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NASA NTRS1985

Neighborhood comparison operator

Digital values in a moving window are compared by an operator having nine comparators connected to line buffers for receiving a succession of central pixels together with eight neighborhood pixels. A single bit of program control determines whether the neighborhood pixels are to be compared with the central pixel or a threshold value. The central pixel is always compared with the threshold. The omparator output plus 2 bits indicating odd-even pixel/line information about the central pixel addresses a lookup table to provide 14 bits of information, including 2 bits which control a selector to pass either the central pixel value, the other 12 bits of table information, or the bit-wise logical OR of all nine pixels through circuit that implements a very wide OR gate.

Gennery, D. B.↗

NASA NTRS2007

The Effects of Radiation on Imagery Sensors in Space

Recent experience using high definition video on the International Space Station reveals camera pixel degradation due to particle radiation to be a much more significant problem with high definition cameras than with standard definition video. Although it may at first appear that increased pixel density on the imager is the logical explanation for this, the ISS implementations of high definition suggest a more complex causal and mediating factor mix. The degree of damage seems to vary from one type of camera to another, and this variation prompts a reconsideration of the possible factors in pixel loss, such as imager size, number of pixels, pixel aperture ratio, imager type (CCD or CMOS), method of error correction/concealment, and the method of compression used for recording or transmission. The problem of imager pixel loss due to particle radiation is not limited to out-of-atmosphere applications. Since particle radiation increases with altitude, it is not surprising to find anecdotal evidence that video cameras subject to many hours of airline travel show an increased incidence of pixel loss. This is even evident in some standard definition video applications, and pixel loss due to particle radiation only stands to become a more salient issue considering the continued diffusion of high definition video cameras in the marketplace.

Mathis, Dylan↗

NASA NTRS1987

Neighborhood comparison operator

Digital values in a moving window are compared by an operator having nine comparators (18) connected to line buffers (16) for receiving a succession of central pixels together with eight neighborhood pixels. A single bit of program control determines whether the neighborhood pixels are to be compared with the central pixel or a threshold value. The central pixel is always compared with the threshold. The comparator output, plus 2 bits indicating odd-even pixel/line information about the central pixel, addresses a lookup table (20) to provide 14 bits of information, including 2 bits which control a selector (22) to pass either the central pixel value, the other 12 bits of table information, or the bit-wise logic OR of all neighboring pixels.

Gennery, Donald B.↗

NASA NTRS2008

Image Edge Extraction via Fuzzy Reasoning

A computer-based technique for detecting edges in gray level digital images employs fuzzy reasoning to analyze whether each pixel in an image is likely on an edge. The image is analyzed on a pixel-by-pixel basis by analyzing gradient levels of pixels in a square window surrounding the pixel being analyzed. An edge path passing through the pixel having the greatest intensity gradient is used as input to a fuzzy membership function, which employs fuzzy singletons and inference rules to assigns a new gray level value to the pixel that is related to the pixel's edginess degree.

Dominquez, Jesus A.↗

NASA NTRS2008

Image edge extraction via fuzzy reasoning

Dominguez, Jesus A.↗

NASA NTRS2012

Sensitivity of Marine Warm Cloud Retrieval Statistics to Algorithm Choices: Examples from MODIS Collection 6

The optical and microphysical structure of warm boundary layer marine clouds is of fundamental importance for understanding a variety of cloud radiation and precipitation processes. With the advent of MODIS (Moderate Resolution Imaging Spectroradiometer) on the NASA EOS Terra and Aqua platforms, simultaneous global/daily 1km retrievals of cloud optical thickness and effective particle size are provided, as well as the derived water path. In addition, the cloud product (MOD06/MYD06 for MODIS Terra and Aqua, respectively) provides separate effective radii results using the l.6, 2.1, and 3.7 ~m spectral channels. Cloud retrieval statistics are highly sensitive to how a pixel identified as being "notclear" by a cloud mask (e.g., the MOD35/MYD35 product) is determined to be useful for an optical retrieval based on a 1-D cloud model. The Collection 5 MODIS retrieval algorithm removed pixels associated with cloud'edges as well as ocean pixels with partly cloudy elements in the 250m MODIS cloud mask - part of the so-called Clear Sky Restoral (CSR) algorithm. Collection 6 attempts retrievals for those two pixel populations, but allows a user to isolate or filter out the populations via CSR pixel-level Quality Assessment (QA) assignments. In this paper, using the preliminary Collection 6 MOD06 product, we present global and regional statistical results of marine warm cloud retrieval sensitivities to the cloud edge and 250m partly cloudy pixel populations. As expected, retrievals for these pixels are generally consistent with a breakdown of the ID cloud model. While optical thickness for these suspect pixel populations may have some utility for radiative studies, the retrievals should be used with extreme caution for process and microphysical studies.

