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)
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yyxzxf
yf
yxzxf
IyxI
sin),(cos2cossin),(cos2cos
2cos2sin),(cos2cos222, 0
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xuiyxcxuiyxcyxayxI
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(2exp,*(2exp,
2exp,*2exp,
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FT of I(x,y)
FFT of the light pattern
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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
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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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tyxyxyxim
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tyxyxxir
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,,,exp*
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sin,2,
2;cos2
0
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yf
yxf
x
t
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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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tyxIT
t
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,'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
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