Interferometry Technology Research Articles

Cuff-less wearable biosensor in continuous noninvasive human radial artery pulse waveform and blood pressure measurement using self-mixing interferometry

In this paper, we propose a compact, wearable biosensor for the noninvasive measurement of human radial artery pulse waveform curve (PWC) and blood pressure (BP). In this system, self-mixing interferometry (SMI) technology is employed to measure the weak arterial vascular deformation, enabling accurate PWC retrieval. Based on the reconstructed PWC features, BP values are precisely estimated by means of deep learning method. Here continuous wavelet transform (CWT), enabling visualization of the relationship between the SMI signal temporal frequency components and the PWC characteristics, is highlighted for PWC flipping points seeking and convolutional neural network (CNN) input parameter acquisition. For the first time, a novel deep learning network preprocessing method is proposed that allows direct feature extraction from the CWT scalogram of SMI signal without the complicated PWC reconstruction algorithm. The robustness and accuracy of our device are validated by a series of clinical measurements, mean absolute error (MAE) and standard deviation (STD) values are calculated and compared with the existing models. We approach minimal BP estimation results (MAE ± STD) of 1.41 ± 1.89 mmHg for systolic blood pressure (SBP) and 1.78 ± 2.01 mmHg for diastolic blood pressure (DBP), respectively. The luxuriant novelties and remarkable performance clearly demonstrate our wearable sensor’s great potential in BP monitoring, and other clinical applications.

Data-Supported Prediction of Surface Settlement Behavior on Opencast Mine Dumps Using Satellite-Based Radar Interferometry Observations

To ensure the safe repurposing of post-mining landscapes, understanding and managing geotechnical risks, particularly ground movements such as settlements on opencast mining dump surfaces, is critical. Satellite-based radar interferometry (InSAR) technology offers highly detailed data on vertical ground movements with a high spatial and temporal resolution. By combining a data-driven approach, using InSAR-generated high-resolution datasets, with model-driven methods such as inverse modeling and classic time–settlement models, the efficient monitoring and prediction of opencast mine dump settlements can be achieved. This dual approach—leveraging advanced data analysis tools and precise modeling—yields valuable insights into spatial settlement behavior. In particular, classic time–settlement models are applied to the InSAR data through least square regression and Taylor approximation. The integration of both approaches enables the more robust, data-validated forecasts of key geotechnical indicators, such as the time to settlement stabilization and the expected maximum settlement over large areas. An application at a mine in central Germany illustrates the method by generating spatial predictions of the settlement behavior over more than 200 ha. In general, the results provide a comprehensive dataset for investigating other factors influencing the settlement behavior of opencast mine dumps.

Two-frame random phase-shifting interferometry immune to the influence of tilted phase-shift.

To expand the reliability of interferometry technology, this paper proposes a random two-frame algorithm with high accuracy, high robustness, and immunity to tilt phase-shift. This method uses the equivalence of inter-frame phase-shift and intra-frame phase difference to mine light intensity pixels carrying new phase-shift from different images. Then, the linear random phase-shift plane is fitted by least squares, and the inverse tangent relationship is used to obtain a high-precision phase distribution. This technology uses the principle of light intensity equivalence to fit the linear phase-shift plane and does not require any iterative process. It can effectively suppress the influence of tilt phase-shift while ensuring computational efficiency. The paper verifies that the proposed algorithm has excellent performance in both tilted and non-tilted conditions through simulation and experimental comparison.

