Search Results (72)

A pixelated instantaneous phase-shifting interferometry (PSI) using a phase-only liquid crystal spatial light modulator (LC-SLM) is developed and experimentally validated. The LC-SLM generates high-frequency spatial phase modulation and introduces pixelated instantaneous phase-shifting between two incident orthogonal linearly polarized beams propagating along the same optical path. A single-frame pixelated phase-shifted interferogram is captured in one exposure, and the wavefront phase is reconstructed subsequently by using the proposed loop retrieval algorithm. In the experimental investigation, an interference region segmentation method based on wavefront-modulated sequential images is firstly developed to realize precise alignment between LC-SLM pixels and CCD pixels. Secondly, based on the PSI setup established, wavefront measurement experiments for system aberration, tilted wavefront and defocused wavefront are performed. Experimental results show that the root-mean-square (RMS) value of the residual wavefront between the retrieved tilted wavefront and its fitting plane is 0.046 λ. Furthermore, the RMS value of the residual wavefront between the defocused wavefront retrieved by the proposed method and the eight-step phase-shifting method is 0.075 λ, which verifies the effectiveness of the proposed approach. This work provides a simple and rapidly deployable solution for single-shot interferometric measurement. Full article

Interferometers are essential tools for quality control of optical surfaces. While interferometric techniques like phase-shifting interferometry offer high accuracy, they involve complex setups, require stringent calibration, and are sensitive to phase shift errors, noise, and surface inhomogeneities. In this research, we introduce an alternative algorithm that integrates Moving Average and Fast Fourier Transform (MAFFT) techniques with Polynomial Fitting. The proposed method achieves results comparable to a Zygo interferometer under standard conditions, with an error margin under 2%. It also maintains measurement stability in noisy environments and in the presence of significant local inhomogeneities, operating in real-time to enable wavefront measurements at 30 Hz. We have validated the algorithm through simulations assessing noise-induced errors and through experimental comparisons with a Zygo interferometer. Full article

Space-based gravitational wave detection relies on laser interferometry to measure picometer-level displacements over ${10}^5$–${10}^6$ km baselines. To integrate ranging and communication within the same optical link without degrading the primary scientific measurement, a low modulation index of 0.1 rad is required, resulting in extremely weak signals and challenging acquisition conditions. This study developed mathematical models for signal acquisition, identifying and analyzing key performance-limiting factors for both Binary Phase Shift Keying (BPSK) and Binary Offset Carrier (BOC) schemes. These factors include spreading factor, acquisition step, modulation index, and carrier-to-noise ratio (CNR). Particularly, the acquisition threshold can be directly calculated from these parameters and applied to the acquisition process of communication and ranging signals. Numerical simulations and evaluations, conducted with TianQin mission parameters, demonstrate that, for a data rate of 62.5 kbps and modulation indices of 0.081 rad (BPSK) or 0.036 rad (BOC), respectively, acquisition (probability ≈ 1) is achieved when the CNR is ≥104 dB·Hz under a false alarm rate of ${10}^{-6}$. These results provide critical theoretical support and practical guidance for optimizing the inter-satellite communication and ranging system design for the space-based gravitational wave detection missions. Full article

Accurate estimation of young forest height is essential for assessing the carbon sequestration potential of vast Siberian boreal forests recovering from wildfires. Satellite radar interferometry, particularly PolInSAR, is a promising tool for this task. However, its application in winter conditions and over sparse young forests remains underexplored. This study proposes a novel method for estimating the height of sparse young pine (Pinus sylvestris) stands using fully polarimetric bistatic TerraSAR-X/TanDEM-X data acquired in winter. The method is based on an analysis of the multimodal distribution of the unwrapped interferometric phase of the surface scattering component, which was isolated via PolInSAR decomposition. We hypothesize that the phase centers correspond to the snow-covered ground (located between tree groups) and the rough surface formed by the upper layer of branches and needles (of the tree groups). The results demonstrate that the difference between the dominant modes of the surface scattering phase distribution correlates with the height of young trees. However, the measurable height difference is limited by the interferometric height of ambiguity. Furthermore, a temporal analysis of the phase and meteorological data revealed a strong correlation between sudden phase shifts and daytime temperature rises around 0 °C. This is interpreted as the formation of a layered snowpack structure with a dense ice crust. This study confirms the potential of X-band PolInSAR for monitoring the structure of young Siberian forests in winter but also highlights a significant limitation: the critical impact of snowpack metamorphism, particularly melt-freeze cycles, on the interferometric phase. The proposed method is only applicable to certain forest regeneration stages where tree height does not exceed the ambiguity limit and snow conditions are stable. Full article

