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MetroProTM

SurfaceTexture

Parameters

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Understanding Surface Texture Parameters

Every parts surface is made up of texture and roughness whichvaries due to manufacturing techniques and the part structure itself.

To understand a components surface and to control themanufacturing process to the degree required in todays modernworld, it is necessary to quantify the surface in both two and threedimensions.

Surface texture parameters can be grouped into these basiccategories: Roughness, Waviness, Spacing, and Hybrid.

TerminologyAreal- A three dimensional surface area.

Cutoff Filter- Determines the wavelength at which the surfacestructure is differentiated between roughness and waviness data.Proper selection of the correct filter cutoff in software is critical tomeasurement accuracy.

Evaluation Length- The area from which data is obtained. It is athree dimensional area that corresponds to the instrument field ofview, or a two dimensional profile that corresponds to the length ofthe slice as defined in the filled plot.

Hybrid Parameters- These parameters are combinations ofspacing and roughness parameters.

Mean Line- A straight line that is generated by calculating aweighted average for each data point resulting in equal areas aboveand below the line. Also known as center line.

Profile-A two dimensional slice through an area.

Roughness Parameters - The finer irregularities in the surfacetexture which are inherent in the production process. These are ameasure of the vertical characteristics of the surface.

Sampling Length- The area selected for assessment andevaluation of the roughness parameter having the cutoff wavelength.

Any surface irregularities spaced farther apart than the samplinglength are considered waviness. Also known as cutoff length.

Spacing Parameters- A measure of the horizontal or lateralcharacteristics of the surface.

Surface Texture- The topography of a surface composed of certaindeviations that are typical of the real surface. It includes roughnessand waviness.

Waviness Parameters - A larger component of surface textureupon which roughness is superimposed.

When two parameter names are shown, the name inparentheses is the name used in ZYGO software.

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Contents

Roughness Parameters pageH ISO Flatness Pt ISO R3z 4R3z ISO Ra Rku Rq Rmax ISO Rp 5Rpm ISO Rq Rt Rtm Rtm ISO 6Rv Rvm ISO Ry Rz Rz ISO 7SPt ISO SR3z ISO SRmax ISO SRpm ISO 8SRtm ISO SRvm ISO SRz 8

SRz ISO SRzX SRzY 9

Waviness ParametersWa Wq Wy 9

Spacing ParametersPc Peak Density Peak Spacing S Sm 10Summits Summit Density Summit Spacing 10Valleys Valley Density Valley Spacing 11

Hybrid Parameters

a q tm Ia Iq Iy 11Rvolume RSurfAreaRatio 12WSurfAreaRatio ISurfAreaRatio 12Bearing Ratio Parameters

Bearing Ratio (Tp) Rk Rk Midpoint 12Rpk Rpk Threshold Rvk Rvk Threshold 12Mr1 Mr2 V1 V2 Stp1 (%) Stp2 (%) 13

Stp3 (%) Upper Stp (%) Lower Stp (%) 13Delta Stp (%) Stp1 Height Stp2 Height Stp3 Height 14Upper Stp Height Lower Stp Height SHtp Mean SHtp 14tp1 (%) tp2 (%) tp3 (%) Upper tp (%) Lower tp (%) 15Delta tp (%) tp1 Height tp2 Height tp3 Height 15Upper tp Height Lower tp Height Htp Mean Htp 16

Material Probability Parameters

Rpq Rvq Rmq (%) Height UPL 16Height LPL Height UVL Height LVL 17Std UPL Std LPL Std UVL Std LVL 17

Rsk ACF 18

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Roughness Parameters

H Swedish height. Theroughness between two

predefined reference lines.The upper line exposes 5%of the data, and the lower lineexposes 90%. H is lesssensitive to data spikes thanRt. Available for profile andareal data.

ISOFlatness

Areal flatness deviation. Themeasure of surface deviationfrom perfectly flat. It is thedistance between two parallelplanes obtained by applying a

Chebychev fit to the surface data. The Chebychev fit isa mathematical technique that effectively uses twoparallel planes to squeeze the surface data points fromboth inside and outside, adjusting the angle to minimizethe distance between the planes.

