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We thank Dr. Yurkin for his considered and constructive critique of our paper. We respond to his insightful comments below and hope that this discussion motivates further communication and cooperation and benefits to the scattering by small particles community. Key Points: Fenni et al. (2021, https://doi.org/10.1029/2020jd034172) main outcome is the enhancement in accuracy and computational cost of MIDAS with use of higher‐order quadrature schemesMajor conclusions of Fenni et al. (2021, https://doi.org/10.1029/2020jd034172) are validated on a large set of realistic arbitrarily‐shaped ice aggregates [ABSTRACT FROM AUTHOR]

In a recent study, a 2-D pseudospectral time-domain (PSTD) full-wave simulator was developed and demonstrated to be capable of efficiently solving large-scale low-frequency (e.g., HF) electromagnetic scattering problems, for example, on the application of radar sounding simulations of planetary clutter and subsurfaces. In this article, the 2-D PSTD simulator is applied to simulate a domain as large as 4000 $\lambda $ (along-track) $\times 1666.67\,\,\lambda $ (cross-track) $\times 33.33\,\,\lambda $ (depth) with $\lambda =15$ m at an HF frequency of 20 MHz. To accomplish the goal, the simulator is further improved to efficiently model/simulate large cross-track slices of dielectric scenes by allowing nonuniform grid sampling in horizontal (lateral) and vertical directions, and the cross-track results are then stitched together along the track to form the simulated radargram. By combining the SHAllow RADar (SHARAD) viewing geometry and Mars Orbital Laser Altimeter (MOLA) digital elevation model (DEM), we simulate SHARAD returns at three different sites on Mars: one at the North Pole and two at Oxia Planum. At all three sites, the PSTD simulated radargrams are compared with measured SHARAD radargrams. Through power-level calibration and reference time adjustment, the PSTD simulated power estimates are further validated by comparing with real power observations from SHARAD with a 5-dB uncertainty and Pearson correlation coefficient of 0.3–0.4 (a $p$ -value on the order of $10^{-9}$), which justifies the use of the 2-D PSTD simulator for emulating surface clutter in planetary radar sounding. This simulator is open source and can be easily modified to support radar sounding simulations in support of other planetary missions with radar sounding instruments. [ABSTRACT FROM AUTHOR]

A compression algorithm for the T-matrix scattering solution from multiple objects and incident fields is derived and examined which we call the Compressed T-Matrix Algorithm (CTMA). The CTMA is derived by applying the SVD and Woodbury matrix-inverse identity to compress the original T-matrix system of equations and simultaneously compress the matrix of right-hand side incident field vectors. This is suited for scattering problems with many incident directions. We quantify the compression rates for different collections of dielectric spheres and draw comparisons to the Characteristic Basis Function Method (CBFM) with which the CTMA shares many structural similarities. [ABSTRACT FROM AUTHOR]

Low-frequency radar sounders have the potential to generate altimetric profiles, but the feasibility of utilizing planetary radar sounding data as an alternative to laser altimetry has not been assessed using existing data to date. Therefore, we have developed, implemented, and evaluated an algorithm to process SHAllow RADar sounder (SHARAD) data on Mars (Experiment Data Records as available on the planetary data system) first into altimetry profiles and ultimately into digital terrain models (DTMs). The minimally processed data are pulse compressed, corrected for ionospheric distortion, zero-Doppler filtered, and incoherently summed. We then apply pulse re-tracking techniques adapted from terrestrial ocean altimetry to identify the surface return. From the surface return we compute the time-of-flight and hence the range from the spacecraft to the surface of the planet. The altimetry groundtracks are then co-registrated with Mars Orbiter Laser Altimeter (MOLA) to remove any biases resulting from residual ionospheric effects or timing issues. The altimetric profiles are finally used to create DTMs based on SHARAD data. While the SHARAD altimetry data have coarser inherent resolution than laser altimeters or imaging radars, we demonstrate that radar sounding data is still a viable source for satellite-based altimetry measurements. This is particularly important for future planetary missions not carrying laser altimeters but radar sounders, such as the upcoming Europa Clipper mission. [ABSTRACT FROM AUTHOR]

Recent work has demonstrated a passive radio sounding approach that uses the Sun as a source for echo detection and ranging. As the Sun is a moving source with a position that is known a priori, we evaluate this technique’s capabilities to measure the echo’s phase history, map topography, and perform synthetic aperture radar (SAR) focusing. Here, we present our approach to implementing passive SAR using a compact, temporally incoherent radio-astronomical source as a signal of opportunity. We first evaluate the passive system’s capabilities to obtain an echo from a rough surface by determining the critical signal-to-noise ratio (SNR) for reliably observing the Sun’s echo reflection with our passive instrument. We then demonstrate that our technique can detect the necessary changes in range, phase, and reflectivity of an echo from the Sun. We next present the experimental results of our passive radar testing using the Sun at Dante’s View, Death Valley, to highlight this technique’s ability to perform 2-D imaging. Finally, with synthetic data, we demonstrate that we can use time-domain backprojection to focus a planar white noise signal, perform passive SAR imaging, and improve the measurement’s SNR and azimuth resolution. The results of passive SAR focusing on white noise highlight the potential for the Sun and Jupiter’s radio emissions to perform surface and subsurface imaging for planetary and terrestrial observations. [ABSTRACT FROM AUTHOR]

