Optical Profilometry and Vibration Optical Profilometry and Vibration Amplitude Measurement with Amplitude Measurement with

Multicore FibersMulticore Fibers

M. M. Naci Naci InciInciPhysics Department, Bogazici University

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• Fourier Transform Profilometry (FTP) • Vibration Amplitude Study with FT Analysis

Optical Profilometry

It employes the wave nature of light to determine shape and dimensions of objects. It uses structured light patterns that are generated through optical interference.

A structured light pattern based on a two-beam optical interference

Advantageous of the Optical Profilometry

Applicable in real-time Non-invasive Applicable to large areas Hight resolution and high sensitivity Computer compatibility

Applications

Industrial otomation Robotic vison Quality control Biomedical applications CAD/CAM modelling

Optical Profilometry:

It is a measurement method based on the wave nature of light, which uses optical interference fringes of the laser beam

How do we obtain a structured light pattern?

(A double-slit Young experiment)

Beam I

Beam II

fiber

fiber

scre

en

FTP’s main advantage is that it uses only a single image to extract profile of an object. In other techniques, 3 or 4 images are required.

Why Fourier Transform Profilometry (FTP)?

Methodology:

Aim: To obtain a direct relationship between the object’s surface topography (z(x,y)) and the phase () of the structured light pattern

Two-beam interference fringe pattern analysis

Light intensity distribution over the surface in concern is

For the Fourier fringe analysis, Eq.1 can be written as

The FT of I(x,y) at the CCD camera is

(1)

(2)

(3)

u0

AC*C

Fringe analysis

C (or C*) is isolated and then translated to the origin by u0 amount.

A(u, v) and C*(u+u0, v) are eliminated by bandpass filtres

Inverse of FT is applied to determine the complex fn. c(x,y) Phase of the structured light pattern is determined as

Phase-unwrapping is applied to correct 2π phase jumps Surface topography and phase of the fringes are related as

u0

A

C*C

n 1

Cla

ddig

n 2

Core

n1 n2>

Optical fiber

Interference with two fibers

Interference with four fibers

Mutual coherence is required between fibre ams to obtain interference pattern

Single source with a 2x2 fiber coupler

Fibre arms are difficuilt to aline properly.Vibration, temperature, polarization, etc. result in

a poor fringe visibility

Alignment is even more difficuilt with 4 fibers

Interferece with a two-core optical fibre

125 m

Interferece with a four-core optical fibre

Four-core fiber

Manufactured by Hesfibel, Kayseri, Turkey(www.hesfibel.com)

yyxzxf

yyxzxf

yf

yxzxf

IyxI

sin),(cos2cossin),(cos2cos

2cos2sin),(cos2cos222, 0

yuxuiyxfyuxuiyxf

yuxuiyxeyuxuiyxe

yuiyxdyuiyxd

xuiyxcxuiyxcyxayxI

0000

0000

00

00

(2exp,*(2exp,

(2exp,*(2exp,

2exp,*2exp,

2exp,*2exp,,),(

fu

0

),(*),(

),(*),(

),(*),(

),(*),(),(),(

0000

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FT of I(x,y)

FFT of the light pattern

),(*),(

),(*),(

),(*),(

),(*),(),(),(

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uvuuFuvuuF

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uvuDuvuD

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Phase

Surface and phase are related as

Experimental Setup

(a) Triangular shape object; (b) projected fringe pattern; (c) reconstructed surface of the object

(a) Sculptured head object and the outlined area shows the analysed surface; (b) projected fringe pattern; (c)reconstructed surface of the object

(a) An object made from sand and the outlined area shows the analysed surface; (b) projected fringe pattern; (c)reconstructed surface of the object

(a) Projected fringe pattern of a flat plate with a 2 mm step. The area in the upper right-hand corner is 2mm higher than the rest of the plate; (b) 2D Fourier spectra of the analyzed pattern (c) Reconstructed surface

K Bulut, MN Inci, Optics & Laser Technology (in press)

A board marker

K Bulut, MN Inci, Optics & Laser Technology (in press)

-6,50 -4,88 -3,25 -1,63 0,00 1,63 3,25 4,88 6,50

y (mm)

0

0,5

1

1,5

2

2,5

3

3,5

4

Su

rfac

e H

eig

ht

(mm

)

Measured

Circle, r =14,4 mm

Comparison between a cross section of the reconstructed surface with a circle of radius 14.4 mm. The RMS error is 0.4 mm.

Vibration Amplitude Measurements

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sincos,sin),(cos2cos

sincos,sin),(cos2cos

2cos2

sincos,sin),(cos2cos222),,(

0

0

00

tyxVyxzyxf

tyxVyxzyxf

yf

tyxVyxzxf

ItyxI

If the object vibrates sinusoidal with an angular frequency ,then the out-of-plane displacement of the object surface at (x, y) is given by

V(x, y): local amplitude of vibration B

A

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tyxyxyxin

tyxyxyxim

tyxyxyxim

yir

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tyxyxxir

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tryx

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y

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trx

trx

,,,exp*

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exp*

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1;sincos,2,,

sin,2,

2;cos2

0

ityxVf

tyx

yxzf

yx

yf

yxf

x

t

r

yx

Since the frame rate of the CCD camera is much lower than the vibration angular frequency ω, the light pattern captured is proportional to the time average of I(x, y ,t) over one period:

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yuxuiyxn

yuxuiyxm

yuxuiyxm

yuiryuir

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dttyxIT

tyxIT

t

'00

'00

'00

'00

'0

'0

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0

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22exp,'

22exp,*)'(

22exp,'

2exp*2exp

2exp,*)'(2exp,'

,,1

,,

0

0

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,,exp1

,exp,'

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yxiryxr

r

T

tr

2

T),(2

yxVf

fu

fu

'00 ;

cos

yxr

yxrJ

,

,'0 C and D are processed to obtain

),(2

yxVf Vibration amplitude is obtained from

4 different vibration amplitudes studied

ST Yilmaz, U Ozugurel, K Bulut, MN Inci, Optics Communications (to be published)

Conclusion

Multicore fiber based optical profilometry and vibration amplitude measuremets are promising.

However, a larger fiber core seperation will improve the resolution of the optical method

Acknowledgement

Karahan Bulut, Tunç Yılmaz, Umut Özuğurel