Platnick, Steven↗

NASA NTRS2013

Measuring and Estimating Normalized Contrast in Infrared Flash Thermography

Infrared flash thermography (IRFT) is used to detect void-like flaws in a test object. The IRFT technique involves heating up the part surface using a flash of flash lamps. The post-flash evolution of the part surface temperature is sensed by an IR camera in terms of pixel intensity of image pixels. The IR technique involves recording of the IR video image data and analysis of the data using the normalized pixel intensity and temperature contrast analysis method for characterization of void-like flaws for depth and width. This work introduces a new definition of the normalized IR pixel intensity contrast and normalized surface temperature contrast. A procedure is provided to compute the pixel intensity contrast from the camera pixel intensity evolution data. The pixel intensity contrast and the corresponding surface temperature contrast differ but are related. This work provides a method to estimate the temperature evolution and the normalized temperature contrast from the measured pixel intensity evolution data and some additional measurements during data acquisition.

Koshti, Ajay M.↗

NASA NTRS2017

Evaluation of Satellite Remote Sensing Albedo Retrievals over the Ablation Area of the Southwestern Greenland Ice Sheet

MODerate resolution Imaging Spectroradiometer (MODIS) albedo products have been validated over spatially uniform, snow-covered areas of the Greenland ice sheet (GrIS) using the so-called single 'point-to-pixel' method. This study expands on this methodology by applying a 'multiple-point-to-pixel' method and examination of spatial autocorrelation (here using semivariogram analysis) by using in situ observations, high-resolution World- View-2 (WV-2) surface reflectances, and MODIS Collection V006 daily blue-sky albedo over a spatially heterogeneous surfaces in the lower ablation zone in southwest Greenland. Our results using 232 ground-based samples within two MODIS pixels, one being more spatial heterogeneous than the other, show little difference in accuracy among narrow and broad band albedos (except for Band 2). Within the more homogenous pixel area, in situ and MODIS albedos were very close (error varied from −4% to +7%) and within the range of ASD standard errors. The semivariogram analysis revealed that the minimum observational footprint needed for a spatially representative sample is 30 m. In contrast, over the more spatially heterogeneous surface pixel, a minimum footprint size was not quantifiable due to spatial autocorrelation, and far exceeds the effective resolution of the MODIS retrievals. Over the high spatial heterogeneity surface pixel, MODIS is lower than ground measurements by 4-7%, partly due to a known in situ undersampling of darker surfaces that often are impassable by foot (e.g., meltwater features and shadowing effects over crevasses). Despite the sampling issue, our analysis errors are very close to the stated general accuracy of the MODIS product of 5%. Thus, our study suggests that the MODIS albedo product performs well in a very heterogeneous, low-albedo, area of the ice sheet ablation zone. Furthermore, we demonstrate that single 'point-to-pixel' methods alone are insufficient in characterizing and validating the variation of surface albedo displayed in the lower ablation area. This is true because the distribution of in situ data deviations from MODIS albedo show a substantial range, with the average values for the 10th and 90th percentiles being −0.30 and 0.43 across all bands. Thus, if only single point is taken for ground validation, and is randomly selected from either distribution tails, the error would appear to be considerable. Given the need for multiple in-situ points, concurrent albedo measurements derived from existing AWSs, (low-flying vehicles (airborne or unmanned) and high-resolution imagery (WV-2)) are needed to resolve high sub-pixel variability in the ablation zone, and thus, further improve our characterization of Greenland's surface albedo.

