Fresnel Images Research Articles

Computer simulation of Fresnel diffraction from double rectangular apertures in one and two dimensions using the iterative Fresnel integrals method

We have applied the iterative Fresnel integrals method for the computation and simulation of the Fresnel diffraction images created by double apertures in one and two dimensions. Necessary formalism has been derived and the relevant computation algorithms have been developed for this application. The computer simulated images show an interesting combination of Fresnel diffraction images with mutual interference effects between the light diffracted from the two apertures. Transition to the expected Fraunhofer diffraction pattern for double apertures or slits is also observed by the simulations.

In situ Lorentz TEM magnetization studies on a Fe–Pd–Co martensitic alloy

Understanding domain wall pinning centers and the resultant mobility of ferroic (ferromagnetic and ferroelastic) walls under an applied magnetic field is of central importance to actuator applications of magnetic shape memory alloys. The movement of ferroic boundaries in a twinned Fe–Pd–Co martensite was analyzed by means of Lorentz mode transmission electron microscopy. An in situ magnetizing sample-holder was used to record the evolution of the magnetic domain structure as a function of the applied field. Fresnel images were recorded at different field values and a phase reconstruction algorithm was used to map the magnetization configuration inside the foil. The motion of magnetic domain walls was found to be strongly influenced by the presence of twin boundaries. Free-standing domain walls became mobile at fields as low as 15 Oe, whereas an order of magnitude higher field was required to depin domain walls that coincided with twin boundaries. The domain wall motion was completely reversible with a notable hysteresis.

Image processing method for laser damage probability measurement by single-shot of laser pulse

An experiment for high efficiency laser-induced damage probability measurement has been implemented using a periodic binary phase grating. With such a grating, a laser beam is transformed into an ensemble array of Gaussian-like spots, which is known as the Fresnel image of the grating. A scientific CCD camera is used to image the laser spot array as well as the damage of the coating sample. The image data is then processed to obtain the peak fluence distribution of the laser spot array based on the calibrated CCD grayscale. By comparing the image of the damaged coating sample with that of the laser spot array, the damage probability of the coating sample can be precisely determined by the use of single-shot of laser pulse.

Visualization of vortex core polarity in NiFe nanodots by tilted Fresnel images

We illustrate an approach which allows determining the out-of-plane component of the vortex core (polarity) in NiFe nanodots using Fresnel imaging in Lorentz electron microscopy. Using tilted Fresnel images, contribution of the polarity is introduced into the Fresnel image. However, this contribution is relatively small and a difference image from two symmetrically tilted Fresnel images must be used to eliminate the strong contribution from the in-plane curling magnetization and non-magnetic contrast. The sense of the polarity appears as a bipolar white-black contrast in the difference image on the tilt axis. A vortex core with a diameter of 16.5 ± 2.5 nm is experimentally measured. Image tilting, displacement and geometrical distortion may disturb the difference image, and hence subtraction of the difference image must be aligned by cross-correlation. The method is also justified by a study of the observed contrast characteristic due to misalignment. The method is confirmed to be superior to similar approach with direct interpretation of information and more information subtracted.

Fresnel-based beamforming for low-cost portable ultrasound

In this paper, we propose a modified electronic Fresnel-based beamforming method for low-cost portable ultrasound systems. This method uses a unique combination of analog and digital beamforming methods. Two versions of Fresnel beamforming are presented in this paper: 4-phase (4 different time delays or phase shifts) and 8-phase (8 different time delays or phase shifts). The advantage of this method is that a system with 4 to 8 transmit channels and 2 receive channels with a network of switches can be used to focus an array with 64 to 128 elements. The simulation and experimental results show that Fresnel beamforming image quality is comparable to traditional delay-and-sum (DAS) beamforming in terms of spatial resolution and contrast-to-noise ratio (CNR) under certain system parameters. With an f-number of 2 and 50% signal bandwidth, the experimental lateral beamwidths are 0.54, 0.67, and 0.66 mm and the axial pulse lengths are 0.50, 0.51, and 0.50 mm for DAS, 8-phase, and 4-phase Fresnel beamforming, respectively. The experimental CNRs are 4.66, 4.42, and 3.98, respectively. These experimental results are in good agreement with simulation results.

Phase calibration of spatial light modulators by means of Fresnel images

Reliable application of spatial light modulators (SLMs) as programmable diffractive optical elements requires a thorough calibration. In this paper, we propose a method for calibrating SLMs based on the evaluation of Fresnel images. Fresnel images generated by a binary phase diffraction grating consist of binary irradiance distributions whose visibility depends on the phase modulation. Displaying on our device a diffraction grating with a binary phase step along one direction and a linearly increasing phase along the orthogonal direction, we perform a complete phase calibration. In this way, the phase modulation for every pixel and for every value of the entrance signal can be determined experimentally. Additionally, data acquisition can be significantly simplified with this scheme.

