Shearing Interference Research Articles

Robust optical singularity detection enabled by spin-synchronized shearing interference

Singular beams carrying phase and polarization singularities have been extensively studied for applications in optical communication, quantum information processing, optical imaging, and other fields. However, developing a robust method to detect optical singularity that is insensitive to wavelength, polarization, and illumination position remains a significant challenge. In this study, we propose and demonstrate a robust optical singularity detection scheme based on spin-synchronized shearing interference (SSSI) using spin-dependent gradient phase modulation of a quarter-wave liquid–crystal polarization grating. Since the spin-dependent gradient phase modulation of the polarization grating is wavelength-independent, and the two circular bases of the incident field can be measured simultaneously, the proposed method is robust to wavelength and polarization. Additionally, we have verified that SSSI performs well in detecting multi-singularity cylindrical vector beam. This work provides a practical and straightforward scheme for robust optical singularity detection.

Error correction analysis of wavefront testing in quadriwave lateral shearing interferometry

Quadriwave lateral shearing interferometry (QWLSI) is based on double birefringent crystals of a beam displacer (DBCs-BD), which can generate the lateral shearing interference wavefront of four beams of overlapped replicas in the DBCs-BD orthogonal directions. When the replica waves are overlapped incident to the analyzer and the direction of the transmission axis is set as 45° or 135°, the QWLSI’s polarization interferogram can be obtained. This paper deduces the principle of QWLSI based on the DBCs-BD and presents the analysis of orthogonal error influence based on the DBCs-BD and the phase retrieval error of QWLSI when shear displacement by tilted incident on the DBCs-BD. In our investigation, we have established the correction range of the PBD’s orthogonal angle error is within −0.5∘−0.5∘, the maximum error in PV is 0.0012λ, and the maximum error in RMS is 1.3789×10−4λ in wavefront reconstruction. Moreover, when the testing light tilts to incident on the PBD in the range of −0.4∘−0.4∘, correction of the shear distance is used for wavefront reconstruction to achieve a high-precision wavefront testing result. Finally, the experiment shows that QWLSI based on the DBCs-BD exhibits feasibility and high precision.

Shear-interference assisted deep-learning for enhancing spatially multiplexing capacity of free-space communication

The information capacity is a critical measure in free-space optical (FSO) communication. Traditional mode-multiplexing techniques employed in optical communication utilizing Laguerre-Gaussian beams (LGBs) necessitate proper topological charge interval to prevent mode-crosstalk. In this paper, we propose a novel approach that integrates deep learning (DL) into the LGB-based optical communication model, incorporating shearing interference techniques. This combination enables the FSO system to achieve the theoretical limit of capacity, resulting in a remarkable 300 % increase in information capacity compared to traditional techniques. Experimental results demonstrate that the constructed neural network attains a flawless pattern recognition accuracy of 100 %. Additionally, we evaluate various partially coherent light scenarios under the influence of beam decoherence. The results reveal that accurate discrimination of multiplexing patterns is maintained when the fringe contrast exceeds 0.43. Even at a degraded contrast level of 0.18, the recognition accuracy remains impressively high at 91.16 %. To demonstrate practicality, we successfully encode and transmit a cyan-magenta-yellow-black (CMYK) color image using the proposed system, achieving a low bit error rate of 7.5 × 10-5. These findings highlight the potential of DL-assisted mode-division multiplexing for future optical communication applications.

Single-shot deterministic complex amplitude imaging with a single-layer metalens.

Conventional imaging systems can only capture light intensity. Meanwhile, the lost phase information may be critical for a variety of applications such as label-free microscopy and optical metrology. Existing phase retrieval techniques typically require a bulky setup, multiframe measurements, or prior information of the target scene. Here, we proposed an extremely compact system for complex amplitude imaging, leveraging the extreme versatility of a single-layer metalens to generate spatially multiplexed and polarization phase-shifted point spread functions. Combining the metalens with a polarization camera, the system can simultaneously record four polarization shearing interference patterns along both in-plane directions, thus allowing the deterministic reconstruction of the complex amplitude light field in a single shot. Using an incoherent light-emitting diode as the illumination, we experimentally demonstrated speckle-noise-free complex amplitude imaging for both static and moving objects with tailored magnification ratio and field of view. The miniaturized and robust system may open the door for complex amplitude imaging in portable devices for point-of-care applications.