Ablation zone↗

NASA NTRS2022

Spatial Characterization of PACE OCI ETU Using Time-Delay Mode

The OCI (Ocean Color Instrument) is the main sensor on the upcoming PACE (Plankton Aerosol Cloud ocean Ecosystem) mission. OCI has two hyperspectral CCD sensors covering 340nm to 885nm and 9 SWIR (Short Wave IR) bands from 940nm to 2260nm. SWIR bands have nominal 1km ground pixel size and CCD bands have native 1/8 km ground pixel size in diagnostic mode that will be aggregated into 1km pixels to improve SNR and meet the data rate constraints. OCI has a rotating telescope that is synchronized to the readout of the CCD and SWIR detectors. Full pre-launch system level testing for the OCI ETU (Engineering Test Unit) was completed in June 2021.With time-delayed scan mode, a sub-pixel level time-delay step is applied to the detector readout. This sub-pixel level time-delay step causes a sub-pixel level shift in the start of the data collection. After collecting time-delay step scans with different step sizes, a scan profile with sub-pixel resolution can be constructed. 1/8 and 1/4 of CCD pixel resolutions were achieved using this mode. In this paper, the OCI time-delayed scan mode will be described as well as how it was used to calculate OCI’s high spatial resolution PSF (Point Spread Function), IFOV (instantaneous Field of View), MTF (Modulation Transfer Function), and BBR (Band to Band Registration).

PACE↗

NASA NTRSDate not supplied

Deep Convective Cloud Calibration Sensitivity Studies in Support of Radiometrically Scaling GEO Imagers With VIIRS

The NASA CERES SYN1deg product provides the scientific community regional hourly TOA and surface broadband fluxes and clouds. For consistent geostationary (GEO) derived fluxes and clouds the GEO imagers are radiometrically scaled to the Aqua-MODIS calibration reference. The CERES project utilizes GEO and MODIS analogous channel coincident, collocated, and co-angled radiance pairs as the primary method to inter-calibrate the GEO imagers. Deep convective clouds (DCC) are bright tropical, near Lambertian, top of atmosphere pseudo invariant Earth targets that do not rely on coincident radiance pairs to radiometrically scale sensors to a common calibration reference. DCC pixels are identified by cold IR window channel brightness temperatures (BT). Successful DCC inter-calibration relies on sufficient sampling of comparable identified DCC pixels between sensors. The DCC identification thresholds, pixel resolution, local time, and geographical sampling should be consistent between sensors. Over 20 GEO imagers during the span of the CERES record have various visible and IR pixel resolutions. Unlike the MODIS and VIIRS imagers, where the visible and IR pixel resolutions are similar, the GEO visible pixel resolution is much finer than the IR pixel resolution. The study will examine the pixel resolution impact on the DCC calibration methodology. The resulting DCC calibration coefficients can be validated against the sensor pair calibration methodology. Accounting for the DCC calibration imager resolution differences will allow the CERES project to utilize the future CLARREO observations as the calibration reference for all GEO, MODIS, and VIIRS imagers across the CERES record.

Conor Haney↗

DOE OSTI2015

Laboratory and testbeam results for thin and epitaxial planar sensors for HL-LHC

The High-Luminosity LHC (HL-LHC) upgrade of the CMS pixel detector will require the development of novel pixel sensors which can withstand the increase in instantaneous luminosity to L = 5 × 10 34 cm –2 s –1 and collect ~ 3000fb –1 of data. The innermost layer of the pixel detector will be exposed to doses of about 10 16 n eq / cm 2 . Hence, new pixel sensors with improved radiation hardness need to be investigated. A variety of silicon materials (Float-zone, Magnetic Czochralski and Epitaxially grown silicon), with thicknesses from 50 μm to 320 μm in p-type and n-type substrates have been fabricated using single-sided processing. The effect of reducing the sensor active thickness to improve radiation hardness by using various techniques (deep diffusion, wafer thinning, or growing epitaxial silicon on a handle wafer) has been studied. Furthermore, the results for electrical characterization, charge collection efficiency, and position resolution of various n-on-p pixel sensors with different substrates and different pixel geometries (different bias dot gaps and pixel implant sizes) will be presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Wide Dynamic Range, 10 kHz Framing Detector for 4D-STEM

