Quadratic Phase Research Articles

Properties and applications of quaternion quadratic phase Fourier transforms

Properties and applications of quaternion quadratic phase Fourier transforms

Peering into Cloud Physics Using Ultra-Fine-Resolution Radar and Lidar Systems

Abstract Cloud microphysical processes, such as droplet activation, condensational growth, and collisional growth, play a central role in the evolution of clouds and precipitation. Accurate representations of these processes in numerical models are challenging partially due to incomplete understanding of them at the process level arising from limited systematic observations. Most surface-based active remote sensors, including today’s operational cloud radars and lidars, have a resolution on the order of tens of meters. This resolution is insufficient to resolve cloud microphysical processes that manifest at finer (meter and submeter) scales. A new set of ultra-high-resolution ground-based radar and lidar systems have been developed to address this observational gap. The newly developed 94-GHz cloud radar has a range resolution down to 2.8 m, or a factor of 10 finer than typical radars, using a large bandwidth and quadratic phase coding techniques. The lidar has a range resolution down to 10 cm, or a factor of 100 finer than typical lidars, using a time-gated time-correlated single-photon-counting technique. Such high-resolution observations were previously only achievable through in situ aircraft measurements. Even then, aircraft measurements do not permit continuous long-term cloud observation as is possible with ground-based remote sensing instruments. In this study, the first-light cloud observations from the new radar and lidar systems are shown to reveal detailed cloud structures that conventional sensors could only perceive in a bulk sense, thus providing new avenues to investigate cloud microphysical processes and their impact on weather and climate.

Adaptive tunicate swarm optimization with partial transmit sequence for phase optimization in MIMO-OFDM

<span>Multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) are widely utilized in wireless systems and maximum data rate communications. The MIMO-OFDM technology increases the efficiency of spectrum utilization. The peak-to-average-power ratio (PAPR) minimization in MIMO-OFDM is a complex task in wireless communications systems. In this research, an adaptive tunicate swarm optimization with partial transmit sequence (ATSO-PTS) algorithm is proposed for a reduction of PAPR in MIMO-OFDM. The nonsquare-matrix-based differential space time coding (N-DSTC) scheme is used for the encoding and decoding process of MIMO-OFDM. The N-DSTC encoding and decoding are linear error-correcting codes that are utilized for message transmission over noisy channels. The pre-specified quadrate phase shift keying (QPSK) symbol is deployed for the modulation and demodulation scheme. On the receiver side, the serial to parallel (S/P) conversion, and fast Fourier transform (FFT) are accomplished, alongside the received data bits being demodulated to obtain the output bits. The proposed ATSO-PTS method achieves better results according to performance metrices PAPR, bit error rate (BER) and signal-to-noise-ratio (SNR), with values of about 2.9, 0.01 and 0.025, respectively. This ensures superior results when compared to the existing methods of twin symbol hybrid optimization applied to partial transmit sequence (TSHO-PTS), selective level mapping and PTS (SLM-PTS), and particle swarm and grey wolf (PS-GW) with PTS, respectively.</span>

Role of chirping in pulsed single-photon spectroscopy

We investigate the precision of estimating the interaction strength between a two-level system (TLS) and a single-photon pulse when the latter is subject to chirping. We consider linear, quadratic, and sinusoidal temporal phases applied to Gaussian and exponential temporal profiles. At the asymptotic time, when the TLS has fully decayed to its ground state, the fundamental precision depends solely on the magnitude of its spectral amplitude. For quadratically phase-modulated Gaussian pulses, this is entirely determined by the spectral bandwidth. We provide expressions for evaluating the fundamental precision for general temporal profiles and phase modulations. Finally, we show that experimentally feasible mode-resolved measurements are optimal, or close to it, for chirped, pulsed single-photon spectroscopy. Published by the American Physical Society 2024

Revisit of uncertainty principles via OPS method approach in the framework of quaternion quadratic phase Fourier transform

Revisit of uncertainty principles via OPS method approach in the framework of quaternion quadratic phase Fourier transform

Generation and control of circular Airy solitons in fractional nonlinear optical systems under different modes

