Phase-stepping Technique Research Articles

Whole-field principal angle and optical path retardation measurements using white light OPD scanning polariscope with first moment algorithm

White-light Optical Path Difference (OPD) scanning polariscope is currently an accepted technique for analyzing photoelastic specimens. While it has proven effective in overcoming limitations associated with phase-stepping and fringe scanning techniques, it is constrained when evaluating optical path retardation smaller than the light source coherence length. To address this limitation, a white-light OPD scanning polariscope, equipped with a first moment algorithm, has been introduced for the comprehensive examination of whole-field principal angle and optical path retardation. This article demonstrates the design and operational principles of the proposed polariscope, details an experimental setup for its deployment, and presents findings from practical applications of this setup. The results confirm the effectiveness and practicality of the proposed polariscope. Furthermore, these results highlight its precision, with standard deviations of 0.176° for principal angle and 6.4 nm for optical path retardation measurements.

Phase stepping through polarizing modulation in electronic speckle pattern interferometry.

We have demonstrated a speckle out-of-plane interferometer that employs phase-stepping procedures by means of polarization modulation. The system generates circular polarization states with opposite signs at each arm of the system, which overlap at the output of the interferometer, to generate phase shifts operating a conventional linear polarizer; the emerging polarization states have been analyzed to obtain the shifts needed to process the optical phase. The phase-stepping technique is demonstrated with a two-step algorithm to measure out-of-plane displacement on a flat metal plate.

A Radial-In-Plane Sensitivity Interferometer with Divergent Illumination for Displacement Measurement

An in-plane radial sensitivity interferometer that uses the divergent illumination for displacement measurement in the radial direction is presented. A description and mathematical model for calculating the sensitivity vector are also presented. The interferometer has two polarizing filters: a circular one and a linear one to implement the phase stepping technique. A measurement of the radial deformation by thermal expansion is performed over an aluminium plate in order to test the interferometer. The results indicate that the maximum contribution of the out-of-plane with respect to the radial-in-plane sensitivity vector is less than 3% and decreases by less than 1% when measurements are performed near the optical axis. The measurement is compared with the results obtained by a finite element analysis on a virtual specimen model.

Optical polarization measurement for measuring deflection radius of the optically anisotropic flexible-polymeric substrate

This study proposes an optical methodology to measure the deflection radius of flexible polymeric substrates; to our best knowledge, this is the first report taking into consideration the optical anisotropy effect of these substrates for such measurements. The relation between the deflection-induced optical phase retardation of two distinct refraction beams and the deflection radius was derived. Full-field phase maps were obtained via a polarization measurement system and the phase-stepping technique. The measurement results for three substrates having nominal deflection radii of 50, 55, and 60 mm were, correspondingly, 51.39 ± 0.37, 57.56 ± 1.00, and 58.71 ± 0.85 mm (error = 2.78%, 4.65%, and 2.15%, respectively); thus, the measurement precision was confirmed.

Optical phase extractions based on reassigned continuous wavelet transform with application to simultaneous displacement and velocity measurement.

Instantaneous frequency extraction of a highly nonstationary optical interferometric fringe signal using continuous wavelet transform with Morlet wavelet often fails in the neighborhood of the null phase gradient. The present work reports that the optimal selection of the central frequency and time variance of the Morlet wavelet reduces the spread of wavelet energy to its adjacent bins, and the reassignment technique further sharpens the energy density and enhances accuracy of the extracted instantaneous frequency of the fringe signal. The developed algorithm is applied to a sinusoidal frequency-modulated fringe signal for which the mean square error percentage in normalized instantaneous frequency is determined to be 0.0032 Hz, which is significantly less than 0.0507 Hz obtained with a conventional continuous wavelet transform. Results are also compared with the existing phase stepping technique and found to be more accurate and free from any ripple like nonlinear error for sinusoidal fringe signals. The proposed technique is applied to a fringe signal obtained with a Michelson interferometer, generating displacement profiles that show advantages over those produced by the phase stepping technique. The applicability of the proposed technique is further extended to an arbitrary phase signal.