Hybrid pixel array detectors (PADs) have expanded the fidelity, frame rate and dynamic range for diffractive imaging in electron microscopes. With their high detective quantum efficiencies (DQE), the noise performance limited is by counting statistics. Consequently, improving the precision and quality of high-speed images requires increasing the linear dynamic range and the maximum usable beam current. Here we describe a new prototype hybrid PAD, our next-generation electron microscope pixel array detector (NG-EMPAD) that expands both the framing speed and dynamic range of our earlier EMPAD design. Like the EMPAD, electrons are detected directly in a 500 μm thick silicon sensor bonded pixel-by-pixel to a custom signal processing integrated circuit (IC). Each pixel in the IC integrates charge carriers produced by the high-energy incident electrons. Here, in-pixel circuitry uses a combination of techniques to extend the dynamic range, including adaptive gain switching and the quantitative excess charge dumping similar to the EMPAD. In-pixel buffering of signals during readout allows acquiring a new image while reading out the previously collected image, yielding an image collection duty cycle of nearly 100%.

36 MATERIALS SCIENCE↗

DOE OSTI2015

WE-EF-207-07: Dual Energy CT with One Full Scan and a Second Sparse-View Scan Using Structure Preserving Iterative Reconstruction (SPIR)

Purpose: Conventional dual energy CT (DECT) reconstructs CT and basis material images from two full-size projection datasets with different energy spectra. To relax the data requirement, we propose an iterative DECT reconstruction algorithm using one full scan and a second sparse-view scan by utilizing redundant structural information of the same object acquired at two different energies. Methods: We first reconstruct a full-scan CT image using filtered-backprojection (FBP) algorithm. The material similarities of each pixel with other pixels are calculated by an exponential function about pixel value differences. We assume that the material similarities of pixels remains in the second CT scan, although pixel values may vary. An iterative method is designed to reconstruct the second CT image from reduced projections. Under the data fidelity constraint, the algorithm minimizes the L2 norm of the difference between pixel value and its estimation, which is the average of other pixel values weighted by their similarities. The proposed algorithm, referred to as structure preserving iterative reconstruction (SPIR), is evaluated on physical phantoms. Results: On the Catphan600 phantom, SPIR-based DECT method with a second 10-view scan reduces the noise standard deviation of a full-scan FBP CT reconstruction by a factor of 4 with well-maintained spatial resolution, while iterative reconstruction using total-variation regularization (TVR) degrades the spatial resolution at the same noise level. The proposed method achieves less than 1% measurement difference on electron density map compared with the conventional two-full-scan DECT. On an anthropomorphic pediatric phantom, our method successfully reconstructs the complicated vertebra structures and decomposes bone and soft tissue. Conclusion: We develop an effective method to reduce the number of views and therefore data acquisition in DECT. We show that SPIR-based DECT using one full scan and a second 10-view scan can provide high-quality DECT images and accurate electron density maps as conventional two-full-scan DECT.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Noise suppression for dual-energy CT via penalized weighted least-square optimization with similarity-based regularization

Purpose: Dual-energy CT (DECT) expands applications of CT imaging in its capability to decompose CT images into material images. However, decomposition via direct matrix inversion leads to large noise amplification and limits quantitative use of DECT. Their group has previously developed a noise suppression algorithm via penalized weighted least-square optimization with edge-preservation regularization (PWLS-EPR). In this paper, the authors improve method performance using the same framework of penalized weighted least-square optimization but with similarity-based regularization (PWLS-SBR), which substantially enhances the quality of decomposed images by retaining a more uniform noise power spectrum (NPS). Methods: The design of PWLS-SBR is based on the fact that averaging pixels of similar materials gives a low-noise image. For each pixel, the authors calculate the similarity to other pixels in its neighborhood by comparing CT values. Using an empirical Gaussian model, the authors assign high/low similarity value to one neighboring pixel if its CT value is close/far to the CT value of the pixel of interest. These similarity values are organized in matrix form, such that multiplication of the similarity matrix to the image vector reduces image noise. The similarity matrices are calculated on both high- and low-energy CT images and averaged. In PWLS-SBR, the authors include a regularization term to minimize the L-2 norm of the difference between the images without and with noise suppression via similarity matrix multiplication. By using all pixel information of the initial CT images rather than just those lying on or near edges, PWLS-SBR is superior to the previously developed PWLS-EPR, as supported by comparison studies on phantoms and a head-and-neck patient. Results: On the line-pair slice of the Catphan{sup ©}600 phantom, PWLS-SBR outperforms PWLS-EPR and retains spatial resolution of 8 lp/cm, comparable to the original CT images, even at 90% reduction in noise standard deviation (STD). Similar performance on spatial resolution is observed on an anthropomorphic head phantom. In addition, results of PWLS-SBR show substantially improved image quality due to preservation of image NPS. On the Catphan{sup ©}600 phantom, NPS using PWLS-SBR has a correlation of 93% with that via direct matrix inversion, while the correlation drops to −52% for PWLS-EPR. Electron density measurement studies indicate high accuracy of PWLS-SBR. On seven different materials, the measured electron densities calculated from the decomposed material images using PWLS-SBR have a root-mean-square error (RMSE) of 1.20%, while the results of PWLS-EPR have a RMSE of 2.21%. In the study on a head-and-neck patient, PWLS-SBR is shown to reduce noise STD by a factor of 3 on material images with image qualities comparable to CT images, whereas fine structures are lost in the PWLS-EPR result. Additionally, PWLS-SBR better preserves low contrast on the tissue image. Conclusions: The authors propose improvements to the regularization term of an optimization framework which performs iterative image-domain decomposition for DECT with noise suppression. The regularization term avoids calculation of image gradient and is based on pixel similarity. The proposed method not only achieves a high decomposition accuracy, but also improves over the previous algorithm on NPS as well as spatial resolution.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Nanosecond Gated CMOS Camera (NSGCC) ICD (Rev. 2.1)

