Hyperbolic Range Research Articles

An improved equivalent acceleration imaging approach for spaceborne sliding spotlight SAR

The traditional hyperbolic range equation model will produce large errors in the spaceborne sliding spotlight synthetic aperture radar with large azimuth time. Although the equivalent acceleration range model (EARM) can deal with the problem of large azimuth scenes well, the interpolation steps from azimuth resampling make the computational burden of algorithm very huge. In response to this problem, this paper improves EARM by dividing the range model into two parts: residual terms of azimuth time and equivalent range expression. The frequency domain imaging algorithm designed for the new range model omits the interpolation step of azimuth resampling. The simulation experiments verify the efficiency and validity of the proposed methodology.

Azimuth Multichannel Reconstruction Based on Advanced Hyperbolic Range Equation

To acquire high-resolution wide-swath (HRWS) imaging capacity, the displaced phase center multichannel azimuth beam (DPCMAB) technology is usually adopted in spaceborne synthetic aperture radar (SAR), while multichannel reconstruction must be carried out before imaging process due to azimuth nonuniform sampling. Up to now, almost all azimuth multichannel reconstruction algorithms have been mainly based on conventional hyperbolic range equation (CHRE), but the accuracy of the CHRE model is usually not suitable for the HRWS mode, especially for high resolution and large squint observation cases. In this study, the azimuth multichannel signal model based on the advanced hyperbolic range equation (AHRE) is established and analyzed. The major difference between multichannel signal models based on CHRE and AHRE is the additional time-varying phase error between azimuth channels. The time-varying phase error is small and can be ignored in the monostatic DPCMAB SAR system, but it must be considered and compensated in the distributed DPCMAB SAR system. In addition to the time-varying phase error, additional Doppler spectrum shift and extended Doppler bandwidth should be considered in the squint case during azimuth multichannel reconstruction. The azimuth multichannel reconstruction algorithm based on AHRE is proposed in this paper. Before multichannel reconstruction and combination, time-varying phase errors between azimuth channels were first compensated, and the range-frequency-dependent de-skewing function was derived to remove the two-dimension (2D) spectrum tilt to avoid azimuth under-sampling. Then, azimuth multichannel data were reconstructed according to the azimuth multichannel impulse response based on AHRE. Finally, the range-frequency dependent re-skewing function was introduced to recover the tilted 2D spectrum. Simulation results on both point and distributed targets validated the proposed azimuth multichannel reconstruction approach.

Modified Chirp Scaling Algorithm for Ultra-High Resolution Spaceborne-SAR

The hyperbolic range equation model (HREM) and equivalent squint range model (ESRM) are applied in traditional chirp scaling algorithm (CSA). However, these range models cannot describe the satellite range history in the high-resolution case accurately because of the long azimuth integration time. The non-negligible phase error caused by this will lead the targets distort. In this paper, a modified chirp scaling algorithm (MCSA) is proposed by introducing a novel high-precision range model. A more accurate signal spectrum is calculated through it. Then, the modified chirp scaling factor, range compression filter, range cell migration correction (RCMC) filter and azimuth compression filter can be derived based on this signal spectrum, and the focused target obtained at last. Finally, the experimental results, to validate the proposed algorithm, adopted by the sliding spotlight synthetic aperture radar (SAR) simulation are provided.

Pre-stack sea bottom detection and swell correction within an expected hyperbolic range for noisy high-resolution 8-channel airgun seismic data

High-resolution marine seismic data degraded by sea swell can be enhanced by swell correction. To correct for swell, two-way travel times are detected for sea bottom locations in seismic traces; linear predicted values are calculated from the previously detected travel times, and correct static shifts between the detected and calculated values before stacking. To pick sea bottom locations for very large numbers of seismic traces, automatic sea bottom detection (SBD) is normally required. However, sea bottom signal degradation by wave noise causes SBD failure. Our first SBD trial using trace-by-trace (TBT) picking from raw and energy ratio data was unsatisfactory, with many of the detected sea bottom values deviating from the correct values due to noise in the field data. However, we achieved reasonable results by considering source–receiver geometry and previously detected sea bottom values. We picked reliable sea bottom values within an expected hyperbolic range (EHR) calculated from the source–receiver offset and group interval. To prevent excessive correction for swell, we excluded unreliable picks that deviated greatly from the linear trend of previously detected sea bottom values, or from the immediately preceding value. Swell correction within the EHR significantly improved the quality of noisy data. We applied this method to noisy field seismic data acquired offshore Yeosu, Korea, and successfully detected the sea bottom, corrected for swell, and improved seismic section. Thus, high-resolution marine seismic data degraded by sea swell can be enhanced by pre-stack swell correction in shot gathers using a hyperbola calculated based on source–receiver geometry.

