Surface Slope Research Articles

Siting Considerations for Satellite Observation of River Discharge

AbstractWith growing global capability for satellite measurement of river discharge (flow) comes a need to understand and reduce error in satellite‐based discharge measurements. Satellite‐based discharge estimates are based on measurements of water surface width, elevation, slope, and potentially velocity. Site selection is important for reducing error and uncertainty in both conventional and satellite‐based discharge measurements because geomorphic river characteristics have strong control over the relationships between discharge and width, water surface elevation (or depth), slope, and velocity. A large ground‐truth data set of 8,445 conventional hydraulic measurements, collected by acoustic Doppler current profilers at 503 stations in the United States, was developed and quality assured to examine correlation between river discharge and water surface width, depth, velocity, and cross‐sectional area. A separate database of river surface slope and discharge time‐series was developed from paired continuous monitoring stations to examine slope‐discharge correlations. Results show that discharge correlates most strongly with velocity, cross‐sectional area, depth, width, and slope, in that order. Uncertainty of satellite discharge estimates is affected by observed hydraulic variable and reach‐specific variability in observed variable(s) characteristics including range of variability, georegistration accuracy, and stability over time of relationships between discharge and observed hydraulic variable.

Multiscale slope analysis and functional correlation with gloss reflectance from photographic papers

A novel multiscale 3D topographic characterization for slope is introduced. Slope is considered as a crucial parameter linking area-scale and 3D curvature analyses. Relationships between surface topography and gloss reflectance in photographic papers are used for an example application. Directional angles, characterizing slopes, are calculated two ways: normals to triangular facets (method 1), and eigenvectors of a covariance matrix based on nine points (method 2). Slope is the steepness of surface inclinations associated with the orientation of local surface features (facets). The impact of slope on gloss reflectance supports the use of pertinent geometric characterizations, i.e., alignment of geometric characterizations with the physical nature of the topographic interaction phenomena. Topographies of 24 photographic papers, were measured with a laser scanning confocal microscope and their gloss reflectance was measured with a micro-TRI-gloss gloss meter. Analyses of slope distributions with bivariate dispersion measures of directional angles and their trigonometric functions revealed strong correlations (R2 > 0.6) between slope distributions and gloss. Bivariate median deviation of secant or tangent of directional angles, demonstrated consistently high correlations across scales, magnifications, and filtrations. This study supports pertinent and useful characterizations grounded in the physics of topographic interaction phenomena to provide insights into relationships between surface topography, e.g., slope and gloss reflectance in photographic papers. This nuanced understanding has potential applications for other applications as well.

Hydraulic River Models From ICESat‐2 Elevation and Water Surface Slope

AbstractForecasting flood and drought events requires accurate modeling tools. Hydraulic river models are based on estimates of riverbed geometry which are traditionally collected in situ. The novel Ice, Cloud and Land Elevation Satellite 2 [ICESat‐2] lidar altimetry mission with 6 simultaneous high‐resolution laser beams provides the opportunity to define river cross‐section geometries as well as observe water surface elevation [WSE] and water surface slope spatially resolved along the river chainage. This paper describes a method to utilize terrain altimetry and water surface slope estimates to define complete river geometries from ICESat‐2 data products, using the diffusive wave approximation to calculate depth in the submerged section not penetrated by the lidar. Exemplifying the method, cross‐sections are defined for a stretch of the Mekong River. Hydrodynamic model results of the stretch are compared with ICESat‐2 WSE estimates and in situ gauging station time series. Insights in river characteristics from satellite imagery and the ICESat‐2 slope estimates allow for fine‐tuning of the cross‐sections using spatially varying Manning numbers. The final model achieves a root mean square error against the ICESat‐2 WSE of 0.676 m and average Kling‐Gupta Efficiency against gauging station time series of 0.880. The method is limited by the diffusive wave approximation resulting in inaccurate cross‐section estimates in sections with supercritical flow or significant acceleration. Errors can be identified from ICESat‐2 WSE estimates and reduced with additional cross‐sections. Combined with hydrological models, the method will allow for cross‐section definition without in situ data.

