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The Surface-Topography Challenge: A Multi-Laboratory Benchmark Study to Advance the Characterization of Topography
Surface performance is critically influenced by topography in virtually all real-world applications. The current standard practice is to describe topography using one of a few industry-standard parameters. The most commonly reported number is Ra, the average absolute deviation of the height from the mean line (at some, not necessarily known or specified, lateral length scale). However, other parameters, particularly those that are scale-dependent, influence surface and interfacial properties; for example the local surface slope is critical for visual appearance, friction, and wear. The present Surface-Topography Challenge was launched to raise awareness for the need of a multi-scale description, but also to assess the reliability of different metrology techniques. In the resulting international collaborative effort, 153 scientists and engineers from 64 research groups and companies across 20 countries characterized statistically equivalent samples from two different surfaces: a “rough” and a “smooth” surface. The results of the 2088 measurements constitute the most comprehensive surface description ever compiled. We find wide disagreement across measurements and techniques when the lateral scale of the measurement is ignored. Consensus is established through scale-dependent parameters while removing data that violates an established resolution criterion and deviates from the majority measurements at each length scale. Our findings suggest best practices for characterizing and specifying topography. The public release of the accumulated data and presented analyses enables global reuse for further scientific investigation and benchmarking.
Topography of the Flattest Surface on Earth: using ICESAT, GPS, and MISR to Measure Salt Surface Topography on Salar de Uyuni, Bolivia
Salt flats are aptly named: they are composed largely of salt, and are maintained as nearly equipotential surfaces via frequent flooding. The salar de Uyuni, on the Altiplano in southwestern Bolivia, is the largest salt flat on Earth, with an area of 9,800 sq km. Except for a few bedrock islands, it has less than 40 cm of relief. The upper-most salt unit averages 5 m thick and contains 50 cu km of nearly pure halite. It includes most of the salt that was in solution in paleolake Minchin, which attained a maximum area of 60,000 sq km and a maximum depth of 150 m, roughly 15 kyr ago. Despite approx. 10 m of differential isostatic rebound since deposition, the salar surface has been actively maintained as an extraordinarily flat and smooth surface by annual flooding during the rainy season. We have used the strong optical absorption properties of water in the visible band to map spatial variations in water depth during a time when the salar was flooded. As water depth increases, the initially pure white surface appears both darker and bluer. We utilized MISR images taken during the interval from April to November 2001. The red and infra-red bands (672 and 867 nm wavelength) were most useful since the water depth is small and the absorption at those wavelengths is quite strong. Nadir pointed MISR images have 275 m spatial resolution. To aid in our evaluation of water depth variations over the saiar surface, we utilized two sources of direct topographic measurements: several ICESAT altimetry tracks cross the area, and a 40x50 km GPS grid was surveyed to calibrate ICESAT. A difficulty in using these data types is that both give salt surface elevations relative to the ellipsoid, whereas the water surface will, in the absence of wind or tidal disturbances, follow an equipotential surface. Geoid height is not known to the required accuracy of a few cm in the central Andes. As a result, before comparing optical absorption from MISR to salt surface topography from GPS or ICESAT, we removed the longest wavelengths from both.
The study of X-ray scattering to determine surface topography of smooth surfaces
The scattering of X-rays from state-of-the-art polished mirrors is discussed with reference to the requirements of the Advanced X-ray Astrophysics Facility telescope. An experimental set-up is described which allows information to be obtained with subarcsecond resolution. A sample of the data obtained is presented along with a possible theoretical model for its interpretation.
Origin of bending in uncoated microcantilever - Surface topography?
We provide direct experimental evidence to show that difference in surface topography on opposite sides of an uncoated microcantilever induces bending, upon exposure to water molecules. Examination on opposite sides of the microcantilever by atomic force microscopy reveals the presence of localized surface features on one side, which renders the induced stress non-uniform. Further, the root mean square inclination angle characterizing the surface topography shows a difference of 73° between the opposite sides. The absence of deflection in another uncoated microcantilever having similar surface topography confirms that in former microcantilever bending is indeed induced by differences in surface topography.
Anomalous near-equilibrium capillary imbibition induced by nanoscale surface topography
Here, this work reports that the nanoscale surface topography induces a crossover from the classical Lucas–Washburn imbibition dynamics to a long-lived anomalously slow regime observed near thermodynamic equilibrium conditions. A compact analytical model considering the interplay between interfacial wetting, thermal motion, and the nanoscale physical topography accounts for experimental observations for the case of capillary rise of different nonvolatile liquids in simple glass tubes. Analytical predictions supported by topographic analysis via atomic force microscopy indicate that topographic features with a specific range of nanoscale dimensions determine the crossover condition and anomalous imbibition rate. Our findings have important implications for the scientific understanding and technical application of capillary imbibition and suggest strategies to control the adsorption of specific liquids in porous materials with complex surface topography.
