Software image alignment for X-ray ... - Wiley Online Library

Journal of Microscopy, Vol. 228, Pt 3 2007, pp. 257–263 Received 14 March 2007; accepted 1 June 2007

Software image alignment for X-ray microtomography with submicrometre resolution using a SEM-based X-ray microscope ∗

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S . M AYO , P. M I L L E R , D. G AO & J. S H E F F I E L D - PA R K E R † ∗

CSIRO Division of Materials Science and Engineering, Private Bag 33, Clayton South, VIC 3169, Australia †XRT Limited, A3.0, 63 Turner Street, Port Melbourne, Victoria 3207, Australia

Key words. phase-contrast, x-ray microscopy.

Summary Improved X-ray sources and optics now enable X-ray imaging resolution down to ∼50 nm for laboratory-based X-ray microscopy systems. This offers the potential for submicrometre resolution in tomography; however, achieving this resolution presents challenges due to system stability. We describe the use of software methods to enable submicrometre resolution of approximately 560 nm. This is a very high resolution for a modest laboratory-based point-projection X-ray tomography system. The hardware is based on a scanning electron microscope, and benefits from inline X-ray phase contrast to improve visibility of fine features. Improving the resolution achievable with the system enables it to be used to address a greater range of samples. Introduction X-ray microscopy and microtomography have been rapidly growing fields in recent years, largely driven by work at synchrotron sources. Synchrotron-based X-ray microscopy typically makes use of diffractive (Baez, 1961; Aristov & Erko, 1994), reflective (Kirkpatrick & Baez, 1948; Bilderback et al., 1994) or refractive (Snigirev et al., 1996; Lengeler et al., 1999) focussing optics and operates in both scanning (Jacobsen et al., 1991; Burge et al., 2000) and imaging (Schmahl et al., 1995; Schneider, 1998) modes. In the soft X-ray regimes using diffractive optics, resolutions down to 15 nm have been achieved for imaging (Burge et al., 1997; Chao et al., 2005) and 2 μm. This resolution limit arises because the successive views are misaligned by 2 μm or more with respect to ‘ideal’ views with a perfect rotation stage. This is exacerbated by the use of eucentric rotation. Although eucentric rotation maintains the position of the sample within the field of view it requires the movement of the X- and Y-axes in addition to the rotation axis, leading to additional misalignments due to stage instability in X and Y. The nature of the misalignment can be considered as two components with different characteristics. The first arises primarily from thermal drift and has a slow consistent image displacement over time, mostly in the vertical direction. Data sets can take 2–8 h to acquire, due to the relatively weak X-ray source, over which time drift of up to 10 μm has been seen to occur although 2–3 μm is more typical. In this case it is slow environmental thermal changes that cause the problems, unlike the synchrotron case where rapid heating from the intense beam can cause thermal changes on a much shorter time scale. The other component of image misalignment, described hereafter as ‘jitter’, is due to limitations of stage repeatability and is characterized by a frame to frame displacement of up to 2 μm from the ‘average’ position. The source of jitter is the limits of stage repeatability and the movements of the rotation and X- and Y-axes occurring between views. This type of problem also occurs in transmission electron microscopy (TEM) and synchrotron microtomography where both hardware and software approaches are used to address it. Using an improved stage and other hardware modification is one approach to dealing with this issue; however, in our method we are using a software approach to correct for image misalignment. The methods used need to be suited to our polychromatic beam (with consequent beam-hardening) and cone-beam geometry that unfortunately rules out some of the methods, such as centre of mass, that have proven successful for

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synchrotron work (Rivers & Wang, 2006). However, other methods drawing on TEM microtomography are applicable. Algorithm testing with synthetic data In the case of the XuM the problem can be somewhat simplified. The geometry of the instrument and stage means that the main form of image misalignment is in the form of translations of the sample in the image plane. Shifts of the sample along the source–detector axis would be expected to lead to changes in magnification; however, with the typical XuM geometry the effect on the image – even for the worst affected pixels – is 30× smaller than for shifts in the image plane and is therefore neglected. Rotations of the sample about an axis normal to the image plane are not a significant problem with the current stage geometry. Other possible sources of error for reconstructions are tilts of the rotation axis in the image plane relative to the image vertical axis, which is addressed by rotating the CCD camera (CCD rotation is the major source of this error as the stage itself is well aligned to the SEM body). The method for aligning the views is similar to the ‘bootstrapping’ methods for TEM tomography described by Dengler (1989). These methods have the advantage of not requiring fiducial markers to be added to the sample. Since our views are already relatively well aligned (e.g. relative to TEM tomographic data) there is no pre-alignment step or change in alignment resolution through the process (as used by Dengler, 1989). The alignment procedure is iterative and includes the following steps. 1. Tomographic reconstruction of data set using the uncorrected views – this produces a reconstructed volume in which the errors in individual views results in 3D blurring relative to an ideal reconstructed volume. 2. Calculation of simulated views equivalent to the actual views from the reconstructed volume – since all the original views have contributed to the simulated views (via the 3D reconstruction) the errors in individual views are averaged out. 3. Alignment of the real views to the simulated views using cross-correlation of the images to find the required shift. 4. Tomographic reconstruction of data set using the aligned views. Steps 2–4 are repeated until a satisfactory reconstruction is achieved. To make the process practical on a desktop computer the view simulations and tomographic reconstructions are carried out on 256 × 256 images; however, the alignment step is carried out on 512 × 512 images (the simulated views are scaled up to this size) and aligned to subpixel accuracy with interpolation. When the alignment is complete a reconstruction is done at the resolution of the original data. Initially this process was tested with some simulated data to determine how well it performed for images with random

