Phase-shifting Interferometry Technique Research Articles

Design and implementation of an electromechanical gear system for optimization of automatic phase-shifting of a Dual Aperture Common-Path Interferometer

In this work, we report experimental results of a proposed gear system for optimization of phase shifts used for extraction of phase between a reference and a test object in a Double Aperture Common Path Interferometer. The electromechanical approach is designed to increase the precision and control of automated transverse translation of a diffraction grating to obtain equidistant displacements, typically carried out manually. Calculations and analytics for the design and operation of the mechanical gear system are presented. The experimental results demonstrate significant error minimizing for equally spaced phase shifts compared to a previously reported implementation of our research group. The proposed system represents a reliable and low-cost implementation to improve the obtaining of suitable interferogram captures for equally spaced phase-shifting interferometry techniques.

Quantitative phase imaging with single-path phase-shifting digital holography using a light-emitting diode

We propose a quantitative phase imaging technique with single-path phase-shifting digital holography using a light-emitting diode (LED). A reference wave is generated from an object wave in the Fourier plane using a single-path interferometer, based on self-reference digital holography. The object wave interferes with the reference wave, and the quantitative phase information of the object wave is recorded as a digital hologram. Quantitative phase images of objects are obtained by applying a phase-shifting interferometry technique. All the light diffracted from the objects can be utilized to generate a digital hologram. Its validity is experimentally demonstrated by constructing an optical system with a wide-field optical microscope.

A Real-Time Automated System for Dual-Aperture Common-Path Interferometer Phase-Shifting

We report a novel fully real-time automatized optomechatronic dual-aperture common-path interferometer system for obtaining the phase difference between two interferograms by using the technique of phase-shifting interferometry. A motorized system is used to shift an additional phase transversally to the optical axis by ruling translation. For each high-resolution ruling displacement step of 0.793 μm, an interferogram is recorded by a CCD camera. The phase difference between the two successive recorded interferograms is then automatically calculated by computational self-calibrated algorithms. The proposed device provides more accurate measuring than typically used manual processes. Real-time phase differences are obtained from a robust low-cost optomechatronic system. Analytical calculation of the phase is performed automatically without the requirement of additional or external tools and processes, reducing the significant rework delay. A set of 47 interferograms were captured in real time then recorded and analyzed, obtaining an average phase shifting of 2.483 rad. Analytic explanation and experimental results are presented.

Alumina abrasive grains mediated grinding induced glass surface and fractal analysis of SiO2 glass

Fabrication of optical components such as passive optics (mirrors, prisms, lenses) or active optics (polarizer’s, laser gain media, adaptive optics) starts from a bulk material and reaches to the required size and shape. To achieve the required specification of the component, a series of process has to be followed from grinding to polishing stage. Initially, in grinding stage, material removal is faster, with more surface damage and less geometric control. During polishing stage, material removal is slower, with no surface damage but with greater geometric control. Hence, to achieve good surface quality, the component or work piece has to be controlled from grinding stage. We present an advanced surface and fractal analysis study on fused silica samples processed with different grit sizes such as 3, 5, 12, and 25 μm aluminium oxide (Al2O3) abrasives. The maximum sub surface damage (SSD) with respect to size of the abrasive grain ranged between 30 μm to 5 μm in empirical module. In theoretical module it varied from 45 μm to 5.4 μm for fused silica glass, mediated with loose abrasive aluminium oxide powder of 25 μm and 3 μm respectively. An experimental investigation is reported on the increasing effect of Al2O3 grit sizes on the surface topography such as average roughness (Ra), which varied from 57 nm to 847 nm for 3 μm and 25 μm Al2O3 abrasives respectively. Three-dimensional image analysis was captured through Phase Shift Interferometry (PSI) and Coherence Correlation Interferometer (CCI) technique. Field Emission Scanning Electron Microscope (FESEM) technique was utilized to characterize the Al2O3 powders and the processed fused silica samples. Later, the images have been analysed using two-dimensional multifractal detrended fluctuation analysis (2D-MFDFA) to understand and confirm the multiple fractal nature on fused silica samples caused by varying grit size of Al2O3 abrasives.

Two-step phase-shifting interferometry for self-interference digital holography

We propose a phase-shifting interferometry technique using only two in-line phase-shifted self-interference holograms. There is no requirement for additional recording or estimation in the measurement. The proposed technique adopts a mathematical model for self-interference digital holography. The effectiveness of the proposed technique is demonstrated by experiments on incoherent digital holographic microscopy and color-multiplexed fluorescence digital holography with computational coherent superposition. Two-color-multiplexed four-step phase-shifting incoherent digital holography is realized for the first time, to the best of our knowledge, using the proposed technique.

