Quantification Of Surface Roughness Research Articles

Measuring Surface Roughness through the Use of Digital Photography and Image Processing

This paper aims to provide a quantitative method that employs image processing in the assessment of surface roughness based on digital photograph field surveys, as in previous studies employing the outdoor integrated digital photography and image processing (O-IDIP) method. Digital photographs were taken on two different days under contrasting outdoor lighting conditions (overcast versus clear sky). Images were captured mounted on a tripod close up to the surface of a 380-year-old wall located at the University of Oxford Botanic Garden in the City of Oxford, UK. Sampling points were established at regular intervals along the border wall and encompassed sections facing west, north, and east, respectively along the survey. Two photographs were taken with a digital camera at each sampling point, one containing a color chart used to calibrate outdoor lighting conditions across images, which was excluded from the other photographic pair. Histogram-based quantification was performed based on images converted to Lab Color mode. The 10-step calibration procedure presented in this paper required more adjustments of contrast. However, more adjustments were not required under a clear sky. Std Dev L measurements were used to establish categories in a simple 3-point roughness index, namely the surface roughness index (SRI). The results denote that pitting did not affect surface roughness measurements. The study shows that it is possible to use Std Dev L measurements to quantify surface roughness on a comparative basis.

Active Whisking-Based Remotely Deployable NDE Sensor

The fundamental sensitivity characterization of a novel whisking sensor for applications in nondestructive evaluation is presented. The whisking sensors, originally developed for proximity detection applications in autonomous robotics are evaluated for measurements of surface roughness and surface form change. These surface parameters are the representatives of the typical changes associated with corrosion and surface breaking defects in real structures. The authors demonstrate that the whisking sensor can be used to accurately quantify surface roughness in the range 14-53 μm with excellent correlation to a standard reference. Furthermore, it is shown that that the sensor can detect 14 mm diameter flat bottomed holes with depths ranging from 0.4 to 1.0 mm. In contrast to conventional ultrasonic and eddy current techniques, the sensor is insensitive to surface liftoff, producing an error of only 1.2% for liftoffs of several mm. This liftoff insensitivity is a highly desirable characteristic for real-world deployment of the sensors, and the authors describe how the sensor can be incorporated into autonomous inspection robots.

A review of quantification of lithic use-wear using laser profilometry: a method based on metrology and fractal analysis

Over a decade of experimental lithic use-wear analysis using laser profilometry has led to the development of a method to measure surface modification due to wear in a reliable fashion. This research demonstrates that surface roughness can be documented on experimental stone tools made from a variety of raw material types, including chert, flint, and obsidian, using the laser profilometer, but that determining root mean square roughness (Rq) and a fractal dimension (Dr) may not always be possible. However, when coupled with scale-sensitive fractal analysis, specifically relative length (RL), and the F-test (MSR), it is possible to mathematically discriminate both used and unused surfaces on flint flakes, as well as used flake surfaces worn against different contact materials. This research has also identified some potential limitations associated with measuring stone tool surfaces using the profilometer, which affect this method's ability to quantify surface roughness on some experimental stone tools.

Effect of dry-out on the fouling of PVDF and PTFE membranes under conditions simulating intermittent seawater membrane distillation (SWMD)

Hydrophobic membranes are perceived to be chemically stable and resistant to dry-out during intermittent membrane distillation (MD) operations. However, distillate quality deterioration has been reported in field tests of solar-powered MD systems. This work investigates the effects of salt deposition, resulting from membrane dry-out, on the properties of two types of commercial hydrophobic membranes commonly used for MD purposes. The membranes are made of polytetrafluoroethylene (PTFE) and polyvinylidenefluoride (PVDF). The intermittent operation was simulated by a series of wet/dry cycles using seawater at MD operational temperatures. Membrane properties including surface contact angle, gas permeability, and mechanical strength were assessed, along with other structural characteristics like pore size distribution. The morphology of the salt-exposed membranes was also investigated using SEM and EDS. Atomic force microscopy (AFM) measurements were carried out to assess surface morphology and quantify surface roughness, in relation to the fouling process. AFM was combined with the use of a CaCO3 colloid probe to assess adhesion forces between CaCO3 and the membranes. DCMD experiments were conducted to study the post-fouling performance of the membranes in the MD process. Significant scaling was detected starting from the first week of seawater exposure, as evidenced by all the characterization techniques used. PVDF and PTFE membranes were observed to behave somewhat differently under these fouling conditions. DCMD experiments proved that membrane wetting was exacerbated by intermittent operation.