Trimodal radiography using sinusoidal phase modulating grating interferometry

X-ray grating interferometry (XGI) provides complementary information to visualize the internal structure of an object better than conventional absorption-based imaging methods, thereby having the potential for future biomedical applications. In XGI, information retrieval is critical for qualitative and quantitative research. However, information retrieval based on the phase-stepping technique usually requires that the absolute spatial translations of these phase-stepping position series lie in the range of only a few hundred nanometers, making this technique prone to mechanical instabilities and motion artifacts. In this paper, trimodal radiography using sinusoidal phase modulating interferometry is studied. The theoretical analysis of the signal retrieval algorithm using four integrating buckets is derived, and numerical experiments are demonstrated. In the proposed method, the phase modulation is generated by shifting the grating following a sinusoidal curve while the signals are retrieved from the four frames obtained by integrating the time-varying intensity over the four quarters of the modulation period. Compared with the previously proposed method, this method is easier to implement due to relaxed requirements on the phase-shifting device; high speed and continuous data averaging will greatly promote the real applications of the X-ray grating interferometer.

Evaluation of the Bending Behaviour of Laminated Glass Beams Via Electronic Speckle Pattern Interferometry

The paper is devoted to the experimental analysis of the kinematical and mechanical behaviour of laminated glass beam structures. In particular, the utilized laminated glass specimens are composed of two glass layers bonded by a polymer layer constituted by Ethylene-vinyl acetate whose thickness has been nominally considered as constant for all the specimens. The experimental behaviour of the analyzed specimens is deduced by applying Electronic Speckle-Pattern Interferometry technique; actually, among optical methods this technique (handled by phase-stepping technique) is very effective to obtain a full-field displacement map and to numerically achieve the longitudinal strain. In particular, this technique has been used to analyse the pure bending behaviour of two-layers specimens characterized by different thicknesses of glass layers. The longitudinal strain, numerically obtained, is the basis for the subsequent analysis of the stress acting on the specimen. The longitudinal stress shows the role of the stacking sequence in the structural behaviour of the analysed specimens opening new approaches to the optimization of such elements. The principal aim of the present paper is the evaluation of the reliability of the methods suggested by the international standards by means of the comparison of the obtained experimental results with those arising from the effective monolithic thickness approach reported in international standards. The effected analyses allow to observe that the numerical results obtainable by using the methods provided by international standards are not very effective especially for thin layers.

Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing

An X-ray Talbot-Lau interferometer scanning setup consisting of three transmission gratings, a laboratory-based X-ray source that emits X-rays vertically, and an image detector on the top has been developed for the application of X-ray phase imaging to moving objects that cannot be tested clearly with conventional absorption contrast. The grating-based X-ray phase imaging method usually employs a phase-stepping (or fringe-scanning) technique by displacing one of the gratings step-by-step while the object stays still. Since this approach is not compatible with a scanner-type application for moving objects, we have developed a new algorithm for achieving the function of phase-stepping without grating displacement. By analyzing the movie of the moiré pattern as the object moves across the field of view, we obtain the absorption, differential phase, and visibility images. The feasibility of the X-ray phase imaging scanner has been successfully demonstrated for a long sample moving at 5 mm/s. This achievement is a breakthrough for the practical industrial application of X-ray phase imaging for screening objects carried on belt-conveyers such as those in factories.

