Quadratic Phase Research Articles

A Method to Suppress Interferences Based on Secondary Compensation with QPC-FDA-MIMO Radar

The traditional phased array radar is unable to distinguish mainlobe deceptive interference from the true target when they share an identical angle. To address this issue, a method is developed to suppress the interference in the joint transmit–receive–Doppler frequency domain, using secondary compensation and quadratic phase code (QPC) with the frequency diversity array multiple-input multiple-output (FDA-MIMO) radar. The QPC technique is employed by encoding the transmitted pulses in various spatial channels, which extends the degrees-of-freedom (DOFs) of the system. To distinguish and suppress the false targets behind the true target by at least one pulse, Doppler compensation is performed and Doppler filters are employed. To distinguish the fast-generated false targets, which are located in the same pulse with the true target, the spatial frequency compensation is implemented, which equivalently relocates the mainlobe interference to the sidelobes. Via the singular spectrum analysis (SSA) technique and the data-dependent beamforming, the interferences within the ambiguity region are suppressed. Simulation results verify the effectiveness of the method.

Experimental demonstration of passive microwave pulse amplification via temporal Talbot effect

The temporal Talbot effect is a passive phenomenon that occurs when a periodic signal propagates through a dispersive medium with a quadratic phase response that modulates the output pulse repetition rate based on the input period. As previously proposed, this effect enables innovative applications such as passive amplification. However, its observation in the microwave regime has been impractical due to the requirement for controlled propagation through a highly dispersive waveguide. To overcome this challenge, we employed an ultra-wide band linearly chirped Bragg grating within a standard microwave X-Band waveguide. By utilizing backwards Talbot array illuminators aided by particle swarm optimization, we achieved passive amplification with a gain of 3.45 dB and 4.03 dB for gaussian and raised cosine pulses, respectively. Furthermore, we numerically verified that with higher quality substrates this gain can be theoretically increased to over 8 dB. Our work paves the way for numerous applications of the Talbot effect in the microwave regime, such as temporal cloaking, sub-noise microwave signal detection, microwave pulse shaping, and microwave noise reduction.

Optical computation of Laplace operator using Pancharatnam-Berry lens of large focal length

We propose an optical Laplace operator consisting of a large-focal-length Pancharatnam-Berry lens placed on the Fourier plane of an optical imaging system and sandwiched with two orthogonal linear polarizers. Theoretical analysis reveals that the isotropic second-order differentiation derives from the quadratic phase attached to the left-handed and right-handed circularly polarized light. The Pancharatnam-Berry lens made of liquid crystal with high transmittance and diffraction efficiency is integrated into different imaging systems to realize edge detection for both amplitude and phase objects, and the results conform to the theory well. This work paves the way to implement Laplace operator in practical applications such as image processing and high-contrast microscopy.

Scintillation mitigation via the cross phase of the Gaussian Schell-model beam in a turbulent atmosphere.

Scintillation is an important problem for laser beams in free space optical (FSO) communications. We derived the analytical expressions for the scintillation index of a Gaussian Schell-model beam with cross phase propagation in a turbulent atmosphere. The numerical results show that the quadratic phase can be used to mitigate turbulence-induced scintillation, and the effects of the turbulent strength and beam parameters at the source plane on the scintillation index are analyzed. The variation trend of the experimentally measured scintillation index is consistent with the numerical results. Our results are expected to be useful for FSO communications.

A Signal Model Based on the Space–Time Coding Array and a Novel Imaging Method Based on the Hybrid Correlation Algorithm for F-SCAN SAR