Development and Comparison of InSAR-Based Land Subsidence Prediction Models

Land subsidence caused by human engineering activities is a serious problem worldwide. We selected Qian’an County as the study area to explore the evolution of land subsidence and predict its deformation trend. This study utilized synthetic aperture radar interferometry (InSAR) technology to process 64 Sentinel-1 data covering the area, and high-precision and high-resolution surface deformation data from January 2017 to December 2021 were obtained to analyze the deformation characteristics and evolution of land subsidence. Then, land subsidence was predicted using the intelligence neural network theory, machine learning methods, time-series prediction models, dynamic data processing techniques, and engineering geology of ground subsidence. This study developed three time-series prediction models: a support vector regression (SVR), a Holt Exponential Smoothing (Holt) model, and multi-layer perceptron (MLP) models. A time-series prediction analysis was conducted using the surface deformation data of the subsidence funnel area of Zhouzi Village, Qian’an County. In addition, the advantages and disadvantages of the three models were compared and analyzed. The results show that the three developed time-series data prediction models can effectively capture the time-series-related characteristics of surface deformation in the study area. The SVR and Holt models are suitable for analyzing fewer external interference factors and shorter periods, while the MLP model has high accuracy and universality, making it suitable for predicting both short-term and long-term surface deformation. Ultimately, our results are valuable for further research on land subsidence prediction.

Plane mirror-optical path coupling noise in telescope off-axis system dimensional stability measurement

The dimensional stability of the off-axis optical system affects its optical performance significantly and may even lead to its failure. Here, we report a heterodyne interferometry technology to measure the telescope’s dimensional stability. In this method, the standard plane mirror, which reflects the measurement laser, is a critical structural component. Additionally, it is one of the primary sources of the noise. The study focuses on the impact of the standard plane mirror’s positional misalignment instability on optical path noise. A mathematical model was established to depict the effects of mirror misalignment instability on the optical path, and experiments were conducted to decouple the noise. The results of the experiment show that the standard plane mirror introduces approximately 1nm/Hz1/2 at 10 mHz of optical path noise into the off-axis system, and the dimensional stability of the off-axis system is about 6.23nm/Hz1/2 at 10 mHz.

Nonlinearity-suppressed micro-probe fiber optic interferometer for accurate long-range displacement measurements

Fiber-optic interferometry technology has advanced rapidly in recent years. However, accurate measurement of the displacement over long ranges remains a challenge. This study reveals that fiber interferometers with Fabry–Perot cavities experience non-elliptic multi-order nonlinear errors due to parasitic interference, leading to nonlinearity correction failures in the case of reflectivity mismatch. We proposes a nonlinearity-suppressed microprobe fiber interferometer to measure long-range displacement with high accuracy. The proposed microprobe interferometer structurally avoids non-elliptic nonlinearities from higher-order harmonics and ensures the effectiveness of the nonlinearity correction method. Moreover, we optimized the micro-sensing probe parameters based on an established multimedia transmission interference model to further improve the measurement accuracy of long-range displacement. Nonlinear errors are reduced from 2.3 nm to 0.92 nm in the application range 0–700 mm. The findings of this study demonstrate that the proposed nonlinearity-suppressed microprobe fiber interferometer is suitable for sub-nanometer accuracy measurements over displacements of several hundred millimeters, especially in limited-space scenarios. It has great potential for industries seeking breakthroughs in long-range displacement measurement, such as robotics, medical devices and manufacturing.

Design and Analysis of Orthogonal Polarization Point Diffraction Pinhole Plate

The pinhole plate is a key component of the point diffraction interferometer (PDI). The reasonable improvement and simulation of this device would enhance the application of point diffraction interferometry technology during the measurement of wavefronts. The traditional point diffraction interferometry measurement method is easily disturbed by environmental noise, making it difficult to obtain high-precision dynamic measurements. This paper introduces a four-step phase-shift PDI that can be employed in a common optical path. By using the principle of the finite-difference time-domain method (FDTD), a simulation model of the orthogonal polarization point diffraction pinhole plate (OP-PDPP) structure is established. The results show that when Cr is used as the film material in the pinhole plate, the parameters include a film thickness of 150 nm, a pinhole diameter of 2 μm, a wire grid period of 150 nm, and a wire grid width of 100 nm; in addition, the comprehensive extinction ratio of the pinhole plate is the greatest and the diffraction wavefront error is the smallest. Finally, the constructed experimental system is used to test the wavefront of a flat sample with a 25.4 mm aperture, and the test results are compared with those of the ZYGO interferometer. The difference in the peak-to-valley (PV) value between the OP-PDI and the ZYGO interferometer measurement is 0.0028λ, with an RMS value difference of 0.0011λ; this verifies the feasibility of the scheme proposed in this paper. The experimental results show that the proposed OP-PDPP is an effective tool for high-precision dynamic measurement.