We evaluate several high‐order quadrature schemes for accuracy and efficacy in obtaining orientation‐averaged single‐scattering properties (SSPs). We use the highly efficient MIDAS to perform electromagnetic scattering calculations to evaluate the gain in efficiency from these schemes. MIDAS is shown to be superior to DDSCAT, a popular discrete dipole approximation (DDA) method. This study is motivated by the fact that quality physical precipitation retrievals rely on using accurate orientation‐averaged SSPs derived from realistic hydrometeors as input to radiative transfer models (RTM). The DDA has been a popular choice for single‐scattering calculations, due to its versatility with respect to target geometry. However, being iterative‐solver‐based (ISB), the most used DDA codes, for example, DDSCAT and ADDA (formerly, Amsterdam DDA), must solve the scattering problem for each orientation of the target separately. As the size parameter and geometric anisotropy of the hydrometeor increase, the number of orientations needed to obtain accurate orientation‐averages can increase drastically and so does the computation cost incurred by the ISB‐DDA methods. MIDAS is a Direct‐Solver‐Based (DSB) code, its decomposition of the original large matrix with a high rank into multiple more manageable smaller matrices of lower ranks makes it much more computationally efficient while maintaining excellent accuracy. In addition, direct solvers consider all requested orientations at once, giving MIDAS further advantage over popular ISB‐DDA methods. MIDAS, when combined with high‐order quadrature for orientation averaging, can be greater than three orders of magnitude more efficient in obtaining RTM‐ready SSPs of complex‐shaped hydrometeors than existing ISB‐DDA methods, with the native quadrature schemes they offer. Key Points: The direct solver‐based MIDAS is used to compute orientation‐averaged single‐scattering properties (SSPs) of realistic complex‐shape hydrometeorsThe number of incident directions needed to achieve SSPs convergence is investigated for several quadrature schemesOrientation‐averaged single‐scattering of realistic hydrometeors is more efficiently calculated with Lebedev quadrature and Spherical Design [ABSTRACT FROM AUTHOR]

We report the analysis of opposite-side ambiguities in single-pass radar sounding interferometry. Nadir pointing radar sounders suffer inherent cross track ambiguities that cannot be separated with the power image alone. Interferometry can be used to interpret these ambiguities when data are collected with multichannel receivers. However, opposite-side surface clutter, volume scattering, and cross track range misalignment create unique interferometric phase and correlation signatures. Such signatures are observed experimentally in data collected by the Polarimetric Airborne Radar Ice Sounder (POLARIS) P-band multichannel radar sounder. We derive analytic expressions to predict the observations and validate them with simulation. In addition, we observe and explain a correlation dropout feature that is due to volume scattering competing with surface clutter in the null of the cross track antenna pattern. The purpose of this article is to explain opposite-side ambiguity signatures in radar sounder interferometry and provide models and techniques for scientific interpretation of interferograms. [ABSTRACT FROM AUTHOR]

This article discusses the implementation of a 2-D pseudospectral time-domain (PSTD) full-wave simulator for solving large-scale low-frequency (e.g., HF) electromagnetic (EM) scattering problems with the application of radar sounding of planetary subsurfaces. Compared to other computational EM algorithms, the PSTD solver is both memory-efficient and accurate for sounding applications. New domain designs are developed to efficiently simulate 2-D scattering of half-space media for normal and oblique incidence from arbitrary wave sources. As a validation of the PSTD simulator, the simulated 2-D scattering radar cross width (RCW) is compared with the analytical solutions of both point targets (dielectric cylinders) and distributed targets (random rough surfaces), for the first time, where the frequency and angular (bistatic scattering) dependence are studied with various choices of grid sampling resolution. Furthermore, the PSTD solver is applied to passive synthetic aperture radar (SAR) sounding problems (single transmitter and several receivers), for the first time, where various scenarios (e.g., cylinder, surface, and volume) are demonstrated and the targets are correctly resolved after focusing, indicating an accurate simulation of the phase history. Finally, an example of using the solver is shown for emulating 3-D large-scale radar sounding problems with cross-track surface and subsurface scattering. This is particularly useful to simulate radar sounding returns and SAR-focused imagery of large-scale subsurface structures to better support planetary missions with radar sounding instruments. [ABSTRACT FROM AUTHOR]