Mid-IR and UV-Vis-NIR Mueller matrix ellipsometry characterization of tunable hyperbolic metamaterials based on self-assembled carbon nanotubes

Mueller matrix ellipsometry over the wide spectral range from the mid-IR to UV is applied to characterize the dielectric function tensor for films of densely packed single-walled carbon nanotubes aligned in the surface plane. These films optically act as metamaterials with an in-plane anisotropic, bulk effective medium response. A parameterized oscillator model is developed to describe electronic interband transitions, π−π⋆ plasmon resonances, and free-carrier absorption. Wide ranges of hyperbolic dispersion are observed and exceptional tuneability of the hyperbolic ranges is demonstrated by comparing results for a film of aligned but unordered carbon nanotubes with a film fabricated under optimized conditions to achieve hexagonally close-packed alignment of the nanotubes. The effect of doping on the optical properties and hyperbolic range is discussed.

Focusing Bistatic Forward-looking Synthetic Aperture Radar Based on An Improved Hyperbolic Range Model and A Modified Omega-K algorithm.

For parallel bistatic forward-looking synthetic aperture radar (SAR) imaging, the instantaneous slant range is a double-square-root expression due to the separate transmitter-receiver system form. The hyperbolic approximation provides a feasible solution to convert the dual square-root expression into a single-square-root expression. However, some high-order terms of the range Taylor expansion have not been considered during the slant range approximation procedure in existing methods, and therefore, inaccurate phase compensation occurs. To obtain a more accurate compensation result, an improved hyperbolic approximation range form with high-order terms is proposed. Then, a modified omega-K algorithm based on the new slant range form is adopted for parallel bistatic forward-looking SAR imaging. Several simulation results validate the effectiveness of the proposed imaging algorithm.

Effects of the Earth’s Curvature and Lunar Revolution on the Imaging Performance of the Moon-Based Synthetic Aperture Radar

In this paper, effects of the earth’s curvature and lunar revolution on the performance of the moon-based synthetic aperture radar (SAR) are examined by a comprehensive analysis of the motion-induced Doppler frequency and Doppler rate on which azimuthal imaging relies. The motion effects include the earth’s self-rotation related to the earth’s curvature and lunar revolution around the earth. An extended hyperbolic range equation (EHRE) is proposed in line of the equivalent velocity and equivalent squint angle, and then the signal model based on the EHRE is established to simulate the moon-based SAR image from which the imaging performance is analyzed. Theoretical analyses show that the earth’s curvature is a dominant factor in determining the moon-based SAR’s Doppler and azimuthal resolution. Furthermore, the earth’s curvature distorts the SAR image by way of rotating the azimuth imaging from the cross-range direction within a certain skewed angle. The overall effects of lunar revolution generate a velocity correction factor and a deviate squint angle, which subsequently deteriorate the azimuthal resolution and image focusing. Results also show that effects of the earth’s curvature and lunar revolution are in connection with relative positions of the ground target and moon-based SAR. To this end, numerical simulations using point target response is carried out to accentuate the necessary for taking account of the Doppler error induced by the lunar revolution.

Improved range model based on parameter estimation for high resolution and high squint LEO SAR

Due to the curve of the LEO synthetic aperture radar (SAR) orbit and the rotation of the earth, the high resolution imaging for LEO SAR is always facing the problem of obtaining accurate range history. Meanwhile, with the increase of squint angle, it will take longer azimuth time to meet the same high resolution. In this paper, an improved hyperbolic range equation (IHRE) is presented to model the accurate range history for high squint LEO SAR. First, the state vectors of satellite are used to estimate the Doppler parameters. Then, the improved hyperbolic range equation is recovered based on the estimation of the Doppler parameters. Compared with other existing methods, the superiority of IHRE is more precise in the condition of high squint LEO SAR which can provide sufficient azimuth time for high resolution imaging. The simulation and analysis validate the precision of the proposed range history model.

A modified Omega-K algorithm for squint circular trace scanning SAR using improved range model

Abstract For squint circular trace scanning SAR (CTSSAR), the circular flight trajectory and squint angle make the conventional hyperbolic range model (CHRM) hard to accurately represent the true range history. Traditional frequency domain algorithms cannot accomplish precise imaging directly. To address this problem, a modified Omega-K algorithm with improved range model is proposed. The algorithm can be divided into two main steps: Range-independent error compensation and range-dependent error compensation. By employing the improved range model, the complex coarse range-independent range phase error is compensated. Then the omega-K algorithm is implemented to remove the residual range-dependent phase error for target focusing. Simulation results validate the effectiveness of the proposed range model together with the imaging algorithm.