Advance and prospect in the study of laser interferometry technology for space gravitational wave detection

Advance and prospect in the study of laser interferometry technology for space gravitational wave detection

Glycyrrhetinic acid blocks SARS-CoV-2 infection by activating the cGAS-STING signalling pathway.

Traditional Chinese medicine (TCM) played an important role in controlling the COVID-19 pandemic, but the scientific basis and its active ingredients are still weakly studied. This study aims to decipher the underlying anti-SARS-CoV-2 mechanisms of glycyrrhetinic acid (GA). GA's anti-SARS-CoV-2 effect was verified both in vitro and in vivo. Homogeneous time-resolved fluorescence assays, biolayer interferometry technology, and molecular docking were employed to examine interactions of GA with human stimulator of interferon genes (hSTING). Immunofluorescence staining, western blot, and RT-qPCR were used to investigate nuclear translocation of interferon regulatory factor 3 (IRF3) and levels of STING target genes. Pharmacokinetics of GA was studied in mice. GA could directly bind to Ser162 and Tyr240 residues of hSTING, thus up-regulating downstream targets and activation of the STING signalling pathway. Such activation is crucial for limiting the replication of SARS-CoV-2 Omicron in Calu-3 cells and protecting against lung injury induced by SARS-CoV-2 Omicron infection in K18-ACE2 transgenic mice. Immunofluorescence staining and western blot indicated that GA increased levels of phosphorylated STING, phosphorylated TANK-binding kinase-1, and cyclic GMP-AMP synthase (cGAS). Importantly, GA increased nuclear translocation of IRF3. Pharmacokinetic analysis of GA in mice indicated it can be absorbed into circulation and detected in the lung at a stable level. Activation of the cGAS-STING pathway through the GA-STING-IRF3 axis is essential for the antiviral activity of GA in mice, providing new insights into the potential translation of GA for treating SARS-CoV-2 in patients.

Coherent manipulation of Brewster angles and phase shifts for both left right circularly polarized beams in chiral medium

The Brewster angles and phase shift of both left right circular polarization beams of the probe field is controlled and modified in this manuscript. Subluminal and superluminal propagation of light having group indices of ±200 has been reported. The group velocities of left circularly polarized (LCP) and right circularly polarized (RCP) beam varies to ±1.5×106 m/s while, delay times varies to ±5ns. The peak values of Brewster angles of LCP and RCP beams are calculated 0.786 radian. The maximum value phase shift of LCP and RCP is reported to 31.45 radian at length L=5λ. Strong oscillation in Brewster angles and phase variations of LCP and RCP beams are investigated with azimuthal quantum number of control field and increasing length of position coordinates. The modified results of this manuscript are useful for interferometry and lasers technology.

Frequency-modulated continuous-wave laser interferometry measurement method based on cross-correlation

