Winter College on Optics: Trends in Laser Development and Multidisciplinary Applications to Science and Industry February 2013

Transcription

1 Winter College on Optics: Trends in Laser Development and Multidisciplinary Applications to Science and Industry 4-15 February 2013 Data capture and tomographic reconstruction of phase microobjects M. Kujawinska WUT Poland

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6 CT computer tomography hard tissue (bones) X rays MRI magnetic resonance Imaging, soft tissue ultrasound tomography Terahertz tomography Optical tomography Diffraction tomography

7 Intensity in a single projection f(x,y) P (, t) f ( x, y) ds Fourier transform of intensity t Reconstruction of object function P(,t) Single projection

8 Sinogram t

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11 Series of projections Filt er Object Sinogram Filtered Sinogram Typical filters Result Reconstruction

12 Reconstruction from small number of projections

13 Presence of noises in projections 2% noise Noncentric rotation of object Radial run-out: 2.5% Presence of background in projections 5% relative background

14 Provide a convenient tool for 3D material properties determination in novel photonics materials and elements Provide experimental data for optimization of novel prototyping and production technologies e.g. - deep lithography with protons (DLP), - laser ablation and laser writing, - hot embossing, - injection molding. Provide a tool for reliability studies of phase photonics elements (essp. for polimer elements or elements being subjected to radiation, temperature, fatigue) Quantities of interest: refractive index, birefringence, residual stresses

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16 The scheme of standard ODT data aquisition system, Co-ordinate system Reconstruction of internal structure by filtered back projection algorithm 1 Ox, y d ~ 2 k P k exp i kx cos ysin 2 0 where or algebraic tomographic reconstruction ~ P dk k P exp ikd

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18 Series interferogram acquisition Integrated phase distribution computing z =1 w P(w,z,) Reconstruction of phase distribution (back-projection algorythm) Scaling to refractive index value ( x, y, z) n( x, y, z) nl, 2d -source wavelength, n l refractive index of immersion liquid, d-object size corresponding to pixel of camera

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22 Fused optical fibre(sm and M M F) I nterferogram Distribution n(x,y,z) - rendering

23 Cross-sections sequence

24 Considerable deviation of refractive index in the middle area ideal profile measured profile

25 [pixels] core Fiber parameters: -fiber diameter 120 -core diameter 8 -core refractive index 1,47 -cladding refractive index pixel=0,33 core cladding core cladding Only central core area was reconstructed propoperly -refractive index determination error is considerable in core area, source of this error is difraction phenomenon on edge of core and cladding; step of refractive index is equal 0,01

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27 n ( x, y, z ) i S(,, z j w d dx d i ) exp( 2 ) 2 0 S(,, zi ) (, w, zi )exp( j2w) dw, spatial frequency of the function (, w,zi - source wavelegth, dx - spatialstep

28 , ) cos 2( sin cos ) sin 2( sin ) sin 2( sin ) cos 2( sin cos cos 2 1 sin 2 sin 2 cos 2 1 cos sin sin cos 2 1 t i ke i i i i i i i i i i V U

29 i )cos 2( sin i i sin 2( )cos 2 i sin 2 2 m v v Output intensity equations 0 /4 0 3/4 i i i a i 1 b i a i 2 b cos cos 0 0 /4 /4 /2 /2 3/4 3/4 i i i i i a i 3 b i a i 4 b i a i 5 b i a i 6 b sin sin cos sin sin sin cos sin 1 i5 i arctan 2 i4 i 1 2 ( i arctan i3)sin 2 ( i4 i6)cos 2 i 1 i 2

30 Elastooptics tomograph

31 Capillary 127m Outer diameter 350 m n o Analysed objects are fibers with channels filled with liquid crystal (nematic LC with n = Due to viscosity forces liquid crystals particles are expected to be oriented paralelly to axis of capillary Expected birefringence B 0.02<B<0.06

32 Experiment: birefringence in a single layer A-A A A birefringence [m] [m]

33 Quantities of interest: n(x,y,z) or n 0 (x,y,z), n e (x,y,z)), and birefringence B(x,y,z)* *) assumption that rotation of anisotropy axes is moderate and birefringence is weak.

34 Experimental and simulation results Experiment Simulations

35 Microscopic image of sample Determined axial stress in sample Axial stress Panda type fiber cladding diameter 125 m, stress members diameter 35 m refractive index of cladding and for matching liquid D field of axial stress Plot of axial stress profile Determined refractive index in sample (for horizontal plane 2D distribution of refractive index Refractive index Distance along profile Plot of refractive index profile

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39 Properties of bio-samples Polarization Sensitive Birefringence Models High-Phase Gradient Depend on Choice of Wavelengths Core of the Cell important Cell boundary important Use of Born / Rytov Models needed

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42 Example: DHM phase contrast video of Chinese Hamster Ovary (CHO) cells during internalization of SiO 2 micro particles ( ) Cell division Phagocytosis SiO 2 micro particle Nucleus Cell division CHO cells

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45 , Co-ordinate system The simplest reconstruction method : filtered back projection 1 Ox, y d k P k exp i kx cos ysin ~ where ~ P dk k P exp ikd

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80 object HT1080 fibroblasts HT1080 fibroblasts Agarose beads 30m PVA coated inside collagen 0,08% inside collagen 0,16% inside Agar 0,15% inside Glycerin outside immersion oil Outside Phosphat Buffered Saline Inner diameter [m] Incubation time h h h result most cells stick to the wall cells stick to the wall and shrink good results, less diffraction U937 Human Leukemia h good results, some cells are in the middle of the fiber, diffraction not important HT1080 fibroblasts h vertical good results, most cells stick to the wall but some are in the middle of the fiber HT1080 fibroblasts h vertical good results, strong cells, centered

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