Pt ISO Total peak-to-valley profile

height. The distancebetween the highest peakand the deepest valley overthe entire evaluation length.The profile data has formremoved but is unfiltered.

R3z Base roughness depth. Thedistance between the thirdhighest peak and the thirdlowest valley. A peak is aportion of the surface abovethe mean line and betweencenter line crossings.

Available for profile and arealdata.

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R3zISO

Base roughness profiledepth. The height of the 3rd

highest peak from the 3rdlowest valley per samplinglength. The base roughnessdepth is found in fivesampling lengths and thenaveraged.

Ra Arithmetical mean deviation.The average roughness ordeviation of all points from aplane fit to the test partsurface. Available for profileand areal data.

Rku Kurtosis is a measure of the randomness of heights, andof the sharpness of a surface. A perfectly randomsurface has a value of 3; the farther the result is from 3,the less random and more repetitive the surface is.

Surfaces with spikes are higher values; bumpy surfacesare lower. Available for profile and areal data.

RmaxISO

Maximum peak-to-valleyprofile height. The greatestpeak-to-valley distance withinany one sampling length.

Rp(Peak)

Highest peak. The maximumdistance between the meanline and the highest pointwithin the sample. It is themaximum data point heightabove the mean line throughthe entire data set. Availablefor profile and areal data.

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RpmISO

Mean peak profile height.The mean peak height based

on one peak per samplinglength. The single highestpeak is found in five samplinglengths and then averaged.

Rq(rms)

Root-mean-square (rms) roughness. The average of themeasured height deviations taken within the evaluation

length or area and measured from the mean linearsurface. Available for profile and areal data. Rq is therms parameter corresponding to Ra.

Rt(PV)

Maximum peak-to-valley height. The absolute valuebetween the highest and lowest peaks. Available forprofile and areal data.

Rtm Mean peak-to-valleyroughness. It is determined

by the difference between thehighest peak and the lowestvalley within multiple samplesin the evaluation area. Forprofile data it is based on fivesample lengths. Available forprofile and areal data.

RtmISO

Mean peak-to-valley profileroughness. The mean peak-to-valley roughness based onone peak and one valley per

sampling length. The singlelargest deviation is found infive sampling lengths andthen averaged.

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Rv(Valley)

Lowest valley. The maximum distance between themean line and the lowest point within the sample. It is

the maximum data point height below the mean linethrough the entire data set. Available for profile andareal data. See Rp.

RvmISO

Mean valley profile depth.The mean valley depth basedon one peak per sampling

length. The single deepestvalley is found in fivesampling lengths and thenaveraged.

Ry(Rmax)

Maximum peak-to-valleyroughness. The vertical

distance between the top ofthe highest peak and thebottom of the deepest valleywithin the sampling length. Itis the maximum of all thepeak-to-valley values.

Rz Ten-point height. Theaverage absolute value of thefive highest peaks and thefive lowest valleys over theevaluation length. Availablefor profile and areal data.

RzISO

Average peak-to-valleyprofile roughness. Theaverage peak-to-valleyroughness based on one

peak and one valley persampling length. The singlelargest deviation is found infive sampling lengths andthen averaged. Identical toRtm ISO.

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For S_ ISO parameters, a surface area is

analyzed by fitting a minimum enclosingrectangle and applying a 5 x 5 sampling grid, fora total of 25 sampling areas. All sampling areastogether make up the evaluation area.

SPtISO

Total peak-to-valley areal height. The distance betweenthe highest peak and the deepest valley over the entire

evaluation area.

SR3zISO

Base roughness areal depth. The height of the 3rdhighest peak from the 3rd lowest valley per samplingarea. The base roughness depth is found in eachsampling area and then averaged.

SRmaxISO

Maximum peak-to-valley height over the entire arealevaluation area.

SRpmISO

Mean peak areal height. The mean peak height basedon one peak per sampling area. The single highest peakis found in each sampling area and then averaged.

SRtm

ISO

Mean peak-to-valley areal roughness. The mean peak-

to-valley roughness based on one peak and one valleyper sampling area. The single largest deviation is foundin each sampling area and then averaged.