Frequency-modulated continuous-wave (FMCW) laser interferometry technology holds significant potential for applications in the fields of ultraprecision manufacturing and high-precision sensing. This paper proposes a novel approach among current phase demodulation methods is based on cross-correlation to address the challenge of this technology. On the basis of nonlinear correction of a distributed feedback laser, the intercepted beat frequency signal was first preprocessed with Z-score signal normalization and a smoothing filter. Subsequently, the interference beat signal was subjected to processing using a correlation method to derive the correlation function. Finally, the phase difference between adjacent beat signals was determined by pinpointing the maximum value of the cross-correlation function, enabling accurate displacement demodulation. Experimental validation was performed by constructing an FMCW laser interferometric displacement measurement system. The results indicated that the standard deviation of the displacement error for the cross-correlation method was 2.41 nm during static measurements. Compared to conventional maximum-point method, the static measurement error of the cross-correlation method has been reduced by 1.43 times. In dynamic measurements in the 500 μm range, The measurement error of the cross-correlation method has been reduced by 6.04 times, avoiding the dynamic measurement positioning problem of conventional feature point demodulation methods and making the measurement results more accurate. This advancement holds substantial practical value in the realm of phase demodulation in laser interferometry.

Penthorum chinense Pursh inhibits ferroptosis in cellular and Caenorhabditis elegans models of Alzheimer's disease

Background: Ferroptosis, a unique type of cell death triggered by iron-dependent lipid peroxidation, plays a critical role in the pathogenesis of Alzheimer's disease (AD), a debilitating condition marked by memory loss and cognitive impairment due to the accumulation of beta-amyloid (Aβ) and hyperphosphorylated Tau protein. Increasing evidence suggests that inhibitors of ferroptosis could be groundbreaking in the treatment of AD. Method: In this study, we established in vitro ferroptosis using erastin-, RSL-3-, hemin-, and iFSP1-induced PC-12 cells. Using MTT along with Hoechst/PI staining, we assessed cell viability and death. To determine various aspects of ferroptosis, we employed fluorescence probes, including DCFDA, JC-1, C11 BODIPY, Mito-Tracker, and PGSK, to measure ROS production, mitochondrial membrane potential, lipid peroxidation, mitochondrial morphology, and intracellular iron levels. Additionally, Western blotting, biolayer interferometry technology, and shRNA were utilized to investigate the underlying molecular mechanisms. Furthermore, p-CAX APP Swe/Ind- and pRK5-EGFP-Tau P301L overexpressing PC-12 cells, along with Caenorhabditis elegans (C. elegans) strains CL4176, CL2331, and BR5270, were employed to examine ferroptosis in AD models. Results: Here, we conducted a screening of our natural medicine libraries and identified the ethanol extract of Penthorum chinense Pursh (PEE), particularly its ethyl acetate fraction (PEF), displayed inhibitory effects on ferroptosis in cells. Specifically, PEF inhibited the generation of ROS, lipid peroxidation, and intracellular iron levels. Furthermore, PEF demonstrated protective effects against H2O2-induced cell death, ROS production, and mitochondrial damage. Mechanistic investigations unveiled PEF's modulation of intracellular iron accumulation, GPX4 expression and activity, and FSP1 expression. In p-CAX APP Swe/Ind and pRK5-EGFP-Tau P301L overexpressing PC-12 cells, PEF significantly reduced cell death, as well as ROS and lipid peroxidase production. Moreover, PEF ameliorated paralysis and slowing rate in Aβ and Tau transgenic C. elegans models, while inhibiting ferroptosis, as evidenced by decreased DHE intensity, lipid peroxidation levels, iron accumulation, and expression of SOD-3 and gst-4. Conclusion: Our findings highlight the suppressive effects of PEF on ferroptosis in AD cellular and C. elegans models. This study helps us better understand how ferroptosis affects AD and emphasizes the potential of PCP as a candidate for AD intervention.

Wide-Area Subsidence Monitoring and Analysis Using Time-Series InSAR Technology: A Case Study of the Turpan Basin