Real-Time Dynamics during Recharging Cycles

This paper describes preliminary results from in situ electrochemical atomic force microscopy (EC AFM) studies and in situ electrochemical small angle x-ray scattering (EC USAXS). Experiments are designed to quantify the morphological evolution during charge and discharge cycles. From the AFM data we measure feature shapes, nucleation density, island distributions and quantify surface roughness using height-height correlation functions. The USAXS scattering data is modeled as a distribution of islands. The goal of our project is to link early time nucleation events with the onset of large-scale instabilities such as dendrites.

Study on estimation method of rock mass discontinuity shear strength based on three-dimensional laser scanning and image technique

The estimation of shear strength of rock mass discontinuity is always a focal, but difficult, problem in the field of geotechnical engineering. Considering the disadvantages and limitation of existing estimation methods, a new approach based on the shadow area percentage (SAP) that can be used to quantify surface roughness is proposed in this article. Firstly, by the help of laser scanning technique, the three-dimensional model of the surface of rock discontinuity was established. Secondly, a light source was simulated, and there would be some shadows produced on the model surface. Thirdly, to obtain the value of SAP of each specimen, the shadow detection technique was introduced for use. Fourthly, compared with the result from direct shear testing and based on statistics, an empirical formula was found among SAP, normal stress, and shear strength. Data of Yujian (鱼简) River were used as an example, and the following conclusions have been made. (1) In the case of equal normal stress, the peak shear stress is positively proportional to the SAP. (2) The formula for estimating was derived, and the predictions of peak-shear strength made with this equation well agreed with the experimental results obtained in laboratory tests.

Characterizing morphology and nonlinear elastic properties of normal and thermally stressed engineered oral mucosal tissues using scanning acoustic microscopy.

This study examines the use of high-resolution ultrasound to monitor changes in the morphology and nonlinear elastic properties of engineered oral mucosal tissues under normal and thermally stressed culture conditions. Nonlinear elastic properties were determined by first developing strain maps from acoustic ultrasound, followed by fitting of nonlinear stress-strain data to a 1-term Ogden model. Testing examined a clinically developed ex vivo produced oral mucosa equivalent (EVPOME). As seeded cells proliferate on an EVPOME surface, they produce a keratinized protective upper layer that fills in and smoothens out surface irregularities. These transformations can also alter the nonlinear stress/strain parameters as EVPOME cells differentiate. This EVPOME behavior is similar to those of natural oral mucosal tissues and in contrast to an unseeded scaffold. If ultrasonic monitoring could be developed, then tissue cultivation could be adjusted in-process to account for biological variations in their development of the stratified cellular layer. In addition to ultrasonic testing, an in-house-built compression system capable of accurate measurements on small (∼1.0-1.5 cm(2)) tissue samples is presented. Results showed a near 2.5-fold difference in the stiffness properties between the unstressed EVPOME and the noncell-seeded acellular scaffold (AlloDerm(®)). There were also 4×greater differences in root mean square values of the thickness in the unseeded AlloDerm compared to the mature unstressed EVPOME; this is a strong indicator for quantifying surface roughness.

Smoothness assessment of corneal stromal surfaces

To assess the accuracy of the scanning electron microscopy (SEM) and present alternative approaches to quantify surface roughness based on numerical analysis. Department of Ophthalmology, Maisonneuve-Rosemont Hospital, University of Montreal, Montreal, Quebec, Canada. Experimental study. Lamellar stromal cuts were performed on human corneas using a femtosecond laser or a microkeratome. The photodisrupted stromal surfaces were processed for SEM, and images were acquired at ×1000 magnification. First, images were evaluated by independent observers. Second, images were analyzed based on first-order and second-order statistics of gray-level intensities. Third, 3-dimensional (3-D) surface reconstructions were generated from pairs of SEM images acquired at 2 angles. Results show that traditional assessment of roughness based on evaluating SEM images by independent observers can be replaced by computer-image texture analysis; an algorithm was developed to avoid subjective and time-consuming observations. The 3-D reconstructions allowed additional characterization of surface properties that was not possible with SEM images alone. Significant fluctuations in surface height were lost, although they could be retrieved using 3-D reconstructions. Image texture analysis allowed objective and repeatable assessment of stromal surface roughness; however, full assessments of surface-height fluctuations required 3-D reconstruction. These complementary methodologies offer a more comprehensive assessment of corneal surface roughness in clinical applications.

