Search Results (17)

We theoretically investigate geometric Stückelberg interferometry in a doubly driven optical lattice clock (OLC). By tuning the relative phase between the two driving fields, we control the relative sign of the effective coupling strengths at the avoided crossings. Within the adiabatic-impulse model, we analyze the time evolution of the two-level system, where nonadiabatic transitions occur only near the crossing points and adiabatic evolution takes place between them. We show that, besides the usual dynamical phase and the Stokes phase, a gauge-invariant noncyclic geometric phase contributes to the final transition probability. This geometric contribution yields a stable $\pi$-phase shift in the Stückelberg interference fringes. Moreover, we demonstrate that, under realistic experimental conditions, this geometric Stückelberg interferometer remains insensitive to inhomogeneities in atom-light coupling arising from the finite temperature of the atomic ensemble. Our results provide a general framework for engineering and detecting geometric phases on the OLC platform. Full article

In the field of optical metrology, wavelength-tunable interferometry is widely used to obtain the phase information of measured objects. Due to the modulo 2π operation, the extracted phase is inherently wrapped into the range of −π to π, which necessitates phase unwrapping to restore the actual phase profile. However, traditional phase-shifting methods suffer from low accuracy caused by phase shift miscalibration, coupling signals, atmospheric turbulence, and measurement noise. To address these issues, this paper proposes a deep learning-based phase-unwrapping method using a deep convolutional neural network, which formulates the unwrapping task as a multiclass classification problem. The proposed method employs an encoder–decoder residual network (ResNet) architecture that treats phase unwrapping as a pixel-wise semantic segmentation task, enabling end-to-end continuous phase reconstruction. It also adopts a 2N − 1 algorithm-based dataset generation strategy that inherently suppresses phase-shift miscalibration and harmonic coupling errors without relying on Zernike polynomial representations. Furthermore, a large-scale data augmentation pipeline (16-fold expansion to 20,992 training samples) endows the network with a strong generalization capability and noise immunity. The quantitative experimental results demonstrate that the proposed method achieves 100% phase-unwrapping accuracy under noise-free conditions and 99.03% accuracy under severe noise (standard deviation = 1.5), substantially outperforming the quality-guided method (QG, 69.87%) and the transport-of-intensity equation method (TIE, 77.53%) under identical conditions. On real interferometric data acquired using a wavelength-tuning interferometer, the proposed method successfully unwraps the phase even under heavy noise where conventional methods fail completely. These results confirm that the proposed method has favorable noise resistance and potential applicability in high-precision optical metrology. Full article

Point diffraction interferometers (PDIs) utilize a near-ideal spherical wavefront generated by point diffraction as the reference, providing a high-quality measurement benchmark independent of reference surface quality. In this work, a compact dual-oblique-fiber heterodyne phase-shifting point diffraction interferometer (DOF-HPSPDI) is proposed. A dual-oblique-fiber point diffraction wavefront generator (DOF-PDWG) is designed to generate the reference and measurement beams separately. The proposed configuration enables efficient utilization of the divergence of the fiber-generated diffracted wavefront, while the reflective structure at the fiber end faces allows the two beams to propagate along a common path. In addition, the close spacing between the two oblique fibers minimizes system errors. Heterodyne phase-shifting interferometry (HPSI) is employed to retrieve the wavefront phase from the interferograms. Theoretical system errors are analyzed through simulations, and experiments verify the feasibility and stability of the proposed system. This work provides a low-cost, compact, and highly stable point diffraction interferometer, offering a promising device for high-precision optical testing and sub-aperture stitching of large-aperture optical components. Full article

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

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

The three spacecraft of the space gravitational wave antenna employ heterodyne interferometry to mitigate the effects of Doppler shift. Constrained by laser relative intensity noise (RIN) and the sampling frequency constraints of phase readout circuits, the widespread adoption of fixed offset frequencies effectively regulates the frequency of heterodyne interferometric beat notes within a reasonable frequency domain of [5 MHz, 25 MHz]. In this work, a high-precision fitness genetic algorithm for heterodyne interferometry is utilized to generate the initial offset frequency distribution scheme. To address issues with unreasonable switching times and offset frequency settings in the initial scheme for partial frequency domains, optimization strategies are proposed from three aspects: frequency domain selection extension, switch times control, and numerical low frequency. Results demonstrate that the optimization of frequency domain selection extension narrows the reasonable frequency domain to [5 MHz, 15 MHz] and [7 MHz, 17 MHz]. Optimization of switch times control ensures that switching times of offset frequency distribution scheme generated under the settings of [6 MHz, 17 MHz] and wider frequency domains can be controlled within a reasonable range of 6 to 13 times. Fixed offset frequency settings are generally reduced by 24.3% after low-frequency optimization. This methodology and result can provide a reliable reference for Program Taiji and even related space gravitational wave antenna projects. Full article