Accuracy and Resolution of SWOT Altimetry: Foundation Seamounts

AbstractWe assess the accuracy and spatial resolution of the surface water and ocean topography (SWOT) swath altimeter for deriving marine gravity anomalies. The analysis is performed at the Foundation Seamounts in the South Pacific where we developed a highly accurate gravity field by combining the long‐wavelength (>40 km) gravity field derived from previous nadir altimeters with the shorter wavelength gravity field from the seafloor topography as constrained by the ship gravity. In this region, the sea surface slope (SSS) of the ocean variability is 50–100 times smaller than the slope signal of the seamounts so can be ignored in the analysis. Each SWOT cycle can deliver SSS accurately with a standard deviation of 2.6 µrad and a spatial resolution of 14 km at typical sea state (significant wave height 4 m), with accuracy diminishing at high significant wave heights (e.g., exceeds 6 m). Averaging repeated SWOT measurements improves the accuracy and resolution. For example, we expect that averaging just 10 repeats (7 months) results in accuracy/resolution that matches the best marine gravity maps based on 230 months of nadir altimetry. With a mission lasting over a year, SWOT promises a substantial leap in marine gravity accuracy and resolution, uncovering previously uncharted details of the seafloor, including thousands of uncharted seamounts.

Shaking table test on damage mechanism of bedrock and overburden layer slope based on the time–frequency analysis method

To systematically analyze the damage caused by bedrock and overburden layer slope under seismic action, a set of large-scale shaking table test was designed and completed. Interpolation of the acceleration amplification coefficient, Hilbert–Huang transform and transfer function was adopted. The damage mechanisms of the bedrock and overburden layer slopes under seismic action are systematically summarized in terms of slope displacement, acceleration field, vibration amplitude, energy, vibration frequency, and damage level. The results show a significant acceleration amplification effect within the slope under seismic action and a localized amplification effect at the top and trailing edges of the slope. With an increase in the input seismic intensity, the difference in the vibration amplitude between the overburden layer and bedrock increased, low-frequency energy of the overburden layer was higher than that of the bedrock, and the vibration frequency of the overburden layer was smaller than that of the bedrock. These differences cause the interface to experience cyclic loading continuously, resulting in the damage degree of the overburden layer at the interface being larger than that of the bedrock, reduction of the shear strength, and eventual formation of landslides. The displacement in the middle of the overburden is always greater than that at the top. Therefore, under the action of an earthquake and gravity, the damage mode of the bedrock and overburden layer slope is such that the leading edge of the critical part pulls and slides at the trailing edge, and multiple tensile cracks are formed on the slope surface.

Influence of Pre- and Post-Contouring Strategies to Downskin Sloped Surfaces in Laser Powder-Bed Fusion (L-PBF) Additive Manufacturing.

Among various metal additive manufacturing (AM) technologies, L-PBF is known for fabricating intricate components. However, due to step edges and powder particle attachments, attaining a good surface finish is challenging, especially on downskin surfaces. Contour scanning has potential to improve surface quality because such scanning may dominate the surface formation of sloped features. This study evaluates the effects of pre- and post-contouring strategies on the sloped downskin surfaces fabricated using a commercial L-PBF system with Ti6Al4V powder. L-PBF parts printed at inclination angles 30°, 45° and 60° were investigated. A double-contouring approach with varying processing conditions was employed and surface characteristics were analyzed using data acquired by white light interferometry. The average surface roughness, Sa, surface skewness, Ssk, and percentage area of powder particles attached onto surfaces were statistically evaluated. The lowest Sa obtained for pre- and post-contoured samples is 14.08 µm and 18.88 µm, respectively. For both strategies, the combination of a low laser power and a high scan speed on the interface of downskin surface and underneath powder results in smoother surfaces. However, while comparing both strategies, pre-contouring gives better surface finish for samples built at similar processing conditions, with a difference of nearly 5 µm in Sa.