High‐Resolution Microfocus X‐Ray Computed Tomography for 3D Surface Roughness Measurements of Additive Manufactured Porous Materials

AbstractSince commercially available profiling systems fail when determining the surface roughness of porous materials, we propose a novel protocol for surface roughness quantification of 3D additive manufactured porous structures based on high‐resolution microfocus X‐ray computed tomography (micro‐CT) images. It allows to non‐destructively assess the roughness of these porous materials at the outer surface as well as inside the structure. The noise in the images and the spatial image resolution both have a significant effect on the accuracy of the micro‐CT‐based roughness measurements. Comparing the roughness parameters of flat substrates determined both with commercially available (optical and contact) profiling systems and the micro‐CT‐based roughness measurement protocol shows that micro‐CT can be applied accurately and in a robust manner for surface roughness quantification of 3D additive manufactured porous materials with a micro‐scale roughness. Depending on the dimensions of the roughness, the micro‐CT acquisition parameters, i.e., frame averaging and spatial image resolution, need to be fine‐tuned. Submicron‐scale roughness can currently not be quantified.

Quantifying Surface Roughness Effects on Phonon Transport in Silicon Nanowires

Although it has been qualitatively demonstrated that surface roughness can reduce the thermal conductivity of crystalline Si nanowires (SiNWs), the underlying reasons remain unknown and warrant quantitative studies and analysis. In this work, vapor-liquid-solid (VLS) grown SiNWs were controllably roughened and then thoroughly characterized with transmission electron microscopy to obtain detailed surface profiles. Once the roughness information (root-mean-square, σ, correlation length, L, and power spectra) was extracted from the surface profile of a specific SiNW, the thermal conductivity of the same SiNW was measured. The thermal conductivity correlated well with the power spectra of surface roughness, which varies as a power law in the 1-100 nm length scale range. These results suggest a new realm of phonon scattering from rough interfaces, which restricts phonon transport below the Casimir limit. Insights gained from this study can help develop a more concrete theoretical understanding of phonon-surface roughness interactions as well as aid the design of next generation thermoelectric devices.

Effect of surface roughness on inactivation of Escherichia coli O157:H7 87-23 by new organic acid-surfactant combinations on alfalfa, broccoli, and radish seeds.

Surface roughness has been reported as one of the factors affecting microbial attachment and removal. Seed surfaces are complex, and different seed varieties have different surface topographies. As a result, a sanitizer effective in eliminating pathogenic bacteria on one seed may not be as effective when applied to another seed. The objectives of this research were (i) to investigate the efficacy of malic acid and thiamine dilaurylsulfate (TDS) combined treatments for inactivation of E. coli O157:H7 strain 87-23 on alfalfa, broccoli, and radish seeds, (ii) to quantify surface roughness of the seeds, and (iii) to determine the correlation between microbial removal and surface roughness. The surface roughness of each seed type was measured by confocal laser scanning microscopy (CLSM) and surface profilometry. Surface roughness (Ra) values of the seeds were then calculated from CLSM data. Seeds inoculated with E. coli O157:H7 87-23 were washed for 20 min in malic acid and TDS solutions and rinsed for 10 min in tap water. Radish seeds had the highest Ra values, followed by broccoli and alfalfa seeds. A combination of 10% malic acid and 1% TDS was more effective than 20,000 ppm of Ca(OCl)(2) for inactivation of E. coli O157:H7 87-23 on broccoli seeds, while the inactivation on radish and alfalfa seeds was not significantly different compared with the 20,000-ppm Ca(OCl)(2) wash. Overall, a negative correlation existed between the seeds' Ra values and microbial removal. Different seeds had different surface roughness, contributing to discrepancies in the ability of the sanitizers to eliminate E. coli O157:H7 87-23 on the seeds. Therefore, the effectiveness of one sanitizer on one seed type should not be translated to all seed varieties.