Focusing of SAR With Curved Trajectory Based on Improved Hyperbolic Range Equation

For a synthetic aperture radar (SAR) system with curved trajectory, which is different from the conventional SAR, the downward velocity and the acceleration result in highly complicated range history, making it hard to achieve a focused target response. The traditional SAR imaging algorithms are not accurate enough to compensate the phase errors introduced from the highly complicated range history. In this letter, considering the impact of complex range history, an improved hyperbolic range equation is proposed to access the 2-D spectrum for curved trajectory SAR imaging. Based on the derived spectrum, frequency-domain imaging algorithm can be performed to focus targets. By analyzing the phase error and comparing with other current range models, the proposed range model is proved to be precise enough to deal with the complex motion model happened in curved trajectory SAR imaging. Simulation experiments are implemented to evaluate the imaging performance of the proposed approach.

Comparison of the Hyperbolic Range of Two-fluid Models on Two-phase Gas-liquid Flows

In this paper, a numerical study is conducted in order to compare hyperbolic range of equations of isotherm two-fluid model governing on two-phase flow inside of pipe using conservative Shock capturing method. Differential equations of the two-fluid model are presented in two forms (i.e. form I and form II). In forms I and II, pressure correction terms are hydrodynamic and hydrostatic, respectively. In order to compare, the hyperbolic range of equations of two-fluid model is presented in two forms. One case (water Faucet Case) in the vertical configuration and two other cases (i.e. Large Relative Velocity Shock Tube Case and Toumi’s Shock Tube Case) in the horizontal configuration were used. The form I of two-fluid model had broader range of well-posing than form II of two-fluid model. The form I of two-fluid model has coefficient that proper selecting of this coefficient ensures hyperbolic roots of the characteristic equation, but in form II, roots of the characteristic equation did not have this capability.

A Chirp Scaling Algorithm for Forward-Looking Linear-Array SAR With Constant Acceleration

For forward-looking linear-array synthetic aperture radar (FLLA-SAR) with constant acceleration, the conventional hyperbolic range model is incorrect, and the range-dependent range cell migration (RCM) cannot be ignored any more. Hence, the traditional chirp scaling (CS) algorithm based on the hyperbolic range model also cannot be used. To overcome these problems, a modified range model for the FLLA-SAR which has taken the platform’s acceleration into consideration is proposed in this letter. Based on the model, an improved CS method is proposed for FLLA-SAR to eliminate the space-variant characteristic of the RCM. Simulation results are presented to validate the range model and the proposed method.

Perfect Absorption With Trapezoidal Gratings Made of Natural Hyperbolic Materials

ABSTRACTBroadband absorption is needed for a wide spectrum of applications such as solar–thermal conversion, radiative cooling, and photodetection. In this work, we theoretically show that trapezoidal gratings made of a natural hyperbolic material on a metal substrate can be used to achieve omnidirectional perfect absorption in a relatively broad spectral region. Hexagonal boron nitride (hBN) is taken as a mid-infrared polar material with hyperbolic characteristic in the wavelength region from 6.2 to 7.3 μm. The anisotropic rigorous-coupled wave analysis is used to calculate the absorptance as well as the local power dissipation and field distributions. The main mechanism for the broadband perfect absorption is elucidated by considering the slow-light effect in a hyperbolic waveguide, which can trap the incident light of different wavelengths in different regions of the trapezoid. The spectral range and bandwidth of near perfect absorption can be adjusted within the hyperbolic range of the material by changing the shape of the trapezoid. Moreover, the substrate can play a role on the reflectance and transmittance of the structure for the wavelengths that do not support the slow-light effect. Similar designs can be applied to other hyperbolic materials to achieve perfect absorption in various wavelength regions.

Equivalent hyperbolic range model for synthetic aperture radar with curved track

In the imagery of synthetic aperture radar with curved track, the traditional hyperbolic range model (HRM) is inaccurate due to the existence of acceleration. Thus, the traditional imaging algorithms of high precision based on HRM such as Omega-K algorithm are no longer available. For this problem, an equivalent HRM which can precisely take the curved track into account is proposed. Then, Omega-K algorithm with some refinements based on this new range model could be used. Simulation results validate the effectiveness of the proposed range model.