SRvmISO

Mean valley areal depth. The mean valley depth basedon one peak per sampling area. The single deepestvalley is found in each sampling area and then

averaged.

SRz Average radial peak-to-valleyareal roughness. The averageof the largest half of manyindividual Rz resultsdetermined by slicing the areal

data array about its center through 360 degrees. The Rzresults are sorted by magnitude and SRz is calculated byaveraging the largest 50% of the Rz values. A line-generation algorithm is used to determine the actualpixel-to-pixel path of each slice; there is no interpolationbetween pixels. SRz covers the entire array, and due toits radial generation it is lay independent.

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SRzISO

Average peak-to-valley areal roughness. The averagepeak to valley roughness based on one peak and one

valley per sampling area. The single largest deviation isfound in each sampling area and then averaged.

SRzX The average of many individual Rz results, determinedby slicing the data array in the x-axis. The individual Rzresults are each based on a profile slice one pixel wide.SRzX is based on the entire array. See SRz.

SRzY The average of many individual Rz results, determinedby slicing the data array in the y-axis. The individual Rzresults are each based on a profile slice one pixel wide.SRzY is based on the entire array. See SRz.

Waviness Parameters

Wa The arithmetic averageroughness, or averagedeviation, of all points from aplane fit to the waviness data.

Wq The root-mean-square (rms) roughness of all points froma plane fit to the waviness data.

Wy(Wmax)

The maximum height of thewaviness data.

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Spacing Parameters

Pc(Peaks)

Peak count or the number ofpeaks included in the

analysis. A peak is definedas a data point whose heightis above a software selectedbandwidth.

PeakDensity

The number of peaks per unit area.

PeakSpacing The average distance between peaks.

S The average spacingbetween local peaks over theevaluation length. A localpeak is the highest pointbetween two adjacent

minima. The averagespacing for the exampleshown is calculated by:

Sm The average spacing

between peaks at the meanline over the evaluationlength. A peak is the highestpoint between an upwardsand downwards crossing ofthe mean line. It iscalculated by summing all

the peak spacing anddividing by the number ofspaces.

Summits The number of summits included in the analysis. Asummit is a point that is higher than the four nearestdata points as determined by a software threshold

value. The higher the threshold, the fewer and steeperthe summits.

SummitDensity

The number of summits per unit area.

SummitSpacing

The average distance between summits.

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Spacing Parameters

Valleys The number of valleys included in the analysis. A valleyis defined as a data point whose height is below a

software selected bandwidth. See Pc.ValleyDensity

The number of valleys per unit area.

ValleySpacing

The average distance between valleys.

Hybrid Parameters

a(Slope Ra)

The arithmetic average surface slope of the entiredata matrix. Slopes are directly related to thereflective properties of the surface. They are usefulfor controlling cosmetic appearances of surfaces, as

well as in controlling reflective surfaces. Results areavailable for overall slopes and in just the x or y axes.In mathematical symbols:

q(Slope rms) The geometric average slope of the entire datamatrix. This result is similar to a except that

individual slopes are averaged by the rms methodrather than arithmetically, emphasizing more extremeslopes. Results are available for overall slopes andin just the x or y axes.

tm(Slope Rtm)

The average peak-to-valley slope of nine sampleareas on the entire data matrix. Results are availablefor overall slopes and in just the x or y axes.

Ia The average surface height, or average deviation, ofall points from a plane fit to the input data. Input datais the data obtained by the instrument; it includesroughness and waviness information.

Iq The root-mean-square deviation of all points from aplane fit to the input data. Input data includesroughness and waviness information.

Iy(Imax)

The maximum height of the input data. Input dataincludes roughness and waviness information.

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Hybrid Parameters

Rvolume The volume of theroughness data as

specified by software asabove or below thesurface.

RSurfAreaRatio The ratio of roughness surface area to the planararea occupied by the data.

WSurfAreaRatio The ratio of waviness surface area to the planar areaoccupied by the data.

ISurfAreaRatio The ratio of input surface area to the planar areaoccupied by the data.