Optical Method for Simultaneous High-Resolution Measurement of Heat and Fluid Flow: The Case of Rayleigh-Bénard Convection

An optical system combining phase-shifting interferometry (PSI) and particle image velocimetry (PIV) is built and verified with simultaneous two-dimensional temperature- and velocity-field measurements of a convective flow. The well-known Rayleigh-B\'enard convection in laminar regime in a cubical cavity filled with water is chosen as the experimental validation case. Three-, four-, and six-bucket temporal phase-shifting equations using a rotating polarizer method are tuned under different light-source power conditions, first without PIV, to produce high-resolution phase-shifted data. The results showed that the three-bucket phase-shifting equation is the most robust method over a wide range of laser powers, while the PIV tracers decreased the PSI precision from 1.5% in the case without tracers to 3.0% when seeded at 0.02 wt%. The temporal and spatial resolution of the PSI measurement is 0.1 s and 6.47 $\ensuremath{\mu}\mathrm{m}$, respectively. Owing to the combined PSI and PIV technique, both temperature and velocity characteristics are obtained, unveiling the existence of several flow bifurcations as the Rayleigh number is increased up to $1.06\ifmmode\times\else\texttimes\fi{}{10}^{5}$. This optical setup is a potential paradigm shift in heat- and fluid-flow visualization, while having a great potential in biosensor development for concurrent velocity-, concentration-, and temperature-field measurements of aerosols and flows with multicomponent species.

Phase detection algorithm using step lengths deviation errors and Hough transform in phase-shifting interferometry

In phase-shifting interferometry (PSI), a set of interferograms with a known phase step displacement is necessary, but incorrect calibration deviation errors can occur in shifter devices. We present a method to recover the phase distribution in the presence of this deviation error through the widely used PSI technique. By applying the radon transform as a profile measurement, our algorithm first estimates the deviations in the phase steps, then these calculations are used to obtain the wrapped phase using the Hough transform as an estimation of coefficients in sinusoidal patterns. Simulation and experimental results have shown good performance. The results reveal that this algorithm is able to detect and decrease the phase error due to miscalibrations.

Data quality assessment of Diffusion Coefficient Measurements in ternary mIXtures 4 (DCMIX4) experiment

Thermodiffusion, which leads to a component separation in a mixture due to the thermal gradient, still does not have an unambiguous microscopic picture. Therefore, experimental studies, especially in convection free environment, are important. As part of the 4th campaign on the DCMIX project, thermodiffusion experiments on three compositions of the toluene-methanol-cyclohexane ternary mixture, on a mixture of fullerene-tetralin-toluene and on a mixture of polystyrene-toluene-cyclohexane have been performed in microgravity conditions on board the International Space Station. A binary mixture of polystyrene-toluene has been filled into the companion cell for the campaign. The Selectable Optical Diagnostics Instrument (SODI), wich is a two-wavelength Mach-Zehnder interferometer for the ternary mixtures, plus a monochromatic Mach-Zehnder interferometer for the binary mixture, has been used in order to obtain the temperature and the concentration fields in the cells. Precisely, it is a 5-steps phase-shifting interferometry technique which is implemented with SODI, producing by means of laser illumination a set of 5 phase-shifted images of π/2 between them as function of the time. A total of 58 runs of various durations and at different mean temperatures have been conducted. Here, we evaluate the contrast of the interferograms, the quality in the phase stepping, the stability of the thermal regulation of the experiments and the level of environmental disturbances on board the space station during the campaign.

A computational phase-shifting interferometric method using a single-shot microinterferogram and its application

In this article, a fast computational phase-shifting interferometry (PSI) method for extracting the phase object from a single-shot two-beam microinterferogram has been proposed. This technique bases on utilizing the features of the two-beam microinterferometry to yield three daughter microinterferograms with accurately known phase shift between them from a recorded mother microinterferogram. The main idea of the proposed method relies on analyzing the recorded mother microinterferogram to compute the width of its bright and dark fringes which resulted equal in this study. Furthermore, we utilize the fact that the complete change from bright fringe to dark fringe or vice versa, in the two-beam microinterferogram, is identical to shift in phase by π radians. The proposed method is characterized by high ability to perform in-situ investigation for the objects on the contrary with the traditional PSI technique. The phase-shifting Pluta interference microscope is used for verifying this computational method for the polypropylene (PP) fiber. The calculated phase distribution values via this method show a good agreement with the obtained results by the phase-shifting Pluta interference microscope for the same fiber sample. Also, the proposed method is utilized to perform accurate in-situ investigation for the structural properties of the polypropylene fiber at different draw ratios. In addition, the proposed method is valid to investigate the fractures modes of fibers in short time comparing to the spatial carrier frequency algorithm and the spatial carrier-frequency phase-shifting (SCFPS) algorithm.

