3d fourier & wavelets analysis module for mountainsmap · plot obtainedby the fast fourier...

Interactive frequency spectrum plots

Interactive power spectrum density plots

Surface isotropy, directionality and periodicity analysis

Autocorrelation and intercorrelation plots

FFT plot editor for advanced filtering

Discrete scale-based wavelets filtering

Continuous wavelet decomposition

FFT-based and wavelets based tools for studying surface-process interactions and for advanced filtering

3D Fourier & Wavelets Analysis Module for MountainsMap+

The Frequency Spectrum study provides an interactiveplot obtained by the Fast Fourier Transform (FFT).

Surfaces (x,y,z). Any x,y point on the frequencyspectrum plot can be selected interactively and thefollowing parameters are calculated:

• Wavelength • Angle • Phase

• Magnitude (amplitude) of the radius in decibels (logscale) or length units (linear scale).

.

Frequency SpectrumSee the wavelength, magnitude, phase and angle of each point on a surface in an interactive frequency spectrum plot

Profiles (x,z). Any wavelength on the frequency spectrumplot can be selected using a vertical sliding cursor andthe following parameters are calculated:

• Wavelength • Magnitude (amplitude) • Phase.

Motor cylinder surface with honing marks. The Frequency Spectrum study provides an interactive plot with a logarithmic scale (left) or a linear scale (right). It calculates parameters for each point on the surface.

Microlens array surface and extracted profile.

Frequency spectrum of the surface.


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Frequency spectrum of the profile.

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Power spectrum density

See the intensity of each wavelength in an interactive PSD plot

The Power Spectrum Density study (for surfaces andprofiles) displays an interactive plot with wavelength onthe x axis and intensity (square of the amplitude) on the yaxis.

Glass surfacebeforeacid attack

PSD plots (using the all directions method)

The amplitude is shown when a wavelength is selectedusing a vertical sliding cursor line.

Example: acid attack on glass

Glass surfaceafteracid attack



FFT plot editor

Carry out advanced filtering, remove noise

The FFT plot editor is used for advanced filtering.

The FFT plot can be edited interactively in order to eliminate wavelengths responsible for artifacts.

After. Alumina surface topography after using the FFT plot editor to remove the artifacts.

Before. Alumina surface topography (8.75 µm x 8.75 µm x 308 nm) measured by AFM. The lines running from left to right are scanning artifacts.


The Texture Direction study analyzes the surface usingthe Fourier transform and shows dominant surfacedirections on a polar or Cartesian plot. It calculates thefollowing parameters:

• Isotropy (%). This is equal to the ISO 25178 Strparameter. It is calculated with smoothing and withminimum and maximum frequency thresholds of 5% and80% respectively. These thresholds can be changed bythe user. The higher the isotropy percentage value themore the surface resembles itself in every direction.

• The three most dominant lay directions of a surface(in degree units).

Isotropy, directionality and periodicity

View dominant surface directions and calculate isotropy and other parameters

Nanowires

The Texture Isotropy study calculates the followingparameters with respect to a user-defined threshold(default 0.2):

• Isotropy (%) • Periodicity (%). • Period (length).

• Direction of the period (degrees).

Texture Direction study: isotropy and dominant directions Autocorrelation plot

Roughness reference standardTexture Isotropy study isotropy and periodicity

Autocorrelation plot

The Autocorrelation operator displays a 3Dautocorrelation plot. The plot helps to distinguishbetween isotropic surfaces (with a circular central node)and anisotropic surfaces (with a central node extendedalong one direction).

The Intercorrelation operator displays an intercorrelationplot.



Texture isotropy

Autocorrelation and intercorrelation

Texture direction


Wavelets filtering means using wavelets of differentfamilies to decompose a profile or surface into a set ofprofiles or surfaces at different levels of scale.

A number of different wavelet families, defined by awavelet function and a scaling function, can be selected.

Wavelets spline filtering is one of the advanced filteringtechniques defined in ISO 16610.

Discrete wavelets filtering (2D profiles and 3D surfaces)Use scale-based filtering as a complement to FFT-based filtering

Select the wavelet family for filtering.

