Phase-shifting Interferometry Research Articles

Fast and precise single-frame phase demodulation interferometry

To achieve real-time phase detection, this paper presents a fast and precise spatial carrier phase-shifting interferometry based on the dynamic mode decomposition strategy. The algorithm initially produces a series of phase-shifted sub-interferograms with the aid of a spatial carrier interferogram. Subsequently, the measured phases are derived with great accuracy from these sub-interferograms through the use of the dynamic mode decomposition strategy, an outstanding non-iterative algorithm. Numerical simulation and experimental comparison show that this method is an efficient and accurate single-frame phase demodulation algorithm. The paper also analyzes the performance of the proposed method based on influencing factors such as random noise level, carrier frequency size, and carrier frequency direction. The results indicate that this method is a fast and accurate phase solution method, offering another effective solution for dynamic real-time phase measurement.

Time-resolved measurement of acoustic density fluctuations using a phase-shifting Mach-Zehnder interferometer.

Phase-shifting interferometry is one of the optical measurement techniques that improves accuracy and resolution by incorporating a controlled phase shift into conventional optical interferometry. In this study, a four-step phase-shifting interferometer is developed to measure the spatiotemporal distribution of acoustic density oscillations of the gas next to a rigid plate. The experimental apparatus consists of a polarizing Mach-Zehnder interferometer with a polarization camera capable of capturing four polarization directions in one shot image and it is used to measure the magnitude and the phase of density fluctuations through a duct of rectangular cross section connected to a loudspeaker. The results are compared with the well-established thermoacoustic theory describing the thermal coupling between acoustic oscillations and rigid boundaries, and the results show a very good agreement for various ratios of the (frequency-dependent) thermal boundary layer thickness to the plate spacing. This measurement technique could be advantageously employed to analyze more complex heat transfer processes involving the coupling of acoustic oscillations with rigid boundaries.

A dual-stage correction approach for high-precision phase-shifter in Fizeau interferometers

This paper proposes a dual-stage correction approach for a high-accuracy phase-shifter in Fizeau laser interferometers, effectively reducing the phase shift errors in PSI (Phase-Shifting interferometry) and improving the precision of surface profile measurements. The precision of PSI depends on the displacement accuracy of the reference mirror, and the function of the phase shifter is to drive the reference mirror to generate wavelength-level displacements with nanometer-level accuracy. The first-stage correction aims to reduce the nonlinearity error of the reference mirror by ULPS (Ultra-High Linearity Phase Shifter). The second-stage correction aims to reduce the average velocity error and plane velocity uniformity error of the reference mirror by AVIC (Auto Velocity Iterative Correction). The experimental results indicate that, after the first-stage correction, ULPS exhibits a 0.05 % nonlinearity, a 2.5 nm repeatability, and a 0.2 nm resolution under a load of 20 kg, and its nonlinearity surpassing all phase-shifters documented in the literature. After the second-stage correction, the average velocity error and plane velocity uniformity error of the reference mirror are reduced to 0.07 %.

Fresnel incoherent compressive holography toward 3D videography via dual-channel simultaneous phase-shifting interferometry.

Fresnel incoherent correlation holography (FINCH) enables high-resolution 3D imaging of objects from several 2D holograms under incoherent light and has many attractive applications in motionless 3D fluorescence imaging. However, FINCH has difficulty implementing 3D imaging of dynamic scenes since multiple phase-shifting holograms need to be recorded for removing the bias term and twin image in the reconstructed scene, which requires the object to remain static during this progress. Here, we propose a dual-channel Fresnel noncoherent compressive holography method. First, a pair of holograms with π phase shifts obtained in a single shot are used for removing the bias term noise. Then, a physic-driven compressive sensing (CS) algorithm is used to achieve twin-image-free reconstruction. In addition, we analyze the reconstruction effect and suitability of the CS algorithm and two-step phase-shift filtering algorithm for objects with different complexities. The experimental results show that the proposed method can record hologram videos of 3D dynamic objects and scenes without sacrificing the imaging field of view or resolution. Moreover, the system refocuses images at arbitrary depth positions via computation, hence providing a new method for fast high-throughput incoherent 3D imaging.