Assessment of park paths and trails to promote physical accessibility among wheelchair users in Saudi Arabia.

Individuals with mobility disabilities are less likely to meet physical activity standards and are at greater risk of developing non-communicable chronic diseases at earlier ages. Public parks are an essential resource for participation in physical activity. However, environmental factors may limit the participation of wheelchair users. The objective of this study was to evaluate the feasibility of using the Path Environment Audit Tool (PEAT) and to explore the wheelchair accessibility of five public parks in Saudi Arabia through descriptive analysis. A descriptive study design was implemented to evaluate wheelchair accessibility features of five public parks in Riyadh, Saudi Arabia, and process, resource, and management assessments were conducted. Phone GPS-App Strava was used to track the segments and measure their distances. Audits in multiple parks using PEAT were time-consuming despite being user-friendly. The descriptive analysis of paths and trails across the five parks showed some positive features, such as adequate bollard/gate clearance, but the path slope and condition of the path surfaces were more variable. This study is the first to examine wheelchair accessibility in public parks in Saudi Arabia. Preliminary audits of paths/trials in five public parks revealed the strengths and weaknesses of accessibility and features that promote physical activity participation for wheelchair users. These findings can guide future use of PEAT in large-scale studies and inform environmental modifications.

Undervalued dry riverbeds: A key factor in equating intermittent river CO2 emissions to perennial rivers

Intermittent rivers in semiarid and arid regions, constituting over half of the world's rivers, alternate the carbon cycle interactions among the biosphere, hydrosphere, and atmosphere. Inadequate quantification of flow duration and river water surface area, along with overlooked CO2 emissions from dry riverbeds, result in notable inaccuracies in global carbon cycle assessments. High-resolution remote sensing images combined with intensive field measurements and hydrological modelling were used to estimate and extract the flow duration, river water surface area and dry riverbed area of Huangfuchuan, an intermittent river watershed that acts as a major tributary of the Yellow River in semiarid Northwest China. CO2 emission rates and partial pressures in water and air across the watershed were in-situ measured. In 2018, the flow duration of Huangfuchuan increased from less than 5 days in the first-order tributary to 150 days in the sixth-order mainstream. River water surface area estimated by remote sensing extraction plus the hydrodynamic model simulation varied from 3.9 to 88.6 km2 under 5 %–95 % discharge frequencies. CO2 emissions from the water-air interface and dry riverbed in 2018 were estimated at 582.3 × 103 and 355.2 × 103 ton, respectively. The estimated total annual emission (937.5 × 103 ton) aligns closely with the range of emissions (67.3 × 103–1377.2 × 103 ton) calculated for the water-air interface alone, derived using DEM river length and hydraulic geometry method. This similarity can be attributed to the overestimation of flow duration and flow velocity, as well as the over- or under-estimation of river water surface area and slope. The new method proposed in this study has large potential to be applied in estimating CO2 emissions from data-scarce intermittent rivers located in mountainous regions and provides a standardized solution in the estimation of CO2 emission. Results of this research reveal the spatiotemporal distribution of CO2 emissions along an intermittent river system and highlight the substantial role of dry riverbed in carbon cycle.

Estimation of Crosswind Disturbances for a Vehicle by LPV‐MHE and its Application to Disturbance Cancellation

Crosswinds and transverse slopes of the road surface affect the motion of a ground vehicle as disturbances. The objective of this paper is to develop a method for estimating crosswind disturbances and lateral force disturbances caused by transverse slopes of the road surface under the variation of the vehicle speed. Firstly, a dynamical model of a vehicle is described as a Linear Parameter‐Varying (LPV) system in which the value of the coefficient matrices vary with the vehicle velocity. Then, an algorithm to estimate the disturbance is derived based on Moving Horizon Estimation (MHE) and applied to the derived LPV system. Furthermore, a simple control law which counteracts the effects of the disturbances on the lateral velocity and the yaw rate in steady‐state based on the estimates of the disturbances is presented. The effectiveness of the proposed method is demonstrated by a numerical example. © 2024 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Assessment of slope stability with study parametric of faults (shear joints) using the lower and upper limit analysis method

