Fourier Series Filtering Concepts

8/6/2019 Fourier Series Filtering Concepts

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Copyright 2002 - Digital Metrology Solutions, Inc. 1

Fitting, Filtering and Analysis:Fitting, Filtering and Analysis:

Feature Extraction in DimensionalFeature Extraction in Dimensional

Metrology ApplicationsMetrology Applications

Mark C. Malburg

International DimensionalInternational Dimensional

Workshop 2002Workshop 2002

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Inside the BoxInside the Box A cloud of data points.


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Inside the BoxInside the Box Fitting


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Inside the BoxInside the Box Filtering


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Thinking Outside the BoxThinking Outside the Box Do the current analysis methods

provide the information that you arelooking for?

Modeling of performance

Correlation with process controls

Failure analysis

???? Why measure in the first place?


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Why measure?Why measure?


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Fitting, Filtering & AnalysisFitting, Filtering & Analysis There are many tools at our disposal for

the better analysis of data!


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Fitting, Filtering & AnalysisFitting, Filtering & Analysis An overview of some of the tools

Applications

Getting the tools into my box

Goal:

Make you think differentlyabout what you are measuring.


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FittingFitting Not much has changed!

Depending on the geometry there are afew options:


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FittingFitting

Fitting alone

doesntaddress all of

the issues


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FilteringFiltering Filter-phobia

I dont want to corrupt my data I dont use filters; they hide things

I want to see the realsurface

The proper use of filtering:

Exploit the features of interest


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A Filtering ToolboxA Filtering Toolbox ISO/TC213 Advisory Group 9

GPS Extraction Techniques Linear Filters

Morphological Filters

Spline Filters Spline Wavelet Filters

Alternating Sequence Filters

Robust Filters

Technical Specifications are being produced


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An easier viewAn easier view


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Traditional FilteringTraditional Filtering Gaussian Filter

End regions are not valid!

2

1)(

=c

x

c

exs


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Improved Gaussian FilteringImproved Gaussian Filtering Spline-based Gaussian Filtering

Filtered data is available all the way to theends of the raw data set!


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Mechanical Filtering (by Math)Mechanical Filtering (by Math) Morphological Filters CLOSING

OPENING


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Powerful filteringPowerful filtering Robust Filters

These filters are insensitive to extremepoints.


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What makes these coolWhat makes these cool Gaussian Filter (sensitive to extremes)

Robust Filter (insensitive to extremes)


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DisclaimerDisclaimer It should be noted that the concept of

sampling is closely connected to theconcept of filtering (mechanical,electronic or mathematical).

There, I said it.


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AnalysisAnalysis Surface texture has been suffering for

many years with a condition known as:

The Parameter Rash

However, many other fields could

benefit from some additional numericaldescriptions.


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AnalysisAnalysis A single number doesnt always

describe the functionality of a surface orinterface.

Examples:

Peak to valley distance, RMS

Rates of change, slope

Bearing Ratio, volumetric analysis

Harmonic Content


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Application Example #1Application Example #1 The Cam Lobe

The underlying, loadcarrying geometry isof interest.

The orientation and

shape of thisunderlying surface isto be characterized.


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Sampling the Cam LobeSampling the Cam Lobe


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Analyzing the Cam LobeAnalyzing the Cam Lobe Simple fitting does

not yield functionalinformation.

The outlierinfluences the formand orientation.

Simple filteringcorrupts the

underlying shape


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Simple filtering isnt enough...Simple filtering isnt enough...


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Combined Fitting/FilteringCombined Fitting/Filtering Suppress the nominal geometry via

Least Squares fitting.


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Combined Fitting/FilteringCombined Fitting/Filtering Remove outliers or apply robust filtering

on the residuals.


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Combined Fitting/FilteringCombined Fitting/Filtering Re-apply the suppressed geometry and

analyze the resulting data.


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Application Example #2Application Example #2 A gasket interface.

A solid surface in contact with aconformable component.

Rigid Surface

Conformable Surface (e.g. gasket)


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Conformable InterfacesConformable Interfaces There is a strong sensitivity to localized

surface variations (curvatures). Typically these are middle wavelengths.


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Traditional FilteringTraditional Filtering Bandpass waviness analysis is

somewhat useful.

Roughness FormWaviness

Transmission


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Bandpass WavinessBandpass Waviness Traditional filtering is used to separate

the data into 3 domains.


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Bandpass WavinessBandpass Waviness The bandpass waviness approach does

not adequately model the interface. Its good, but not great.


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Combined Filtering & AnalysisCombined Filtering & Analysis A better approach is to combine robust

filtering with morphological filtering.


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Combined Filtering & AnalysisCombined Filtering & Analysis First a robust filter is applied.


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Combined Filtering & AnalysisCombined Filtering & Analysis Next a morphological closing filter is

applied to the waviness profile.


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Combined Filtering & AnalysisCombined Filtering & Analysis The resulting profiles represent

conformability and the resulting gaps.


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Combined Filtering & AnalysisCombined Filtering & Analysis The cutoff and closing radius can be

tuned to simulate gasket properties. The gap area (between the morphological

and robust filtered profiles) can be

calculated as a functional analysis.


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Combined Filtering & AnalysisCombined Filtering & Analysis Similar peak-to-valley values, but

different performance:

Gap area is key!


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Old dogs, new tricksOld dogs, new tricks

How can I use this stuffHow can I use this stuff

on my machine?on my machine?

Answer:SoftwareAdd-Ins(Helpers)


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Direct Hardware InterfacingDirect Hardware Interfacing Example: Analog to digital conversion of

analog probe signal Requires calibration and often requires

other control interfacing.


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Serial InterfacingSerial Interfacing Many instruments provide data output

via a serial (RS-232 or other) port.


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Software InterfacingSoftware Interfacing Some instrument software packages

provide an interface for externalapplications.

Spawning of external applications

Dynamic Data Exchange (DDE)

Object Linking and Embedding (OLE/COM)

DDE/OLE


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File Based InterfacingFile Based Interfacing The control software simply stores a file.

The add-in package monitors the file andloads it when changed.

1. Save

3. Auto-Load

2. Monitor


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Fitting, Filtering & AnalysisFitting, Filtering & AnalysisSummary:

Several analysis tools are available tobetter exploit the features of interest.

Choose wisely Grasshopper!

These tools can be applied to manyexisting measurement systems.


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Thank you!Thank you!

[email protected]

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Fourier Series Filtering Concepts

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