With advances in scientific foundations and engineering practice, segmented mirrors—a key architecture for realizing extremely large apertures and high-resolution imaging—have become foundational across space astronomy, ground-based telescopes, and advanced manufacturing. In recent years, interferometry, which leverages optical coherence and phase sensitivity, has become a powerful tool for inter-segment co-phasing. Its capabilities have advanced markedly owing to developments in multi-wavelength techniques, high-speed high-dynamic-range detectors, and instantaneous phase-shifting methods. Relative to non-interferometric sensing, interferometry directly encodes and unwraps phase. This enables a unified framework that combines millimeter-scale dynamic range with nanometer-level resolution throughout coarse acquisition, fine phasing, and in situ maintenance. This paper first outlines the degrees of freedom and error sources in segmented mirrors. It then reviews the configurations and acquisition strategies of shearing, Mach–Zehnder, Michelson, Fizeau, and PISTIL interferometers, and systematizes interferogram processing methods—such as phase-shifting, synthetic-wavelength techniques, and digital holography—for retrieving piston and tip/tilt. Accuracy of piston is λ/50–λ/100, and tip/tilt accuracy can reach the arcsecond level, with resolution at the nanometer scale. Finally, we discuss pathways to extend interferometric metrology from segmented mirrors to other discontinuous surfaces (e.g., segmented detectors, segmented gratings, microlens arrays) and outlines future research directions. Full article

This paper presents a voltage-controlled phase shifter (VCPS) capable of 360° continuous adjustment, applied in laser frequency-locking systems to obtain maximum amplitude error signals with minimal dispersion. The phase-shifting unit is realized through CMOS integrated circuit design, utilizing comparators, logic gate control modules, and filters. Simulations verify the VCPS, composed of three cascaded units, achieves 360° continuous phase adjustment. A printed circuit board (PCB) was fabricated with the integration of electronic components. The test results demonstrate that the VCPS exhibits a continuous 360° phase shift in one direction with increasing control voltage. It operates from kHz to 50 MHz and maintains a peak-to-peak output amplitude of 5 V or 10 V. The proposed VCPS has been successfully applied in cold-atom interferometry, quantum memory experiments, and optical frequency standards. Full article

Optical interferometry provides high-precision displacement and angle measurement solutions for a wide range of cutting-edge industrial applications. One of the key factors to achieve such precision lies in highly accurate optical encoder signal processing, as well as the calibration and compensation techniques customized for specific measurement principles. Optical interferometric techniques, including laser interferometry and grating interferometry, are usually classified into homodyne and heterodyne systems according to their working principles. In homodyne interferometry, the displacement is determined by analyzing the phase variation of amplitude-modulated signals, and common demodulation methods include error calibration methods and ellipse parameter estimation methods. Heterodyne interferometry obtains displacement information through the phase variation of beat-frequency signals generated by the interference of two light beams with shifted frequencies, and its demodulation techniques include pulse-counting methods, quadrature phase-locked methods, and Kalman filtering. This paper comprehensively reviews the widely used signal processing techniques in optical interferometric measurements over the past two decades and conducts a comparative analysis based on the characteristics of different methods to highlight their respective advantages and limitations. Finally, the hardware platforms commonly used for optical interference signal processing are introduced. Full article

