Wavelets Analysis
Mountains® 6 Optional Module
Visualize Analyze
Report
Visualize and analyze the scale levels at which
phenomena occur, apply wavelets filtering
Wavelets Analysis
Mountains 6 Optional Module
Discrete wavelets filtering (2D profiles and 3D surfaces)
Use scale-based filtering as a complement to FFT-based filtering
Wavelets filtering means using wavelets of different families
to decompose a 2D (x, z) profile or 3D (x, y, z) surface into a
set of profiles or surfaces at different levels of scale. Wavelet
families are defined by a wavelet function and a scaling
function. They include Coiflet (1-5), Daubechies (1-10),
Discrete Meyer, Spline and Symlet (1-8).
Profiles or surfaces are displayed at different levels of scale.
You select the scale levels contained in the low-pass
(waviness) and high-pass (roughness) filter interactively and
preview the results. When you apply the wavelets filter,
profiles/surfaces are output at all scale levels together with
the waviness and roughness profiles/surfaces.
Wavelet spline filtering is one of the advanced filtering
techniques defined in ISO 16610.
Wavelet filtering of a profile

Select the wavelet family for filtering
the profile.

Visualize all of the scale levels in the
profile.


Select the number of levels to be
included in the high-pass
(roughness) profile (shown in blue).

Visualize the resulting low-pass
(waviness) profile and high-pass
(roughness) profile.

Apply the wavelets filter and carry
out further analysis of profiles at
different levels of scale, the waviness
profile and the roughness profile.


Wavelet filtering of a surface

Select the wavelet family for filtering
the surface.

Visualize all of the scale levels in the
surface.

Select the number of levels to be
included in the high-pass
(roughness) surface (gray
background).
2

Visualize the resulting low-pass
(waviness) surface and high-pass
(roughness) surface.

Apply the wavelets filter and carry
out further analysis of surfaces at
different levels of scale, the waviness
surface and the roughness surface.



Mountains
Wavelets
Analysis
6 – Wavelets Analysis
Mountains 6 Optional
OptionalModule
Module
Visualize and analyze a surface at different levels of scale
Wavelet Filtering generates a composite surface image
showing all of the scale levels of a surface. From this
composite image you can generate a 4D image and walk
through and manipulate 3D images of the surface at each
level of scale.
In addition you can extract a scale level for individual analysis
using all of the analytical tools in Mountains 6.
Visualization of a surface at each level of scale.
A scale level can be extracted for individual
analysis.
3
Mountains
Wavelets
Analysis
6 – Wavelets Analysis
Mountains 6 Optional
OptionalModule
Module
Example: wavelets filtering and multi-scale visualization of latex particles
AFM latex particles surface 5 µm x 5 µm
after form removal.
Waviness surface after wavelets filtering
Roughness surface after wavelets filtering
Decomposition of the latex surface into six scale levels using Wavelets filtering
4
3
Mountains
Wavelets
Analysis
6 – Wavelets Analysis
Mountains 6 Optional
OptionalModule
Module
Continuous Wavelet Decomposition (2D profiles)
Study scale levels and spatial locations where phenomena occur
The Continuous Wavelet Decomposition study shows the
scales and spatial locations where phenomena occur on 2D
(x, z) profiles.
scale
intensity
spatial location
A Continuous Wavelet Decomposition study of an abrasive profile. The X axis
is length (same as the X axis of the profile). The logarithmic Y axis shows the
scales at which phenomena occur. The color-coded Z axis shows their
intensity.
Settings for the study are shown in the dialog box
above.
A number of wavelet families can be selected:
Coiflet (1-5), Daubechies (1-10), Discrete Meyer,
Gauss (1-8), Mexican Hat, Morlet and Symlet (1-8).
In addition it is possible to:
• specify the decomposition range (the upper and
lower limits of the scales shown 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 achieve optimum resolution).
4
5
Mountains
Wavelets
Analysis
6 – Wavelets Analysis
Mountains 6 Optional
OptionalModule
Module
Selected features
Mountains® 6 Wavelets Analysis Optional Module
Discrete wavelet filtering (3D surfaces and 2D profiles)
Continuous wavelet decomposition (2D 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 or surfaces at
different levels of scale.
• Visualize and analyze surfaces and profiles at different levels of scale.
• Select the scale levels contained in the low-pass (waviness) and high-pass
(roughness) filter interactively.
• Visualize and analyze waviness and roughness surfaces and profiles.
• Walk through and manipulate 3D images of a surface at each level of scale.
• Extract a scale level for individual analysis.
• Apply Coiflet (1-5), Daubechies (1-10), Discrete Meyer, Gauss (1-8), Mexican Hat,
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 and intensity on the Z axis.
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Digital Surf SARL, 16 rue Lavoisier, 25000 Besançon, France
Tel +33 3 81 50 48 00 Fax +33 3 81 50 92 24
contact@digitalsurf.fr www.digitalsurf.com
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Specifications subject to change without prior notice