Slope instability is widespread throughout the world, has become well known to geotechnical engineers, and poses a major challenge. The causes of slope slippage vary, which is why it is considered important and dangerous. Until now, researchers are trying to understand this phenomenon and the extent to which it is affected by surrounding elements, such as the slope ratio, slope height, water level, soil properties, and other physical and chemical properties. In this research, we will discuss one of the characteristics, which is the presence of cracks on slopes. The presence of combined shear on slopes poses a challenge to geotechnical engineers to determine field mechanical parameters, analyze, and study these slopes. In this research, we studied the effect of faulting on slopes. We changed the crack in the slope in five cases, and in each case we changed the length of the crack (21.5 m, 16.2 m, 11.2 m, 7.5 m, 3.5 m) and its location (five places) in order to understand a fracture. Slope behavior as a result of the effect of crack length and location on the safety factor, failure of the slope surface, and deformations of this slope using the top and bottom analysis method. This study provides valuable insights into the effects of fault zones on slope stability using OptumG2 software. It is helpful for us to use these results to better understand slope sliding, and from this, we can reduce the risk of sliding in areas where cracked soil is present.

Pit Lake Slope Stability under Water Level Variations

This paper presents the results of a geotechnical investigation regarding the slope stability in a pit lake, emphasizing the impact of water level variations. Advanced analysis techniques were utilized for this study. The research was performed by using fully coupled flow-deformation analyses. For the fully coupled approach, Bishop’s effective-stress equation was used, and for the description of soil hydraulic behavior, the Van Genuchten’s model was applied. The analysis of slope stability associated with reservoir water level changes revealed that the slope tended to become unstable as the water level decreased; the stability factor was negatively related to the rate of water level reduction. Concerning the water level fluctuations, the analyses revealed that the soil mass seemed to become less stable as the rate of water level change increased. Under a specific range of rates of water level variation, the safety factor became higher as the number of fluctuations increased. Additionally, the simulation results concerning the water level rising indicate that the pressure due to the external water level acts on the slope surface with a positive impact on the stability factor. The results obtained reflect the effects under a specific site condition, but they can be used as a reference for evaluating slope stability in a pit lake design.

A deflected ray model of the transit time difference in ultrasonic flow meters applied to non-ideal flow profiles

Transit time difference (TTD) ultrasonic meters have widespread applications due to their high dynamic range, lack of moving parts and low maintenance requirements. In earlier work, the TTD is considered to arise due to the fluid flow changing the effective speed of sound along a fixed ray path, but recent publications have introduced a new way of viewing how the TTD arises. The flow velocity in the axial direction does not affect the speed of sound in the direction normal to the pipe wall. Therefore, in a clamp-on meter with the fluid at constant temperature and pressure, the transit time in the liquid must be constant with changing flow rate. The TTD then arises due to the ray path in the water being deflected, and the received wavefront travelling some extra distance along the pipe axis, which results in a different transit through the transducer wedge than for zero flow conditions. In a meter with wetted transducers, the mechanism causing the TTD is slightly different. The deflected ray travels a different distance in the fluid along the direction normal to the pipe walls due to the transducer surface being at an angle to the flow direction, and this is responsible for the TTD that is measured.Previous work has focused on calculating the magnitude of the ray deflection effect in clamp-on meters for ideal flow conditions, where the flow velocity does not depend on the position in the pipe. In this article, the ray deflection is calculated for a series of analytic profiles, and it is shown that the two models result in the same calculated TTD for both clamp-on meters and meters with wetted transducers at low flow speeds. The hydraulic correction factors calculated using the model which considers a change in the effective speed of sound are recovered using the ray deflection models. The resulting equations for beam deflection are the same as those for the conventional fixed ray path model, but the beam deflection model is more physically realistic and presents new opportunities for calibration methods utilising carefully controlled movement of the transducers. The conventional model typically has a correction factor which is allowed to vary in cases where the flows are expected to approach the speed of sound to account for the effect of ray deflection. However, the ray deflection model automatically takes this into account, so is expected to be useful in these circumstances.

