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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 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) Why Fourier Transform Profilometry (FTP)? 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 Light intensity distribution over the surface in concern is (1) For the Fourier fringe analysis, Eq.1 can be written as (2) The FT of I(x,y) at the CCD camera is (3) A C C* u0 A Fringe analysis C* C u0 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 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 Interferece with a four-core optical fibre Four-core fiber Manufactured by Hesfibel, Kayseri, Turkey (www.hesfibel.com) x cos z ( x, y) sin 2 cos 2 y I x, y 2 I 0 2 2 cos 2 f f x cos z ( x, y) sin y cos 2 x cos z ( x, y) sin y cos 2 f f I ( x, y ) ax, y cx, y exp i2u0 x c * x, y exp i2u0 x d x, y exp i2u0 y d * x, y exp i2u0 y ex, y exp i2 (u0 x u0 y e * x, y exp i2 (u0 x u0 y f x, y exp i2 (u0 x u0 y f * x, y exp i2 (u0 x u0 y u 0 f FT of I(x,y) I (u, v) A(u, v) C (u u 0 , v) C * (u u 0 , v) D(u, v u 0 ) D * (u, v u 0 ) E (u u 0 , v u 0 ) E * (u u 0 , v u 0 ) F (u u 0 , v u 0 ) F * (u u 0 , v u 0 ) FFT of the light pattern I (u, v) A(u, v) C (u u 0 , v) C * (u u 0 , v) D(u, v u 0 ) D * (u, v u 0 ) E (u u 0 , v u 0 ) E * (u u 0 , v u 0 ) F (u u 0 , v u 0 ) F * (u u 0 , v u 0 ) 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) 4 3 2,5 2 1,5 1 Surface Height (mm) 3,5 Measured 0,5 Circle, r =14,4 mm -6,50 -4,88 -3,25 -1,63 0,00 1,63 3,25 4,88 0 6,50 y (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 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 zx, y, t z 0 x, y V x, y cos t V(x, y): local amplitude of vibration A B x cos z 0 ( x, y ) sin V x, y cos t sin I ( x, y, t ) 2 I 0 2 2 cos 2 f 2 cos 2 y f x cos y z 0 ( x, y ) sin V x, y cos t sin cos 2 f x cos y z 0 ( x, y) sin V x, y cos t sin cos 2 f I x, y, t p r exp i x x r x, y t x, y, t r * exp i x x r x, y t x, y, t r exp i y y r * exp i y y m exp i x x y y r x, y t x, y, t m * exp i x x y y r x, y t x, y, t n exp i x x y y r x, y t x, y, t n * exp i x x y y r x, y t x, y, t x cos ; y y 2 y f f r x, y 2 z 0 x, y sin f t x, y, t 2 V x, y cos t sin ; i 1 f x x 2 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: I x, y , t T t 1 I x, y, t dt T 0 p r ' x, y exp i 2u 0 x (r ' ) * x, y exp i 2u 0 x m' x, y exp i 2u x 2u y (m' ) * x, y exp i 2u x 2u y n' x, y exp i 2u x 2u y (n' ) * x, y exp i 2u x 2u y r exp i 2u 0' y r * exp i 2u 0' y ' 0 0 ' 0 0 ' 0 0 0 ' 0 2 V ( x, y ) f T 1 r ' x, y r exp i r x, y exp it x, y, t dt T 0 r exp i r x, y J 0 u0 cos ; u 0' f f T 2 C and D are processed to obtain J 0 Vibration amplitude is obtained from r ' x, y r x, y 2 V ( x, y ) f 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