In this paper, the dynamics of the circular Airy beam (CAB) in the spatial fractional nonlinear Schrödinger equation (FNLSE) optical system are investigated. The propagation characteristics of CABs modulated by the quadratic phase modulation (QPM) in a Kerr (cubic) nonlinear medium under power function diffractive modulation modes and parabolic potentials are numerically simulated by using a step-by-step Fourier method. Specifically, the threshold for CABs to form solitons in the Kerr medium is controlled by the Lévy index and the QPM coefficient. Secondly, the parabolic potential has the ability to stabilize the FNLSE optical system, making it easier for the formation of CAB solitons. The addition of QPM allows the refocusing of the split beam caused by the Lévy index, and it can change the position and intensity of solitons. Finally, we also study the transmission evolution of QPM-modulated CABs in the Kerr medium under the power function diffraction modulation mode. We can obtain different types of solitons by varying the power function modulation coefficients. A dark soliton with high stability is formed, and we can control its size. Results show that it is possible to optimize the parameter settings (parabolic potential coefficients, power function modulation coefficients, QPM coefficients, Lévy indices, and nonlinear Kerr intensity coefficients) to obtain different types of solitons as well as to modulate the soliton transport. It provides more degrees of freedom for the study of CAB soliton propagation in the Kerr media, which is of great significance and application in fields of nonlinear optical transport, particle manipulation, and optical metrology.

Propagation of M-shaped and W-shaped similaritons in birefringent tapered graded-index nonlinear fiber amplifiers

We study the self-similar transmission of optical beams inside an inhomogeneous birefringent tapered graded-index nonlinear fiber amplifier within the framework of generalized coupled Schrödinger equations with spatially inhomogeneous nonlinearity, group velocity dispersion, tapering and gain or loss. New kinds of similariton solutions for the governing model are constructed by means of the similarity transformation method. Especially, the M-shaped and W-shaped similariton pulses are found successfully for the first time, which do not exist in single-mode waveguide amplifier. In addition, bright–dark similaritons are found in the presence of tapering effect. It is shown that these waveforms exhibit a quadratic phase structure, which leads to chirped self-similar pulses. In addition, we determine the relationships among the tapering profile, gain or loss distribution, nonlinearity, and similariton width, which provide the required conditions for controlling the self-similar wave dynamics. Moreover, we discuss the dynamical evolution of the similariton pulses under the influence of special tapering profiles, which are of physical importance in practical applications. The results show that through selecting the appropriate tapering, dispersion and nonlinearity profiles, we can control the dynamics of similaritons effectively.

The control for multiple kinds of solitons generated in the nonlinear fractional Schrödinger optical system based on Hermite-Gaussian beams

In this paper, we investigate the control for Hermite-Gaussian (HG) solitons in the nonlinear fractional Schrödinger equation (FSE) by sequentially applying power function modulations, cosine modulations, parabolic potentials, and quadratic phase modulations (QPM). In the photorefractive media, the HG beam forms scattered breathing solitons when the fractional diffraction effect equilibrates with nonlinear effect. Under the power function modulation, the soliton maintains an equidistant linear transmission along the z-axis, and the number of solitons is equal to the mode. In the cosine modulation, the soliton distorts and its energy rapidly decreases after a certain distance of transmission. The time of the distortion varies with the Lévy index, photorefractive coefficient, modulation frequency and order. The freak spots exhibit a “flower” shape pattern. If a parabolic potential is introduced, the HG beam forms crawling soliton pairs or merges into a single bounded breathing soliton by adjusting the correlation among the Lévy index, nonlinear and parabolic coefficients. By increasing the nonlinear coefficient in the negative QPM regime, the defocusing HG beam emits several “filiform” breathing solitons during its propagation, which move in a parallel straight line to each other. The HG beam is transformed into a single fine breathing soliton after being focused under a positive QPM. The time of the formation and breathing rate varies with the Lévy index, QPM and nonlinear coefficients. Moreover, the number of solitons changes irregularly with modes. These results are significant for applications in optical communication, optical device design, and optical signal processing.

Nonlinear vibro-acoustic modulation for microcrack detection of steel strands based on S-transform bispectrum

Fatigue crack detection is an important issue to ensure the safety of steel strands. The key to solve this problem is to extract the nonlinear response generated by fatigue cracks. In this paper, the nonlinear VAM method is used to detect the structural cracks. The structure with fatigue cracks is excited using low-frequency pumping and high-frequency probing, and the power spectrum analysis of the modulated signal is carried out. In view of the shortcomings of spectral analysis, a new method combining S-transform and bispectrum is proposed, which is called S-transform bispectrum. S transform contains the phase factor, which can retain the absolute phase characteristics of each frequency, and has good time–frequency multi-scale focusing performance. The bispectrum can suppress Gaussian noise, retain phase information, and quantitatively describe the quadratic phase coupling in the signal. Then the simulation and experiment of damaged straight rod, helical rod, and steel strands are carried out. The results show that the proposed method can effectively detect the nonlinear features by using the sideband peaks in the S-transform bispectrum three-dimensional plot, and the nonlinear features are important to identify the structure with damage. At the same time, in order to prove the ability of S-transform bispectrum, an S-transform bispectrum detector is used to verify it, which is superior to the spectrum in terms of its ability to localize modulation sidebands. The proposed S-transform bispectrum has a good application prospect and provides a new tool for structural damage detection.