Simulation analysis of iterative wavefront reconstruction algorithm for center-offset radial shearing interference

Simulation analysis of iterative wavefront reconstruction algorithm for center-offset radial shearing interference

Mutual aid instead of mutual restraint: interactive probing for topological charge and phase of a vortex beam of large aberrations

An imperfect propagation environment or optical system would introduce wavefront aberrations to vortex beams. The phase aberrations and orbital angular momentum in a vortex beam are proved to be mutually restrictive in parameter measurement. Aberrations make traditional topological charge (TC) probing methods ineffective while the phase singularity makes phase retrieval difficult due to the aliasing between the wrapped phase jump and the vortex phase jump. An interactive probing method is proposed to make measurements of the aberrated phase and orbital angular momentum in a vortex beam assist rather than hinder each other. The phase unwrapping is liberated from the phase singularity by an annular shearing interference technique while the TC value is determined by a Moiré technique immune to aberrations. Simulation and experimental results proving the method effective are presented. It is of great significance to judge the characteristics of vortex beams passing through non-ideal environments and optical systems.

Dynamic imaging of three-dimensional temperature field via three-directional wavelength modulated lateral shearing interferometry

A three-directional wavelength modulated lateral shearing interference system was proposed for the dynamic three-dimensional visualization of a temperature field. The laser emitted from a distributed feedback (DFB) laser was divided into three beams by a fiber beam splitter. The beams were spatially expanded and passed through the flame in three directions of 0°, 120° and 240°, respectively. The three interferograms formed by reflections from the front and back surfaces of the parallel glass plates were spatially converged into the lens of a high-speed camera. Multiple plane mirrors were utilized to reflect the beams. The size of the region of interest (ROI) was −20 ∼ 20 mm in both x and z directions and 5 ∼ 30 mm in y direction, with a spatial resolution of 200 μm in all directions. A three-dimensional sensitivity matrix was modeled, and the simultaneous algebraic reconstruction technique (SART) was used for layer-by-layer imaging to achieve three-dimensional flame monitoring. Numerical simulations verified the effectiveness of the algorithm qualitatively and quantitatively. In experiments, the temperature distributions of four cases of flames, namely, steady diffused flame, partially blocked diffused flame, dynamic acoustically excited flame and the flame after ignition, were reconstructed at 1k frames per second (fps). The flame structures and temporal variations of temperature distributions were clearly visualized, demonstrating the ability of the system in fast monitoring of three-dimensional dynamic temperature fields.

New-Type Shearing Interference Detection System Based on Double-Grating Structure for Suppressing the Skylight Background.

To overcome the influence of the daytime skylight background on long-distance optical detection, a new type of shearing interference detection system was proposed to improve the detection performance of the traditional detection system for finding dark objects such as dim stars during the daytime. This article focuses on the basic principle and mathematical model as well as the simulation and experimental research of the new type of shearing interference detection system. The comparison of the detection performance between this new-type detection system and the traditional system is also carried out in this article. The experimental results show that the detection performance of the new type of shearing interference detection system is significantly better than that of the traditional system, and the image signal-to-noise ratio of this new-type system (about 13.2) is much higher than that of the best result of the traditional detection system (about 5.1).

Effects and elimination of image grating defocusing on a double-Ronchi shearing interference field.

Double-Ronchi shearing interferometry is a promising wavefront aberration measurement system for advanced lithography projection lens systems. The image grating defocusing is a key systematic error of the interferometer. However, the effects and elimination of this error have not been systematically researched. In this work, the interference field effects caused by the image grating defocusing are analyzed based on the theories of scalar diffraction, and a method to eliminate the effects is proposed. The theoretical analysis has been verified by a simulation and experiments. The results show that the error of image grating defocusing is mainly expressed as the Zernike Z4 term and Z9 term in the reconstructed wavefront, and the coefficients of Z4, and Z9, respectively, are related to NA2, NA4, and the defocus distance z. When the numerical aperture (NA) of the under-test projection lens is 0.6, 99.8384% of the errors caused by the image grating defocusing can be removed. When the NA is reduced to 0.3, 99.9854% of the errors can be removed. Additionally, when the NA is less than 0.1, almost all the errors can be eliminated.