An Improved Range Model and Omega-K-Based Imaging Algorithm for High-Squint SAR With Curved Trajectory and Constant Acceleration

For high-squint synthetic aperture radar (SAR) with curved trajectory, the traditional hyperbolic range model (HRM) is inaccurate, and the variation of velocity caused by constant acceleration in azimuth dimension cannot be ignored. Thus, the traditional omega-K imaging algorithms based on HRM are no longer available. For this problem, this letter proposes an improved range model, which can precisely take account for the curved trajectory. Then, a modified omega-K algorithm based on this new range model is proposed for high-squint SAR imaging. Simulation results validate the effectiveness of the improved range model and imaging algorithm.

Extended nonlinear chirp scaling algorithm for highly squinted missile-borne synthetic aperture radar with diving acceleration

An extended nonlinear chirp scaling (NLCS) algorithm is proposed to process data of highly squinted, high-resolution, missile-borne synthetic aperture radar (SAR) diving with a constant acceleration. Due to the complex diving movement, the traditional signal model and focusing algorithm are no longer suited for missile-borne SAR signal processing. Therefore, an accurate range equation is presented, named as the equivalent hyperbolic range model (EHRM), which is more accurate and concise compared with the conventional fourth-order polynomial range equation. Based on the EHRM, a two-dimensional point target reference spectrum is derived, and an extended NLCS algorithm for missile-borne SAR image formation is developed. In the algorithm, a linear range walk correction is used to significantly remove the range-azimuth cross coupling, and an azimuth NLCS processing is adopted to solve the azimuth space variant focusing problem. Moreover, the operations of the proposed algorithm are carried out without any interpolation, thus having small computational loads. Finally, the simulation results and real-data processing results validate the proposed focusing algorithm.

Processing of Very High Resolution Spaceborne Sliding Spotlight SAR Data Using Velocity Scaling

In spaceborne synthetic aperture radar, the sliding spotlight mode can acquire high resolution and large azimuth scene size simultaneously. However, when the resolution is very high and the azimuth scene size is large, the traditional hyperbolic range model (HRM) is inaccurate and the variation of the equivalent velocity in azimuth dimension cannot be ignored. Thus, the traditional imaging algorithms based on HRM are no longer available. For this problem, this paper proposes an equivalent acceleration range model, which can precisely take into account the spaceborne curved orbit. Then, velocity scaling algorithm based on this new range model is proposed to meet the needs of very high resolution and large azimuth scene size. The results of the simulation validate the effectiveness of the new range model and the imaging algorithm.

Resolution calculation and analysis in high‐resolution spaceborne SAR

In high-resolution spaceborne synthetic aperture radar (SAR), the hyperbolic range equation assumption fails to precisely describe the range history; thus, the traditional resolution analysis used for a spaceborne SAR design is imprecise. A curved orbit geometrical model based on the modified equivalent squint range model is graphically presented by vector notation. According to the model, the vectorial calculation of resolution is analytically presented, based on the gradient method. Additionally, a physical model is introduced to derive the effective integration time, which is quite difficult to derive due to the three-dimensional curved orbit. Simulation results are presented to validate the proposed method.

Focusing of geosynchronous SAR with nonlinear chirp scaling algorithm

In geosynchronous (GEO) synthetic aperture radar (SAR), the satellite track is curvilinear and the typical assumption of ‘stop-and-go’ breaks down due to the increase of orbit altitude. Thus, standard imaging algorithms based on the conventional hyperbolic range equation (CHRE) become inadequate. A four-order range equation taking the ‘stop-and-go’ errors into consideration is adopted to improve the accuracy in the approximation of the range history for GEO SAR. Then, an accurate two-dimensional spectrum is analytically deduced under the curved trajectory model, and a modified nonlinear chirp scaling (NLCS) algorithm is proposed according to this new spectrum. Simulation results validate that the proposed algorithm has better performance than the CHRE-based NLCS algorithm in the GEO cases.

Extension of Wavenumber Domain Focusing for spotlight COSMO-SkyMed SAR Data

In this work we describe a method to handle curved orbits in wavenumber domain focusing algorithm for high-resolution SAR data acquired by Low Earth Orbit satellites using spotlight mode. The standard wavenumber domain focusing algorithm make assumptions that start to be invalid when applied to high-resolution spotlight SAR data acquired in spaceborne low Earth orbit (LEO) configurations. The assumption of a hyperbolic range history is no longer accurate for sub-metric spatial resolutions due to the satellite curved orbit. The proposed method is used to estimate the satellite velocity and closest-approach range distance of the rectified effective orbit which minimizes the phase errors over the whole scene coverage. This allows to use all frequency domain focusing kernels developed to focus SAR images acquired with a stripmap mode. We use this method with the ω- k algorithm, and its approximation Fast ω-k (Fω-k), demonstrating its effectiveness to focus COSMO-SkyMed (CSK) SAR images obtaining, respectively, sub-metric and metric azimuth spatial resolution.