Fourier-transform-only method for random phase shifting interferometry

An accurate and computationally simple phase shifting interferometry (PSI) method is developed to reconstruct phase maps without a priori knowledge of the phase shift. Previous methods developed for random PSI either do not address general sources of error or require complex iterative processes and increased computational time. Here we demonstrate a novel method that is able to extract the phase using only Fourier transform (FT). With spatial FT analysis, randomly phase-shifted data is reordered to allow performing temporal FT on the intensity, which is a function of the phase shift. Since the entire process, including order analysis and phase calculation, is based only on Fourier analysis, it is rapid, easy to implement, and addresses general sources of error. The method exhibits high performance in experiments containing random phase shifts. Moreover, simulations incorporating common experimental error sources such as random intensity noise, intensity harmonics, and phase shift errors demonstrate that the proposed method performs as good as or better than the state-of-the-art phase reconstruction techniques in terms of accuracy and time.

Adaptive phase-shifting interferometry based on a phase-shifting digital holography algorithm.

Phase-shifting interferometry (PSI) requires accurate phase shifts between interferograms for realizing high-accuracy phase retrieval. This paper presents an adaptive PSI through synchronously capturing phase shifts measurement interferograms and phase measurement interferograms, in which the former is a series of spatial carrier frequency phase-shifting interferograms generated by an additional assembly and the phase shifts are calculated with the single-spectrum phase shifts measurement algorithm (SS-PSMA), the latter is employed for phase retrieval with an adaptive phase-shifting digital holography algorithm (PSDHA) based on complex amplitude recovery. In addition to exhibiting excellent reliability, high-accuracy phase retrieval (0.02 rad), and short calculation time (<25 ms), the proposed adaptive PSDHA is suitable for various interferograms with different fringe shapes and numbers. Importantly, both simulation analysis and experimental result demonstrate that this adaptive PSI based on PSDHA can effectively eliminate phase-shifting errors caused by phase shifter and external disturbance, ensuring high-accuracy phase shifts measurement and phase retrieval, meanwhile significantly reducing phase-shifting interferograms acquisition time and phase retrieval calculation time.

Quantitative visualization on boundary heat transfer of supercritical CO2 mini-channel through-flow (Re=104) via pixelated phase-shifting interferometry

This study is focused on measuring the transient boundary heat transfer in supercritical CO2 mini-channel flows under local heat application. A pixelated-array masked phase-shifting interferometer system and quantitative data procedures have been established for sCO2 boundary flow. The experiments have been conducted at a Reynolds number level of 104, spanning across both subcritical and supercritical regions (5.0 ∼ 7.9 MPa). High resolution local density and temperature have been extracted from the raw interferograms by developing a digital phase-shifting algorithm. The temporal and spatial evolutions of Nu show good agreement with classic correlations. The effects of differential pressures (10.87 ∼ 52.59 Pa) and heat fluxes (2014, 5500, 14,057 W/m2), along with their associated heat transfer behaviors, have been quantitatively examined under transient scenarios using the current method. The results show: (1) although the Re number is high, such small thermal perturbations can be clearly visualized in the entire window, which shows the capability of field extraction of the current method proposed for complicated supercritical boundary flows; (2) rapid density decrease (1.0 kg/m3) occurs locally, while small temperature differences (0.01 K) are observed, which also lead to local Nu variations under different operation conditions; (3) detailed convective patterns and time evolution of Nu curve groups identified for subcritical, near-critical and supercritical states.

Nanoscale Examination of Artistic Surfaces Utilizing 3D Non-Contact Optical Scanning Technology

The assessment of painting surfaces at the microscale has been historically impeded by challenges related to limited resolution and accuracy in traditional methodologies. This study pioneers the utilization of non-contact 3D optical scanning technology, meticulously calibrated for nanoscale precision, to unravel the intricate features residing on painting surfaces. The initial phase employs the Point Diffraction Interferometer (PDI) for 3D optical scanning, incorporating meticulously optimized parameters tailored to nanoscale analysis. Subsequent phases involve the application of Phase Shifting Interferometry (PSI) and Holographic Interferometry (HI). PSI is employed to discern morphological alterations, while HI captures the nuanced color and optical characteristics embedded in the painting surfaces. To enhance the continuity of phase information, the Goldstein algorithm is introduced during phase stitching, fortifying the method’s robustness against discontinuities. Further refinement is achieved through the Iterative Closest Point (ICP) algorithm, orchestrating precise 3D data reconstruction. This process encompasses multi-view stereo matching and surface fitting, ensuring a meticulous representation of the painting surface geometry. The study meticulously presents detailed 3D optical scanning results, probing into the painting surface’s performance concerning nanoscale resolution, measurement accuracy, and color consistency. The unveiled findings showcase a remarkable minimum feature capture capability of 1.8 at nanoscale resolution. The quantitative assessment, encapsulated by a Root Mean Square Error (RMSE) ranging from 0.001 to 0.012 for 100 scanned data points, and a Standard Deviation (STD) oscillating between 0.0008 to 0.0018, attests to the method’s efficacy. This effectiveness is underscored by its capacity to deliver a thorough and intricate analysis of painting surface performance at the nanoscale.