The F-SCAN principle is a better alternative to the scan-on-receive technique (SCORE) based on digital beamforming (DBF), which can avoid low gain caused by a conventional broad beam in the case of a wide swath. In F-SCAN SAR, a pencil beam scans the entire target area from far to near, providing high energy independent of the position and ensuring a low range ambiguity-to-signal ratio (RASR). Moreover, echo compression can be achieved via appropriate system parameter configuration, significantly shortening the receive window and reducing the amount of data. A wider range swath can, therefore, be achieved. However, for this novel F-SCAN SAR working mode, signal modeling and imaging processing are key issues that needed to be addressed. In this paper, the far-field synthetic antenna pattern of the space–time coding array (STCA) is first derived and analyzed, based on which the signal modeling of the F-SCAN SAR is carried out. Then, according to the signal model and echo characteristics, a novel imaging processing method based on the hybrid correlation algorithm is presented for the F-SCAN SAR. First, the dechirp operation is performed to compensate for the quadratic phase of the range time. The range compressed result is obtained after a range Fourier transform, where different range targets are successfully separated and range aliasing is avoided. Then, the modified azimuth reference function is correlated with the echo at each range cell to complete range cell migration correction (RCMC) and azimuth compensation. The received signal parameters and the Doppler parameters of each range cell are derived to update the azimuth reference function. Finally, accurate focused results are obtained in the range-frequency, azimuth-time domain. The simulation results indicate that the signal model based on the STCA can satisfy the requirements of the F-SCAN principle, and the proposed imaging algorithm can complete the precise focusing processing of the F-SCAN SAR echo.

A Coherent Integration and Parameter Estimation Method for Constant Radial Acceleration Weak Target via SOKT-IAR-LVD

In order to enhance the detection and parameter estimation capacity to the maneuvering target with complex motions, a low complexity coherent integration and parameter estimation method named SOKT-IAR-LVD is proposed in this paper. In SOKT-IAR-LVD, first, the second-order keystone transform (SOKT) is utilized to eliminate the range curvature induced by target acceleration. Second, improved axis rotation (IAR) is applied to regulate the linear range migration by rotating the fast time axis and the target envelope is aligned along the slow time axis with a quadratic phase characteristic. At last, the target signal is coherently integrated via the Lv’s Distribution (LVD) transform. The target motion parameters, including range, velocity, and acceleration, are estimated by the IAR and LVD results. The integration gain and computational load of SOKT-IAR-LVD are analyzed. Without needing to estimate the Doppler ambiguity number and target acceleration, the computational burden of SOKT-IAR-LVD is three orders of magnitude lower than that of the Radon-Lv’s Distribution (RLVD) method. Simulation results demonstrate that the detection performance of SOKT-IAR-LVD is almost the same as that of RLVD and that the required input SNR of SOKT-IAR-LVD is 17.4 dB lower than that of SOKT–Radon Fourier transform (SOKT-RFT) when the detection threshold is set to 12 dB.

Volumetric T2 -weighted spin echo imaging with improved SNR using localized quadratic encoding and a spiral readout trajectory.

To demonstrate T2 -weighted (single-echo) spin-echo (SE) imaging with near-optimal acquisition efficiency by applying SNR-efficient RF slice encoding and spiral readout. A quadratic-phase (frequency swept) excitation RF pulse replaced the conventional excitation in T2 -weighted SE sequence to excite a thick slab that is internally spatially encoded by a variable phase along the slice direction. Highly overlapping slabs centered at every desired slice location were acquired in multiple passes, such that the entire imaging volume was excited by contiguous slabs in any given pass. Following 90° excitation, each slab was refocused with a conventional 180° RF to produce a SE signal, followed by a spiral in-out readout. A noise-insensitive reconstruction removed the quadratic phase in the spatial frequency domain, yielding desired slice resolution and improved SNR. Increasing the RF frequency sweep (hence, excitation width) allowed more frequent encoding of each slice over the multiple passes, improving final image SNR, until crosstalk ensued at excessive slab widths compared to their center-to-center spacing. With an optimized slab width, the proposed technique used all passes to acquire every prescribed slice, with substantially improved SNR over conventional SE or 2D-turbo-spin-echo (TSE) scans. Quantitative SNR measurements indicated similar SNR as 3D-TSE, but radiologist scoring favored 3D-TSE, mainly because of spiral-related artifacts and possibly because of regularized reconstructions in 3D-TSE. Using SNR-efficient slice excitation scheme and spiral readout helped eliminate SNR and temporal inefficiencies in conventional T2 -weighted imaging, yielding SNR independent of TR or number of passes.