Bearing Ratio Parameters

Bearing

Ratio (Tp)

Bearing ratio is the ratio (expressed as a percentage)

of the length of the bearing surface at any specifieddepth in the evaluation area. It simulates the effect ofwear on a bearing surface. Bearing Ratio results areavailable for profile data (tp) and surface area (Stp).

Rk Core Roughness Depth -The long term running

surface which will influencethe performance and life ofthe bearing surface.

RkMidpoint

The middle point of the Rk region; it is an absoluteheight.

Rpk Reduced Peak Height - The top portion of the surfacethat will be worn away in the run-in period.

RpkThreshold

The threshold between theRpk and Rk regions; it is anabsolute height.

Rvk Reduced Valley Depth - The lowest part of thesurface that retains lubricant.

RvkThreshold

The threshold between the Rk and Rvk regions; it is anabsolute height.

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Hybrid Parameters

Mr1 Peak Material Component - The material ratio atwhich Rpk and Rk meet. It represents the upper limit

of the core roughness profile. This parameter isderived from the bearing ratio plot.

Mr2 Valley Material Component - The material ratio atwhich Rvk and Rk meet. It represents the lower limitof the core roughness profile. This parameter isderived from the bearing ratio plot.

V1 Volume 1 - the volume of the material that will beremoved during the run-in period. Part of the bearingratio analysis.

V2 Volume 2 - The potential volume of retained lubricant.Part of the bearing ratio analysis.

Stp1 (%) The areal bearing ratio(expressed as apercentage) at the heightspecified by the Stp1Height control, relative tothe selected StpReference location and

Stp1 (%) Offset value.

Stp2 (%) The areal bearing ratio (expressed as a percentage)at the height specified by the Stp2 Height control,relative to the selected Stp Reference location andStp2 (%) Offset value.

Stp3 (%) The areal bearing ratio (expressed as a percentage)

at the height specified by the Stp3 Height control,relative to the selected Stp Reference location andStp3 (%) Offset value.

UpperStp (%)

The areal bearing ratio (expressed as a percentage)at the location specified by the Upper Stp Heightcontrol, relative to the selected Stp Reference

location.LowerStp (%)

The areal bearing ratio (expressed as a percentage)at the location specified by the Lower Stp Heightcontrol, relative to the selected Stp Referencelocation.

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Hybrid Parameters

DeltaStp (%)

The difference in the areal bearing ratio (expressedas a percentage) between the Upper and Lower

Stp (%) values.Stp1Height

The height of the arealbearing ratio curve whereit intersects the percentagespecified by the Stp1 (%)control, relative to the

selected Stp Referencelocation.

Stp2Height

The height of the areal bearing ratio curve where itintersects the percentage specified by the Stp2 (%)control, relative to the selected Stp Referencelocation.

Stp3Height

The height of the areal bearing ratio curve where itintersects the percentage specified by the Stp3 (%)control, relative to the selected Stp Referencelocation.

UpperStp Height

The height of the areal bearing ratio curve at thelocation specified by the Upper Stp (%) control,

relative to the selected Stp Reference locationLowerStp Height

The height of the areal bearing ratio curve at thelocation specified by the Lower Stp (%) control,relative to the selected Stp Reference location.

SHtp Height between two points on the areal bearing ratiocurve as specified by the Upper Stp (%) and Lower

Stp (%) controls. It is used to help determine materialremoval over multiple processes.

MeanSHtp

The average of all the height values between the twopoints on the areal bearing ratio curve specified bythe Upper Stp (%) and Lower Stp (%) controls.

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Hybrid Parameters

tp1 (%) The profile bearing ratio(expressed as apercentage) at the heightspecified by the tp1Height control, relative tothe selected tp Referencelocation and the tp1 (%)Offset control value.

tp2 (%) The profile bearing ratio (expressed as a percentage)at the height specified by the tp2 Height control,relative to the selected tp Reference location and thetp2 (%) Offset control value.

tp3 (%) The profile bearing ratio (expressed as a percentage)at the height specified by the tp3 Height control,

relative to the selected tp Reference location and thetp3 (%) Offset control value.