High-precision micro-displacement measurement in a modified reversal shearing interferometer using vortex beams

We propose a novel micro-displacement measurement system that employs a modified reversal shearing interference structure based on vortex beam interference. The micro-displacement in the measurement path caused a change in the light path and resulted in an optical path difference (OPD) between the reference and measurement paths. This OPD led to the rotation of the petal-like pattern obtained by the interference between two paths. The rotation angle of the petal-like pattern was proportional to the OPD caused by micro-displacement. We used the virtual phase-shifting method to extract the helical phase front, and the Radon transform to measure the angle of the helical phase front. We achieved a high-accuracy micro-displacement measurement with a measurement error of less than 0.067 nm when using a vortex beam with a topological charge of six. This system has an extremely simple structure and is easy to adjust. It is of great significance to the miniaturized design of high-precision displacement sensors.

Quadriwave lateral shearing interferometry based on double birefringent crystals of beam displacer.

A quadriwave lateral shearing interferometry (QWLSI) is proposed based on double birefringent crystals of a beam displacer (DBCs-BD). The DBCs-BD is formed by adopting two birefringent crystals of a polarization beam displacer (PBD), which can generate the lateral shearing interference waves of four beams of overlapped replicas in the DBCs-BD orthogonal directions. When the replica waves are overlapped incident to the analyzer, and the direction of the transmission axis is set as 45° or 135°, the QWLSI's polarization interferogram can be obtained. The high-precision phase can be obtained by simple spectrum denoising and performing the Fourier transform of the resulting interferogram. We deduce the principle of QWLSI in detail, and the wavefront distribution can be achieved by the phase calculation. The experiment shows that the DBCs-BD-QWLSI exhibits feasibility and high precision.

Effects of illumination non-uniformity on the double-Ronchi lateral shearing interference field.

Double-Ronchi shearing interferometry is a promising technique for insitu wavefront aberration measurement of the projection lens in photolithography systems. In practice, the non-uniformity of illumination is an important issue affecting the interference field, which has not been systematically researched. In this work, the interference field errors caused by non-uniform illumination distributions are analyzed utilizing the theories of scalar diffraction. The theoretical analysis has been verified by simulation and fundamental experiments. Results show that the uniformity requirements for the abrupt annular, Gaussian, and uniform random illumination distribution (RD) are 0.9434, 0.8439, and 0.2751, respectively, with a shear ratio of 5% and a relative wavefront reconstruction error of 1%. The uniformity of the three distributions is reduced to 0.6513, 0.5864, and 0.1234, respectively, with the shear ratio shrunk to 3%. When the shear ratio is less than 1%, there is no specific requirement for illumination uniformity.

Phase unwrapping algorithm for images with local high-density noise.

Due to undersampling and the local phase with local high-density noise, it is still difficult to develop a robustphase unwrapping algorithm. In order to resolve this issue, here, we propose what we believe to be a novel multiple path-following phase unwrapping (MPIPU) algorithm based on the shearing interference principle to recover the undersampling phase (non-noise). By calculating the unwrapping coefficient k, the phase iteration filling algorithm based on least-squares is developed for the high-density noise region in order to reconstruct the three-dimensional surface topography of interferometric synthetic aperture radar (InSAR) data. The proposed algorithm takes advantage of the MPIPU's ability to fill in the missing phase with fitting data and can successfully suppress the error transfer caused by the blocky noise phase iteration process. Several experiments are conducted using both simulated and actual InSAR image data. The experimental findings show that the proposed method can achieve robust phase unwrapping performance on a phase of local high-density noise.

