 2D structures were distinguished was imaging them at different defocusing values. While for 2D structures all the four GNPs acquire Fresnel fringes at the same defocusing value, for 3D structures at least one particle is at a different plane with respect to the others, and so it acquires Fresnel fringes at a different defocusing value. The second method we show is imaging of the structures at different angles. While a single TEM image gives only a 2D projection of the structure, by combining information achieved from imaging at several tilting angles one may verify the structural construct.

X-Ray propagation imaging of a lipid bilayer in solution

We have used X-ray propagation imaging to visualize a less than 5 nm thick native lipid bilayer membrane freely suspended in aqueous solution. Contrast is formed by free space propagation of hard X-rays, with the membrane illuminated by a nano-focused, partially coherent synchrotron beam, at a controllable distance (defocus) behind the focal spot. Quantitative fitting of the magnified Fresnel fringes shows the transition from membranes swollen with solvent to the native bilayer, containing structural information at near-molecular resolution along the dimension perpendicular to the bilayer. We show first applications of this hybrid technique of propagation imaging and near-field diffraction to the investigation of ultra-thin organic films formed in micro-fluidic devices, namely the formation of a lipid bilayer by the adhesion of two constitutive monolayers.

Local electron tomography using angular variations of surface tangents: Stomo version 2

Local electron tomography using angular variations of surface tangents: Stomo version 2

Twin-electron biprism

In order to obtain a large deflection angle without increasing the applied voltage to an electron biprism, we have developed a 'twin-electron biprism' (TBP), which is composed of two filament electrodes and a pair of ground plates. The observed interference-fringe spacing revealed that the deflection angle created by a TBP was about twice larger than that by a 'conventional electron biprism'. Also, we have suggested, in a double-electron biprism interferometry, the optimal disposition of a TBP for reducing the intensity of Fresnel fringes recorded in an electron hologram.

Deconvolution by finite‐size‐source effects of x‐ray phase‐contrast images

In the hard x-ray region, the cross sections for the phase shift of low-Z elements are about 1000 times larger than the absorption ones. As a consequence, phase contrast is detectable even when absorption contrast is minimal or absent. Therefore, phase-contrast imaging could become a valid alternative to absorption contrast without delivering high dose to tissue/human body parts. To enhance the quality of phase-contrast images without increasing the dose, a possible approach could be the partial deconvolution of the finite source size effects by experimental phase-contrast images. The deconvolution procedure, the authors propose, employs the acquisition of two images on a suitable well-known test sample, one in contact and the other in phase-contrast conditions. Both acquired images are used along with a simulated phase-contrast image (obtained from the test sample in ideal conditions of pointlike source illumination) to correctly retrieve the experimental source distribution function. This information allows a generic experimental phase-contrast image, acquired in the same conditions, to be partially deconvolved by finite source size effects. The performed experimental tests indicate that deconvolved images are equivalent to those which would be obtained with a source 40% smaller than the actual size. In turn, this finding is equivalent to an increase of the "effective" lateral spatial coherence length. The corresponding quality improvement of the phase-contrast imaging is directly deducible by the presence of many Fresnel fringes, much better visible with respect to the original experimental phase-contrast images. The use of a test standard sample, always possible in every experimental setup, to partially deconvolve the finite-size-source blurring effects shows that higher quality phase-contrast images could be readily available, making easier diagnoses and tissue/sample analyses. The method could give, in the future, the possibility to further lower the delivered dose to patients, organs, and tissues when compact room-sized and brilliant microfocus x-ray sources will be available for clinical applications in hospitals.

X-Ray Phase Contrast Imaging of Freestanding Lipid Model Membranes

Membranes are considered as the most important interfaces in biology, and can be visualized under physiological conditions by optical techniques such as phase contrast and fluorescence light microscopy. While the contour lines and large lateral domains of biological membranes can be imaged, the density profile of the membrane and associated changes cannot be resolved by visible light. We report on hard x-ray phase contrast imaging of black lipid membranes (BLMs), which are freely suspended over a micro machined aperture in an aqueous solution. This new way of membrane structure analysis allows investigating bio molecular and organic sub-stances in aqueous environments by parallel and divergent beam propagation imaging, using partially coherent multi-keV x-ray radiation. The width of the thinning film is significantly smaller than the detector pixel size, but can be resolved from quantitative analysis of the intensity fringes in the Fresnel diffraction regime down to its native thickness of about 5nm. We have put forward a simplified but extendable model, which enables the theoretical description of image formation and charac-terization of membrane thickness and its decrease during the thinning process from a bulk to a bimolecular film. The structural changes can be obtained from both the loss of contrast and the asymmetry of the detected Fresnel fringes. On the basis of the recent experiments, future investigations will be performed to study the inte-ractions of membranes, as they are for example known from synaptic fusion, with high spatial resolution.