Large Phase Errors Research Articles

Simple implementation of aperture modulation quantitative differential phase contrast imaging

As one of the quantitative phase imaging methods, aperture modulation quantitative differential phase contrast (amqDPC) imaging has isotropic lateral resolution, being widely used in many fields such as biological cell morphology detection. However, the devices required to implement it are poorly controlled and very expensive. In addition, due to the weak phase approximation, there is a large axial phase error, and the full spectrum center pass during aperture modulation will cause distortion. Therefore, a method that enables simple and low-cost implementation of amqDPC, high axial phase accuracy, and isotopic lateral resolution is reported. Through simulations and experimental verifications, axial accuracy is greatly improved in the phase range of [0, π], and an isotropic lateral resolution of 870 nm can be achieved. In addition, experiments on transparent glass circular step sample and mouse kidney tissue slice also prove the practicability of this method. According to this study, researchers can accurately and simply measure the axial height of a slightly thick sample, which is achieved by capturing two intensity images to reconstruct a quantitative phase.

Validity of the effective sound speed approximation in parabolic equation models for wind turbine noise propagation.

Parabolic equation (PE) based methods are widely used in outdoor acoustics because they can solve acoustic propagation problems above a mixed ground in a refractive and scattering atmosphere. However, recent research has shown phase error due to the effective sound speed approximation (ESSA). To overcome these limitations, a new PE formulation derived without the ESSA has been proposed recently. We investigate the impact of such phase error on wind turbine noise modeling, as the classical wide-angle parabolic equation (WAPE) with ESSA is widely used in the research community. We propose a comparison between the classical WAPE with ESSA and the new WAPE derived without the ESSA in the context of wind turbine noise. We highlight large phase error (several dB) on monochromatic calculations with a point source. Using an extended sound source representative of a wind turbine, we show small phase error (<1 dB) in a wind turbine noise context where sound level variability far from the source is of several dB. The validity of previous works using WAPE with ESSA is, thus, not questioned, although we do recommend the use of the new WAPE derived without the ESSA to accurately model the effect of wind speed on sound propagation.

Silicon optical phased array with calibration-free phase shifters.

Optical phased array (OPA) based on silicon photonics is considered as a promising candidate for realizing solid-state beam steering. However, the high refractive index contrast of the silicon waveguides leads to conventional silicon based OPA suffering from large random phase errors, which require complex post-processing such as time-consuming phase calibration. We propose and demonstrate a calibration-free silicon OPA with optimized optical waveguides width as well as the compact 90° waveguide bends beyond the single mode regime. By using grouped cascaded phase shifters, it is able to reduce the number of control electrodes from N to log2(N). A 16-channel OPA has been demonstrated with continuous beam steering over the field of view controlled by only four control voltages without any calibration.

Pseudo Wigner-Ville distribution for 3D white light scanning interferometric measurement.

White light scanning interferometry is a commonly used optical measurement method for three-dimensional (3D) surface profiles. In the case of large phase errors, accurate height values can generally be obtained indirectly from the interferometric signal envelope information derived using various envelope extraction methods. However, the current envelope extraction algorithms have the disadvantages of low robustness, increasing the half-width of the envelope information, and requiring correct parameter settings in advance. In this study, the pseudo Wigner-Ville distribution is modified and applied to white light scanning interferometric 3D measurement to avoid the above-mentioned drawbacks. Simulations and experiments are performed in a single-frequency mode (only the approximate central wave-number is used to guide both the proposed and wavelet transform methods). The simulation results prove that the proposed method has a 31.7% higher reconstruction accuracy than the wavelet transform method under a 25 dB signal to noise ratio condition. Concurrently, the proposed method is insensitive to the change in the central wavelength with a constant central wave-number parameter and has a good extraction effect for a long coherent length. The experiments measure standard step objects (VLSI standard, 1.761 ± 0.01 µm), and the reconstruction height error of the proposed method is 0.0035 µm. Simulations and experiments show that the proposed method can adaptively provide accurate envelope information after half-width reduction under the condition that only the approximate central wave-number a priori knowledge is used. Simultaneously, the proposed method is shown to be robust and effective.