Study on the Characteristics and Evolution Laws of Seepage Damage in Red Mud Tailings Dams

Seepage damage is a significant factor leading to red mud tailings dam failures. Laboratory tests on seepage damage were conducted to investigate the damage characteristics and distribution laws of red mud tailings dams, including soil pressure, infiltration line, pore water pressure, dam displacement, and crack evolution. The findings revealed the seepage damage mechanisms of red mud slopes, offering insights for the safe operation and seepage damage prevention of red mud tailings dams. The results showed that the higher the water level is in the red mud tailings dam, the higher position the infiltration line is when it reaches the slope face. At the highest infiltration line point of the slope surface, the increase of pore water pressure is the highest and the change of horizontal soil pressure is the highest. Consequently, increased pore water pressure leads to decreased effective stress and shear strength, increasing the susceptibility to damage. Cracks resulting from seepage damage predominantly form below the infiltration line; the higher the infiltration lines is on the slope surface, the higher the position of the main crack formations is. The displacement of the dam body primarily occurs due to the continuous expansion of major cracks; the higher the infiltration lines are on the slope surface, the larger the displacement of the dam body is.

Enhancing stability analysis of open-pit slopes via integrated 3D numerical modeling and data monitoring

The slope at Zhahanur open-pit mine (China) has experienced significant and prolonged deformation, posing a considerable risk to life and property within the mining area. To analyse the deformation and failure mechanism of the rock slope, geotechnical investigations, numerical simulations, and long-term movement monitoring were undertaken. In order to improve the efficiency of slope pretreatment, a point elimination method was proposed for the slope surface, and a 3D geological model of mining area was established. A systematic analysis was performed on monitoring data from surface slope radar and underground inclinometers, enabling the identification of the potential sliding surface and deformation pattern of northern slope in a rational manner. Additionally, through three-dimensional numerical simulation, the feasibility of the mining scheme that incorporates waste dump inside the pit was explored. These simulations accurately captured the varying deformation patterns at different levels and exhibited good agreement with available field monitoring data. The findings revealed a composite multi-stage slope failure pattern primarily controlled by weak layers. The safety factors associated to two competing slip surfaces were determined to be 1.20 and 1.15, respectively. To ensure the safe extraction of coal resources from the deformed slope, a combined mining scheme of in-pit dumping and mining is proposed in the study. The proposed scheme was shown to meet the production needs, with a minimum safety factor of 1.08 for rock slope under the mining scheme. By integrating various field monitoring techniques with numerical simulations, a collaborative monitoring scheme was devised to effectively and promptly identify potential sliding surface and implement necessary mining and control measures to ensure slope stability. This comprehensive approach provides valuable insights into the deformation behavior of the rock slope and facilitates the implementation of proactive measures to mitigate risks associated with slope instability.

Comparative Analysis of the Slope Stability Using Slide and Plaxis 2D Software: A Case Study of Tombel Pozzolan Quarry (South-West Cameroon)

The presented study attempted to use coupled finite element numerical (FEM) and analytical limit equilibrium (LEM) procedures to provide comparative graphical charts demonstrating the geometry, the groundwater condition, the safety factor, and the characteristics of the support, which were implemented in the Dangote Pozzolan quarry at Tombel to preventing the slope instability’s occurrence. Field and laboratory work have been carried out to collect and characterize data. The results obtained with the LEM procedure via Slide 2D showed a safety factor of 0.87, indicating an unstable slope compared to a safety factor of 1.0 obtained with the FEM procedure via Plaxis 2D corresponding to a limited equilibrium state of the slope. The characteristics of the support that can be used to stabilize the slopes are geotextile support of 100% strip coverage, a tensile strength of 100 kN/m, an adhesion property of 4 kPa, and a frictional angle of 40°. The geotextile is anchored at the slope surface. After the support has been introduced, and the new safety factor calculated, the support automatically increased the safety factor value from 0.87 to 1.51 by using Slide 2D and from 1.0 to 1.98 by using Plaxis 2D, which is from an unstable state to a very stable state.

