Enhanced Surface Metrology1

Enhanced

Surface

Metrology

Russell M. Kurtz

RAN Science &

Technology, LLC

Ryder Nesbitt

Hexagon Metrology, Inc.

Enhanced Surface Metrology

There is a constant search for more accurate measurement

Traditionally 3 Parameters

COST

MEASURMENT SPEED

ACCURACY

Traditional Tradeoffs

Cheap, Fast, Inaccurate

Expensive, Slow, Accurate


We Present a

Method of

Adding

One More

Tradeoff

Parameter

MEASUREMENT

PRECISION

Measurement Precision

(perpendicular to the surface)

vs.

Sample Correlation

(along the surface)


Through

application of

statistical

sampling and

curve fitting...

... we can improve

precision by

approximately the

same amount that we

increase correlation


Theory & Methods

POINT CLOUDS

The number of

points in a 3-D

space, each

corresponding to a

point on the

surface of the item


Described as Deviation from CAD

Three possible deviation causes:

1. The real surface deviation from nominal

2. Consistent measurement inaccuracies

3. Random measurement inaccuracies or

other random noise

δr

δm

δn


Slide 1


Slide 2


Slide 3


Slide 4


Our Focus: Noise (δn) Reduction

defectvisible with

low noisehidden by

moderate noise

10 x 10 mm portion of a surface, nominally spherical, defect height = ~1.5 µm


Methods of Noise Reduction

A. Arithmetic Mean over a Square Sampling Area

zcalc

x0,h

0( ) =w

mnn=-N 2

N 2

å zmeas

x0+ m,h

0+ n( )

m=-M 2

M 2

å

wmnn=-N 2

N 2

åm=-M 2

M 2

å

B. Arithmetic Mean over a Circular Region• wmn = 1 over the range m2 + n2 ≤ (M/2)2, again with M = N

• This statistical process uses 78.5% as many samples as the

square, and is expected to reduce noise by a factor of 0.886M.

C. Gaussian Sampling Process over Square Region

w

mn= e

-2 m2+n2( ) M 2( )2


Sample Correlation, 5 pixel wide

Square

Circular

Gaussian


Targeting Task Performance Model

Probability of Identifying a 3-µm Feature with No

Noise Reduction


Experiments

Flat Sample: WLS400

block made of ceramic with a polished white surface finish


Experiments

Flat Sample: WLS400

Measurement Noise and Actual Surface Deviation

Before Statistical Noise

ReductionAfter Statistical Noise

Reduction


Experiments

Sphere Sample: WLS400

Test on a known sphere, whose diameter was specified

to be 1.5000±0.0001 in. but whose surface was

specified smooth only to ±0.001 in. We scanned a

section of the upper half of the sphere, a circular area

whose diameter was 27.20 mm.


Experiments


Measurement Noise and Actual Surface Deviation

Before Statistical Noise

ReductionAfter Statistical Noise

Reduction


Experiments


Surface of the sphere with locations measured from its center.

Surface color shows deviation from nominal (after noise reduction)


Experiments

Interferometric Measurement

Test on a flat, metallic surface

(aluminum), mechanically polished to RA ≈ 60.

We used a Mach-Zender interferometer to obtain an

interferogram covering a square 1 cm on a side.

The illumination wavelength was 532 nm.


Experiments

Interferometric Measurement

Original Interferogram

A B

C D

Original fit to a sinusoid

with intensity varying

from 0 to 1

The

difference

is the

noise

pattern

After

noise

reduction


Summary & Conclusions

We have developed a statistical method for noise

reduction of three-dimensional metrology systems.

The method involves combination of measurement

values over a range of points, and permits weighting

the points (enabling the user to, for example, assign

confidence values to the various measurements).



On the flat surface, we reduced the deviation from

nominal by more than a factor of two.

The sphere was specified to an accuracy of ±25.4

µm, and we measured that its accuracy was ±15.8 µm.

With the interferometric measurement we determined

that the surface deviated 16.0% from perfect flatness.



These improvements indicate that the statistical surface

metrology enhancement method can be useful in

detecting small features.

Enhanced

Surface

Metrology

Russell M. Kurtz

RAN Science & Technology,

LLC

Ryder Nesbitt

Hexagon Metrology, Inc.

Enhanced Surface Metrology1

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