Ground subsidence often occurs over a large area. Although traditional monitoring methods have high accuracy, they cannot perform wide-area ground deformation monitoring. Synthetic Aperture Radar (SAR) interferometry (InSAR) technology utilizes phase information in SAR images to extract surface deformation information in a low-cost, large-scale, high-precision, and high-efficiency manner. With the increasing availability of SAR satellite data and the rapid development of InSAR technology, it provides the possibility for wide-area ground deformation monitoring using InSAR technology. Traditional time-series InSAR methods have cumbersome processing procedures, have large computational requirements, and rely heavily on manual intervention, resulting in relatively low efficiency. This study proposes a strategy for wide-area InSAR multi-scale deformation monitoring to address this issue. The strategy first rapidly acquires ground deformation information using Stacking technology, then identifies the main subsidence areas by setting deformation rate thresholds and visual interpretation, and finally employs advanced TS-InSAR technology to obtain detailed deformation time series for the main subsidence areas. The Turpan Basin in Xinjiang, China, was selected as the study area (7474.50 km2) to validate the proposed method. The results are as follows: (1) The basin is generally stable, but there is ground subsidence in the southern plain area, mainly affecting farmland. (2) From 2016 to 2019, the maximum subsidence rate in the farmland area was approximately 0.13 m/yr, with a maximum cumulative subsidence of about 0.25 m, affecting a total area of approximately 952.49 km2. The subsidence mainly occurred from late spring to mid-autumn, while lifting or subsidence mitigation occurred from late autumn to early spring. The study also analyzed the impacts of rainfall, geographical environment, and human activities on subsidence and found that multiple factors, including water resource reduction, overexploitation, geological characteristics, and the expansion of human activities, contributed to the subsidence problem in the Turpan Basin. This method contributes to wide-area InSAR deformation monitoring and the application of InSAR technology in engineering.

Overview and Analysis of Ground Subsidence along China’s Urban Subway Network Based on Synthetic Aperture Radar Interferometry

Deformation along a subway rail network is related to the safe operation of the subway and the stability of construction facilities on the surface, making long-term deformation monitoring imperative. Long-term monitoring of surface deformation along the subway network and statistical analysis of the overall deformation situation are lacking in China. Therefore, targeting 35 Chinese cities whose subway mileage exceeds 50 km, we extracted their surface deformation along subway networks between 2018 and 2022, using spaceborne synthetic aperture radar (SAR) interferometry (InSAR) technology and Sentinel-1 satellite data. We verified the results with the continuous global navigation satellite system (GNSS) stations’ data and found that the root mean square error (RMSE) of the InSAR results was 3.75 mm/year. Statistical analysis showed that ground subsidence along the subways was more prominent in Beijing, Tianjin, and other areas in the North China Plain, namely Kunming (which is dominated by karst landforms), as well as Shanghai, Guangzhou, Qingdao, and other coastal cities. In addition, an analysis revealed that the severity of surface subsidence correlated positively with a city’s gross domestic product (GDP) with a Pearson correlation of 0.787, since the higher the GDP, the more frequent the construction and maintenance of subway, and the more commuters there are, which in turn exacerbates the disturbance to the surface. Additionally, the type of land cover also affects the ground deformation. Our findings provide a reference for constructing, operating, and maintaining the urban subway systems in China.

Formation design for interplanetary shock imaging interferometric array

Continuous monitoring of interplanetary coronal mass ejections (CMEs) plays a vital role in modelling of CME heliospheric propagation and improving space weather prediction, which remains a significant challenge due to the lack of effective observations. The type II radio bursts produced by CME-driven interplanetary shocks provide an opportunity for us to imaging the CMEs and their shocks through interferometry technology. This paper proposes a concept for the program of CME/shock imaging through low-frequency radio interferometry based on satellite formation. The formation consists of one mother satellite and seven daughter satellites, forming an interferometric array with the equivalent aperture size of 100 km to conduct three-dimensional tomography of CME/shock at 0.1 MHz ∼ 30 MHz. Two types of satellite formations, including a linear formation and a coplanar formation, are designed to provide different options of baseline distributions. Then, the fuel budgets for formation deployment and maintenance are analyzed. Besides, GNSS (Global Navigation Satellite System) differential positioning is discussed for relative measurement between the mother and daughter satellites. Finally, imaging simulations are performed to demonstrate the imaging performances of the interferometric array. The proposed interferometric formation will furnish essential insights into the Earth-directed CME propagation and provide critical and unprecedented observation data for space weather forecasting.

