Grating Interferometer Research Articles

Optical Fiber Interferometers Based on Arc-Induced Long Period Gratings at INESC TEC.

In this work, we review the most important achievements of an INESC TEC long-period-grating-based fiber optic Michelson and Mach–Zehnder configuration modal interferometer with coherence addressing and heterodyne interrogation as a sensing structure for measuring environmental refractive index and temperature. The theory for Long Period Grating (LPG) interferometers and coherence addressing and heterodyne interrogation is presented. To increase the sensitivity to external refractive index and temperature, several LPG interferometers parameters are studied, including order of cladding mode, a reduction of the fiber diameter, different type of fiber, cavity length and the antisymmetric nature of cladding modes.

Efficient 2D Optical Beamforming Network With Sub Partitioning Capability Based on Raised Cosine Chirped Fiber Grating and Mach-Zehnder Delay Interferometer

In this paper, a two-dimensional true time delay optical beamforming network (OBFN) has been proposed with sub partitioning capability for 3X3 phased array antenna (PAA) with operating frequency in X-Band. The architecture is based on raised cosine apodised chirp fiber Bragg grating (CFBG) and Mach-Zehnder delay interferometer (MZDI). Compared to unapodised CFBG, raised cosine apodization drastically reduces the ripple as well as sidelobes and gives a flat response in the passband of reflection spectrum. Multiwavelength optical signals with a wavelength difference of 0.3 nm are used to steer 10 GHz RF signal in elevation and azimuth direction. Further, broad angular control of beam radiation due to sub partitioned PAA is also demonstrated. The RF signal beam is steered in elevation at -62.2,-31.9, and-10.8 degrees, and in azimuth at 123.6 and 55.9 degrees. Theoretical analysis of the OBFN has been presented and validated with the experimental results. At the best of our knowledge, delay characteristics of raised cosine apodised CFBG have been theoretically explored for the first time with mathematical formulation and a comparative discussion is given with the measured data.

High-efficiency polarization-independent gold-coated crossed grating under normal incidence

A gold-coated crossed grating (GCCG) is designed and fabricated to improve the signal contrast and signal-noise-ratio (SNR) of the grating interferometer (GI) with the high-efficiency polarization-independent property. The proposed grating based on two dimensional (2D) periodic gold nanocylinder structure can diffract both TE and TM polarizations into four first orders with measured diffraction efficiency (DE) of more than 21.8% and total DE of more than 88.8% at 780 nm incident wavelength under normal incidence, which shows the highest DE and brings much benefits to the SNR and compactness in practical applications. Moreover, the optimized GCCG also shows great tolerances of duty cycle, groove depth, and sidewall angle for grating fabrication. The measured DEs from the experimental results substantiate themselves with the numerical calculations. Additionally, the measured DE of the (±1, 0) order and (0, ±1) order all exceed 18% at the wavelength range from 750 nm to 810 nm and present great polarization independence at the polarization angle varying from 0° to 90°. The experimental results show the excellent performance of GCCG for improving heterodyne grating interferometer and indicate great potential for applications in microscopy techniques, semiconductor manufacturing, and material processing.

Laser Ablated Periodic Nanostructures on Titanium and Steel Implants Influence Adhesion and Osteogenic Differentiation of Mesenchymal Stem Cells.

Metal implants used in trauma surgeries are sometimes difficult to remove after the completion of the healing process due to the strong integration with the bone tissue. Periodic surface micro- and nanostructures can directly influence cell adhesion and differentiation on metallic implant materials. However, the fabrication of such structures with classical lithographic methods is too slow and cost-intensive to be of practical relevance. Therefore, we used laser beam interference ablation structuring to systematically generate periodic nanostructures on titanium and steel plates. The newly developed laser process uses a special grating interferometer in combination with an industrial laser scanner and ultrashort pulse laser source, allowing for fast, precise, and cost-effective modification of metal surfaces in a single step process. A total of 30 different periodic topologies reaching from linear over crossed to complex crossed nanostructures with varying depths were generated on steel and titanium plates and tested in bone cell culture. Reduced cell adhesion was found for four different structure types, while cell morphology was influenced by two different structures. Furthermore, we observed impaired osteogenic differentiation for three structures, indicating reduced bone formation around the implant. This efficient way of surface structuring in combination with new insights about its influence on bone cells could lead to newly designed implant surfaces for trauma surgeries with reduced adhesion, resulting in faster removal times, reduced operation times, and reduced complication rates.