Multiwavelength-multiplexed phase-shifting incoherent color digital holography.

We propose multiwavelength-multiplexed phase-shifting incoherent color digital holography. In this technique, a monochrome image sensor records wavelength-multiplexed, phase-shifted, and incoherent holograms, and a phase-shifting interferometry technique selectively extracts object waves at multiple wavelengths from the several recorded holograms. Spatially incoherent light that contains multiple wavelengths illuminates objects, and multiwavelength-incoherent object waves are simultaneously obtained without using any wavelength filters. Its effectiveness is experimentally demonstrated for transparent and reflective objects.

Thermal lens investigation in EuF2.11, PrF3, and Na0.38Ho0.62F2.24 crystals for magnetooptical applications

Thermal lens, absorption coefficient for 1076 nm radiation and spectral dependence of the Verdet constant were measured in PrF3, EuF2.11 and Na0.38Ho0.62F2.24 crystals for magneto-optical applications. As evaluated in the 400–1310 nm wavelength range, the Verdet constant of the EuF2.11 crystals is ~30% higher than that of the TGG crystals, an at the wavelength of 1557 nm it is 100% higher. The Verdet constant of PrF3 crystals is ~5% lower than in TGG throughout the studied wavelength range. Na0.38Ho0.62F2.24 crystals have the lowest (among the studied crystals) value of the Verdet constant that is 50–80% lower than in TGG.The thermal lens was measured by the phase-shift interferometry technique and has the sign opposite to that of the TGG lens for all considered crystal. The thermo-optical constant P and the dependence of the thermal lens on the absorbed power were calculated. It is shown that the optical power of thermal lens in PrF3, EuF2.11 and Na0.38Ho0.62F2.24 at equal absorbed laser power is, respectively, 1.3, 1.7 and 1.8 times higher than in TGG.

Thermal lens in magneto-active fluoride crystals

The thermal lens magneto-active CeF3, KTb3F10 and Na0.37Tb0.63F2.26 fluorides was investigated by the phase-shift interferometry technique. It was shown that the fluorides introduce a much weaker thermal lens into the laser beam than a traditional TGG crystal. The advantage is 3, 20, and 6 times for CeF3, KTb3F10 and Na0.37Tb0.63F2.26, respectively, with allowance for the need to increase length for achieving the same angle of rotation of the polarization plane because of the smaller Verdet constant. The measurement results were used to calculate the focal shift and the thermo-optical parameter αP/κ for the studied materials.

Fast phase-shifting technique for 3-D surface micro-topography measurement

This paper presents a two-step phase-shifting interferometry technique for fast inspection of uniformity of optoelectronic samples. The in-line configuration was applied to make full use of the space-bandwidth product (SBP) of the camera and hence can resolve finer spatial details of the sample. Two-step phase-shifting (TSPS) algorithm was used to reconstruct the object with only two in-line interferograms generated when a quarter wave plate (QWP) is placed in the light path of one arm of the Mach-Zehnder interferometer. Experimental results show that the extracted phases calculated by the TSPS technique match with the phases extracted by the three-step phase-shifting (THSPS) technique.

Model-based multi-fringe interferometry using Zernike polynomials

In this paper, a general phase retrieval method is proposed, which is based on one single interferogram with a small amount of fringes (either tilt or power). Zernike polynomials are used to characterize the phase to be measured; the phase distribution is reconstructed by a non-linear least squares method. Experiments show that the proposed method can obtain satisfactory results compared to the standard phase-shifting interferometry technique. Additionally, the retrace errors of proposed method can be neglected because of the few fringes; it does not need any auxiliary phase shifting facilities (low cost) and it is easy to implement without the process of phase unwrapping.

Surface topography measurement of plasma-facing materials by dual-wavelength phase-shifting speckle interferometry technique

A dual-wavelength phase-shifting speckle interferometry approach has been proposed to diagnose the topography of plasma-facing materials (PFMs) in tokamak. The conventional speckle interferometric surface measurement, which uses single-wavelength, can offer excellent vertical resolution, but limitation in measuring large height step and phase ambiguity would occur during their application. To solve the problem, a dual-wavelength method was developed. Experiments were conducted on molybdenum (Mo) sample, which is related to PFMs of experimental advanced superconducting tokamak (EAST), and a laser ablation method was adopted to simulate the erosion happed on PFMs. The laser ablation craters were measured by both single-wavelength and dual-wavelength phase-shifting speckle interferometry, and a multistep phase-shifting method has been investigated for their effectiveness on reducing noise in calculating the phase map. This work demonstrates the superiority of the dual-wavelength speckle interferometry and the feasibility of applying the measurement system in topographic measurement of PFMs in EAST.

Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry

We present a proof-of-principle demonstration of a method to characterize \textit{any} pure spatial qudit of arbitrary dimension $d$, which is based on the classic phase shift interferometry technique. In the proposed scheme a total of only $4 d$ measurement outcomes are needed, implying a significant reduction with respect to the standard schemes for quantum state tomography which require of the order of $d^2$. By using this technique, we have experimentally reconstructed a large number of states ranging from $d=2$ up to $14$ with mean fidelity values higher than $0.97$. For that purpose the qudits were codified in the discretized transverse momentum-position of single photons, once they are sent through an aperture with $d$ slits. We provide an experimental implementation of the method based in a Mach-Zehnder interferometer, which allows to reduce the number of measurement settings to 4 since the $d$ slits can be measured simultaneously. Furthermore, it can be adapted to consider the reconstruction of the unknown state from the outcome frequencies of $4d-3$ fixed projectors independently of the encoding or the nature of the quantum system, allowing to implement the reconstruction method in a general experiment.

Extended depth-range dual-wavelength interferometry based on iterative two-step temporal phase-unwrapping

For dual-wavelength interferometry (DWI), we propose an extended depth-range phase-shifting interferometry technique of extracting phase distributions from randomly phase-shifted interferograms. First, the generalized phase-shifting algorithm is utilized to retrieve the single-wavelength phase from interferograms with random phase shifts. Then, the phase difference and phase-sum are calculated from the wrapped single-wavelength phases, and iterative two-step temporal phase-unwrapping is introduced to unwrap the phase-sum. Finally, the height of objects is determined. Simulations and experiments are conducted to demonstrate the excellent precision and overall performance of the proposed method. As the limitation of being exclusively applicable to interferograms with special phase shifts is broken, the proposed method will greatly facilitate the practical application of DWI. Furthermore, because the phase-sum and iterative two-step temporal phase-unwrapping is introduced to extend the depth-range, the sensitivity and precision of the retrieved phase are greatly improved.

Application of 3D Nanorelief Sharp-Edge Detection Method in the Optical Interference Microscope

As is well known, the phase-shifting interferometry techniques allow to reach longitudinal resolution to ~ 0.1 nm, but the value of lateral resolution remains at the level of ~ 1 mm. For providing of high lateral resolution of linear measurements in the interference microscope profilometer it was proposed to use a position detection sensor of sharp edge. Principle of sensor’s measurement is based on registration of laser spot intensity scattered by the measurement sample surface under displacement of sample in the lateral direction. The paper shows the prototype scheme of measurement system containing the Linnik interferometer used for surface nanorelief measurement and a position detection module of sharp edge. Measurement process and experimental results are presented. The combining of measurement results performed by the Linnik interferometer and a position detection sensor of sharp edge can allow us to precisely (better then diffraction limit) define the position of sharp edge on the reconstructed surface nanorelief.

The measurement of plasma-facing materials’ topography variation by means of temporal phase-shifting speckle interferometry technique

Temporal phase-shifting speckle interferometry is proposed to measure plasma-facing materials’ (PFMs) topography variation in tokamak. In this approach, laser ablation method is used to simulate erosion and redeposition, and polished molybdenum/tungsten (Mo/W) samples which are related to PFMs have been tested. The geometric topography of the ablated area was reconstructed successfully via a numerical model developed in this work. The results demonstrate the feasibility of temporal phase-shifting speckle interferometry applied to topography measurement of PFMs.

Quantitative refractive index distribution of single cell by combining phase-shifting interferometry and AFM imaging

Cell refractive index, an intrinsic optical parameter, is closely correlated with the intracellular mass and concentration. By combining optical phase-shifting interferometry (PSI) and atomic force microscope (AFM) imaging, we constructed a label free, non-invasive and quantitative refractive index of single cell measurement system, in which the accurate phase map of single cell was retrieved with PSI technique and the cell morphology with nanoscale resolution was achieved with AFM imaging. Based on the proposed AFM/PSI system, we achieved quantitative refractive index distributions of single red blood cell and Jurkat cell, respectively. Further, the quantitative change of refractive index distribution during Daunorubicin (DNR)-induced Jurkat cell apoptosis was presented, and then the content changes of intracellular biochemical components were achieved. Importantly, these results were consistent with Raman spectral analysis, indicating that the proposed PSI/AFM based refractive index system is likely to become a useful tool for intracellular biochemical components analysis measurement, and this will facilitate its application for revealing cell structure and pathological state from a new perspective.