Recent Developments of Microtomography at GeoSoilEnviroCARS Mark Rivers GeoSoilEnviroCARS, Advanced Photon Source University of Chicago

Outline of Talk Tomography at extreme conditions High pressure High speed (High temperature, low temperature) Recent technical developments Reconstruction speeds Visible light optics Ring artifact reduction Rotation stage imprecision

Absorption Tomography Setup 13-BM-D station at APS X-ray Source Parallel monochromatic x-rays, 8-65 keV APS bending magnet source, 20 keV critical energy 1-50mm field of view in horizontal, up to 6 mm in vertical Imaging System YAG or CdWO4 single crystal scintillator 5X to 20X microscope objectives, or macro lens 1300 x 1030 pixel, 12-bit CCD camera Data collection Rotate sample 180 degrees, acquire images every 0.25 degrees Data collection time: 10 minutes Reconstruction time: 5 minutes X-rays Rotation stage Sample Scintillator Microscope objective CCD camera Visible light

Differential Absorption Tomography Clint Willson (Louisiana State University) 8mm diameter sand column with aqueous phase containing Cs and organic phase containing I. 32.5 keV, below I and Cs K absorption edges 33.2 keV, above I and below Cs K absorption edges 36.0 keV, above I and Cs K absorption edges 33.2 - 32.5 keV, showing distribution of I in the organic phase 36.0 - 33.2, showing distribution of Cs in the aqueous phase

High-P tomography: Instrumentation Die set Harmonic Drive Transport Rails 250 T press frame Hydraulic ram Thrust bearings Max. load 50 tons

High pressure tomography: setup Current pressure maxium=10GPa (100 kbar) Goal: 20 GPa (200 kbar) Fe – S alloy Top view CCD detector Al2O3 Microscope objective Phosphor (YAG) Monochromator Mirror Sample Rotation Drickamer Incident X-rays (white) Visible light Transmitted X-rays Monochromatic beam

803 µm vitreous forsterite sphere Anvil BE BN Fe0.9S0.1 0 tons Gaudio, Lesher, Wang, Nishiyama

High-Speed Radiography of Granular Particle Jets John Royer, University of Chicago Physics Dept. Sphere falling into a granular particle (e.g. sand) bed produces a jet These images are above the surface, done with visible light 1 atmosphere Reduced pressure

Want to understand what is happening below the surface Used “pink” x-ray beam, high speed radiography 100 msec exposure time, 5000 frames/sec

Processing Times Data processing is done in 2 steps using IDL graphical user-interface Pre-processing: dark current and flat field normalization, zinger removal Sinogram calculation and reconstuction Reconstruction is done with Gridrec FFT-based C code from Brookhaven. No measureable difference from FBP, but >15X faster. Recently changed from Intel MKL or Numerical Recipes FFT to the FFTW package. 3-4 times faster. Upgraded to dual 3.4 GHz Intel, 8GB RAM, 64-bit Linux, 64-bit IDL, FFTW is built single-threaded, second CPU is idle for other tasks Columns Slices Projections Preprocessing time for volume Sinogram time per slice Recon. time per slice Recon. time for volume 650 515 720 30 0.11 0.19 170 1024 105 0.17 0.58 774 1300 1030 900 200 0.25 0.62

Optics Improvements Sand and fluid, 33.269 keV, Z slice We have been using Mitutoyu long working distance microscope objectives with various tube lens to achieve the desired fields of view. This often involved shorter tube lens than the nominal 200mm tube length. Recently purchased a Nikon macro lens. This lens allows various fields of view, depending on how the lens is focus, and what extension tubes if any are used. We have now compared images collected with very similar pixel sizes using the Mitutoyu lenses and the Nikon lens. It is clear that at least at fields of view > 6mm the Nikon lens is significantly sharper. Sand and fluid, 33.269 keV, Z slice Mitutoyu 5X, 17.5mm tube, 11.1 micron pixels Nikon lens, PK-11A extender, 11.2 micron pixels