Radial orbit error reduction and sea surface topography determination using satellite altimetry
A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.
Azobenzene-based sinusoidal surface topography drives focal adhesion confinement and guides collective migration of epithelial cells
Surface topography is a key parameter in regulating the morphology and behavior of single cells. At multicellular level, coordinated cell displacements drive many biological events such as embryonic morphogenesis. However, the effect of surface topography on collective migration of epithelium has not been studied in detail. Mastering the connection between surface features and collective cellular behaviour is highly important for novel approaches in tissue engineering and repair. Herein, we used photopatterned microtopographies on azobenzene-containing materials and showed that smooth topographical cues with proper period and orientation can efficiently orchestrate cell alignment in growing epithelium. Furthermore, the experimental system allowed us to investigate how the orientation of the topographical features can alter the speed of wound closure in vitro. Our findings indicate that the extracellular microenvironment topography coordinates their focal adhesion distribution and alignment. These topographic cues are able to guide the collective migration of multicellular systems, even when cell–cell junctions are disrupted.
Imaging surface topography with coherent x-ray reflectivity: Theory, kinematics, and simulations
A theoretical formalism is described for understanding coherent x-ray reflectivity (CXR) from the surface of a semi-infinite crystal having a variable surface topography, described by the height profile ℎ(𝑥,𝑦). The surface topography is imaged as a complex “effective density,” obtained from the phasing and inversion of the coherent x-ray reflectivity data, measured through a rocking scan centered at a vertical momentum transfer 𝑄$^{0}_{𝑧}$ and a vertical range Δ𝑄 𝑧 . The formalism predicts that the effective density has an amplitude with a maximum located at the surface height for each position within the surface plane. The phase of the effective density has a lateral variation that is controlled by the surface height and a vertical variation that reflects a combination of the interfacial structure and specific choice of measurement conditions. This understanding enables direct observation of nanometer-scale interfacial topography, i.e., ℎ(𝑥,𝑦)𝑐 𝑠 (where 𝑐 𝑠 is the vertical substrate lattice parameter) with Å-scale sensitivity to surface height. Numerical simulations illustrate and confirm the theoretical results. These results show how the interpretation of the interfacial density phase obtained by CXR data inversion (i.e., surface topography with respect to a flat surface) is conceptually similar to that previously known for Bragg coherent diffraction imaging (BCDI) measurements of isolated nanoparticles (i.e., lattice displacements with respect to an ideal crystal lattice). This suggests that CXR can be thought of as a form of dark field imaging with respect to the bright field BCDI approach. An implication of these results is that interfacial imaging may bypass some of the significant challenges associated with BCDI imaging of multiple particles having different orientations.
Radar measurements of the surface topography and roughness of Mars
Mars surface topography and roughness from radar measurements
Surface topography due to convection in a variable viscosity fluid - Application to short wavelength gravity anomalies in the central Pacific Ocean
Finite difference calculations of thermal convection in a fluid layer with a viscosity exponentially decreasing with temperature are performed in the context of examining the topography and gravity anomalies due to mantle convection. The surface topography and gravity anomalies are shown to be positive over regions of ascending flow and negative over regions of descending flow; at large Rayleigh numbers the amplitude of surface topography is inferred to depend on Rayleigh number to the power of 7/9. Compositional stratifications of the mantle is proposed as a mechanism for confining small-scale convection to a thin layer. A comparative analysis of the results with other available models is included.
Registration and fusion of large-scale melt pool temperature and morphology monitoring data demonstrated for surface topography prediction in LPBF
In-situ monitoring technologies for laser powder bed fusion (LPBF) additive manufacturing often face one key challenge, extracting the ultrafast melt pool (MP) signatures for understanding the localized part properties. Further, the spatial information of each monitored MP signature is essential for correlating the MP – part property. This spatial information is often unavailable especially from commercial LPBF printers. Many MP monitoring methods have been reported and utilized. However, very few of these have the MP’s spatial information. To overcome this challenge, in this work we report a method for spatially registering the key MP signatures (MP intensity, temperature, and area) to the monitored print parts. The MP signatures are obtained from our coaxial high-speed single-camera based two-wavelength imaging pyrometry (STWIP) system and the MP spatial information is obtained from an off-axis camera system. A machine learning aided image analysis method is employed to retrieve the spatial distribution of MPs within the corresponding part’s coordinates system. Then, the MP signature maps (MPSMs) are reconstructed by mapping the STWIP measured MP signatures to the registered MP coordinates. Further, a long short-term memory (LSTM) neural network is developed for estimating the layer surface topography from the registered MPSMs. The obtained results indicate that the layer surface topography can be more accurately estimated by using MP temperature signature rather than MP intensity and/or area signatures as in common practice. Finally, our developed methods for MP monitoring, registration, and MP-surface topography prediction offer advanced capabilities for the online detection of process anomalies and part defects.
