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

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

3. 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.

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

5. Advantageous of the Optical Profilometry  Applicable in real-time  Non-invasive  Applicable to large areas  Hight resolution and high sensitivity  Computer compatibility

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

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

8. How do we obtain a structured light pattern?  (A double-slit Young experiment) Beam I Beam II

9. fiber screen

10. 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)?

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

12. 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)

13. u0u0 A C*C

14. Fringe analysis 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 u0u0 A C*C* C

15. n1n1 Claddig n2n2 Core n1n1 n2n2 > Optical fiber

16. Interference with two fibers

17. Interference with four fibers

18. 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

19. Alignment is even more difficuilt with 4 fibers

20. Interferece with a two-core optical fibre 125  m

21. Interferece with a four-core optical fibre

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

24. FT of I(x,y)

25. FFT of the light pattern

26. Phase Surface and phase are related as

27. Experimental Setup

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

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

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

31. (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)

32. A board marker K Bulut, MN Inci, Optics & Laser Technology (in press)

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

34. Vibration Amplitude Measurements

36. 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

38. 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:

39. C and D are processed to obtain Vibration amplitude is obtained from

41. 4 different vibration amplitudes studied ST Yilmaz, U Ozugurel, K Bulut, MN Inci, Optics Communications (to be published)

42. 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