Optical double-image cryptosystem based on a joint transform correlator in a linear canonical domain

In this work, we present a new optical double-image encryption method based on a joint transform correlator (JTC) and the linear canonical domain for the simultaneous authentication of two images. This new extension of the encryption system overcame the vulnerability of the method based on the JTC and the conventional 4f-optical processor in the Fourier domain. Although the simultaneous authentication process is satisfied in the Fourier domain, the data content is partially disclosed in false validation. Therefore, we introduce a quadratic phase encryption system of the linear canonical transform (LCT) domain in this method. The linear canonical transform domain adds more degrees of freedom to the security method due to the six LCT orders. In addition, the double-image encryption scheme became secure against intruder attacks, and it was difficult to recognize confidential information during the negative validation process. A cryptanalysis is performed in terms of a chosen-plaintext attack (CPA) and chosen-ciphertext attack (CCA). Numerical simulations demonstrate the feasibility, security, and effectiveness of the proposed system.

Time Delay Estimation for Acoustic Temperature Measurement of Loose Coal Based on Quadratic Correlation PHAT-β Algorithm

The acoustic temperature measurement method has a broad application prospect due to its advantages of high precision, non-contact, etc. It is expected to become a new method for hidden fire source detection in mines. The acoustic time of flight (TOF) can directly affect the accuracy of acoustic temperature measurement. We proposed a quadratic correlation-based phase transform weighting (PHAT-β) algorithm for estimating the time delay of the acoustic temperature measurement of a loose coal. Validation was performed using an independently built experimental system for acoustic temperature measurement of loose coals under multi-factor coupling. The results show that the PHAT-β algorithm estimated acoustic TOF values closest to the reference line as the sound travelling distance increased. The results of coal temperature inversion experiments show that the absolute error of the PHAT-β algorithm never exceeds 1 °C, with a maximum value of 0.862 °C. Using the ROTH weighted error maximum, when the particle of the coal samples is 3.0–5.0 cm, the absolute error maximum is 4.896 °C, which is a difference of 3.693 °C from the error minimum of 1.203 °C in this particle size interval. The accuracy of six algorithms was ranked as PHAT-β > GCC > PHAT > SCOT > HB > ROTH, further validating the accuracy and reliability of the PHAT-β algorithm.

Manipulating circular Airy beam dynamics with quadratic phase modulation in fractional systems under some diffraction modulations and potentials.

Based on a split-step Fourier algorithm, the transmission of circular Airy beams with quadratic phase modulation (QPM) is investigated in the fractional Schrödinger equation (FSE) under diffraction modulations (periodic modulation, linear modulation and power function modulation) and external potentials (parabolic potential and linear potential). The results show that QPM is able to change the focusing position and intensity, as well as the transmission trajectory of the beam. In a periodic modulation, the circular Airy beam (CAB) exhibits periodic variation characteristics, and the beam splitting is retarded under the action of the QPM. The self-focusing distance of the beam is significantly reduced, and its transmission trajectory and beam width are altered by the QPM under the linear modulation. The CAB progressively evolves into a non-diffraction beam under the power function modulation, and the QPM is able to reduce the light intensity and increase the beam width as the Lévy index decreases. In a parabolic potential, CABs display autofocusing and defocusing behavior, and the QPM affects the intensity distribution and optical width of the beam. The CAB is deflected and evolves periodically in a linear potential. The beam width increases and gradually stabilizes with the addition of the QPM. The propagation of CABs controlled with QPM in parabolic and linear potentials is also analyzed in the frequency domain. The results demonstrate that we can control the transmission of CABs in an FSE optical system by rationally setting parameters such as QPM, modulation coefficients, and external potentials.

IBAQ: Frequency-Domain Backdoor Attack Threatening Autonomous Driving via Quadratic Phase

The rapid evolution of backdoor attacks has emerged as a significant threat to the security of autonomous driving models. An attacker injects a backdoor into the model by adding triggers to the samples, which can be activated to manipulate the model’s inference. Backdoor attacks can lead to severe consequences, such as misidentifying traffic signs during autonomous driving, posing a risk of causing traffic accidents. Recently, there has been a gradual evolution of frequency-domain backdoor attacks. However, since the change of both amplitude and its corresponding phase will significantly affect image appearance, most of the existing frequency-domain backdoor attacks change only the amplitude, which results in a suboptimal efficacy of the attack. In this work, we propose an attack called IBAQ, to solve this problem by blurring semantic information of the trigger image through the quadratic phase. Initially, we convert the trigger and benign sample to YCrCb space. Then, we perform the fast Fourier transform on the Y channel, blending the trigger image’s amplitude and quadratic phase linearly with the benign sample’s amplitude and phase. IBAQ achieves covert injection of trigger information within amplitude and phase, enhancing the attack effect. We validate the effectiveness and stealthiness of IBAQ through comprehensive experiments.