Visualize all of the scale levels. Use the sliding horizontal line cursor to interactively define the cut-off between the roughness scale levels and the waviness scale levels.

The roughness/waviness cut-off can be changed interactively at any time.

Check the resulting waviness and roughness profiles/surfaces – if necessary go back to the previous step to fine tune the cut-off.

Apply the wavelets filter.

Profiles or surfaces are displayed at different levels ofscale. The scale levels contained in waviness androughness profiles/surfaces are selected interactively.

When the wavelets filter is applied, profiles/surfaces areoutput at all scale levels and the waviness and roughnessprofiles/surfaces are output.



Wavelets filteringof a profile/surface




Measured surface after form removal

Example: wavelets filtering and multi-scale visualization of latex particles

Wavelets transform: the surface is decomposed into six scale levels

Roughness/WavinessCutoffselected interactively

X X

Waviness Surface(scale level 6 only in this example)

Roughness Surface(scale levels 1-5)

Scale levels 1-5 selected for roughness surface


The Continuous WaveletDecomposition studyshows the scales andspatial locations wherephenomena occur on 2D(x, z) profiles.

Continuous Wavelet Decomposition (2D profiles)Study scale levels and spatial locations where phenomena occur

Settings for the study.

A number of wavelet families can be selected and it is possible to:

• specify the decomposition range (the upper and lower limits of the scalesshown on the y axis)

• use a linear or logarithmic y axis, and

• specify the number of horizontal lines in the study image (in order to achieveoptimum resolution).

Continuous Wavelet Decomposition study of an abrasive profile. The x axis is length (same asthe x axis of the profile). The logarithmic y axis shows the scales at which phenomena occur.The color-coded z axis shows their intensity.

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© 1996-2016 Digital Surf. All rights reserved. Specifications subject to change without prior notice.

Digital Surf Head Office & R&D CenterDigital Surf, 16 rue Lavoisier,

25000 Besançon, FranceTel +33 3 81 50 48 00 [email protected] www.digitalsurf.com

3D Fourier & Wavelets Analysis Module for MountainsMap®: Version 7.0 Doc Revision: 20160627

3D Fourier & Wavelets Analysis Module for MountainsMap®

Frequency spectrum • Display interactive frequency spectrum plot for a 3D surface or 2D profile.• Surfaces: select any x,y point in the plot interactively to calculate wavelength, angle, amplitude and phase at that point.• Profiles: select any wavelength interactively to calculate amplitide and phase. • Apply a Hanning window function to eliminate insignificant spectral lines.

Power spectrum density(PSD)

• Display interactive PSD plot (wavelength on x axis, intensity on y axis) for a surface or profile.• Select any wavelength interactively and calculate amplitude.• Use the horizontal or all directions method for calculations.• Apply Hanning window function.

Isotropy, directionality & periodicity

• Calculate isotropy (%) with default/user-defined minimum and maximum thresholds.• Display dominant surface directions on a direction rose.• Calculate periodicity (%), period (length), and direction of the period (degrees).

Autocorrelation & intercorrelation

• Autocorrelation plot.• Intercorrelation plot.

FFT plot editor • Remove frequencies using thresholding or exclude wavelengths interactively.

Discrete wavelet filtering(surfaces and profiles)

• Apply Coiflet (1-5), Daubechies (1-10), Discrete Meyer, Spline and Symlet (1-8)wavelets (defined by a wavelet function and a scaling function).• Decompose a 2D (x, z) profile or 3D (x, y, z) surface into a set of profiles orsurfaces at different levels of scale.• Select the scale levels to be contained in the waviness and roughnessprofile/surface interactively.• Output surfaces/profiles at all scale levels.• Output roughness and waviness surfaces/profiles.

Continuous wavelet decomposition (profiles)

• Apply Coiflet (1-5), Daubechies (1-10), Discrete Meyer, Gauss (1-8), MexicanHat, Morlet and Symlet (1-8) wavelets.• Visualize the scales and spatial locations where phenomena occur on 2D (x, z)profiles with spatial location shown on the x axis, scale on the y axis andintensity on the z axis.

3d fourier & wavelets analysis module for mountainsmap · plot obtainedby the fast fourier...

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