Аналіз деформацій земної поверхні у районі гірничих виробок рудника «Калуш» за даними радіолокаційного знімання 2018–2022

The purpose of this work is to analyze the current state of geodynamic activity of the earth’s surface in the territory of the city of Kalush based on satellite radar monitoring data for the period 2018-2022. Method. The input data for the study were 36 medium-resolution (C-band) radar images of the Sentinel-1A satellite. The method of persistent scatterers (PSInSAR), which is an advanced technology of differential interferometry (DInSAR), was used to process the results of radar acquisition. The PSI method was implemented using the Stanford Method for Persistent Scatterer (StaMPS) software package. The results. Maps of the average rates of deformation of the earth’s surface in the area of the mine fields of the “Kalush” mine were obtained. The rate of subsidence of the territories above the mining works reaches 4 mm/year. The accuracy of determining the deformation rates is an order of magnitude higher than their values, which indicates the reliability of the obtained results. The nature of subsidence, for most areas, has a linear model of deformation processes. The maximum rates of deformation of the earth’s surface are observed over the Khotyn sylvinite field, but the rates of subsidence have decreased significantly compared to the previous data of the monitoring carried out in 2016-2017. The scientific novelty consists in obtaining the updated results of the monitoring of the territories above the mining operations of the Kalush mine using the InSAR method for the period from June 2018 to December 2022. The practical significance of the research results is not only in determining the quantitative indicators of deformations, but also in obtaining data for further planning and improvement of the complex geodynamic monitoring system using ground and satellite measurements.

Discovery of drug targets based on traditional Chinese medicine microspheres (TCM-MPs) fishing strategy combined with bio-layer interferometry (BLI) technology

Target discovery of natural products is a key step in the development of new drugs, and it is also a difficult speed-limiting step. In this study, a traditional Chinese medicine microspheres (TCM-MPs) target fishing strategy was developed to discover the key drug targets from complex system. The microspheres are composed of Fe3O4 magnetic nanolayer, oleic acid modified layer, the photoaffinity group (4- [3-(Trifluoromethyl)-3H-diazirin-3-yl] benzoic acid, TAD) layer and active small molecule layer from inside to outside. TAD produces highly reactive carbene under ultraviolet light, which can realize the self-assembly and fixation of drug active small molecules with non-selective properties. Here, taking Shenqi Jiangtang Granules (SJG) as an example, the constructed TCM-MPs was used to fish the related proteins of human glomerular mesangial cells (HMCs) lysate. 28 differential proteins were screened. According to the target analysis based on bioinformatics, GNAS was selected as the key target, which participated in insulin secretion and cAMP signaling pathway. To further verify the interaction effect of GNAS and small molecules, a reverse fishing technique was established based on bio-layer interferometry (BLI) coupled with UHPLC-Q/TOF-MS/MS. The results displayed that 26 small molecules may potentially interact with GNAS, and 7 of them were found to have strong binding activity. In vitro experiments for HMCs have shown that 7 active compounds can significantly activate the cAMP pathway by binding to GNAS. The developed TCM-MPs target fishing strategy combined with BLI reverse fishing technology to screen out key proteins that directly interact with active ingredients from complex target protein systems is significant for the discovery of drug targets for complex systems of TCM.

Insights into Zwitterionic Surfactant Interactions at the Oil-Water Interface by Interferometry Experiments and MDS Calculations.