Development of Aperture-Type Near-Field Reflection Spectroscopy and Its Application to Single Silver Nanoplates

We developed an aperture-type near-field reflection spectral imaging method to obtain optical properties of materials with a nanometer spatial resolution. We adopted a phase-stepping technique to extract genuine near-field signals of a sample from the observed intensity spectra dominated by the large background, in a multiplex manner. We performed near-field reflection spectral imaging of a single silver nanoplate to evaluate the developed system and also to examine near-field optical properties of the nanoplate. The near-field reflection spectrum of the nanoplate shows multiple resonant features that are not observable by conventional methods. The near-field reflection image taken at the resonance shows unique spatial features attributable to the plasmon mode resonantly excited. The developed system is applicable to transparent samples as well as opaque ones and enables spectral as well as spatial characteristics of the samples to be revealed.

4D measurements of biological and synthetic structures using a dynamic interferometer

Considering the deficiency of time elapsed for phase-stepping interferometric techniques and the need of developing non-contact and on-line measurement with high accuracy, a single-shot phase-shifting triple-interferometer (PSTI) is developed for analysis of characteristics of transparent structures and optical path difference (OPD) measurements. In the proposed PSTI, coupled three interferometers which generate four interference patterns, and a polarizer array is used as phase shifters to produce four spatially separated interferograms with π/2-phase shifts, which are recorded in a single capture by a camera. The configuration of the PSTI allows dynamic measurements (4D measurements) and does not require vibration isolation. We have applied the developed system to examine the size and OPD of cells, and the slope of thin films

Evaluation of continuous filament mat influence on the bending behaviour of GFRP pultruded material via Electronic Speckle Pattern Interferometry

Pultrusion is a process allowing the production of unidirectional (roving) fibre-reinforced polymer (FRP) structural elements with constant cross section. Recently, also civil engineers focused their attention on pultruded composite materials as alternative to traditional ones (e.g., concrete, steel). Furthermore, to improve the transverse strength and stiffness with respect to the fibres direction, continuous filament mat (CFM) is often placed within the stacking sequence. The CFM influence on the global mechanical behaviour is not considered by appropriate actual international standards. In this paper, the influence of the CFM layers on the mechanical behaviour of glass fibres pultruded composite material is investigated. In particular, the bending behaviour is analyzed by performing a four-point bending test on specimens extracted from an H-shape member. The experimental analysis was carried out via Electronic Speckle-Pattern Interferometry (ESPI) (handled by phase-stepping technique) to obtain a full-field displacement map and to numerically achieve the longitudinal strains. By imposing the equilibrium conditions and assuming the compression and tensile roving Young's moduli as constant, the CFM Young's moduli are determined. Finally, the mean stress acting on the material is obtained showing that CFM layers have to be considered to correctly evaluate the maximum stress and to optimize the design phase.

A Direct Approach to In-Plane Stress Separation using Photoelastic Ptychography.

The elastic properties of materials, either under external load or in a relaxed state, influence their mechanical behaviour. Conventional optical approaches based on techniques such as photoelasticity or thermoelasticity can be used for full-field analysis of the stress distribution within a specimen. The circular polariscope in combination with holographic photoelasticity allows the sum and difference of principal stress components to be determined by exploiting the temporary birefringent properties of materials under load. Phase stepping and interferometric techniques have been proposed as a method for separating the in-plane stress components in two-dimensional photoelasticity experiments. In this paper we describe and demonstrate an alternative approach based on photoelastic ptychography which is able to obtain quantitative stress information from far fewer measurements than is required for interferometric based approaches. The complex light intensity equations based on Jones calculus for this setup are derived. We then apply this approach to the problem of a disc under diametrical compression. The experimental results are validated against the analytical solution derived by Hertz for the theoretical displacement fields for an elastic disc subject to point loading.

Helical X-ray phase-contrast computed tomography without phase stepping.

