2443-27 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
CT computer tomography hard tissue (bones) X rays MRI magnetic resonance Imaging, soft tissue ultrasound tomography Terahertz tomography Optical tomography Diffraction tomography
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
Sinogram t
Series of projections Filt er Object Sinogram Filtered Sinogram Typical filters Result Reconstruction
Reconstruction from small number of projections 8 16 32
Presence of noises in projections 2% noise Noncentric rotation of object Radial run-out: 2.5% Presence of background in projections 5% relative background
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
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
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
Fused optical fibre(sm and M M F) I nterferogram Distribution n(x,y,z) - rendering
Cross-sections sequence
Considerable deviation of refractive index in the middle area ideal profile measured profile
[pixels] core Fiber parameters: -fiber diameter 120 -core diameter 8 -core refractive index 1,47 -cladding refractive index 1.46 1 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
100 200 300 400 500 600 100 200 300 400 500 600 100 100 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 100 100 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 100 100 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 100 200 300 400 100 200 300 400 500 600 700 800 900 1000 500 600 100 200 300 400 500 600 100 200 300 400 500 600 100 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 100 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 100 100 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 100 200 300 400 100 200 300 400 500 600 700 800 900 1000 500 600 100 200 300 400 500 600 100 200 300 400 500 600 100 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 100 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 100 100 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 100 200 300 400 100 200 300 400 500 600 700 800 900 1000 500 600 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 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
, 1 0 1 1 ) 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
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 3 6 5 i3)sin 2 ( i4 i6)cos 2 i 1 i 2
Elastooptics tomograph
Capillary 127m Outer diameter 350 m n o Analysed objects are fibers with channels filled with liquid crystal (nematic LC with n = 0.010.02 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
20 40 0.04 0.035 Experiment: birefringence in a single layer 0.025 A-A A 60 80 100 120 140 160 180 0.03 0.025 0.02 0.015 0.01 0.005 0 A birefringence 0.02 0.015 0.01 0.005 0 200 20 40 60 80 100 120 140 160 180 200 [m] -0.005-0.005 20 40 60 80 100 120 140 160 180 200 [m]
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.
Experimental and simulation results Experiment Simulations
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 1.4584 and for matching liquid 1.4582 2D field of axial stress Plot of axial stress profile Determined refractive index in sample (for horizontal plane 2D distribution of refractive index Refractive index 1.465 1.46 1.455 1.45 1.445 1.44 0 50 100 150 200 250 Distance along profile Plot of refractive index profile
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
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
, Co-ordinate system The simplest reconstruction method : filtered back projection 1 Ox, y d k P k exp i kx cos ysin 2 2 0 ~ where ~ P dk k P exp ikd
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 + + + 128 1h + + + 128 0h + + 111 0h result most cells stick to the wall cells stick to the wall and shrink good results, less diffraction U937 Human Leukemia + + + 212 0h good results, some cells are in the middle of the fiber, diffraction not important HT1080 fibroblasts + + + 212 24h vertical good results, most cells stick to the wall but some are in the middle of the fiber HT1080 fibroblasts + + + 111 24h vertical good results, strong cells, centered