Ballistic dynamics of emergent soliton from Airy pulse in a medium with linear optical potential

We numerically investigate the propagation dynamics of Airy pulse in dispersive and nonlinear medium with time-dependent external optical potential. These time-dependent optical potentials are created by the co-propagating strong pump wave. In the presence of linear optical potential, soliton shedding from signal Airy pulse is observed, which demonstrates ballistic motion. However, emergent soliton can either be advanced or delayed depending upon the sign of the potential and the extent of temporal advancement or delay is directly proportional to the magnitude of the potential strength. In addition, the temporal shift of the emergent soliton is found to be dependent on the input pulse power. Moreover, we show ballistic motion of the emergent soliton by incorporating an initial linear phase as well as linear chirp (quadratic phase) parameters in the input Airy pulse. Furthermore, the effect of truncation factor on the propagation dynamics is explored. These results provide new insights on the manipulation of the signal Airy pulse dynamics in dispersive and nonlinear media.

Speckle suppression in arbitrary parallel holographic illumination by the spatial frequency regaining method.

This Letter proposes a spatial frequency regaining method for parallel holographic illumination (SFR-PHI) to suppress speckle noise in phase-only computer-generated holography (CGH). Based on the accurate calculation of the beam bandwidth, this method uses the bandwidth-limited quadratic initial phase and weighted constraint iteration to generate the optimized phase hologram, which can provide the accurate spatial frequency of multiple illumination patterns. The results show that SFR-PHI performs superiorly in speckle suppression for generating dozens of illumination patterns in parallel and with arbitrary shapes and numbers. Compared with other speckle-suppression methods, it exhibits significant advantages in terms of accuracy and modulation efficiency.

Analytical design framework for metasurface projection optics

Beam steering and pattern/image projection have recently emerged as promising applications for optical metasurfaces, potentially bringing significant benefits to fields such as automotive and consumer electronics. To date, designs of metasurfaces for these applications have resorted to iterative numerical optimization. In this paper, we derive analytical solutions to enable computationally efficient design of flat optics systems for optical beam steering and pattern projection. For a single-layer metasurface, we show that a quadratic phase profile yields optimal beam quality. Doublet metasurfaces offer additional control over the beam forming characteristics, and as an example, we demonstrate on-demand distortion correction following analytically derived designs.

Parkinsonian Tremor Detection with Compact Convolutional Transformer from Bispectrum Representation of tri-Axial Accelerometer Signals.

After the breakthroughs of Transformer networks in Natural Language Processing (NLP) tasks, they have led to exciting progress in visual tasks as well. Nonetheless, there has been a parallel growth in the number of parameters and the amount of training data, which led to the conclusion that Transformers are not suited for small datasets. This paper is the first to convey the feasibility of Compact Convolutional Transformers (CCT) for the prediction of Parkinsonian postural tremor based on the Bispectrum (BS) representation of IMU accelerometer time series. The dataset includes tri-axial accelerometer signals collected unobtrusively in-the-wild while subjects are on a phone call, and labelled by neurologists and signal processing experts. The BS is a noise-immune, higher-order representation that reflects a signal's deviation from Gaussianity and measures quadratic phase coupling. We performed comparative classification experiments using the CCT, pre-trained CNNs such as VGG-16 and ResNet-50, and the conventional Vision Transformer (ViT). Our model achieves competitive prediction accuracy and F1 score of 96% with only 1.016 M trainable parameters, compared to the ViT with 21.659 M trainable parameters, in a five-fold cross-validation scheme. Our model also outperforms pre-trained CNNs such as VGG-16 and ResNet-50. Furthermore, we show that the performance gains are maintained when training on a larger dataset of BS images. Our effort here is motivated by the hypothesis that data-efficient transformers outperform transfer learning using pre-trained CNNs, paving the way for promising deep learning architecture for small-scale, novel and noisy medical imaging datasets.Clinical relevance- Novel deep learning model for unobtrusive prediction of Parkinsonian Postural Tremor from Bispectrum image representation of tri-axial accelerometer signals collected in-the-wild.