X-ray phase-contrast computed tomography (PCCT) using grating interferometry provides enhanced soft-tissue contrast. The possibility to use standard polychromatic laboratory sources enables an implementation into a clinical setting. Thus, PCCT has gained significant attention in recent years. However, phase-contrast CT scans still require significantly increased measurement times in comparison to conventional attenuation-based CT imaging. This is mainly due to a time-consuming stepping of a grating, which is necessary for an accurate retrieval of the phase information. In this paper, we demonstrate a novel scan technique, which directly allows the determination of the phase signal without a phase-stepping procedure. The presented work is based on moiré fringe scanning, which allows fast data acquisition in radiographic applications such as mammography or in-line product analysis. Here, we demonstrate its extension to tomography enabling a continuous helical sample rotation as routinely performed in clinical CT systems. Compared to standard phase-stepping techniques, the proposed helical fringe-scanning procedure enables faster measurements, an extended field of view and relaxes the stability requirements of the system, since the gratings remain stationary. Finally, our approach exceeds previously introduced methods by not relying on spatial interpolation to acquire the phase-contrast signal.

Speckle Interferometry Analysis of Full-bending Behavior of GFRP Pultruded Material

The use of Glass Fiber Reinforced Polymer materials (GFRP) has increased in the last years even among civil structural engineering due to their high specific strength, lightweight and excellent corrosion resistance. With application of the pultrusion method, the manufacture of large-scale profiles with various cross-section forms became potentially possible with relatively low costs. Usually two different technological approaches are available to realize the element: in the first one a mat-roving-mat sequence is adopted, in the second one only roving is present. Continuous filament mat (CFM, fibers distributed randomly in all directions) is often used to build up laminate thickness quickly, as well as to enhance transversal strength and stiffness. Besides, the intrinsic particular features of GFRP materials require the application of new techniques of mechanical analysis to define a correct material model. Many papers study the mechanical behavior of GFRP structural elements at a macroscopic scale even in particular environmental conditions. From the other hand full-field contactless techniques (e.g. digital image correlation, thermal stress analysis, speckle interferometry) are effective tools to correctly model complex mechanical behavior and to define the consequent parameters. Among these techniques, Electronic Speckle-Pattern Interferometry (ESPI) has been asserted as very effective due to the technological improvements of the laser sources. One of the significant advantages of ESPI is to produce real-time fringe patterns on objects with optically rough surfaces, with a displacement sensitivity of the order of the light wavelength. Aim of the paper is to apply ESPI handled by phase-stepping technique to the experimental study of GFRP materials in the case of mat-roving-mat sequence.

Sampling grating approach for X-ray differential phase contrast imaging

Grating-based X-ray differential phase contrast imaging (GDPCI) typically employs the phase-stepping technique to extract an object's phase information. This method requires heavy radiation dosage and is time consuming. Another potential approach is the reverse projection (RP) method, which, however, relies on a synchrotron radiation source to obtain highly sensitive differential phase contrast(DPC) signal. Here, we present an alternative approach that enables the RP method to be used with a conventional X-ray source and substantially improves the sensitivity of the DPC signal by replacing the analyzer grating of the GDPCI with a sampling grating. This development represents a significant step towards obtaining fast and low-dosage DPC images in medical, biological, and industrial applications.

Adjustment of the Parallelism of two Mirrors for Wide Angle Divided Mirror Michelson Wind Imaging Interferometer

Abstract Many ways have been developed to measure atmospheric winds by detecting the Doppler shifts of airglow emission lines. The Michelson Interferometer is widely used because of its simple principle. To get the Doppler shifts to calculate the wind velocity, researchers developed four-phase-step and divided mirror technology respectively. But they face challenges in many fields. So a wide angle Michelson Interferometer combining with divided mirror and phase stepping technique is used in this paper. A new algorithm is proposed in this paper to adjust the parallelism of the two mirrors for the Michelson Interferometer. Thus a high precision parallelism of the two mirrors can be obtained to get the phase shift and calculate wind velocity. The interval of the two mirrors has maximum difference less than one tenth wavelength. The experiments were performed in visible channel to prove the feasibility of this proposed algorithm. It can also be used in other fields demanding two surfaces parallel with high precision.

X-ray phase-contrast tomography of renal ischemia-reperfusion damage.