Image Quality Analysis of X-ray Grating Interferometer Using Integrating-bucket Method

Abstract Grating-based x-ray phase-contrast imaging has the potential to enhance image quality and provide inner structure details non-destructively. In this work, using grating-based x-ray phase-contrast imaging system and employing integrating-bucket method, the quantitative expressions of signal-to-noise ratios due to photon statistics and mechanical error are analyzed in detail. Photon statistical noise and mechanical error are the main sources affecting the image noise in x-ray grating interferometry. Integrating-bucket method is a new phase extraction method translated to x-ray grating interferometry; hence, its image quality analysis would be of great importance to get high-quality phase image. The authors’ conclusions provide an alternate method to get high-quality refraction signal using grating interferometer, and hence increases applicability of grating interferometry in preclinical and clinical usage.

Characterization of oriented microstructures through anisotropic small-angle scattering by 2D neutron dark-field imaging

Within neutron imaging, different methods have been developed with the aim to go beyond the conventional contrast modalities, such as grating interferometry. Existing grating interferometers are sensitive to scattering in a single direction only, and thus investigations of anisotropic scattering structures imply the need for a circular scan of either the sample or the gratings. Here we propose an approach that allows assessment of anisotropic scattering in a single acquisition mode and to broaden the range of the investigation with respect to the probed correlation lengths. This is achieved by a far-field grating interferometer with a tailored 2D-design. The combination of a directional neutron dark-field imaging approach with a scan of the sample to detector distance yields to the characterization of the local 2D real-space correlation functions of a strongly oriented sample analogous to conventional small-angle scattering. Our results usher in quantitative and spatially resolved investigations of anisotropic and strongly oriented systems beyond current capabilities.

Operando Visualization of Water Distribution in Gas Diffusion Media of PEFCs with an Optimized Neutron Grating Interferometer

We demonstrated the use of a neutron grating interferometer setup (nGI) with a significantly improved contrast-to-noise ratio of the operando dark-field (DF) contrast visualization of water in gas diffusion media (GDM). The nGI parameters were optimized in such a way that we could perform DF imaging of a fully operational fuel cell including two GDM layers (anode and cathode side). The DF contrast is sensitive to the size and shape of microstructures and is in principle not influenced by large water clusters present in flow field channels. Thus, DF imaging can be applied to analyze water present in GDM overlapping with channels, which is not possible by attenuation contrast imaging when the cell is placed perpendicular to the beam direction. In GDM regions overlapping with ribs the distinction of hydrophilic and hydrophobic areas is facilitated as well compared to attenuation contrast imaging. Finally, we show that disturbing artefacts introduced by moving water clusters in the channels are considerably reduced by applying a golden ratio phase stepping scan strategy.

Predicting fringe visibility in dual-phase grating interferometry with polychromatic X-ray sources.

Dual phase grating X-ray interferometry is radiation dose-efficient as compared to common Talbot-Lau grating interferometry. The authors developed a general quantitative theory to predict the fringe visibility in dual-phase grating X-ray interferometry with polychromatic X-ray sources. The derived formulas are applicable to setups with phase gratings of any phase modulation and with either monochromatic or polychromatic X-rays. Numerical simulations are presented to validate the derived formulas. The theory provides useful tools for design optimization of dual-phase grating X-ray interferometers.