Suppression of Mainlobe Jammers with Quadratic Element Pulse Coding in MIMO Radar

The problem of suppressing mainlobe deceptive jammers, which spoof radar systems by generating multiple false targets, has attracted widespread attention. To tackle this problem, in this paper, the multiple-input multiple-output (MIMO) radar system was utilized by applying a quadratic element phase code (QEPC) to the transmitted pulses of different elements. In the receiver, by utilizing the spatial frequency and Doppler frequency offset generated after decoding, the jammers were equivalently distributed in the sidelobes of the joint Doppler-transmit-receive domain and were distinguishable from the true target. Then, further spatial frequency compensation and Doppler compensation were performed to align the true target to the zero point in the transmit spatial and Doppler domains. Moreover, by designing appropriate coding coefficients, the jammers were suppressed by data-independent Doppler-transmit-receive three-dimensional beamforming. However, the beamforming performance was sensitive to angular estimation mismatches, resulting in performance degradation of jammer suppression. To this end, a center-boundary null-broadening control (CBNBC) approach was used to broaden the nulls in the equivalent beampattern by generating multiple artificial jammers with preset powers around the nulls. Thus, the false targets (FTs) with deviations were sufficiently suppressed in the broadened notches. Numerical simulations and theoretical analysis demonstrated the performance of the developed jammer suppression method.

Phase aberration adaptive compensation in digital holography based on phase imitation and metric optimization.

We proposed a numerical and accurate quadratic phase aberration compensation method in digital holography. A phase imitation method based on Gaussian 1σ-criterion is used to obtain the morphological features of the object phase using partial differential, filtering and integration successively. We also propose an adaptive compensation method based on a maximum-minimum-average- α-standard deviation (MMAαSD) evaluation metric to obtain optimal compensated coefficients by minimizing the above metric of the compensation function. The effectiveness and robustness of our method are demonstrated by simulation and experiments.

Generating ultrashort visible light pulses based on multidimensional solitary states in gas-filled hollow core fiber

Multidimensional solitary states (MDSS) are self-sustaining light wave packets confined in multiple dimensions in multimode fibers. In this work, we experimentally demonstrate the generation of MDSS, driven by a few hundreds of femtoseconds (fs) of long frequency doubled pulses from a Titanium:Sapphire chirped pulsed amplifier in a nitrous oxide-filled hollow core fiber (HCF). The MDSS output, resulting from intermodal interactions in a Raman-active gas-filled large core diameter HCF, features a broadband, red-shifted spectrum in the visible spectral region with a characteristic negative quadratic spectral phase. Therefore, the output with broadband spectra and negative chirp results in the generation of sub-30 fs pulses upon propagation through glass windows and a spectral filter. Backed with experimental observations and multidimensional simulations, we demonstrate that the sign of the frequency chirp of input pulses influences the spectral broadening in the HCF in the high gas-dispersion regime. We observed that the MDSS red-shifted pulses have a clean spatial profile. Therefore, the experimental requirements on the input beam size and quality to achieve a clean MDSS beam profile at the output of large core HCFs can be relaxed. Hence, this work extends the validation of the MDSS phenomenon toward the ultraviolet-visible region of the electromagnetic spectrum, thus providing an alternate source with a clean spatial beam profile for various applications in the field of ultrafast spectroscopy.

Quadratic phase S-Transform: Properties and uncertainty principles

In this paper, a novel quadratic phase S-transform (QPST) is proposed, by generalizing the S-transform (ST) with five parameters a, b, c,d and e. QPST displays the time and quadratic phase domain-frequency information jointly in the time-frequency plane. Firstly, we define the novel QPST and give its relation with quadratic phase Fourier transform (QPFT). Secondly, several important properties of newly defined QPST, such as conjugation, translation, modulation, orthogonality relation and reconstruction formula are derived. Finally, we formulate several classes of uncertainty inequalities, such as the Heisenberg uncertainty inequality and logarithmic uncertainty inequality.

Dynamic response of floating offshore wind turbines under freak waves with large crest and deep trough

Floating offshore wind turbines (FOWTs) are at high risk being attacked by freak waves with profiles of large crest or deep trough, which could damage the structures or weaken the efficiency of power generation. This study developed a numerical model to address the dynamic response of an in-place FOWT under the action of freak waves with large crest and deep trough. Based on the modulation method of freak wave profiles, various random wave trains embedded freak waves were firstly generated in the numerical wave tank. Noted that these waves generated match Gaussian seas. Then, the effect of freak waves was investigated extensively through the FOWT motions, axial acceleration on nacelle, tether forces as well as wave loads and wave fields in time domain and time-frequency domain. The results show that the occurrence of freak waves significantly amplified the dynamic response of FOWT and the impact lasted for approximately 20 spectral peak periods. Under freak waves, the effect of quadratic phase coupling on nacelle acceleration was first observed. The large crest led to a larger horizontal excursion. While the deep trough caused a larger pitch inducing a larger axial acceleration on nacelle. In addition, the nonlinear interaction (between FOWT and freak waves) caused by the large crest was stronger than that caused by deep trough.