Low-Cost Metamaterial Antennas: Forward-Looking Imaging Experiment and Analysis.

A phase error correction method is proposed to compensate for the phase error in super-resolution correlated imaging based on metamaterial antennas. The varying carrier frequencies of a metamaterial antenna can generate the random radiation field for super-resolution correlation imaging, but the variation of the signal carrier frequency leads to large phase errors in the imaging results. In this proposed method, the sampling matrix in the super-resolution correlated imaging algorithm is used to compensate for the phase errors. Each element of the matrix is multiplied by a compensation phase corresponding to the phase error, and the error is subtly removed from the algorithm. In the experiment, the antenna pattern at each frequency of the metamaterial antenna is measured and recorded. In addition, an external field experiment is also carried out, and the collected data are imaged with the improved algorithm. Experimental results show that this technology can effectively solve the effect of phase errors on imaging results caused by signal carrier frequency changes.

Phase error analysis and unwrapping error suppression in phase-sensitive optical time domain reflectometry.

Phase-sensitive optical time domain reflectometry becomes an effective tool to realize distributed sensing, and the optical phase of the received light is usually used to quantify the strain for both dynamic and static measurement. The analysis on the overall phase error has been improved by considering the proportionality of the detection noise to the local optical power. The estimation accuracy is greatly improved by using the proposed theory, the probability density of the estimation accuracy over 99% is > 0.6, ∼39 times larger than the previously reported method. The phase unwrapping may malfunction due to the noisy signal, causing large phase errors. Point break detection algorithms are used to locate the incorrect phase unwrapping points, so the temporal evolution of the phase retrieved at each position can be divided into several sections with different offset. The phase unwrapping error is then suppressed by removing the offset.

High-Precision Temperature Inversion Algorithm for Correlative Microwave Radiometer.

In order to achieve high precision from non-contact temperature measurement, the hardware structure of a broadband correlative microwave radiometer, calibration algorithm, and temperature inversion algorithm are innovatively designed in this paper. The correlative radiometer is much more sensitive than a full power radiometer, but its accuracy is challenging to improve due to relatively large phase error. In this study, an error correction algorithm is designed, which reduces the phase error from 69.08° to 4.02°. Based on integral calibration on the microwave temperature measuring system with a known radiation source, the linear relationship between the output voltage and the brightness temperature of the object is obtained. Since the metal aluminum plate, antenna, and transmission line will have a non-linear influence on the receiver system, their temperature characteristics and the brightness temperature of the object are used as the inputs of the neural network to obtain a higher accuracy of inversion temperature. The temperature prediction mean square error of a back propagation (BP) neural network is 0.629 °C, and its maximum error is 3.351 °C. This paper innovatively proposed the high-precision PSO-LM-BP temperature inversion algorithm. According to the global search ability of the particle swarm optimization (PSO) algorithm, the initial weight of the network can be determined effectively, and the Levenberg–Marquardt (LM) algorithm makes use of the second derivative information, which has higher convergence accuracy and iteration efficiency. The mean square error of the PSO-LM-BP temperature inversion algorithm is 0.002 °C, and its maximum error is 0.209 °C.