Spherical harmonic expansion of the Levitus Sea surface topography
Prior information for the stationary sea surface topography (SST) may be needed in altimetric solutions that intend to simultaneously improve the gravity field and determine the SST. For this purpose the oceanographically derived SST estimates are represented by a spherical harmonic expansion. The spherical harmonic coefficients are computed from a least squares adjustment of the data covering the majority of the oceanic regions of the world. Several tests are made to determine the optimum maximum degree of solution and the best configuration of the geometry of the data in order to obtain a solution that fits the data and also provides a good spectral representation of the SST.
The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models
The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort.
3D surface topography study of the biofunctionalized nanocrystalline Ti-6Zr-4Nb/Ca-P
In this work surface of the sintered Ti-6Zr-4Nb nanocrystalline alloy was electrochemically biofunctionalized. The porous surface was produced by anodic oxidation in 1 M H{sub 3}PO{sub 4} + 2%HF electrolyte at 10 V for 30 min. Next the calcium-phosphate (Ca-P) layer was deposited, onto the formed porous surface, using cathodic potential - 5 V kept for 60 min in 0.042 M Ca(NO{sub 3}){sub 2} + 0.025 M (NH{sub 4}){sub 2}HPO{sub 4} + 0.1 M HCl electrolyte. The deposited Ca-P layer anchored in the pores. The biofunctionalized surface was studied by XRD, SEM and EDS. In vitro tests culture of normal human osteoblast (NHOst) cells showed very good cells proliferation, colonization and multilayering. Using optical profiler, roughness and hybrid 3D surface topography parameters were estimated. Correlation between surface composition, morphology, roughness and biocompatibility results was done. It has been shown by us that surface with appropriate chemical composition and topography, after combined electrochemical anodic and cathodic surface treatment, supports osteoblast adhesion and proliferation. 3D topography measurements using optical profiler play a key role in the biomaterials surface analysis. - Highlights: Black-Right-Pointing-Pointer Nanocrystalline Ti-6Zr-4Nb/Ca-P material was produced for hard tissue implant applications. Black-Right-Pointing-Pointer Calcium-phosphate results in surface biofunctionalization. Black-Right-Pointing-Pointer The biofunctionalized surface shows good in-vitro behavior.
On the simultaneous improvement of a satellite orbit and determination of sea surface topography using altimeter data
A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface toography with minimum wavelengths of about 500 km and to reduce the radial orbit errors caused by geopotential uncertainties. The modeling of these errors is made using the linearized Lagrangian perturbation theory. Observation equations are developed using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information can then provide estimates of parametrs representing the sea surface topography and corrections to the orbit. The potential of the method is demonstrated in a solution where simulated geopotential errors and the Levitus sea surface topography are used to generate the observables for a Seasat 3 day arc. The simulation results suggest that the method can be used to efficiently process real altimeter data.
Exploring the impact of surface topography on Rayleigh-Bénard dry convection in the Pi cloud chamber using OpenFOAM: In cylindrical and rectangular geometries
The Pi convection-cloud chamber can generate steady-state turbulence in both rectangular and cylindrical shapes via Rayleigh-Bénard convection (RBC) by maintaining warm bottom and cold top surfaces. Although most experiments in the Pi chamber were conducted in cylindrical shapes, all previous Pi chamber simulations were conducted in a rectangular shape due to the limitations of those models to discretize a cylindrical domain when using the finite difference method therein. Here, we use OpenFOAM, an open-source finite-volume-based Computational Fluid Dynamics (CFD) software package, to conduct Large-Eddy Simulation (LES) of dry RBC in the Pi chamber at high Rayleigh numbers (10 8 to 10 9 ). Results show that large-scale circulation (LSC) direction varies in the chamber with a constant side wall temperature. Imposing a slight temperature imbalance at the side wall ranging from 0.1 to 0.7 degrees can lock the LSC, aligning better with Pi chamber observations, particularly at higher Rayleigh numbers. In addition, we examine the impact of surface topography on LSC and heat transfer in RBC systems within cylindrical and rectangular shapes under varying conditions. Results show that roughing top/bottom surfaces by adding bars of a few tens millimeters height can strengthen thermal plumes and enhance temperature fluctuations in the chamber. Furthermore, we observe that different bar height configurations lead to notable changes in LSC orientation and thermal stratification, highlighting the complex interactions between surface features and convection patterns. This finding highlights how surface topography and chamber geometry affect Rayleigh-Bénard convection, improving understanding of turbulent heat transfer and atmospheric boundary-layer processes. Direct Numerical Simulations (DNS) are also conducted to validate LES results. In conclusion, while LES effectively captures qualitative behaviors seen in DNS, it tends to underestimate velocity variances near walls, illustrating a trade-off between computational efficiency and accuracy.
Lunar surface topography
Surveyor I spacecraft photographs evaluated for lunar surface topography