Quantification of surface roughness of parts processed by laminated object manufacturing

Additive manufacturing (AM) technology is essentially performed using a layered manufacturing (LM) process. Because more complex 3D physical models can be efficiently fabricated without geometric limitation by the technology, a remarkable reduction in production life cycle has been achieved. However, due to the LM process, a deterioration of the surface quality of the parts processed by AM may occasionally occur, which is the primary reason that the surface problem has been a key issue in AM. In this paper, a methodology is proposed to quantify the surface roughness of the parts processed by laminated object manufacturing (LOM), which is a typical technology in AM. The surface profiles of the parts were investigated, a schematic was constructed by considering the LOM process factor geometrically, and a theoretical approach to quantify average surface roughness according to surface angle variation is presented. The expressions required for numerical computation were deduced and defined. By comparing the measured data and computed values, the proposed approach was verified. Additionally, the effects of the process variables related to surface quality were evaluated and analyzed.

Measurement of the radius of Mercury by radio occultation during the MESSENGER flybys

The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft completed three flybys of Mercury in 2008–2009. During the first and third of those flybys, MESSENGER passed behind the planet from the perspective of Earth, occulting the radio-frequency (RF) transmissions. The occultation start and end times, recovered with 0.1 s accuracy or better by fitting edge-diffraction patterns to the RF power history, are used to estimate Mercury's radius at the tangent point of the RF path. To relate the measured radius to the planet shape, we evaluate local topography using images to identify the high-elevation feature that defines the RF path or using altimeter data to quantify surface roughness. Radius measurements are accurate to 150 m, and uncertainty in the average radius of the surrounding terrain, after adjustments are made from the local high at the tangent point of the RF path, is 350 m. The results are consistent with Mercury's equatorial shape as inferred from observations by the Mercury Laser Altimeter and ground-based radar. The three independent estimates of radius from occultation events collectively yield a mean radius for Mercury of 2439.2±0.5 km.

Suitability of terrestrial laser scanning for studying surface roughness effects on concentrated flow erosion processes in rangelands

Surface roughness is thought to affect concentrated flow erosion – a major mechanism of soil loss on disturbed rangelands. However, quantifying surface roughness in the field at appropriately fine spatial scales is laborious and the scale at which to conduct meaningful roughness measurements is difficult to discern. Rapid, objective, and repeatable field methods are therefore needed to accurately measure surface roughness across a range of spatial scales to advance our understanding and modeling of concentrated flow erosion processes. Surface roughness can be derived from surface topography mapped at the sub-cm level using a field-portable terrestrial laser scanner (TLS). To test the suitability of terrestrial laser scanning for studying surface roughness effects on erosion processes in rangelands, we used concentrated flow simulation techniques at 8.5 m2 plots that were randomly placed at rangeland sites in southeastern Oregon and southwestern Idaho, USA. Local surface roughness (locRMSH) was calculated as the standard deviation of TLS mapped surface heights within moving windows varying in size from 30 × 30 to 90 × 90 mm. The mean locRMSH of the eroded area and entire plot were negatively correlated (r2 > 0.71, RMSE 0.74, RMSE < 90.07 g min− 1, respectively) with concentrated flow erosion. The strength of the locRMSH–erosion relationship and regression model parameters were affected by the moving window size, emphasizing the scale dependence of the locRMSH–erosion relationship. Adjusting locRMSH for slope effects decreased the strength of the locRMSH–erosion relationship from r2 < 0.83 to < 0.26. Our results indicate that TLS is a useful tool to enhance our current understanding of the effect of surface roughness on overland flow erosion processes and advance hydrologic and erosion model parameter development. Further research is needed to evaluate the locRMSH – concentrated flow erosion relationship over a wider range of soil properties, surface conditions, and spatial extents.

Artificial weathering of Spanish granites subjected to salt crystallization tests: Surface roughness quantification