In this work, the interaction performance of zwitterionic surfactant [dodecyl dimethyl sulfopropyl betaine (DSB-12) and hexadecyl dimethyl sulfopropyl betaine (DSB-16)] at the n-octadecane oil surface is investigated from experimental and simulation insights. For a macroscopic experiment, interfacial interferometry technology was developed for real-time monitor interaction performances and to obtain the quantitative interfacial thickness and mass results. The Langmuir model was characterized by thermodynamic analysis, deducing the aggregation spontaneity of DSB-16 > DSB-12 with ΔGagg(DSB-16) = -5.94 kJ mol-1 < ΔGagg(DSB-12) = 24.08 kJ mol-1. A three-step dynamic model (adsorption, arrangement, and aggregation) was characterized by kinetic analysis, indicating arrangement process as slow-limiting step with k2(arr) < k1(ads), k3(agg). For microscopic simulation, and molecular dynamic (MD) method was utilized to theoretically investigate interaction performances and obtain the interfacial configuration and energy results. The interaction stability and interaction strength were indicated to be DSB-16 > DSB-12 with differences of final energy ΔEfin = 48-88 kcal mol-1. The interaction mechanism was explained by proposing the model of "response enhancement" and "deposition activity" for DSB-16 interactions, and "response decrease" and "elution activity" for DSB-12 interactions. The different performances can be attributed to the different interaction forms and forces of surfactants. This work provided a platform for performance and mechanism investigation between the surfactant molecule and oil surface, which is of great significance in reservoir exploitation and enhanced oil recovery (EOR).

Formation-flying interferometry in geocentric orbits

Context. Spacecraft formation flying serves as a method of astronomical instrumentation that enables the construction of large virtual structures in space. The formation-flying interferometry generally requires very high control accuracy, and extraterrestrial orbits are typically selected. To pave the way for comprehensive missions, proposals have been made for preliminary space missions, involving nano- or small satellites, to demonstrate formation-flying interferometry technologies, especially in low Earth orbits. From a theoretical perspective, however, it is unknown where and to what extent feasible regions for formation-flying interferometry should exist in geocentric orbits. Aims. This study aims to demonstrate the feasibility of formation-flying interferometry in geocentric orbits in which various perturbation sources exist. Geocentric orbits offer the advantage of economic accessibility and the availability of proven formation-flying technologies tailored for Earth orbits. Its feasibility depends on the existence of specific orbits that satisfy a small-disturbance environment with good observation conditions. Methods. Spacecraft motions in Earth orbits subjected to perturbations are analytically modeled based on celestial mechanics. The magnitudes of the accelerations required to counteract these perturbations are characterized by parameters such as the semimajor axis and the size of the formation. Results. Small-perturbation regions tend to appear in higher-altitude and shorter-separation regions in geocentric orbits. Candidate orbits are identified in high Earth orbits for the triangular laser-interferometric gravitational-wave telescope, which is 100 km in size, and in medium Earth orbits for the linear astronomical interferometer, which is 0.5 km in size. A low Earth orbit with a separation of approximately 0.1 km may be suitable for experimental purposes. Conclusions. Geocentric orbits are potentially applicable for various types of formation-flying interferometry.

Analysis of phase calculation error introduced by the extinction ratio in instantaneous phase shifting interference.

Instantaneous phase shifting interferometry technology, the core component of which is the pixel micropolarizer camera, has been widely used in commercial interferometers. This technology has the superiority of single-frame acquisition, vibration insensitivity, and no need for phase shifting devices. However, due to manufacturing defects and accuracy limitations, the extinction ratios (ER) of the micropolarizer array are different and fairly small, directly affecting the phase calculation accuracy. This paper initially derives a theoretical expression for the phase calculation error introduced by the extinction ratio (ER) and proposes the error correction model to reduce phase calculation errors caused by the extinction ratio. The theoretical analysis can serve as an important basis for accurately assessing the polarization characteristics of a pixel micropolarizer camera. Quantifying the impact of the extinction ratios provides significant support for the selection of polarization equipment. In addition, the paper proposes a calibration model to improve measurement accuracy, which can serve as an effective means to reduce the impact of the extinction ratio (ER). The innovative research content revealed the influence of extinction ratio (ER), serving as a valuable complement to the existing analysis and research on extinction ratio (ER).