Quadratic phase mismatch in multisoliton interferograms based on time-stretched dispersive Fourier transformation

Quadratic phase mismatch in multisoliton interferograms based on time-stretched dispersive Fourier transformation

Linear-space-variant model for Fourier ptychographic microscopy.

Fourier ptychographic microscopy (FPM) needs to realize well-accepted reconstruction by image segmentation and discarding problematic data due to artifacts caused by vignetting. However, the imaging results have long suffered from uneven color blocks and the consequent digital stitching artifacts, failing to bring satisfying experiences to researchers and users over the past decade since the invention of FPM. In fact, the fundamental reason for vignetting artifacts lies in that the acquired data does not match the adopted linear-space-invariant (LSI) forward model, i.e., the actual object function is modulated by a quadratic phase factor during data acquisition, which has been neglected in the advancement of FPM. In this Letter, we rederive a linear-space-variant (LSV) model for FPM and design the corresponding loss function for FPM, termed LSV-FPM. Utilizing LSV-FPM for optimization enables the efficient removal of wrinkle artifacts caused by vignetting in the reconstruction results, without the need of segmenting or discarding images. The effectiveness of LSV-FPM is validated through data acquired in both 4f and finite conjugate single-lens systems.

New quadratic phase Wigner distribution and ambiguity function with applications to LFM signals

New quadratic phase Wigner distribution and ambiguity function with applications to LFM signals

Spatiotemporal encoding MRI in a portable low-field system.

Demonstrate the potential of spatiotemporal encoding (SPEN) MRI to deliver largely undistorted 2D, 3D, and diffusion weighted images on a 110 mT portable system. SPEN's quadratic phase modulation was used to subsample the low-bandwidth dimension of echo planar acquisitions, delivering alias-free images with an enhanced immunity to image distortions in a laboratory-built, low-field, portable MRI system lacking multiple receivers. Healthy brain images with different SPEN time-bandwidth products and subsampling factors were collected. These compared favorably to EPI acquisitions including topup corrections. Robust 3D and diffusion weighted SPEN images of diagnostic value were demonstrated, with 2.5 mm isotropic resolutions achieved in 3 min scans. This performance took advantage of the low specific absorption rate and relative long TEs associated with low-field MRI. SPEN MRI provides a robust and advantageous fast acquisition approach to obtain faithful 3D images and DWI data in low-cost, portable, low-field systems without parallel acceleration.

Motor Current Time-Varying Quadratic Phase Coupling Analysis and Its Application in Traction Motor Fault Detection Under Varying-Speed Condition

Motor Current Time-Varying Quadratic Phase Coupling Analysis and Its Application in Traction Motor Fault Detection Under Varying-Speed Condition

Focusing characteristics of space-variant quadratic phase modulated linearly polarized Bessel–Gaussian vortex beam

Focusing characteristics of space-variant quadratic phase modulated linearly polarized Bessel–Gaussian vortex beam

Detection of quadratic phase coupling by cross-bicoherence and spectral Granger causality in bifrequencies interactions

Quadratic Phase Coupling (QPC) serves as an essential statistical instrument for evaluating nonlinear synchronization within multivariate time series data, especially in signal processing and neuroscience fields. This study explores the precision of QPC detection using numerical estimates derived from cross-bicoherence and bivariate Granger causality within a straightforward, yet noisy, instantaneous multiplier model. It further assesses the impact of accidental statistically significant bifrequency interactions, introducing new metrics such as the ratio of bispectral quadratic phase coupling and the ratio of bivariate Granger causality quadratic phase coupling. Ratios nearing 1 signify a high degree of accuracy in detecting QPC. The coupling strength between interacting channels is identified as a key element that introduces nonlinearities, influencing the signal-to-noise ratio in the output channel. The model is tested across 59 experimental conditions of simulated recordings, with each condition evaluated against six coupling strength values, covering a wide range of carrier frequencies to examine a broad spectrum of scenarios. The findings demonstrate that the bispectral method outperforms bivariate Granger causality, particularly in identifying specific QPC under conditions of very weak couplings and in the presence of noise. The detection of specific QPC is crucial for neuroscience applications aimed at better understanding the temporal and spatial coordination between different brain regions.