Synchronous Phase-Shifting Shearing Interferometry Based on Polarization Grating

Synchronous Phase-Shifting Shearing Interferometry Based on Polarization Grating

Research on the application of information technology modeling based concrete reinforcement construction for bridge projects

Abstract This paper discusses the application of concrete in bridge and house reinforcement, especially for detecting tiny defects during construction. Taking the optical principle of shear device and the principle of scattering interferometry as the theoretical basis, the article proposes a nondestructive testing technique applicable to concrete construction in bridge engineering. This technique can effectively detect the tiny defects in the structure by combining the time phase shift interferometry. The research and analysis show that the digital shear scattering interferometric detection system proposed in this paper performs well in defect detection, and its calculated defect values are highly similar to the actual data with an error of less than 6%. The system can also present different responses in time according to the different lengths or depths of the defects. Further applications showed that the vibration resistance of the bridges was significantly improved after the concrete reinforcement construction using the defects detected by the system, and the self-oscillation cycles were reduced by 8.1% and 11.8%, respectively. Overall, the study provides an efficient technical method for detecting and treating defects in concrete reinforcement works.

Two-frame random phase shifting interferometry based on constrained Kalman filter without pre-filtering

This paper discusses a phase estimation algorithm in two-frame phase-shifting interferometry using a constrained Kalman filter without the need of pre-filtering operation for the background intensity removal. A state-space model is developed and state estimation is performed based on the extended Kalman filter. The Kalman smoother algorithm is utilized to improve the accuracy of state estimation. A comparative study is presented between the proposed and four state-of-art phase estimation methods. Both simulation and experimental results show good accuracy and noise robustness of the proposed method over a wide range of phase shifts.

Wavefront imaging of a biological sample using DMD-based single-pixel phase-shifting interferometric techniques: An experimental comparison

Single-pixel wavefront imaging (SWI) is an innovative technique for simultaneously measuring the amplitude and phase of an unknown field, which is particularly important for wavefront imaging in invisible wavelengths and under low light conditions. However, most of the existing SWI techniques are still in the technical development stage. Here, we provide a comprehensive analysis and comparison of the SWI methods using DMD-based single-pixel multi-step phase-shifting interferometric techniques. Through experimental demonstrations, we first compare the performances of the techniques using the Hadamard basis, Fourier basis, and discrete cosine transform (DCT) basis. Further, the performances of the Hadamard basis-based SWI (HSWI) technique using phase-shifting interferometry with the different reference strategies are investigated while the binary grating, Lee, and super-pixel methods are applied to control the DMD for realizing the necessary complex amplitude modulations there. Experimental results suggest the grating-phase-shifting-based HSWI performs best, in which one can use the checkerboard reference for the maximum field of view or select the peripheral reference for a better imaging resolution; and it can do 2 fps wavefront imaging of the sample at 10 % downsampling rate with a resolution of 128 × 128 pixels. Our work provides researchers with a guideline to choose a suitable SWI technique for their applications.

Robust phase demodulation algorithm for single-frame interferogram

This paper presents a robust phase demodulation algorithm (PDA) for single-frame interferogram based on preprocessing and watershed segmentation transformation. Compared to existing methods, the PDA can be applied to closed fringe or non-closed fringe patterns with low number of fringes indiscriminately. The proposed PDA includes two main parts, one is the preprocessing stage based on the empirical mode decomposition and Hilbert spiral transformation for background and noise removal, as well as normalization, and the other one is the correction of the wrapped phase obtained by arccosine through the watershed segmentation transformation. Through numerical simulations, the robustness of PDA to high noise and different kinds of fringe patterns is proved. The experimental evaluation of the proposed algorithm focuses on surface shape measurement of optical components, and the comparative analysis of the first 36 Zernike coefficients demonstrates that the PDA has high accuracy and the phase is good accordance with that obtained by phase-shifting interferometry.