Dual Polarization DQPSK ROF System with Duo Binary Precoding and Hybrid Amplification for Effective Hybrid SMF FSO Transmission Medium

This article demonstrates the utilization of a hybrid amplification technique on the transmission part of the proposed hybrid medium transmission system which includes both using Single Mode Fiber (SMF) with 60 km and Free Space Optic (FSO) with a range between 5 km and 25 km. It has included four weather situations with an investigation of the FSO medium-based system performance. The system uses 64 channels based on Dual Polarization-Differential Quadratic Phase Shift Keying (DP-DQPSK) Dense Wavelength Division Multiplexing (DWDM) for the Radio over Fiber (RoF) system using the Duo Binary coding scheme to improve the system efficiency in general and the cross-talk in particular. The investigations will include using the hybrid amplifiers of Erbium Doped Fiber Amplifier (EDFA) and Optical Amplifier (OA) for transmission. The analysis results show that using the hybrid amplification could improve the transmission to reach 25 km for light air case, meanwhile, for light haze, it could reach up to 20 km. Moderate haze could improve transmission efficiency for a distance of 7 km. Finally, for moderate rain situations, the transmission could be further improved to cover a distance of up to 5 km.

Automatic elimination of phase aberrations in digital holography based on Gaussian 1σ- criterion and histogram segmentation.

We propose a numerical and automatic quadratic phase aberration elimination method in digital holography for phase-contrast imaging. A histogram segmentation method based on Gaussian 1σ-criterion is used to obtain the accurate coefficients of quadratic aberrations using the weighted least-squares algorithm. This method needs no manual intervention for specimen-free zone or prior parameters of optical components. We also propose a maximum-minimum-average-standard deviation (MMASD) metric to quantitatively evaluate the effectiveness of quadratic aberration elimination. Simulation and experimental results are demonstrated to verify the efficacy of our proposed method over the traditional least-squares algorithm.

Multiresonant metasurfaces for arbitrarily broad bandwidth pulse chirping and dispersion compensation

We show that ultrathin metasurfaces with a specific multiresonant response can enable simultaneously arbitrarily strong and arbitrarily broadband dispersion compensation, pulse (de)chirping, and compression or broadening. This breakthrough overcomes the fundamental limitations of both conventional nonresonant approaches (bulky) and modern singly resonant metasurfaces (narrowband) for quadratic phase manipulations of electromagnetic signals. The required nonuniform trains of resonances in the electric and magnetic sheet conductivities that completely control phase delay, group delay, and chirp are rigorously derived and the limitations imposed by fundamental physical constraints are thoroughly discussed. Subsequently, a practical, truncated approximation by finite sequences of physically realizable linear resonances is constructed and the associated error is quantified. By appropriate spectral ordering of the resonances, operation can be achieved either in transmission or reflection mode, enabling full space coverage. The proposed concept is not limited to dispersion compensation, but introduces a generic and powerful ultrathin platform for the spatiotemporal control of broadband real-world signals with a myriad of applications in modern optics, microwave photonics, radar, and communication systems.

Scannable Dual-Focus Metalens with Hybrid Phase.

Metalenses with two foci in the longitudinal or transverse direction, called bifocal or dual-focus metalenses, are promising building blocks in tomography techniques, data storage, and optical tweezers. For practical applications, relative movement between the beam and specimen is required, and beam scanning is highly desirable for high-speed operation without vibration. However, dual-focus metalenses employ a hyperbolic phase that experiences off-axis aberrations, which is not suitable for beam scanning. Here, we demonstrated a scannable dual-focus metalens by employing a new phase called "hybrid phase". The hybrid phase consists of a hyperbolic phase inside and a quadratic phase outside to reduce off-axis aberrations while maintaining a high numerical aperture. We show that the two foci of the scannable dual-focus metalens move together without severe distortion for incident angles of up to 2.5°. Our design easily extends to the case of multifocusing, which is essential for various applications ranging from imaging to manipulation.