Another example of improvement in optics Meteorite, 38 keV, Y slices Mitutoyu 5X, 17.5mm tube, 11.1 micron pixels Nikon lens, PK-11A extender, 11.2 micron pixels

Ring Artifact Reduction - Algorithm Compute average of all rows in sinogram This should be a smooth function with little high-frequency content Compute a smoothed version of the average with user-selectable smoothing width. Unsmoothed version minus smoothed version is the correction factor for that pixel Subtract the correction from that pixel in every projection

Ring Artifact Reduction - Sinograms Sinogram before correction Sinogram after correction with 21-point smoothing

Ring Artifact Reduction - Reconstructions No correction 9-point smooth 21-point smooth

Ring Artifacts – A Puzzle We often found ring artifacts even after applying the preceeding algorithm Ring artifact suppression=Off Ring artifact suppression=9 point

Ring Artifacts – the Flat Field Problem We finally realized that these rings were arising from the flat fields This image was reconstructed simply assuming a constant flat field of 4000 counts! Many fewer rings! Ring artifact suppression=Off Ring artifact suppression=9 point

Ring Artifacts – Major Improvement We were previously interpolating the flat fields with time to best estimate the flat field when each projection was taken This introduced 2 serious problems: Noise in the flat field images resulted in anomalous pixels (rings) in many projections The resulting “rings” were only partial rings, not semi-circles, because each noisy pixel was only used over an angular range of 12-25 degrees. This greatly reduced the efficacy of the ring artifact reduction algorithm Solution was easy: Average all the flat fields, rather than interpolating them Better solution would be to collect many flat fields periodically, then average and interpolate

Ring Artifacts – Using Flat Field Averaging Ring artifact suppression=Off Ring artifact suppression=9 point

Ring Artifacts – Another Example Old default, flat field interpolation, 9-point smooth for reduction New default, flat field averaging, 9-point smooth for reduction

Rotation Stage Imperfections When doing high-resolution tomography we have seen small horizontal shifts in the sinogram at some angles. This is due to mechanical imprecision (eccentricity, wobble) in the stage Sinogram with small horizontal shifts at some angles Enlargement of lower right, showing shifts more prominently

Rotation Stage Corrections Developed an algorithm to correct these shifts using only the sinogram data itself. The center of gravity of each row of the sinogram (average of horizontal distance X –log(I/I0)) itself must describe a sine wave Fit the sine wave to the center of gravity for the sinogram of each slice. Measure the deviation from the best-fit sine wave Some of that deviation is noise, some is systematic error due to mechanical shifts in the stage The mechanical shifts should be the same for every slice, thus we can reduce noise by averaging over all slices Must reject slices with no meaningful center-of-gravity, i.e. slices with just air or with complete absorption

Rotation Stage Corrections

Rotation Stage Corrections - Sinograms Enlargement of sinogram before correction Enlargement of sinogram after correction

Rotation Stage Corrections - Reconstructions Reconstruction before correction Reconstruction after correction

Rotation Stage Corrections - Reconstructions Enlargement of reconstruction before correction Enlargement of reconstruction after correction

Rotation Stage Corrections – Laser Autocollimator Measurements Used Newport LAE500 laser autocollimator with high-precision reflective ball to measure rotation motion in horizontal and vertical Mounted ball near center of rotation, fit sine-wave for expected motion Deviations from sine-wave are errors in horizontal and vertical

Laser Autocollimator Measurements Old Newport URM-80 Stage

Laser Autocollimator Measurements New Newport URM-80 Stage

Rotation Stage Corrections – Conclusions Software can automatically correct for rotation axis imperfection Our stage was particularly bad at ~3-4 microns, but as resolution is pushed to sub-micron tomography there will be a real benefit from these corrections Laser autocollimator is very useful for evaluating stages