Analysis of the influence of simultaneous phase-shifting shearing interference polarizer

The aspheric surface testing system based on the shearing interference principle is used to better analyze how the installation and fabrication errors of linear polarizer affects the precision of the aspheric surface. The effects of the angle error of the linear polarizer and the phase-shifting error of the wave plate on the reconstruction of the aspheric surface are studied. Constructing the model of the Jones matrix with the error term system, the reconstruction surface and residual after the corresponding error system are obtained using the four-step phase-shifting and differential Zernike method. The polarizer array of an angle of θ was varied from ( θ − 1 deg ) to ( θ + 2 deg ) every 0.2 deg, and the changes of the fitting surface and the residual surface were simulated. The phase-shifting error of the simulated one-fourth wave plate was <λ / 300. Then, the change of the fitting surface and residual surface when these two errors exist at the same time were simulated. The simulation results show that the influence of the phase-shifting error of the wave plate on the fitting surface is much greater than the angle error of the polarizer array. When assembling the interference system, the phase-shifting error of the wave plate should be <λ / 300 when the light transmission angle error of the polarizer array is between −0.2 deg and 0.2 deg, which will ensure the testing precision of the aspheric surface testing system.

Simultaneous two-step phase-shifting lateral shearing interferometry for aspherical surface based on an orthogonal shear displacer

A novel simultaneous two-step phase-shifting lateral shearing interferometry for aspherical surface based on an orthogonal shear displacer (OSD) is proposed, it is an effective technological measure of aspherical surface measurement, to effectively solve the non-uniformity of light intensity and limited transmission order caused by the beam displacer device. The OSD system is formed by the adoption of two-crystal polarization parallel beam displacers (PBDs), which makes it achieve the orthogonal shearing in the x- and y-directions simultaneously. A quarter-wave plate (QWP) is used to generate the desired phase-shifting, and four beam lateral shearing interference waves are simply generated in OSD orthogonal directions without any bulky and complicated optical components. The phase maps of the aspherical surface can be instantly obtained using the spatial phase-shifting technique with a polarization pixelated mask (or called micro-polarization array: MPA) integrated into CCD. In this study, the proposed method was theoretically described and simulation results were analyzed. The simultaneous two-step phase-shifting lateral shearing interference fringes can be extracted in real-time with the MPA. The experiment results compared with the ZYGO interferometer were performed, and proved that the measurement error is not more than 2%. This interferometry has made it possible to improve the stability and feasibility of aspherical surface testing experiments.

Single-Shot Quantitative Polarization Imaging of Complex Birefringent Structure Dynamics.

Polarization light microscopes are powerful tools for probing molecular order and orientation in birefringent materials. While a number of polarization microscopy techniques are available to access steady-state properties of birefringent samples, quantitative measurements of the molecular orientation dynamics on the millisecond time scale have remained a challenge. We propose polarized shearing interference microscopy (PSIM), a single-shot quantitative polarization imaging method, for extracting the retardance and orientation angle of the laser beam transmitting through optically anisotropic specimens with complex structures. The measurement accuracy and imaging performance of PSIM are validated by imaging a birefringent resolution target and a bovine tendon specimen. We demonstrate that PSIM can quantify the dynamics of a flowing lyotropic chromonic liquid crystal in a microfluidic channel at an imaging speed of 506 frames per second (only limited by the camera frame rate), with a field-of-view of up to 350 × 350 μm2 and a diffraction-limit spatial resolution of ~2 μm. We envision that PSIM will find a broad range of applications in quantitative material characterization under dynamical conditions.

Structures and topological defects in pressure-driven lyotropic chromonic liquid crystals

Lyotropic chromonic liquid crystals are water-based materials composed of self-assembled cylindrical aggregates. Their behavior under flow is poorly understood, and quantitatively resolving the optical retardance of the flowing liquid crystal has so far been limited by the imaging speed of current polarization-resolved imaging techniques. Here, we employ a single-shot quantitative polarization imaging method, termed polarized shearing interference microscopy, to quantify the spatial distribution and the dynamics of the structures emerging in nematic disodium cromoglycate solutions in a microfluidic channel. We show that pure-twist disclination loops nucleate in the bulk flow over a range of shear rates. These loops are elongated in the flow direction and exhibit a constant aspect ratio that is governed by the nonnegligible splay-bend anisotropy at the loop boundary. The size of the loops is set by the balance between nucleation forces and annihilation forces acting on the disclination. The fluctuations of the pure-twist disclination loops reflect the tumbling character of nematic disodium cromoglycate. Our study, including experiment, simulation, and scaling analysis, provides a comprehensive understanding of the structure and dynamics of pressure-driven lyotropic chromonic liquid crystals and might open new routes for using these materials to control assembly and flow of biological systems or particles in microfluidic devices.