High-dynamical-range angular measurement based on Heterodyne Phase Shifting Interferometry

A novel Heterodyne Phase Shifting Interferometer (HPSI) with nano-radians resolution and tens of milli-radians measurement range is developed. Instead of using a PZT-driven mirror to generate phase shift, the interferometer uses the heterodyne scheme. Such that the non-linearity and hysteresis effects of PZT are overcome. The non-linearity within the full range is less than 0.0005. Applying an intensity-modulated beam to test the angular measurement performance, the angular measurement noise level is 1.5nrad/Hz1/2. Due to the large dynamical range and good linearity, this HPSI is a good choice for precision angular metrology.

Accurate computer simulation phase-shifting digital interferometry for measurement of the optical properties of Zamzam water in the visible spectrum Nasser A. Moustafa1,2, Hasan Assaedi2, Thamer H. Albaqami2 1Physics Department, Faculty of Science, H

Accurate computer simulation phase-shifting digital interferometry for measurement of the optical properties of Zamzam water in the visible spectrum Nasser A. Moustafa1,2, Hasan Assaedi2, Thamer H. Albaqami2 1Physics Department, Faculty of Science, H

Adjustable accuracy of phase steps in a double-aperture common-path interferometer by rotating and displacing grating at Fourier plane

Detuning errors limit the accuracy of phase extraction in phase-shifting interferometry (PSI). To improve this accuracy, the systems to control the phase shifter dispositive must be highly accurate, involving high technology, exhaustive calibration, high cost, and constant maintenance. This manuscript presents a method for improving the accuracy of the phase step generated at the Fourier plane by rotating and displacing the grating in a double-aperture common-path interferometer. It is demonstrated that both the detuning errors and the phase extraction uncertainty decrease with the grating rotation angle. The experimental implementation is very simple, as it does not require any sophisticated mechanical system to improve the accuracy, no exhaustive calibration, and no additional mechanical and optical dispositive. With the present approach, the PSI method could be achieved very simply and with high accuracy by using a low-accuracy actuator. The theoretical model and experimental results are presented to demonstrate the present proposal.

Incoherent digital holography with two polarization-sensitive phase-only spatial light modulators and reduced number of exposures.

I propose methods for reducing the number of exposures in incoherent digital holography with two polarization-sensitive phase-only spatial light modulators (IDH with TPP-SLMs). In IDH with TPP-SLMs, no polarization filters are required, and not only three-dimensional (3D), but polarization information is also obtained. However, seven exposures are required to conduct filter-free polarimetric incoherent holography. In this article, the optical designs and modified phase-shifting interferometry to reduce the number of recordings are described. IDH with TPP-SLMs has the potential for filter-free single-shot multidimensional incoherent holographic imaging.

Determination of the Surface Displacement Field under Dynamic Loads by the Method of Phase-Shifting Correlation Speckle Pattern Interferometry

Determination of the Surface Displacement Field under Dynamic Loads by the Method of Phase-Shifting Correlation Speckle Pattern Interferometry

Experimental and quantitative evaluation of frequency modulation caused by Doppler effect around high-speed moving sound source.

High-speed train noise remains a wayside environmental issue. For accurate noise prediction, the characteristics of a moving sound source must be revealed. In this work, the frequency modulation of sound waves emitted from a high-speed moving sound source was experimentally investigated. In the experiment, the sound field around a running train model emitting a 40 kHz pure tone was measured by an optical measurement technique, parallel phase-shifting interferometry, which can visualize instantaneous sound fields. For quantitative evaluation, a lens distortion correction was also developed and adopted for the visualization results. From the measured result of a sound source moving at a running speed of 280 km/h, the frequency modulation, known as the Doppler effect, was observed, and the measured frequency agreed well with the theoretical values.

Complex amplitude extraction from a set of interferograms by simultaneous modulation of amplitude and phase steps

The measurement of an optical field arises in various fields of science and engineering, including holography, crystallography, microscopy, and many others. Nowadays, there are several methods to estimate amplitude and phase including Shack–Hartman wavefront sensor, algorithms type Gerchberg–Saxton, algorithm-based on the transport of irradiance equation, holographic, interferometric, among others. This paper introduces an interferometric method for retrieving the complex amplitude from a set of interferograms modulated simultaneously in visibility and phase steps. Instead of phase only as the method of so-called phase-shifting interferometry. This approach is based on the modulation of amplitude and phase steps and is presented for the case of synchronous detection and coherence light. It is validated with a numerical noise study, turning out to be accurate and robust to detuning errors, with low distortion, and a very high signal-to-noise. The experiment is carried out on a Mach–Zehnder interferometer adapted to modulate the reference amplitude, and the phase steps by modulation of polarization, instead of phase steps only as in phase-shifting interferometry.