Optical Profilometry and Vibration Amplitude Measurement with Multicore

Optical Profilometry and Vibration Amplitude Measurement with Multicore Fibers M. Naci Inci Physics Department, Bogazici University

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

Optical Profilometry n 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.

n 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 n n n 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? Beam I am Be II (A double-slit Young experiment)

er fib en re sc

Why Fourier Transform Profilometry (FTP)? n 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.

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 Ø Light intensity distribution over the surface in concern is (1) Ø For the Fourier fringe analysis, Eq. 1 can be written as (2) Ø The FT of I(x, y) at the CCD camera is (3)

A C C* u 0

A Fringe analysis C* C u 0 n n n C (or C*) is isolated and then translated to the origin by u 0 amount. A(u, v) and C*(u+u 0, 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

2 Optical fiber Co re Cl ad dig n 1 n n 1 > n 2

Interference with two fibers

Interference with four fibers

Mutual coherence is required between fibre ams to obtain interference pattern Single source with a 2 x 2 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

12 5 m Interferece with a two-core optical fibre

Interferece with a four-core optical fibre

Four-core fiber Manufactured by Hesfibel, Kayseri, Turkey (www. hesfibel. com)

FT of I(x, y)

n FFT of the light pattern

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 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 2 mm higher than the rest of the plate; (b) 2 D 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)

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

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

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:

C and D are processed to obtain 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