Applying the Fokker\u2013Planck equation to grating-based x-ray phase and dark-field imaging

X-ray imaging has conventionally relied upon attenuation to provide contrast. In recent years, two complementary modalities have been added; (a) phase contrast, which can capture low-density samples that are difficult to see using attenuation, and (b) dark-field x-ray imaging, which reveals the presence of sub-pixel sample structures. These three modalities can be accessed using a crystal analyser, a grating interferometer or by looking at a directly-resolved grid, grating or speckle pattern. Grating and grid-based methods extract a differential phase signal by measuring how far a feature in the illumination has been shifted transversely due to the presence of a sample. The dark-field signal is extracted by measuring how the visibility of the structured illumination is decreased, typically due to the presence of sub-pixel structures in a sample. The strength of the dark-field signal may depend on the grating period, the pixel size and the set-up distances, and additional dark-field signal contributions may be seen as a result of strong phase effects or other factors. In this paper we show that the finite-difference form of the Fokker–Planck equation can be applied to describe the drift (phase signal) and diffusion (dark-field signal) of the periodic or structured illumination used in phase contrast x-ray imaging with gratings, in order to better understand any cross-talk between attenuation, phase and dark-field x-ray signals. In future work, this mathematical description could be used as a basis for new approaches to the inverse problem of recovering both phase and dark-field information.

Wavefront Measurement Using a Grating Interferometer in the X-ray Region

Wavefront Measurement Using a Grating Interferometer in the X-ray Region

Displacement measuring grating interferometer: a review

A grating interferometer, called the “optical encoder,” is a commonly used tool for precise displacement measurements. In contrast to a laser interferometer, a grating interferometer is insensitive to the air refractive index and can be easily applied to multi-degree-of-freedom measurements, which has made it an extensively researched and widely used device. Classified based on the measuring principle and optical configuration, a grating interferometer experiences three distinct stages of development: homodyne, heterodyne, and spatially separated heterodyne. Compared with the former two, the spatially separated heterodyne grating interferometer could achieve a better resolution with a feature of eliminating periodic nonlinear errors. Meanwhile, numerous structures of grating interferometers with a high optical fold factor, a large measurement range, good usability, and multi-degree-of-freedom measurements have been investigated. The development of incremental displacement measuring grating interferometers achieved in recent years is summarized in detail, and studies on error analysis of a grating interferometer are briefly introduced.

An Optical MEMS Acoustic Sensor Based on Grating Interferometer.

Acoustic detection is of great significance because of its wide applications. This paper reports a Micro-Electro-Mechanical System (MEMS) acoustic sensor based on grating interferometer. In the MEMS structure, a diaphragm and a micro-grating made up the interference cavity. A short-cavity structure was designed and fabricated to reduce the impact of temperature on the cavity length in order to improve its stability against environment temperature variations. Besides this, through holes were designed in the substrate of the grating to reduce the air damping of the short-cavity structure. A silicon diaphragm with a 16.919 µm deep cavity and 2.4 µm period grating were fabricated by an improved MEMS process. The fabricated sensor chip was packaged on a conditioning circuit with a laser diode and a photodetector for acoustic detection. The output voltage signal in response to an acoustic wave is of high quality. The sensitivity of the acoustic sensor is up to −15.14 dB re 1 V/Pa @ 1 kHz. The output signal of the high-stability acoustic sensor almost unchanged as the environment temperature ranged from 5 °C to 55 °C.

A Simulation Study on the Transfer Characteristics of the Talbot Pattern Through Scintillation Screens in the Grating Interferometer

A Simulation Study on the Transfer Characteristics of the Talbot Pattern Through Scintillation Screens in the Grating Interferometer

Double-Diffracted Spatially Separated Heterodyne Grating Interferometer and Analysis on its Alignment Tolerance

An optical configuration of double-diffracted spatially separated heterodyne grating interferometer with a mechanical fixture was designed. To further investigate its features and provide robust measurements, the alignment tolerance in double-diffracted spatially separated heterodyne grating interferometer was qualitatively and quantitatively analyzed. Except for the offset error causing no influence on the interfering signal, the effect of the other four errors, roll, yaw, pitch angles, and stand-off error were geometrically analyzed and mathematically modeled. The simulation result quantified the position mismatches of output beams in a double-diffracted configuration and found the crucial structural parameters related to the intensity of interfering signals. Experiments based on the grating interferometer with a mechanical fixture and the same optical configuration built by independent optical components were implemented, whose results agreed with the simulation. Besides, the results showed that the proposed grating interferometer structure could tolerate the ±1100 arcsec roll movement, ±440 arcsec yaw movement, ±280 arcsec pitch movement, and ±0.6 mm stand-off error when -10 dB intensity loss is afforded.