A Versatile Algorithm for Autofocusing SAR Images

Introduction.Random deviations of the antenna phase centre of a synthetic aperture radar (SAR) are a source of phase errors for the received signal. These phase errors frequently cause blurring of the radar image. The image quality can be improved using various autofocus algorithms. Such algorithms estimate phase errors via optimization of an objective function, which defines the radar image quality. The image entropy and sharpness are well known examples of objective functions. The objective function extremum can be found by fast optimization methods, whose realization is a challenging computing task.Aim.To synthesize a versatile and computationally simple autofocusing algorithm allowing any objective function to used without changing its structure significantly.Materials and methods.An algorithm based on substituting the selected objective function with a simpler surrogate objective function, whose extremum can be found by a direct method, is proposed. This method has been referred as the MM optimization in scientific literature. It is proposed to use a quadratic function as a surrogate objective function.Results.The synthesized algorithm is straightforward, not requiring recursive methods for finding the optimal solution. These advantages determine the enhanced speed and stability of the proposed algorithm. Adjusting the algorithm for the selected objective function requires minimal software changes. Compared to the algorithm using a linear surrogate objective function, the proposed algorithm provides a 1.5 times decrease in the standard deviation of the phase error estimate, with an approximately 10 % decrease in the number of iterations.Conclusion.The proposed autofocusing algorithm can be used in synthetic aperture radars to compensate the arising phase errors. The algorithm is based on the MM-optimization of the quadratic surrogate objective functions for radar images. The computer simulation results confirm the efficiency of the proposed algorithm even in case of large phase errors.

M-PSK Demodulator With Joint Carrier and Timing Recovery

In this brief, we propose a new digital receiver for Phase-Shift Keying (PSK) modulation based on the integration of the conventional digital Costas Loop circuit with a new timing recovery method. The timing recovery is applied to the PSK demodulator using an Iterative Learning Control (ILC) law and it is based on the minimization of the intersymbol interference using only one sample per symbol. The main advantage of the proposed timing recovery method is the insensitivity to frequency offsets which results in improved performance and robustness of the Costas Loop circuit. Experiments comparing a conventional receiver (cascade of Costas Loop and Early-Late Timing Synchronizer) to the proposed receiver in scenarios characterized by low signal-to-noise ratios and large frequency and phase errors, show that the time needed to reduce the errors of the proposed receiver is seven times smaller than the conventional receiver. Moreover, the impact of the proposed method on the necessary hardware resources (area and power consumption) is negligible.

High contrast at small separation – II. Impact on the dark hole of a realistic optical set-up with two deformable mirrors

ABSTRACT Future large space- or ground-based telescopes will offer the resolution and sensitivity to probe the habitable zone of a large sample of nearby stars for exo-Earth imaging. To this end, such facilities are expected to be equipped with a high-contrast instrument to efficiently suppress the light from an observed star to image these close-in companions. These observatories will include features such as segmented primary mirrors, secondary mirrors, and struts, leading to diffraction effects on the star image that will limit the instrument contrast. To overcome these constraints, a promising method consists in combining coronagraphy and wavefront shaping to reduce starlight at small separations and generate a dark region within the image to enhance the exoplanet signal. We aim to study the limitations of this combination when observing short-orbit planets. Our analysis is focused on SPEED, the Nice test bed with coronagraphy, wavefront shaping with deformable mirrors (DMs), and complex telescope aperture shape to determine the main realistic parameters that limit contrast at small separations. We develop an end-to-end simulator of this bench with Fresnel propagation effects to study the impact of large phase and amplitude errors from the test-bed optical components and defects from the wavefront shaping system on the final image contrast. We numerically show that the DM finite stroke and non-functional actuators, coronagraph manufacturing errors, and near-focal-plane phase errors represent the major limitations for high-contrast imaging of exoplanets at small separations. We also show that a carefully defined optical set-up opens the path to high contrast at small separation.

Software compensation for the coupling error of a single-mode fiber coil under time-varying temperature and magnetic field

Previous studies have shown that there exists a large nonreciprocal phase error in the single-mode fiber coil of a depolarized interference fiber optic gyroscope (De-IFOG) under time-varying temperature and magnetic field, which evidently weakens its environmental adaptability. A real-time software compensation method considering the coupling effect of time-varying temperature and magnetic field is first proposed and verified experimentally. After compensation, the error of De-IFOG decreases from 50 deg / h to 6 deg / h when the magnitude of the magnetic field is 10 G and temperature uniformly increases from 10°C to 60°C with time-varying rate of 36 ° C / h. The compensation method is of great significance in De-IFOG engineering applications.