Use of laser speckle shearing interferometric vibration measurement system for acoustic-to-seismic landmine detection

To study the application of laser shearing speckle interferometric vibration measurement technology in acoustic resonance landmine detection, we present an experimental and theoretical study of the method for laser shearing speckle interferometric landmine detection based on time-average. The relationship between the out-of-plane displacement gradient generated by the sound wave on the ground and the phase change of the shearing interference laser is analyzed. A high-power loudspeaker is used as the source of sound wave excitation, and the laser shearing speckle interferometric vibration measurement system is used in landmine detection experiments to investigate the changes of laser shearing speckle interference fringes under different experimental conditions such as sound wave intensity, detection target, buried depth, and soil environment. The study reveals that it is feasible and effective to use laser shearing speckle interferometry to detect landmines, and it provides a theoretical and methodological basis for realizing the rapid scanning of acoustic-optic landmine detection.

Broad-band phase retrieval method for transient radial shearing interference using chirp Z transform technique* *Project supported by the National Natural Science Foundation of China (Grant No. 61705254) and the Key Research and Development Program of Shaanxi Province of China (Grant No. 2020GY-114).

The transient radial shearing interferometry technique based on fast Fourier transform (FFT) provides a means for the measurement of the wavefront phase of transient light field. However, which factors affect the spatial bandwidth of the wavefront phase measurement of this technology and how to achieve high-precision measurement of the broad-band transient wavefront phase are problems that need to be studied further. To this end, a theoretical model of phase-retrieved bandwidth of radial shearing interferometry is established in this paper. The influence of the spatial carrier frequency and the calculation window on phase-retrieved bandwidth is analyzed, and the optimal carrier frequency and calculation window are obtained. On this basis, a broad-band transient radial shearing interference phase-retrieval method based on chirp Z transform (CZT) is proposed, and the corresponding algorithm is given. Through theoretical simulation, a known phase is used to generate the interferogram and it is retrieved by the traditional method and the proposed method respectively. The residual wavefront RMS of the traditional method is 0.146λ, and it is 0.037λ for the proposed method, which manifests an improvement of accuracy by an order of magnitude. At the same time, different levels of signal-to-noise ratios (SNRs) from 50 dB to 10 dB of the interferogram are simulated, and the RMS of the residual wavefront is from 0.040λ to 0.066λ. In terms of experiments, an experimental verification device based on a phase-only spatial light modulator is built, and the known phase on the modulator is retrieved from the actual interferogram. The RMS of the residual wavefront retrieved through FFT is 0.112λ, and it decreases to 0.035λ through CZT. The experimental results verify the effectiveness of the method proposed in this paper. Furthermore, the method can be used in other types of spatial carrier frequency interference, such as lateral shearing interference, rotational shearing interference, flipping shearing interference, and four-wave shearing interference.

Analysis of Embedded Optical Interferometry in Transparent Elastic Grating for Optical Detection of Ultrasonic Waves.

In this paper, we propose a theoretical framework to explain how the transparent elastic grating structure can be employed to enhance the mechanical and optical properties for ultrasonic detection. Incident ultrasonic waves can compress the flexible material, where the change in thickness of the elastic film can be measured through an optical interferometer. Herein, the polydimethylsiloxane (PDMS) was employed in the design of a thin film grating pattern. The PDMS grating with the grating period shorter than the ultrasound wavelength allowed the ultrasound to be coupled into surface acoustic wave (SAW) mode. The grating gaps provided spaces for the PDMS grating to be compressed when the ultrasound illuminated on it. This grating pattern can provide an embedded thin film based optical interferometer through Fabry–Perot resonant modes. Several optical thin film-based technologies for ultrasonic detection were compared. The proposed elastic grating gave rise to higher sensitivity to ultrasonic detection than a surface plasmon resonance-based sensor, a uniform PDMS thin film, a PDMS sensor with shearing interference, and a conventional Fabry–Perot-based sensor. The PDMS grating achieved the enhancement of sensitivity up to 1.3 × 10−5 Pa−1 and figure of merit of 1.4 × 10−5 Pa−1 which were higher than those of conventional Fabry–Perot structure by 7 times and 4 times, respectively.