In this paper, an automatic phase-shifting interferometer has been developed using a homemade liquid-crystal phase shifter, which demonstrates a low-cost, fully automated technical solution for measuring the phase information of optical waves in devices. Conventional phase-shifting interferometers usually rely on PZT piezoelectric phase shifters, which are complex, require additional half-inverse and half-transparent optics to build the optical path, and are expensive. To overcome these limitations, we used a laboratory-made liquid-crystal waveplate as a phase shifter and integrated it into a Mach–Zehnder phase-shifting interferometer. The system is controlled by an STM32 microcontroller and self-developed measurement software, and it utilizes a four-step phase-shift interferometry algorithm and the CPULSI phase-unwrapping algorithm to achieve automatic phase measurements. Phase test experiments using a standard plano-convex lens and a homemade liquid-crystal grating as test objects demonstrate the feasibility and accuracy of the device by the fact that the measured focal lengths are in good agreement with the nominal values, and the phase distributions of the gratings are also in good agreement with the predefined values. This study validates the potential of liquid-crystal-based phase shifters for low-cost, fully automated optical phase measurements, providing a simpler and cheaper alternative to conventional methods. Full article

High aspect ratio (HAR) sample-induced aberrations seriously affect the topography measurement for the bottom of the microstructure by coherence scanning interferometry (CSI). Previous research proposed an aberration compensating method using deformable mirrors at the conjugate position of the pupil. However, it failed to compensate for the shift-variant aberrations introduced by the HAR hybrid trench array composed of multiple trenches with different parameters. Here, we propose a computational aberration correction method for measuring the topography of the HAR structure by the particle swarm optimization (PSO) algorithm without constructing a database and prior knowledge, and a phase filter in the spatial frequency domain is constructed to restore interference signals distorted by shift-variant aberrations. Since the aberrations of each sampling point are basically unchanged in the field of view corresponding to a single trench, each trench under test can be considered as a separate isoplanatic region. Therefore, a multi-channel aberration correction scheme utilizing the virtual phase filter based on isoplanatic region segmentation is established for hybrid trench array samples. The PSO algorithm is adopted to derive the optimal Zernike polynomial coefficients representing the filter, in which the interference fringe contrast is taken as the optimization criterion. Additionally, aberrations introduce phase distortion within the 3D transfer function (3D-TF), and the 3D-TF bandwidth remains unchanged. Accordingly, we set the non-zero part of the 3D-TF as a window function to preprocess the interferogram by filtering out the signals outside the window. Finally, experiments are performed in a single trench sample and two hybrid trench array samples with depths ranging from 100 to 300 μm and widths from 10 to 30 μm to verify the effectiveness and accuracy of the proposed method. Full article

This study employs the simultaneous phase-shift interferometry (SPSI) system to diagnose laser-induced plasma (LIP) and shock wave (SW). In high-density LIP diagnostics, the Faraday rotation effect causes probe light polarization deflection, rendering traditional fixed-phase-demodulation methods ineffective, the Carré phase-recovery algorithm is adopted and its applicability is verified. Uncertainty analysis and precision verification show that the total phase shift uncertainty is controlled within 0.045 radians, equivalent to a refractive index accuracy of $8.55\times {10}^{-6}$, with sensitivity to weak perturbations improved by approximately one order of magnitude compared to conventional carrier-frequency interferometry. Experimental results demonstrate that the SPSI system precisely captures the initial spatiotemporal evolution of LIP and tracks shock waves at varying attenuation levels, exhibiting notable advantages in weak shock wave detection. This research validates the SPSI system’s high sensitivity to transient weak perturbations, offering a valuable diagnostic tool for high-vacuum plasmas, low-pressure shock waves, and stress waves in optical materials. Full article