Determination of magnetic vortex polarity from a single Lorentz Fresnel image

Nanoscale confinement of the magnetization in a magnetic element often results in the creation of a vortex structure. The vortex equilibrium state is characterized by the curling of the in-plane magnetization (chirality) and an out-of-plane core magnetization. The polarity of the vortex core can point up or down, independent of the chirality, and, thus, magnetic elements with a vortex core are interesting as four-state logic elements. We present an easy-to-use, quantitative method for the determination of both chirality and polarity from a single Fresnel image. This method offers direct evidence of the three-dimensional structure of a magnetic vortex and has significant advantages over the more complex methods currently in use.

Easy axis magnetization reversal in cobalt antidot arrays

The magnetization reversal in square lattice cobalt antidot arrays with the applied field at 45° to the antidot rows was investigated using Lorentz electron microscopy in the Fresnel mode. While the hysteresis loops from magneto-optical Kerr effect measurements only reflect the easy axis character of the reversal, several different reversal processes were identified in the Fresnel images depending on the field history. Details of this complex magnetization reversal were elucidated with micromagnetic simulations.

A micro-displacement encoder using a thin-film resonant photodetector with directional sensitivity

A micro-displacement encoder based on compact Moire configuration is developed using a resonant photodetector with directional sensitivity for oblique incidence. The photodetector consists of a thin-film silicon photodiode and a resonant grating (index grating). The fabricated photodetector is directly located in a Fresnel image zone of a scale grating. Therefore, the optical arrangement of the proposed encoder is simple. Using a guided-mode resonance, the photodetector detects selectively the interference of the ± 1st-order beams diffracted from the scale grating, while suppressing the sensitivity for the 0th-order beam. The 0th-order beam causes undesired signal modulation for the air gap fluctuation of the encoder. In the experiment, sub-micron resolution and robustness to the air gap variation have been confirmed. The directional sensitivity and the encoder performances have also been analyzed theoretically.

Anti-phase boundaries and magnetic domain structures in Ni 2MnGa-type Heusler alloys

The microstructure and magnetic domain structure of austenitic Heusler Ni 2MnGa are investigated as a function of heat treatment to study the interplay of anti-phase boundaries and magnetic domain walls. Conventional electron microscopy observations on arc-melted polycrystalline samples show that anti-phase boundaries in this system are invisible for standard two-beam imaging conditions, due to the large extinction distance of the Heusler superlattice reflections. Lorentz Fresnel and Foucault observations on quenched samples reveal a wavy magnetic domain morphology, reminiscent of curved anti-phase boundaries. A close inspection of the domain images indicates that the anti-phase boundaries have a magnetization state different from that of the matrix. Fresnel image simulations for a simple magnetization model are in good agreement with the observations. Magnetic coercivity measurements show a decrease in coercivity with annealing, which correlates with the microscopy observations of reduced anti-phase boundary density for annealed samples.

Metrology for Fresnel measuring method

The metrological characterization of a Fresnel method for measuring the dimensions of objects is investigated. In this method, free space, as an optical element, transforms the input image of the inspected object into its Fresnel image with great accuracy. The major sources of systematic measurement error are estimated analytically including non-uniform illumination of the object, the interference effect of the edge images of the diffracting object, the integration properties of the linear multi-element photodetector, the influence of the extended size of a partially coherent light source and the volumetric properties of a 3D object. It is proposed that algorithms are used to account for any error components; effective algorithms for this are proposed.

Aspects regarding measurement of thickness of intergranular glassy films

Materials such as Si(3)N(4), SiC and SrTiO(3) can have grain boundaries characterized by the presence of a thin intergranular amorphous film of nearly constant thickness, in some cases (e.g. Si(3)N(4)) almost independent of the orientation of the bounding grains, but dependent on the composition of the ceramic. Microscopy techniques such as high-resolution lattice fringe imaging, Fresnel fringe imaging and diffuse dark field imaging have been applied to the study of intergranular glassy films. The theme of the current investigation is the use of Fresnel fringes and Fourier filtering for the measurement of the thickness of intergranular glassy films. Fresnel fringes hidden in high-resolution micrographs can be used to objectively demarcate the glass-crystal interface and to measure the thickness of intergranular glassy films. Image line profiles obtained from Fourier filtering the high-resolution micrographs can yield better estimates of the thickness. Using image simulation, various kinds of deviation from an ideal square-well potential profile and their effects on the Fresnel image contrast are considered. A method is also put forth to objectively retrieve Fresnel fringe spacing data by Fourier filtering Fresnel contrast images. Difficulties arising from the use of the standard Fresnel fringe extrapolation technique are outlined and an alternative method for the measurement of the thickness of intergranular glassy films, based on zero-defocus (in-focus) Fresnel contrast images is suggested. The experimental work is from two ceramic systems: Lu-Mg-doped Si(3)N(4) and SrTiO(3) (stoichiometric and nonstoichiometric). Further, a comparison is made between the standard high-resolution lattice fringe technique, the standard Fresnel fringe extrapolation technique and the methods of analyses introduced in the current work, to illustrate their utility and merits. Taking experimental difficulties into account, this work is intended to be a practical tool kit for the study of intergranular glassy films.