Laboratory Demonstration of Grating Embedded Mirrors for Single-Shot Heliostat Optical Metrology

Abstract Concentrated solar power (CSP) plants need to monitor the surface slope error of thousands of heliostats with sub-milliradian accuracy. Large numbers of heliostats installed in harsh environments mean that measurement speed and durability are key design considerations for metrology systems. We present a compact, accurate, and high-speed heliostat slope error metrology system that is robust to the harsh environmental conditions at CSP plants. The system is composed of (1) grating embedded mirrors (GEMs), which have multiple different phase diffraction gratings written within a glass mirror substrate, and (2) a compact optical system, the diffractive auto-stigmatic Hartmann camera (DASHCam). Using focused ultrafast laser pulses, we write phase gratings within second-surface float glass mirror without damaging the reflective coating on the backside. The gratings direct a small fraction of incident light to non-specular directions, which the DASHCam senses from a virtual center of curvature to measure the mirror slopes at each grating patch. In a CSP plant, each heliostat mirror would be a GEM, and the DASHCam would rapidly measure slope and canting errors during heliostat manufacturing, installation, or operation. We fabricated 0.1 meter-diameter GEMs with 24 grating patches, built a prototype DASHCam system, and tested the system repeatability and accuracy by comparing against a Fizeau interferometer. Our results show, in a laboratory environment, 24μrad root mean square (RMS) measurement repeatability and 47μrad RMS accuracy, with single-shot image capture. The combination of GEMs and DASHCam is a promising metrology approach that could lead to improved optical accuracy of heliostats throughout their life cycle. This work serves as a proof of principle for this system.

Flood Propagation Characteristics in a Plain Lake: The Role of Multiple River Interactions

Plain lakes play a crucial role in the hydrological cycle of a watershed, but their interactions with adjacent rivers and downstream water bodies can create complex river–lake relationships, often leading to frequent flooding disasters. Taking Poyang Lake as an example, this paper delves into its interaction with the Yangtze River, revealing the spatiotemporal patterns of flood propagation within the lake and its impact on surrounding flood control measures. The aim is to provide insights for flood management in similar environments worldwide. This study employs a comprehensive approach combining hydrological statistical analysis and two-dimensional hydrodynamic modeling, based on extensive hydrological, topographic, and socio-economic data. The results indicate that the annual maximum outflow from Poyang Lake is primarily controlled by floods within the watershed, while the highest annual lake water level is predominantly influenced by floods from the Yangtze River. The peak discharge typically reaches the lake outlet within 48 h, with the peak water level taking slightly longer at 54 h. However, water storage in the lake can shorten the time that it takes for the peak discharge to arrive. When converging with floods from the Yangtze River, the peak water level may be delayed by up to 10 days, due to the top-supporting interaction. Furthermore, floods from the “Five Rivers” propagate differently within the lake, affecting various lake regions to differing degrees. Notably, floods from the Fu River cause the most significant rise in the lake’s water level under the same flow rate. The top-supporting effect from the Yangtze River also significantly impacts the water surface slope of Poyang Lake. When the Yangtze River flood discharge significantly exceeds that of the “Five Rivers” (i.e., when the top-supporting intensity value, f, exceeds four), the lake surface becomes as flat as a reservoir. During major floods in the watershed, the water level difference in the lake can increase dramatically, potentially creating a “dynamic storage capacity” of up to 840 million cubic meters.