A high-resolution grating interferometric micro-displacement sensor utilizing the subdivision interpolation technique is proposed and experimentally demonstrated. As the interference laser intensity varies sinusoidally with displacement, subdivision interpolation is a promising technique to achieve micro-displacement detection with a high resolution and linearity. However, interpolation errors occur due to the phase imbalance, offset error, and amplitude mismatch between the orthogonal signals. To address these issues, a subdivision interpolation circuit, along with 90-degree phase-shifter and high-precision DC bias-voltage techniques, converts an analog sinusoidal signal into standard incremental digital signals. This novel methodology ensures that its performance is least affected by the nonidealities induced by fabrication and assembly errors. Detailed design, analysis, and experimentation studies have been conducted to validate the proposed methodology. The experimental results demonstrate that the micro-displacement sensor based on grating interferometry achieved a displacement resolution of less than 1.9 nm, an accuracy of 99.8%, and a subdivision interpolation factor of 208. This research provides a significant guide for achieving high-precision grating interferometric displacement measurements. Full article

Fiber-optic tip sensors offer significant potential in biomedical applications due to their high sensitivity, compact size, and resistance to electromagnetic interference. This study focuses on advancing phase demodulation techniques for ultra-short Fabry–Pérot cavities within limited spectral bandwidths to enhance their application in biomedicine and diagnostics. We propose a novel sparse-sampled white-light interferometry system for respiratory monitoring, utilizing a monolithic integrated semiconductor tunable laser for quasi-continuous frequency scanning across 191.2–196.15 THz at a sampling rate of 5 kHz. A four-step phase-shifting algorithm (PSA) ensures precise phase demodulation, enabling high sensitivity for short-cavity fiber-optic sensors under constrained spectral bandwidth conditions. Humidity sensors fabricated via a self-growing polymerization process further enhance the system’s functionality. The experimental results demonstrate the system’s capability to accurately capture diverse breathing patterns—including normal, rapid, and deep states—with fast response and recovery times. These findings establish the system’s potential for real-time respiratory monitoring in clinical and point-of-care settings. Full article

This paper proposes and implements a novel scheme for recording signals from fibre optic sensors based on tandem low-coherence interferometry with an integrated optical reference interferometer. The circuit allows precision control of the phase shift. Additionally, the paper illustrates the potential for detecting vibration and object deformation using fibre optic Fabry–Perot sensors connected to the registration system. Full article

Fringe projection profilometry (FPP) is extensively utilized for the 3D measurement of various specimens. However, traditional FPP typically requires at least three phase-shifted fringe patterns to achieve a high-quality phase map. In this study, we introduce a single-shot FPP method based on common path polarization interferometry. In our method, the projected fringe pattern is created through the interference of two orthogonal circularly polarized light beams modulated by a liquid crystal spatial light modulator (LC-SLM). A polarization camera is employed to capture the reflected fringe pattern, enabling the simultaneous acquisition of four-step phase-shifting fringe patterns. The system benefits from advanced anti-vibration capabilities attributable to the common path self-interference optical path design. Furthermore, the utilization of a low-coherence LED light source results in reduced noise levels compared to a laser light source. The experimental results demonstrate that our proposed method can yield 3D measurement outcomes with high accuracy and efficiency. Full article

The ionospheric effects in repeat-pass SAR interferometry (InSAR) have become a rising concern with the increasing interest in low-frequency SAR. The ionosphere will introduce serious phase errors in the interferogram, which should be properly corrected. In this paper, the influence of the wavenumber shift on the Range Split-Spectrum (RSS) method is analyzed quantitatively. It is shown that the split-spectrum processing deteriorates the coherence of the sub-band interferogram and then greatly reduces the estimation accuracy. The RSS method combined with common band filtering (CBF) can improve the coherence of sub-band interferograms and estimation accuracy, but the estimation is biased due to the RSS model mismatch. To address the problem, a modified truncated singular value decomposition (MTSVD) based multi-sub-band RSS method is proposed in this paper. The proposed method divides the range common spectrum into multiple sub-bands to jointly estimate the ionospheric phase. The performance of the proposed method is analyzed and validated based on simulation experiments. The results show that the proposed method has stronger robustness and higher accuracy. Full article