Synthetic aperture radar autofocus based on phaseless measurements

We introduce a new framework for compressed sensing (CS) in synthetic aperture radar (SAR) imaging in the case of model error. Conventional CS-based autofocus methods solve a joint optimization problem to achieve both model error parameter estimation and SAR image formation simultaneously. Owing to the possibly nonconvex feature of the joint optimization problem, however, these algorithms may get stuck in local optima having large phase errors and thus fail to reconstruct the image. In contrast, we use phaseless measurements and pose imaging as a convex optimization problem. To solve the convex problem, we use the alternating direction method of multipliers-based approach, which is computationally efficient and easy to implement. The results from simulations with both point targets and extended targets validate the effectiveness of the proposed method.

Evaluating Phase Errors in Phase-Sensitive Optical Time-Domain Reflectometry based on I/Q Demodulation

The phase errors resulting from in-phase/quadrature (I/Q) demodulation in phase-sensitive optical time-domain reflectometry (φOTDR) are investigated theoretically, numerically, and experimentally for two phase recovery schemes: one employing Kramers–Kronig (KK)-based coherent detection, and a second one based on a direct-detection scheme using an imbalanced Mach–Zehnder interferometer, a 3 × 3 coupler and 3 photodetectors. Mathematical models for the estimation of the differential phase variance are proposed and experimentally validated for these two schemes. The probability density function of the phase variance verifies an uneven longitudinal distribution of the phase errors in the two cases. Results point out that KK-based φOTDR sensors have no special advantages in terms of noise performance compared to standard full I/Q coherent detection, so that large phase errors can be verified at fading locations, leading to severe phase unwrapping problems. On the contrary, the direct-detection scheme based on interferometer is highly dependent on the signal difference between photodetectors, showing higher robustness against fading even if its probability density function is wider than the KK-based case. Experimental results also show the advantages of selecting data points with high in-phase and quadrature amplitudes to achieve reliable vibration measurements, especially in KK-based φOTDR sensors.

CZT Algorithm for Multiple-Receiver Synthetic Aperture Sonar

The compensation of slant range motion errors needs to be carried out after range pulse compression in the signal processing of multiple-receiver synthetic aperture sonar (SAS). Whereas range pulse compression cannot be performed as the first step in multiple-receiver SAS chirp scaling (CS) algorithm, as it requires the transmitted signal to be linearly frequency modulated. For this reason, it is difficult to combine CS algorithm with motion compensation. Besides, those imaging algorithms based on interpolation, such as range-Doppler algorithm and wavenumber domain algorithm, have plenty of computation load and large phase errors. Aimed at these problems, a CZT algorithm for multiple-receiver SAS in the non-stop-hop-stop mode is proposed in this paper. The proposed algorithm can correct range cell migration utilizing chirp-z transform, which avoids interpolation. Furthermore, the algorithm is easily combined with motion compensation as it can process pulse-compressed data directly. This paper describes the algorithm in 9 key steps, including the principle of correcting range cell migration utilizing chirp-z transform in discrete domain. In the simulation and sea trial data processing, the proposed algorithm provides image quality equal to the CS algorithm, and the algorithm is slightly more efficient than CS algorithm when combined with motion compensation.

Squint-looking differential synthetic aperture ladar: signal processing and experimental demonstration.

Squint-looking differential synthetic aperture ladar (DSAL) is reported with detailed signal processing mathematics and high-resolution experimental demonstrations. Based on the DSAL principle and standard squint-looking synthetic aperture radar theory, the data processing procedures on squint-looking DSAL image formation are obtained. The experimental DSAL setup, operating in "step-stop" strip map mode, adopts a frequency chirped laser with a wavelength of 1550 nm as the illuminating source and a specially designed random phase generator to introduce large common mode random phase error (RPE) into the phase history data of both receiving sub-apertures. High-resolution DSAL images of a cooperative target at a distance of 1.85 m and squint-looking angle of $-{10}^\circ$-10∘ or $+{10}^\circ$+10∘ are demonstrated. The DSAL images, with or without large RPE, are all well focused by straightforwardly following the given data processing steps. The result illustrates that the DSAL technique is robust in removing common mode phase errors in squint-looking configuration.