PurposeThe aim of the study was to investigate microstructural changes occurring in unilateral renal ischemia-reperfusion injury in a murine animal model using synchrotron radiation.Material and MethodsThe effects of renal ischemia-reperfusion were investigated in a murine animal model of unilateral ischemia. Kidney samples were harvested on day 18. Grating-Based Phase-Contrast Imaging (GB-PCI) of the paraffin-embedded kidney samples was performed at a Synchrotron Radiation Facility (beam energy of 19 keV). To obtain phase information, a two-grating Talbot interferometer was used applying the phase stepping technique. The imaging system provided an effective pixel size of 7.5 µm. The resulting attenuation and differential phase projections were tomographically reconstructed using filtered back-projection. Semi-automated segmentation and volumetry and correlation to histopathology were performed.ResultsGB-PCI provided good discrimination of the cortex, outer and inner medulla in non-ischemic control kidneys. Post-ischemic kidneys showed a reduced compartmental differentiation, particularly of the outer stripe of the outer medulla, which could not be differentiated from the inner stripe. Compared to the contralateral kidney, after ischemia a volume loss was detected, while the inner medulla mainly retained its volume (ratio 0.94). Post-ischemic kidneys exhibited severe tissue damage as evidenced by tubular atrophy and dilatation, moderate inflammatory infiltration, loss of brush borders and tubular protein cylinders.ConclusionIn conclusion GB-PCI with synchrotron radiation allows for non-destructive microstructural assessment of parenchymal kidney disease and vessel architecture. If translation to lab-based approaches generates sufficient density resolution, and with a time-optimized image analysis protocol, GB-PCI may ultimately serve as a non-invasive, non-enhanced alternative for imaging of pathological changes of the kidney.

Imaging interference microscope for nanometrology

Here we report the development of the primary nanometrology capacity at the National Metrology Institute of Brazil (INMETRO). An interference microscope of the Linnik type has been developed and subjected to optimization and characterization studies. The recording of the fringes is done by an automated CCD system with 2 possible processing approaches: interferometric pattern processing and the phase stepping technique. Current progress in the development of the hardware and software adequate for sub- nanometer resolution of the instrument is reported. A study of systematical errors of the interference microscope has been performed. The instrument is aimed for international key comparisons of step height standards.

An adjustable sensitivity shadow moiré technique for surface morphology measurement

In this paper, an adjustable sensitivity of measurement system based on the shadow moiré technique is proposed. In this measurement system, an adjusting mechanism can control the illumination angle to change the moiré contour intervals and vary the moiré fringe spacing correspondingly. In the experiments of this paper, the suitable density of the moiré fringe can effectively reduce the influence of the noise of the image and keep adequate accuracy of the measurement system simultaneously. An accurate evaluation method for determining the sensitivity is proposed for the measurement system. By using the phase stepping technique, the proposed measurement system can analyse the fringe pattern and measure the surface profile accurately. Some samples are measured to validate the feasibility of the proposed system, and the experimental results verify the effectiveness of the developed three-dimensional profilometer to be applied for various microscale measurement applications.

Phase-stepping technique for highly sensitive microscopic surface plasmon resonance biosensor.

In this paper, the phase-stepping technique is applied to improve a phase-sensitive surface plasmon resonance biosensor based on differential interferometry between focused radially polarized and azimuthally polarized cylindrical vector beams. Detailed analysis is presented for the phase-stepping method, and the least squares unwrapping algorithm is employed to detect the phase distribution in correspondence to the refractive index of sample. Benefiting from the phase-stepping technique, both the measurement speed and sensitivity are improved significantly. The proposed sensor maintains high sensitivity of 9.4×10-7 RIU/1° and a wide dynamic range of 0.35RIU simultaneously. Furthermore, the real-time binding reaction process of bovine serum albumin with antibody is monitored to verify the system for potential biological applications.