The Ultra-Fast X-ray Imager (UXI) program is an ongoing effort at Sandia National Laboratories to create high speed, multi-frame, time-gated Read Out Integrated Circuits (ROICs), and a corresponding suite of photodetectors to image a wide variety of High Energy Density (HED) physics experiments on both Sandia’s Z-Machine and LLNL’s National Ignition Facility (NIF). Several cameras have been designed over the length of the program; one of the most recent is the Icarus, which is an improvement on past imagers (Furi and Hippogriff). A second sensor that can be connected is the Daedalus sensor. The Icarus is a 1024 × 512-pixel array with either 25 μm or 8 µm spatial resolution containing four frames of storage per pixel and has improved timing generation and distribution components while achieved 2 ns time gating. The Daedalus sensor is also a 1024 x 512-pixel array with 25 µm special resolution containing three frames of storage per pixel and has an increased set of features for a wider variety of applications from interlacing of rows in each frame to configurability of all shutters. See Section 14 for details regarding the Icarus implementation of the firmware and Section 15 for details regarding the Daedalus implementation. Due to the unique test environments UXI sensors are targeted for, full custom hardware was required to physically mount an Icarus or Daedalus sensor, manage its various functions, and read out pixel data for transfer to a host computer. Beyond experimental functionality, the hardware also needed to accommodate sensor characterization requirements. Lawrence Livermore National Laboratory’s ‘Version 4.0 Board’ was the result of these efforts. It mounts all the components required to fully utilize the Icarus and Daedalus sensors including analog to digital converters to convert pixel data and various system voltages to digital form for readout and analysis, DAC channels for remote configuration of critical bias voltages, static random-access memories to buffer pixel data, RS422 and Gigabit Ethernet communications for remote access, and an FPGA to tie these components together. This document describes the FPGA electrical interfaces in detail to allow the reader a greater understanding of the device, and to facilitate implementation of custom software to control and manage it. The Version 4.0 Board is a continuation of the Nano-second Gated CMOS hardware design that retains much of the functionality of the Version 1.0 Board while adding features including a DAC instead of digital potentiometers, as well as sensors for pressure and radiation. The Version 4.0 board is intended for applications requiring tight form-factor enclosures. It is composed of two stacking boards; one holds the FPGA and regulators to power the various components of the board while the other contains the mating connector to the sensor, image-readoff ADCs, the DAC, and other components.