Novel acceleration compensation method for highly squint mode SAR with curve trajectory

Due to the influence of air currents and the control of the platform's own power system, acceleration is often present in the motion platform equipped with synthetic aperture radar (SAR) system, which causes the actual trajectory of the platform to be curved. When the acceleration is large or the azimuth accumulation time is long, a large envelope error or phase error will be caused. This problem will be more obvious in highly squint mode SAR. On the other hand, the acceleration may also cause the situation where the absolute value of the Doppler frequency rate is extremely small, resulting in the azimuthal time-bandwidth product that is too small to satisfy the requirements of the stationary phase principle. To solve the above problems, a novel acceleration compensation method based on inertial navigation information is proposed in this article. By integrating the acceleration and velocity information provided by the inertial navigation system, the position information of maneuvering platform is obtained. Then the actual trajectory of the platform is constructed. On this basis, the envelope and phase errors caused by the acceleration are estimated. The results of real data processing verify the correctness of the analysis and the effectiveness of the proposed method.

A new accurate discretization method for high-frequency component mechatronics systems

Modern mechatronics systems are implemented digitally. However, the magnitude and phase errors caused in the discretization process severely restrain the control performance in systems with high-frequency components where only a few sampled data points are available per period. This paper presents a new accurate discretization method for mechatronics systems that provide good performance even when intrinsic frequency components are close to the Nyquist frequency which is one-half of the sampling frequency. The bilinear transform method is most commonly used, but it causes oscillations when the initial state error of the output is not zero or when rapid changes occur in the input signal. Several variations of the bilinear transform method have been proposed to improve these problems, but as a tradeoff, they introduce large magnitude and/or phase errors at high frequencies. In this paper, a more accurate discretization method is developed, which combines a modified bilinear transform method with a new method to compensate for the frequency and damping ratio warping caused by approximate discretization. The proposed method reduces the magnitude and phase errors over the entire frequency range. The proposed method is experimentally evaluated in a mechatronics system with a mechanical resonance frequency that is about 0.6 times the Nyquist frequency.

Slippage boosted spectral cleaning in a seeded free-electron laser

The realization of fully coherent light sources at extreme ultraviolet to x-ray region has been a long-standing challenge for laser technologies. While modern single pass free-electron lasers (FELs) hold the ability to produce very intense x-ray radiation on few-femtosecond timescale, the output radiation pulses usually have noisy spectra and limited temporal coherence since the amplification starts from electron noise. A promising way for producing stable transform-limited pulses is based on the harmonic up-conversion techniques with a conventional laser as the seed. However, it is found that the insignificant phase error in the seed laser may be eventually multiplied by the harmonic number, leading to a degradation of the output temporal coherence at x-ray wavelength. Here, we report for the first time on the demonstration of a slippage boosted spectral cleaning technique to mitigate the impact of seed laser induced phase errors and to significantly improve the temporal coherence of a seeded FEL with large phase errors in the seed laser. Experimental results indicate the possibility of generating fully coherent x-ray radiation pulses with this technique.

大随机相位误差下条带模式合成孔径激光雷达成像实验

大随机相位误差下条带模式合成孔径激光雷达成像实验

Performance of differential synthetic aperture ladar versus phase-gradient autofocus at large phase errors and low return levels

The performance of differential synthetic aperture ladar (DSAL) processing versus phase-gradient autofocus (PGA) technique in SAL image formation is demonstrated experimentally using phase history data (PHD) with large random phase errors and various target returns generated from a laboratory DSAL setup operating at 1550-nm wavelength. Results show that at strong return levels, both DSAL and PGA are very robust in focusing high-resolution images from the PHD; whereas, as target returns become weak and PHD is dominated by noise, the iterative PGA performs less effectively than the DSAL does. It is concluded that, on the whole, the DSAL technique is possibly more robust than PGA in both effectiveness and efficiencies.