Evaluasi Faktor-Faktor Penyebab Longsor dan Kesesuaian Mitigasi

Management and maintenance of slopes require proper knowledge of slope conditions so that appropriate mitigation measures can be implemented. The activities required for the management of slopes include slope inventory, slope inspection, slope risk level assessment, and risk mitigation measures. The objective of this study was to observe the slope conditions and causes of past slope failures, determine the appropriate mitigation measures, and analyze the suitability of landslide mitigation measures and causes of slope failures. The research locations are road segment No. 36 (Kota Lahat – Simpang Air Dingin), No. 37 (Simpang Air Dingin – Pagar Alam), and No. 38 (Pagar Alam – Tanjung Sakti – batas Bengkulu). The research was initiated by analyzing data collected by the South Sumatra National Road Management Agency (BPJNSS) from 2018 to 2021. The field observation was conducted on ten locations where the slope had been repaired after slope failure events. The suitability of mitigation with the factors that cause landslides was analyzed using the slope management system method suggested by the Ministry of PUPR. The results showed that most slope failures were triggered by high-intensity rain falling on slope surfaces containing high humidity due to previous rainfall. The common types of slope mitigation are reducing the forces that cause movement, increasing the resisting forces by controlling seepage, and the use of anchors.

Linear systems characterization of the topographical spatial resolution of optical instruments

Lateral resolving power is a key performance attribute of Fizeau interferometers, confocal microscopes, interference microscopes, and other instruments measuring surface form and texture. Within a well-defined scope of applicability, limited by surface slope, texture, and continuity, a linear response model provides a starting point for characterizing spatial resolution under ideal conditions. Presently, the instrument transfer function (ITF) is a standardized way to quantify linear response to surface height variations as a function of spatial frequency. In this paper, we build on the ITF idea and introduce terms, mathematical definitions, and appropriate physical units for applying a linear systems model to surface topography measurement. These new terms include topographical equivalents of the point-, line-, and edge-spread functions, as well as a complex-valued transfer function that extends the ITF concept to systems with spatial-frequency-dependent topography distortions. As an example, we consider the experimental determination of lateral resolving power of a coherence scanning interference microscope using a step-height surface feature to measure the ITF directly. The experiment illustrates the proposed mathematical definitions and provides a direct comparison to theoretical calculations performed using a scalar diffraction model.

Biomechanical effects of adding an articulating toe joint to a passive foot prosthesis for incline and decline walking.

Walking on sloped surfaces is challenging for many lower limb prosthesis users, in part due to the limited ankle range of motion provided by typical prosthetic ankle-foot devices. Adding a toe joint could potentially benefit users by providing an additional degree of flexibility to adapt to sloped surfaces, but this remains untested. The objective of this study was to characterize the effect of a prosthesis with an articulating toe joint on the preferences and gait biomechanics of individuals with unilateral below-knee limb loss walking on slopes. Nine active prosthesis users walked on an instrumented treadmill at a +5° incline and -5° decline while wearing an experimental foot prosthesis in two configurations: a Flexible toe joint and a Locked-out toe joint. Three participants preferred the Flexible toe joint over the Locked-out toe joint for incline and decline walking. Eight of nine participants went on to participate in a biomechanical data collection. The Flexible toe joint decreased prosthesis Push-off work by 2 Joules during both incline (p = 0.008; g = -0.63) and decline (p = 0.008; g = -0.65) walking. During incline walking, prosthetic limb knee flexion at toe-off was 3° greater in the Flexible configuration compared to the Locked (p = 0.008; g = 0.42). Overall, these results indicate that adding a toe joint to a passive foot prosthesis has relatively small effects on joint kinematics and kinetics during sloped walking. This study is part of a larger body of work that also assessed the impact of a prosthetic toe joint for level and uneven terrain walking and stair ascent/descent. Collectively, toe joints do not appear to substantially or consistently alter lower limb mechanics for active unilateral below-knee prosthesis users. Our findings also demonstrate that user preference for passive prosthetic technology may be both subject-specific and task-specific. Future work could investigate the inter-individual preferences and potential benefits of a prosthetic toe joint for lower-mobility individuals.