Due to its high precision, phase-shifting interferometry (PSI) is a commonly used optical component detection method in interferometers. However, traditional PSI, which is susceptible to environmental factors, is costly, with piezoelectric ceramic transducer (PZT) being a major contributor to the high cost of interferometers. In contrast, two-frame random interferometry does not require precise multiple phase shifts, which only needs one random phase shift, reducing control costs and time requirements, as well as mitigating the impact of environmental factors (mechanical vibrations and air turbulence) when acquiring multiple interferograms. A novel method for wavefront reconstruction using two-frame random interferometry based on Swin-Unet is proposed. Besides, improvements have been made on the basis of the established algorithm to develop a new wavefront reconstruction method named Phase U-Net plus (PUN+). According to training the Swin-Unet and PUN+ with a large amount of simulated data generated by physical models, both of the methods accurately compute the wrapped phase from two frames of interferograms with an unknown phase step (except for multiples of $\pi$). The superior performance of both methods is effectively showcased by reconstructing phases from both simulated and real interferograms, in comprehensive comparisons with several classical algorithms. The proposed Swin-Unet outperforms PUN+ in reconstructing the wrapped phase and unwrapped phase. Full article

Curators have developed preventive conservation strategies and usually try to control the temperature (T) and relative humidity (RH) variations in the museum rooms to stabilise the artworks. The control systems chosen by museums depend on the size and age of the building, the financial means and the strategies that can be adapted. However, there is a lack of methods that can monitor mechanical changes or chemical reactions of objects in real-time or regularly. It would therefore ideally be preferable to monitor each of them to alert them to preserve them. For this purpose, a non-destructive, non-contact, full-field technique, Digital Holographic Speckle Pattern Interferometry (DHSPI), has already been developed and allows direct tracking of changes on the surface of artworks. This technique is based on phase-shifting speckle interferometry and gives the deformation of the surface below the level of the micro-meter of the analysed object. In order to monitor the deformation continuously, a large number of images are acquired by DHSPI and have to be processed. The existing process consists of removing noise from the interferogram, unwrapping this image, and deriving and displaying a 2D or 3D deformation map. In order to improve the time and accuracy of processing the imaging data, a simpler and faster processing method is developed. Using Matlab^®, a denoising methodology for the interference pattern generated during data acquisition is created, based on a stationary wavelet transform. The unwrapped image is calculated using the CPULSI (Calibrated Phase Unwrapping based on Least-Squares and Iterations) algorithm as it gives the fastest results among the tested methods. The unwrapped phase is then transformed into surface displacement. This process performs these steps for each interferogram automatically. It allows access to 2D or 3D deformation maps. Full article

In the past two decades, ground-based synthetic aperture radars (GB-SARs) have developed rapidly, providing a large amount of SAR data in minutes or even seconds. However, the real-time processing of big data is a challenge for the existing GB-SAR interferometry (GB-InSAR) technology. In this paper, we propose a near-real-time GB-InSAR method for monitoring slope surface deformation. The proposed method uses short baseline SAR data to generate interferograms to improve temporal coherence and reduce atmospheric interference. Then, based on the wrapped phase of each interferogram, a network method is used to estimate and remove systematic errors (such as atmospheric delay, radar center shift error, etc.). After the phase unwrapping, a least squares estimator is used for the overall solution to obtain the initial deformation parameters. When new data are added, a sequential estimator is used to combine the previous processing results and dynamically update the deformation parameters. Sequential estimators could avoid repeated calculations and improve data processing efficiency. Finally, the method is validated with the measured data. The results show that the average deviation between the proposed method and the overall estimation was less than 0.01 mm, which could be considered a consistent estimation accuracy. In addition, the calculation time of the sequential estimator was less sensitive than the total amount of data, and the time-consuming growth rate of each additional period of data was about 1/10 of the overall calculation. In summary, the new method could quickly and effectively obtain high-precision surface deformation information and meet the needs of near-real-time slope deformation monitoring. Full article