This article presents a design for implementing an ultrawideband (UWB) software-defined radar (SDRadar) using a bandwidth reconstruction technique, called frequency stacking, for a stepped frequency signal to create a synthetic wideband waveform (SWW). Practical methods of overcoming traditional limitations of SDRadar and stepped chirp radar are introduced, and the performance is demonstrated using a commercial battery-powered universal software radio peripheral (USRP) software-defined radio (SDR). Application-specific considerations are made and performance tradeoffs are demonstrated. Furthermore, the method is shown to be the coherence solution for otherwise noncoherent low-cost communications’ SDR systems. The proposed design has multiple applications in low-cost, reconfigurable ground-penetrating radar (GPR) and small unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) platforms. [ABSTRACT FROM AUTHOR]

This work is a collection of radar equations for low-frequency radar sounding and radar in general that emphasize the form of the radar equation for different target and source geometries. This is meant as a handbook for scientists and engineers that work with or analyze radar sounder systems and interpret radar sounding echoes. Lookup tables summarize the results and derivations are provided for each equation. [ABSTRACT FROM AUTHOR]

The homodyned-K (HK) distribution is a three-parameter density function used to study mixed-species radar and ultrasound scattering phenomena. We analyze the distribution that results from corrupting the HK with additive Gaussian noise (HKN). This modification enables analytic study of the HK in the presence of system thermal noise in radar and ultrasound systems. The moments of intensity of the HKN are derived and a new moment method parameter estimation algorithm is tested in simulation. [ABSTRACT FROM AUTHOR]

This paper reports a method to analyze surface clutter discrimination for radar sounding interferometry. Nadir-looking low-frequency radar sounders cannot easily resolve off-nadir surface echoes from subsurface nadir echoes. Sounders equipped with multichannel receivers can use interferometric phase to discriminate whether a feature is at nadir or not. We developed a method to evaluate the performance of this application of interferometry and used it to analyze the selected Radar for Europa Assessment and Sounding: Ocean to Near-surface (REASON) instrument on NASA's Europa Clipper mission to Jupiter's moon Europa. [ABSTRACT FROM AUTHOR]

This paper reports the analysis of the geometric power fall-off of Fresnel zone scattering in radar sounding. Radar sounders can take advantage of strong coherent scattering from Fresnel zones at nadir which grow with sensor altitude. The strength of the signal and the actual rate of power fall-off, however, depend heavily on the surface properties. We first use the radar equation to separate geometric versus scattering mechanisms driving $R^{2}$ , $R^{3}$ , or $R^{4}$ fall-off. The Fresnel zone for planetary surfaces, where body curvature has an effect, is derived and its implications discussed. We show the impact of Gaussian and fractal surface roughness on the exponent of power fall-off and the transition from coherent to incoherent scattering. This is done in simulation and analytically to derive coherence loss functions. Finally, we study the effect of incoherent area fraction within the Fresnel zone. These results are intended to be used in radar link budgets, performance metrics, and scientific interpretation of sounding data. [ABSTRACT FROM AUTHOR]

This letter reports a method to compute the multilook interferometric phase probability density function (pdf) used in interferometric synthetic aperture radar (InSAR). The method is fast and accurate for at least 10 000 looks and the full range of interferometric correlations. This is accomplished by computing the products of large and small numbers in the underlying hypergeometric series logarithmically and by deriving a single-term recursion relation to accelerate the computation. This letter extends the usable range of inputs to the multilook interferometric phase pdf for radar systems with a large number of looks and the entire practical range of interferometric correlation. [ABSTRACT FROM PUBLISHER]

Automated 3D breast ultrasound (ABUS) has shown several advantages over the conventional handheld systems and promising results in screening women with dense breasts. In addition, ABUS seems to offer a unique opportunity for mapping in vivo the normal ducts thus improving our understanding of normal/malignant relationships in the adult female breast. Preliminary results of such a study are reported here. Six lactating, nursing volunteers were scanned with the Invenia™ ABUS system (GE Healthcare, WI, USA). The women were imaged before and after breastfeeding their infants. Ductal patterns were generated from the manual segmentations of two experts. Results were qualitatively compared to published work. Descriptive statistics and the t -test were applied to characterize the population and variabilities. Milk filled ducts in lactating women offered a natural contrast agent but empty ducts may also be observed under light breast compression. Most of the ducts were detected and 3D maps were generated. An increased localized activity of milk filled ducts was observed in the lower outer quadrants of all breasts. Ducts from the upper quadrants show involvement in women breastfeeding the longest (11–18 months). Intra- and inter-volunteer variabilities were significant. The ABUS system provided sufficient information to detect and segment most of the breast ducts. The observed localized activity of the ducts agrees with results from prior similar studies and raises new important issues regarding the role of duct involution on cancer development. Further testing is justified as is the development of computer algorithms for automated 3D ductal structure generation. [ABSTRACT FROM AUTHOR]