Unified approach to describe optical pulse generation by propagation of periodically phase-modulated CW laser light

The analysis of optical pulse generation by phase modulation of narrowband continuous-wave light, and subsequent propagation through a group-delay-dispersion circuit, is usually performed in terms of the so-called bunching parameter. This heuristic approach does not provide theoretical support for the electrooptic flat-top-pulse generation reported recently. Here, we perform a waveform synthesis in terms of the Fresnel images of the periodically phase-modulated input light. In particular, we demonstrate flat-top-pulse generation with a duty ratio of 50% at a quarter of the Talbot condition for the sinusoidal phase modulation. Finally, we propose a binary modulation format to generate a well-defined square-wave-type optical bit pattern.

Computer simulation of Fresnel diffraction from rectangular apertures and obstacles using the Fresnel integrals approach

In this paper, we describe a new computer simulation technique of generating Fresnel diffraction images from rectangular apertures of arbitrary dimensions by using Fresnel integrals instead of the more common fast Fourier transform methods. The simulation can be performed in almost any PC using the software MATLAB. Diffraction images can be generated for any wavelength of light and for any aperture–screen and aperture-source distances. Images for rectangular obstacles can also be simulated. Details of the algorithm and program are presented, as well as the interesting insights than can be gained from using the program. Finally, it is shown that the simulated images reduce to the simple Fraunhofer diffraction patterns for certain limiting situations.

Automated small tilt-angle measurement using Lau interferometry

A technique for a tilt-angle measurement of reflecting objects based on the Lau interferometry coupled with the moire readout has been proposed. A white-light incoherent source illuminates a set of two gratings, resulting in the generation of the Fresnel image due to the Lau effect. The Fresnel image is projected onto a reflecting object. The image reflected from the object is superimposed onto an identical grating, which results in the formation of a moiré fringe pattern. The inclination angle of moiré fringes is a function of tilt angle of the object. Theory and experimental arrangement of the proposed technique is presented and results of the investigation are reported.

Magnetic potential in patterned materials determined using energy-dependent Lorentz phase microscopy

The phase of an electron wave, which has traveled through a magnetic sample, is modified by the magnetic and electrostatic potentials of the material. The ability to reconstruct this phase is a powerful method for quantitatively studying the magnetic structure of the sample. Recently, the ``transport-of-intensity'' equation (TIE) has been applied to phase reconstruction using Lorentz transmission electron microscopy (LTEM) data. For magnetic analyses, it is important to separate the influence of the electrostatic potential on the electron wave. In this paper, an energy-dependent TIE analysis is presented in order to differentiate the magnetic and electrostatic contributions. This approach is developed using ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ and Co patterned films in which the contribution of the electrostatic potential is significant compared to that of the magnetic potential. A good fit to theory is obtained, showing that the contribution of the electrostatic potential to the phase is dependent on the energy of the electrons, namely the applied accelerating voltage, while that of the magnetic potential is not. The energy-dependent analysis shows that neglecting the contribution of the electrostatic potential in continuous films of constant thickness can be reasonable. For patterned materials, this methodology determines which features in Fresnel and Foucault contrast LTEM images originate from the magnetic potential and can remove the electrostatic contribution in order to enable a quantitative reconstruction of the magnetic structure. In addition, the different magnetic samples are used to explain the sensitivity limits of the TIE methodology in respect to quantitative measurements of magnetic properties.

Lorentz Phase Imaging and In-situ Lorentz Microscopy of Patterned Co-Arrays.