For hundreds of years, two types of granite (Zarzalejo and Alpedrete) from the Madrid region, Spain, have been extensively used as building stones. Fresh specimens of both stone types have been sampled from their respective quarries and subjected to sodium sulphate salt crystallization test (SCT). The resulting physical and chemical weathering patterns have been characterized by polarized light optical and environmental scanning electron microscopy. Water absorption under vacuum conditions and mercury intrusion porosimetry techniques were used to determine the pre- and post-SCT porosity and pore size distribution. The following non-destructive techniques were performed to assess stone durability and decay: ultrasound velocity (US) and surface roughness determination (SR) of intra- and inter-granular quartz, feldspar and biotite minerals at the centre as well as at the corners and edges of specimen surfaces. Before the SCT, US values were lower and SR values higher in Zarzalejo (ZAR) than Alpedrete (ALP) granite. After SCT, the US values declined while SR rose in both types of granites, with greater average differences in ZAR than ALP for both parameters. Feldspar and biotite and their inter-granular contacts were found to be the weakest and therefore the most decay-prone areas of the stone. The initial SR parameters were generally higher and rose more steeply after SCT at the corners and around the edges of the specimens. While behaviour was found to be similar in the two types of granite, variations were greater in ZAR, the less durable and more decay-prone of the two. Surface roughness measurement of mineral grains in granite stones is a very useful, in situ, non-destructive technique for quantifying salt crystallization-mediated physical and chemical weathering. The resulting quantification of decay and of related durability provides insight into the future behaviour of this type of stone, commonly used in historic buildings.

Use of Low-Cost Multistripe Laser Triangulation (MLT) Scanning Technology for Three-Dimensional, Quantitative Paleoichnological and Neoichnological Studies

Abstract The purpose of this paper is to test the application of a new, low-cost ($2995.00 US), multistripe laser triangulation (MLT) scanner and three-dimensional (3D) software for semiquantitative and quantitative analyses of ichnofossils and modern traces. The goal of this research is to improve on existing analytical techniques and apply new methods to 3D digital models of ichnofossils and modern traces. Objectives are to (1) provide researchers with new ways to develop and test hypotheses quantitatively in the fields of paleoichnology, neoichnology, sedimentology, and soil science, and (2) discuss uses, advantages, and limitations of MLT technology related to ichnology. We scanned and created digital models of a variety of mostly continental ichnofossils and modern terrestrial traces produced by invertebrates and vertebrates. Visual methods applied include making uniformly colored specimen surfaces, stereo pairs, anaglyph stereo images, animations, and cross sections. Quantitative methods applied include measuring distances, tortuosity indices, and angles, and producing contour maps of tracks. Two of the most useful properties measurable from digital models are surface area (SA) and volume (V); these are used rarely in ichnology because they are difficult to measure with traditional methods. We use SA to calculate area exploited and introduce a method of quantifying surface roughness adapted from research on soil surfaces. We measure V of burrows, tracks, and coprolites, as well as introduce a new measure termed “volume exploited.” We hypothesize that different tracemakers make burrows with characteristic V to SA ratios; this is partially supported by statistical tests of previously published data. We also use V to SA ratios to determine relative compactness—a metric adapted from building physics. Digital models ensure perpetuity of specimens because they preserve 3D data that can be used to make physical copies, placed in museums, and disseminated easily to researchers and educational institutions of all levels. Data from digital models can be used to interpret ichnocoenoses, bioturbation rates, and pedogenic properties and processes in soils and paleosols. Note that MLT scanning digitizes only surfaces of objects, so it is best suited for exogenic traces and casts of endogenic traces.

Spatiotemporal variations of soil surface roughness from in-situ laser scanning

Microtopography and roughness are highly dynamic properties of the soil surface and important factors governing surface runoff and erosion processes. While various remote sensing technologies were successfully applied for topography measurements at different spatial scales, there is a lack of field studies that collected systematically microtopography data over long observation periods. In this paper an approach to measure and quantify surface roughness in the field based on laser scanning technologies is presented. Between June 2004 and November 2005 97 in-situ measurements were conducted in a test site with two different sandy substrates in vegetation-free conditions. Two-dimensional high-resolution (1 mm) datasets where generated for eight micro erosion plots of 0.25 to 2.9 m2 in size. Dynamics and pattern formation were quantified for surface roughness and surface height changes. Roughness patterns at different scales were analyzed by local roughness indices using sliding windows of 3 to 55 mm in size. Results show strong spatial and temporal dynamics in surface roughness as well as substrate-specific variations. Temporal roughness variations could be detected and were linked to precipitation patterns. The methods presented in this paper are considered suitable to generate high-resolution datasets on spatiotemporal and multi-scale microtopography patterns and to advance the understanding of surface processes at small scales in natural environments.