Uppertp (%)

The profile bearing ratio (expressed as a percentage)at the location specified by the Upper tp Heightcontrol, relative to the selected tp Reference location.

Lowertp (%) The profile bearing ratio (expressed as a percentage)at the location specified by the Lower tp Heightcontrol, relative to the selected tp Reference location.

Deltatp (%)

The difference in the profile bearing ratio (expressedas a percentage) between the Upper and Lower tp(%) values.

tp1 Height The height of the profilebearing ratio curve whereit intersects thepercentage specified bythe tp1 (%) control,relative to the selected tpReference location.

tp2 Height The height of the profile bearing ratio curve where itintersects the percentage specified by the tp2 (%)control, relative to the selected tp Reference location.

tp3 Height The height of the profile bearing ratio curve where itintersects the percentage specified by the tp3 (%)

control, relative to the selected tp Reference location.

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Hybrid Parameters

Uppertp Height

The height of the profile bearing ratio curve where itintersects the percentage specified by the Uppertp (%) control, relative to the selected tp Referencelocation.

Lowertp Height

The height of the profile bearing ratio curve where itintersects the percentage specified by the Lowertp (%) control, relative to the selected tp Referencelocation.

Htp Height between two points on the profile bearing ratiocurve as specified by the Upper tp (%) and Lowertp (%) controls.

Mean Htp The average of all the height values between the twopoints on the profile bearing ratio curve specified by

the Upper tp (%) and Lower tp (%) controls.Material Probability Parameters

Rpq The root-mean-squareaverage of the heightdeviations in the peak orplateau portion of the

Material Probability plot.

Rvq The root-mean-square average of the heightdeviations in the valley portion of the MaterialProbability plot. This result is useful as a predictor oforiginal surface roughness before the removal ofmore material in subsequent processes. See Rpq.

Rmq (%) The material ratio(expressed as apercentage) at the peak-to-valley transition.

Height

UPL

The height at the upper

peak or plateau limit. UPLis set with inspectors in theMaterial Probability plot.

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Hybrid Parameters

HeightLPL

The height at the lower peak or plateau limit aslocated by the software in the Material Probabilityanalysis.

HeightUVL

The height at the upper valley limit, as located by thesoftware in the Material Probability analysis.

HeightLVL

The height at the lowervalley limit. LVL is set with

inspectors in the MaterialProbability plot.

Std UPL The standard deviation atthe upper peak or plateaulimit. UPL is set withinspectors in the MaterialProbability plot.

Std LPL The standard deviation at the lower peak or plateaulimit, as located by the software in the MaterialProbability analysis.

Std UVL The standard deviation at the upper valley limit, as

located by the software in the Material Probabilityanalysis.

Std LVL The standard deviation atthe lower valley limit. LVLis set with inspectors in theMaterial Probability plot.

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Hybrid Parameters

Other Hybrid Parameters

Rsk Skewness. A measure of symmetry of the profileabout the mean line. Negative skew indicates apredominance of valleys, while positive skewindicates a peaky surface. Bearing surfaces shouldhave negative skew.

ACF

(Auto-covariance)

Autocorrelation function orAutocovariance. Used todetermine the periodicity ofa surface; it shows thedominant spatial frequencies

along a cross section of thetest surface. ACF is a measure of self-similarity ofa profile - the extent to which a surface waveformpattern repeats. If the surface is random, the plotdrops rapidly to zero. If the plot oscillates aroundzero in a periodic manner, then the surface has adominant spatial frequency. Correlation Length is the

length along the x-axis where the Autocovariancefunction first crosses zero.

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Compliance with International Standards

ZYGO is an industrial leader in surface texture metrology and

complies with numerous international standards for surface textureparameters, including:

ANSI The American National Standards Institute ISO International Standards Organization JIS Japanese Industry Standard

World HeadquartersZygo Corporation

Laurel Brook RoadMiddlefield, CT 06455USA

Tel: 860-347-8506Fax: 860-347-8372Email: [email protected]: www.zygo.com

For a complete list of ZYGO offices,representatives, and distributorsvisit www.zygo.com.

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