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. Full article

Straightness error compensation is a critical process for high-accuracy topography measurement. In this paper, a straightness measurement system was presented based on the principle of fringe interferometry. This system consisted of a moving optical flat and a stationary prism placed close to each other. With a properly aligned incident light beam, the air wedge between the optical flat and the prism would generate the interferogram, which was captured by a digital camera. When the optical flat was moving with the motion stage, the variation in air wedge thickness due to the imperfect straightness of the guideway would lead to a phase shift of the interferogram. The phase shift could be calculated, and the air wedge thickness could be measured accordingly using the image processing algorithm developed in-house. This air wedge thickness was directly correlated with the straightness of the motion stage. A commercial confocal sensor was employed as the reference system. Experimental results showed that the repeatability of the proposed film interferometer represented by σ was within 25 nm. The measurement deviation between the film interferometer and the reference confocal sensor was within ±0.1 µm. Compared with other interferometric straightness measurement technologies, the presented methodology was featured by a simplified design and good environment robustness. The presented system could potentially be able to measure straightness in both linear and angular values, and the main focus was to analyze its linear value measurement capability. Full article

The increasing rate of antimicrobial resistance (AMR) in pathogenic bacteria is a global threat to human and veterinary medicine. Beyond antibiotics, antimicrobial peptides (AMPs) might be an alternative to inhibit the growth of bacteria, including AMR pathogens, on different surfaces. Biofilm formation, which starts out as bacterial adhesion, poses additional challenges for antibiotics targeting bacterial cells. The objective of this study was to establish a real-time method for the monitoring of the inhibition of (a) bacterial adhesion to a defined substrate and (b) biofilm formation by AMPs using an innovative thermal sensor. We provide evidence that the thermal sensor enables continuous monitoring of the effect of two potent AMPs, protamine and OH-CATH-30, on surface colonization of bovine mastitis-associated Escherichia (E.) coli and Staphylococcus (S.) aureus. The bacteria were grown under static conditions on the surface of the sensor membrane, on which temperature oscillations generated by a heater structure were detected by an amorphous germanium thermistor. Bacterial adhesion, which was confirmed by white light interferometry, caused a detectable amplitude change and phase shift. To our knowledge, the thermal measurement system has never been used to assess the effect of AMPs on bacterial adhesion in real time before. The system could be used to screen and evaluate bacterial adhesion inhibition of both known and novel AMPs. Full article

Tracking moving masses in several degrees of freedom with high precision and large dynamic range is a central aspect in many current and future gravitational physics experiments. Laser interferometers have been established as one of the tools of choice for such measurement schemes. Using sinusoidal phase modulation homodyne interferometry allows a drastic reduction of the complexity of the optical setup, a key limitation of multi-channel interferometry. By shifting the complexity of the setup to the signal processing stage, these methods enable devices with a size and weight not feasible using conventional techniques. In this paper we present the design of a novel sensor topology based on deep frequency modulation interferometry: the self-referenced single-element dual-interferometer (SEDI) inertial sensor, which takes simplification one step further by accommodating two interferometers in one optic. Using a combination of computer models and analytical methods we show that an inertial sensor with sub-picometer precision for frequencies above 10 mHz, in a package of a few cubic inches, seems feasible with our approach. Moreover we show that by combining two of these devices it is possible to reach sub-picometer precision down to 2 mHz. In combination with the given compactness, this makes the SEDI sensor a promising approach for applications in high precision inertial sensing for both next-generation space-based gravity missions employing drag-free control, and ground-based experiments employing inertial isolation systems with optical readout. Full article

A convenient and powerful method is proposed and presented to find the unknown phase shifts in three-step generalized phase-shifting interferometry. A slight-tilt reference of 0.1 degrees is employed. As a result, the developed theory shows that the unknown phase shifts can be simply extracted by subtraction operations. Also, from the theory developed, the tilt angle of the tilt reference can also be calculated, which is important as it allows us to extract the object wave precisely. Numerical simulations and optical experiments were performed to demonstrate the validity and efficiency of the proposed method. The proposed slight-tilt reference allows the full and efficient use of the space-bandwidth product of the limited resolution of digital recording devices as compared to the situation in standard off-axis holography where typically several degrees for off-axis angle is employed. Full article

The measurement of in-plane displacement in two orthogonal directions is of considerable significance for modern industries. This paper reports on a spatial carrier phase-shift digital speckle pattern interferometry (DSPI) for the simultaneous measurement of in-plane displacement in two orthogonal directions. The object is illuminated from a single direction and observed from four symmetrical directions simultaneously. One pair of the four observation directions is sensitive to in-plane displacement in one direction, and the other pair is sensitive to in-plane displacement in the perpendicular direction, resulting in the displacement in two directions being measured independently. The polarization property of light is used to avoid cross-interference between the two pairs of beams. Spatial carrier frequencies are generated by aperture misalignment, and the displacement in two directions is modulated onto the same interferogram. With a spatial carrier phase-shift technique, the displacement can be separated in the frequency domain and the phase can be evaluated from a single interferogram in real time. The capability of DSPI is described by theoretical discussions and experiments. Full article