Understanding magnetic structures and properties of patterned and ordinary magnetic films at nanometer length-scale is the area of immense technological and fundamental scientific importance. The key feature to such success is the ability to achieve visual quantitative information on domain configurations with a maximum ''magnetic'' resolution. Several methods have been developed to meet these demands (Kerr and Faraday effects, differential phase contrast microscopy, magnetic force microscopy, SEMPA etc.). In particular, the modern off-axis electron holography allows retrieval of the electron-wave phase shifts down to 2{pi}/N (with typical N = 10-20, approaching in the limit N {approx} 100) in TEM equipped with field emission gun, which is already successfully employed for studies of magnetic materials at nanometer scale. However, it remains technically demanding, sensitive to noise and needs highly coherent electron sources. As possible alternative we developed a new method of Lorentz phase microscopy [1,2] based on the Fourier solution [3] of magnetic transport-of-intensity (MTIE) equation. This approach has certain advantages, since it is less sensitive to noise and does not need high coherence of the source required by the holography. In addition, it can be realized in any TEM without basic hardware changes. Our approach considers the electron-wave refraction inmore » magnetic materials (magnetic refraction) and became possible due to general progress in understanding of noninterferometric phase retrieval [4-6] dealing with optical refraction. This approach can also be treated as further development of Fresnel microscopy, used so far for imaging of in-situ magnetization process in magnetic materials studied by TEM. Figs. 1-3 show some examples of what kind information can be retrieved from the conventional Fresnel images using the new approach. Most of these results can be compared with electron-holographic data. Using this approach we can shed more light on fine details of in-situ magnetization process in magnetic materials and films studied by TEM. As an example, Fig.4 illustrates the evolution of domain configurations in 25-nm thick Co-elements patterned on silicon nitride membrane as function of applied field, ranging from +70 to -70 Oe. The Lorentz phase microscopy allows better understanding the role of magnetization ripple (41 Oe) in nucleation of reverse domains (28 Oe), or vortex formation (-4.4 Oe) followed by the reverse domains expansion and final annihilation of domain walls (41/-41 Oe) at the sample edges. It is believed that due to technical simplicity the Lorentz phase microscopy will find more applications in the nearest future.« less

Structural matching of ferroelectric domains and associated distortion inpotassium titanyl phosphate crystals

The surface deformation and atomic-level distortions associated withcrystal structural matching at ferroelectric inversion domain wallsare investigated in periodically poled potassium titanyl phosphate(KTP) crystals. A deformation, of the order of 10−8 min scale and having the periodicity of the domains, is observed at the surfaces byoptical interferometry. It is discussed in terms of the piezoelectric effect. Thematching of the crystal structures at the domain walls is studied by combining thehard x-ray Fresnel phase-imaging technique with Bragg diffraction imagingmethods (‘Bragg–Fresnel imaging’) and using synchrotron radiation. Quantitativeanalysis of the contrast of the Bragg–Fresnel images recorded as a function of thepropagation distance is demonstrated to allow the determination of how thedomains are matched at the atomic (unit cell) level, even though the spatialresolution of the images is on the scale of micrometres. The atom P(1) isdetermined as the linking atom for connecting the inversion domains across thewall in KTP crystals for domain walls forced by electric-field processing to beparallel to (100). In addition to this, it is shown that a shift of 1/2(a + b)between atoms in the original and inverted structures is introduced as a result ofthe domain inversion operation.

Measurement of magnetic domain wall width using energy-filtered Fresnel images.

Magnetic domain walls in Nd2Fe14B have been examined using a series of energy-filtered Fresnel images in the field emission gun transmission electron microscope (FEGTEM). We describe the changes in the intensity distribution of the convergent wall image as a function of defocus, foil thickness and domain wall width. The effect of tilted domain walls and beam convergence on the fringe pattern is also discussed. A comparison of the experimental intensity profile with that from simulations allows the domain wall width to be determined. Measurement of very narrow walls is made possible only by using a relatively thick foil, which necessitates energy-filtering to allow quantitative comparison with simulations. The magnetic domain wall width in Nd2Fe14B was found to be 3 +/- 2 nm.

Stability of magnetic vortices in flat submicron permalloy cylinders

We have investigated the magnetic properties of flat permalloy cylinders by Lorentz transmission electron microscopy and micromagnetic simulations. The magnetization patterns during in situ magnetizing experiments have been imaged and they revealed that the magnetization reversal of the cylindrically shaped dots investigated is determined by the formation and annihilation of magnetic vortices. Furthermore, the experiments and micromagnetic simulations showed a dependence of the vortex annihilation field not only on the aspect ratio but also on the absolute thickness of the cylinders. The diameter of the cylindrical dots was varied between 150 and 1000 nm, and the thicknesses were 3, 5.5, 8.3, 15, and 20 nm, respectively. The formation of inhomogeneous magnetization patterns prior to vortex evolution was observed and by a comparison of the experimental to simulated Fresnel images these patterns can be identified as S- and C-like states.