42 ENGINEERING↗

DOE OSTI2025

The ETROC2 as the Final Version for CMS Endcap Timing Layer (ETL) Upgrade

The ETROC (Endcap Timing Readout Chip) is being developed for the LGAD-based CMS Endcap Timing Layer (ETL) at HL-LHC. The ETL on each side of the interaction region will be instrumented with a two-disk system of MIP-sensitive LGAD (Low Gain Avalanche Diodes) silicon devices, read out by ETROCs for precision timing measurement with down to ~30 ps timing resolution per track. The ETROC is designed to handle a 16 x 16 pixel cell matrix, with each pixel being 1.3 mm x 1.3 mm to match the LGAD sensor pixel size. The front-end design for preamplifier and discriminator has been specifically optimized for the reduced LGAD signals, with enough flexibilities to meet the ETL specific needs for time resolution, power budget and radiation profile. The ETROC chip is implemented in a commercial 65nm CMOS process. Each channel consists of a preamplifier, a discriminator, a TDC used for TOA (Time Of Arrival) and TOT (Time Over Threshold) measurements, and a memory for data storage and readout. An in-pixel auto threshold calibration is included, along with a self-testing pattern generator. The TOT is used for time-walk correction of the TOA measurement. The detailed hit information (TOA and TOT) from each cell will be read out from a local circular buffer after each Level-1 Accept (about 1 MHz). In addition, a charge injection circuit is implemented to allow for testing and calibration. For more detailed monitoring of the signal pulses, waveform sampling circuits are included for one pixel. The clock distribution is based on a 16x16 H-tree design with a shielding structure to alleviate potential interference. The global peripheral circuits include a PLL, a phase shifter, an I2C slave controller, a fast control block, a global readout, and a data driver along with an efuse and temperature sensor. The ETROC builds event data frames for each L1A selected event and is also capable of providing L1 trigger information for user-defined delayed hits. The main design challenge is how to extract precision timing information from the small LGAD signals in the presence of high irradiation fluence, while keeping the power consumption and digital activity low. The ETL design goal for the time resolution of 50 ps per hit is required to achieve a 35 ps arrival time measurement for a MIP particle, which has its track registered in two ETL disk layers. The LGAD contribution is known to be about 30 ps, this means that the jitter from the ETROC has to be kept below 40 ps. The ETROC2 is the first full size full functionality prototype design fully compatible with the final chip specifications for CMS ETL and now becomes the final version. The ETROC2 chips have been extensively tested. We will present here new testing results including the bump bonding yield improvement study, the time walk correction (TWC) generality study with one pixel TWC applying to all pixels, the final SEU testing using both heavy ion and proton beam, more beam test studies including different sensors, and readiness for the ETROC2 production for CMS ETL upgrade.

Liu, Tiehui [Fermilab] (ORCID:0009000765225605)↗

NASA NTRS1983

Assessment of Thematic Mapper band-to-band registration by the block correlation method

Rectangular blocks of pixels from one band image were statistically correlated against blocks centered on identical pixels from a second band image. The block pairs were shifted in pixel increments both vertically and horizontally with respect to each other and the correlation coefficient to the maximum correlation was taken as the best estimate of registration error for each block pair. For the band combinations of the Arkansas scene studied, the misregistration of TM spectral bands within the noncooled focal plane lie well within the 0.2 pixel target specification. Misregistration between the middle IR bands is well within this specification also. The thermal IR band has an apparent misregistration with TM band 7 of approximately 3 pixels in each direction. The TM band 3 has a misregistration of approximately 0.2 pixel in the across-scan direction and 0.5 pixel in the along-scan direction, with both TM bands 5 and 7.

Card, D. H.↗

NASA NTRS1983

Methodology for interpretation of SST retrievals using the AVHRR split window algorithm

Intercomparisons of sea surface temperature (SST) products derived from the operational NOAA-7 AVHRR-II algorithm and in situ observations are made. The 1982 data sets consist of ship survey data during the winter from the Mid-Atlantic Bight (MAB), ship and buoy measurements during April and September in the Gulf of Mexico and shipboard observations during April off the N.W. Spanish coast. The analyses included single pixel comparisons and the warmest pixel technique for 2 x 2 pixel and 10 x 10 pixel areas. The reason for using multi-pixel areas was for avoiding cloud contaminated pixels in the vicinity of the field measurements. Care must be taken when applying the warmest pixel technique near oceanic fronts. The Gulf of Mexico results clearly indicate a persistent degradation in algorithm accuracy due to El Chichon aerosols. The MAB and Spanish data sets indicate that very accurate estimates can be achieved if care is taken to avoid clouds and oceanic fronts.

Barbieri, R. W.↗