Add-drop filter with complex waveguide Bragg grating and multimode interferometer operating on arbitrarily spaced channels.

We present a silicon nitride/silicon dioxide add-drop filter operating on arbitrarily spaced channels using multimode interferometers (MMIs) and complex waveguide Bragg gratings (CWBGs). The add-drop filter shows a rejection ratio of >40 dB on all five channels, with a line width of 1.2nm and an on-chip loss of <1 dB. By designing the CWBG with the Layer Peeling/Layer Adding algorithm, this MMI-CWBG add-drop filter platform has the capability for ultrabroadband add-drop operation on arbitrarily spaced channels.

Brain Connectivity Exposed by Anisotropic X-ray Dark-field Tomography

To understand the interaction of different parts of the human brain it is essential to know how they are connected. Such connections are predominantly related to the brain’s white matter, which forms the neuronal pathways, the axons. These axons, also referred to as nerve fibers, have a size on the micrometer scale and are therefore too small to be imaged by standard X-ray systems. In this paper, we use a grating interferometer and a method based on Anisotropic X-ray Dark-field Tomography (AXDT) with the goal to generate a three-dimensional tomographic reconstruction of these functional structures. A first preclinical survey shows that we successfully reconstruct the orientations of the brain fibers connectivity with our approach.

Self-Mixing Grating Interferometer With Dual Laser Diodes for Sensing of 2-D Dynamic Displacement

In this paper, a novel self-mixing grating interferometer (SMGI) with dual laser diodes (LDs) is proposed for 2-D dynamic displacement measurement. The light beams emitted from the LDs are incident onto a reflection grating with ±1st order auto-collimation diffraction angles and then diffracted back into the lasers, respectively, which can cause self-mixing interference effect in each LD. Theoretical analysis on the SMGI signals corresponding to 2-D displacement is presented and verified with the experimental observations. Measurement results of 2-D dynamic displacement demonstrate that the proposed system can achieve the measurement resolution better than 10 nm. The proposed SMGI sensing system has the advantages of high stability, compact mechanical structure, and relatively straightforward operation.

Comparison of image properties in full-field phase X-ray microscopes based on grating interferometry and Zernike's phase contrast optics

A grating interferometer (GI) system has been installed in an X-ray microscope equipped with a Zernike phase contrast (ZPC) system and a Cu rotating anode X-ray source. The GI and ZPC systems are switchable, and their performances of phase information extraction have been compared. The GI system is based on a Lau interferometer consisting of an absorption grating and a π/2 phase grating, which extracts a magnified phase shift map of a sample via a phase-stepping measurement. The ZPC system generates a phase contrast image by using a phase plate and a corresponding condenser device. The ZPC system and the GI system are compared in terms of detectability of phase objects. By the Fourier analysis of images of a logarithmic ruler pattern, the spatial resolution was found to be identical between the two systems. Although the sensitivity depends on the sample size, the signal-to-noise ratio of polystyrene spheres with a few microns in diameter was used for sensitivity comparison, showing the superior sensitivity of the GI system to that of the ZPC system. The quantitativeness of the GI system with the phase-stepping measurement was also demonstrated over the ZPC system, which generates halo and shade-off artifacts. The GI system exhibits twin image artifacts that need to be resolved for practical applications of the technique.

Computed Tomography from a Single Grating X-Ray Interferometer at a Laboratory Liquid-Metal-Jet Source

Computed Tomography from a Single Grating X-Ray Interferometer at a Laboratory Liquid-Metal-Jet Source

Phase derivative thermo-spatiogram for distributed temperature sensing based on chirped grating-Michelson Interferometer

A novel thermometric measurement based on chirped fiber Bragg grating (CFBG) and Michelson Interferometer is proposed. The interrogation technique is based on the linear relation between the temperature and the phase derivative function of the grating, which is determined through Fourier transformation of the output spectrum. The Michelson interferometer configuration offers the flexibility in adjusting the position of coupling coefficient curve in the spatiogram, enabling the interrogation to be done at a shorter optical spectrum record length which can reduce the interrogation time and computation load.