Bright Inkjet Printed Macromolecular Organic Light emitting Diodes on Flexible Substrates

AbstractWe present results of printing solution-processable organic light emitting diodes (OLEDs) based on electrophosphorescent Ir(III) stellate polyhedral oligomeric silsesquioxane (POSS) macromolecules. The macromolecules are doped into a polymer-based ink containing a hole transporting polymer, poly(9-vinylcarbazole) (PVK) and an electron transporting material, 2-4-biphenylyl-5-4-tertbutyl-phenyl-1,3,4-oxadiazole (PBD), and the resulting ink is printed on a layer of poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS) spin-coated on indium tin oxide (ITO). An exciton-blocking layer consisting of 2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline (BCP) is thermally evaporated onto the printed ink layers, followed by a LiF/Al cathode. While the photoluminescence (PL) spectrum of printed ink on glass indicates a significant contribution from the PVK:PBD exciplex, electroluminescence measurements (EL) suggest a much smaller effect of these states, which implies significant charge trapping at dopant molecular sites. Our latest experiments with devices printed on PEDOT:PSS/ITO/glass indicate that the devices exhibit high luminances (∼ 13,000 cd/m2 at 70 mA/cm2) and a fairly consistent quantum efficiency (∼ 2.5%) across a wide range of luminances. The corresponding figures for spin-coated devices are expectedly higher, with efficiencies ∼ 4.5% at similar levels of brightness. We use white light interferometry as a non-contact technique to quantify surface roughness and thickness of printed layers. Our current results thus indicate that inkjet printing of macromolecular phosphor doped polymer inks is suitable for fabrication of OLEDs with high brightness, in spite of the low glass transition temperature of some of the species. Our initial work with these devices on flexible ITO-coated plastic substrates shows devices with moderately high luminance values (∼ 2,500 cd/m2 at 35 mA/cm2). Our more recent devices show higher brightnesses (∼ 9, 600 cd/m2). We are working on the development of inkjet printing materials and processes for pure macromolecular OLEDs that are not performance and reliability limited by the presence of the PVK:PBD matrix with low glass transition temperatures. This requires the development of macromolecules that subsume all the functions of the host matrix and have high enough Tg to be usable in high concentrations needed. In conjunction with the inkjet printing technology demonstrated in this work, this has the potential to yield low-cost manufacturing of these devices.

Influence of argon-ion bombardment of titanium surfaces on the cell behavior

Several studies in vitro and in vivo accomplished in dental implants have demonstrated that the chemical and physical properties of biomaterials are able to regulate the initial tecidual response around the implant. This tecidual response depends directly on the hydrophily, roughness, texture and chemical composition of the surface. Plasma treatment can be used to improve the surface properties of commercial pure Ti, in order to create different surface topographies, changes in roughness, and modifications in the surface wettability. In this study a surface modification in titanium Cp degree II was carried out, through the plasma treatment and using argon-ion bombardment. A comparison of surface properties and their influence on the cells behavior was also accomplished, besides the quantification of surface roughness, wettability and cellular proliferation. The results showed that the argon-ion bombardment influences the surface energy value, surface roughness and the surface topography of Ti materials. These parameters influence the cellular proliferation process.

Roughness of Hawaiian volcanic terrains

We performed analyses of topographic variation (surface roughness) using a new 2‐D mapping method which shows that understanding the relationship between data resolution, Hurst exponent, y intercept, RMS deviation, and cell size is important for assessing surface processes. We use this new method to assess flows at six field sites in Kilauea caldera, Hawaii, using three data sets at different resolutions, TOPSAR (10 m/pixel), airborne lidar (1 m/pixel), and tripod‐mounted lidar (0.02–0.03 m/pixel). The flows studied include ponded pahoehoe flows, compound pahoehoe flows, and jumbled, slabby pahoehoe. The 2‐D quantification of surface roughness for the Kilauea lava flows indicates that features formed during emplacement and modification of the flows exhibit statistically distinct roughness signatures. The 2‐D method provides a tool for unit mapping based on surface roughness. Key findings indicate that the new 2‐D method provides more robust results than 1‐D methods for surface roughness because of larger 2‐D sample sizes and the removal of 1‐D directional bias leading to a reduction in error. Furthermore, data set resolution relative to the scale of the features under study is important to consider when designing a 2‐D surface roughness study. Future applications to topographic data sets from Mars will provide information on flow emplacement conditions and spatial and temporal evolution of volcanic provinces on Mars.