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Fig. 3. Test of algorithm with random shifts applied to view series generated from a synthetic data set: (a) slice through original synthetic data set, (b) reconstructed slice from views with random shifts applied and (c) reconstructed slice after 7 cycles of algorithm.

misalignment relative to images with misalignment arising from drift and stage positioning error. The simulated data were drawn from an actual low-magnification tomographic reconstruction. At low magnification (and hence low resolution) there is no significant misalignment of images detectable. A simulated series of views was generated from this reconstructed volume. For the first test random artificial misalignments of up to ±10 pixels in X and Y were applied to the simulated views – this corresponds to a drift of 2 μm at typical magnifications used in the XuM. Figure 3 shows a slice through the original volume, a reconstructed slice from the misaligned views, and the reconstructed slice after some cycles of correction. The correction was considered to have converged once there was good qualitative resemblance to the original data and when no further improvement was obtained with additional iterations. This shows that only a few cycles are required to restore the reconstruction to close to the original. Each cycle takes approximately half an hour making a convergence time of approximately 3.5 h in this case. For the second test the simulated views were shifted according to slow sinusoidal functions in X and Y with an amplitude of 10 pixels. This was to simulate a slow

drift of the sort that may occur due to thermal expansion. Figure 4 shows the reconstruction from the shifted images and the reconstruction after 7 (3.5 h) and 27 (13.5 h) cycles of correction. The algorithm as currently implemented is slow, but could be speeded up with further work. As can be seen from the simulations it takes significantly more cycles to correct the images for drift than for jitter. This is because errors due to jitter cause a geometrically uniform blurring in an uncorrected tomographic reconstruction, whereas with a slow drift the misalignment of an image is correlated to its position in the sequence and the resulting tomographic reconstruction has geometric distortions. This results in less satisfactory simulated views for alignment of the original images. It should be noted that actual data sets contain both components of drift and jitter in their misalignment. It may be possible to speed up the image alignment process by using alternative approaches to address the more predictable slow drift prior to applying the iterative algorithm. Application to real data A data set of a glass fibre coated with carbon dag (a polymer loaded with graphite flakes) was used to test the image

Fig. 4. (a) Reconstruction from view series (generated from same data set in Fig. 3a) with sinusoidal drifts applied, (b) reconstructed slice after 7 cycles of algorithm and (c) after 27 cycles.  C 2007 CSIRO Journal compilation  C 2007 The Royal Microscopical Society, Journal of Microscopy, 228, 257–263

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Fig. 5. Reconstructed slices through a tomographic reconstruction of a glass fibre coated in carbon dag, (a) before and (b) after cycles of processing to correct wobble (which in the case of this data set was >5 μm). The corrected image is much clearer and shows features down to 0.5 μm as indicated by the arrows, (c) and (d) show an XZ slice and YZ slice, respectively, through the reconstructed volume. The red lines indicate profiles of just resolved pairs of fibres with the corresponding intensity profiles shown below. Fitted lines show approximately 0.45 μm between minima in either case; however, as there are so few pixels in each section this cannot be taken as a strict measurement of resolution. Instead we note that with reasonable certainty the resolution is between 3 and 5 pixels or 0.56 ± 0.14 μm.

alignment method. The fibre was 16 μm across and the total sample diameter approximately 30 μm. A tomographic data set of 360 views with 1◦ steps was acquired using an SEM accelerating voltage of 15 kV and a tantalum foil target of 500 nm thickness. In this case the system

was optimized for flux rather than maximum resolution in which case a thinner foil would have been used. The source size was of the order of 100–200 nm and the X-ray output therefore dominated by the 8 keV Ta Lα line together with a substantial bremsstrahlung contribution. As the detector is

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a deep-depletion, direct-detection CCD, the X-ray range sits comfortably in the detector’s most sensitive range of 3–10 keV. For this data set the pixels were binned so that 2 × 2 CCD pixels (each of 20 μm across) correspond to a single image pixel of effective size 40 μm. The source to sample distance (R 1 ) was 0.95 mm and the source to detector distance (R 1 + R 2 ) was 259 mm. Resolution as limited by Fresnel diffraction can be estimated for this √ geometry by (λR 1 ). Thus in this case with wavelength of ∼1.5 Å the resolution is limited to around 0.37 μm. The data were processed using the single image phaseretrieval algorithm referred to above (Paganin et al., 2002) to remove Fresnel fringes from each view to enable reconstruction to be free of artefacts. Strictly speaking this algorithm is only quantitatively correct when applied to images of homogenous samples; however, it can be used successfully for removing Fresnel fringes from images of non-homogenous samples. The data were then normalized and used as input to the Feldkamp cone-beam algorithm to produce a 3D reconstruction of the object. Figure 5(a) shows the tomographic cross-section prior to image alignment and Fig. 5(b) shows the cross-section after correction. In the corrected cross-section the graphite flakes within the carbon dag are clearly visible. In order to estimate resolution, intensity profiles were taken across pairs of just-resolved carbon fibres observed in some tomographic slices. Examples of two of these are shown in Fig. 5(c) and (d) together with the intensity profiles. The spacing between the just resolved features is approximately 3– 5 pixels (at 0.14 μm per pixel) and indicates that the resolution is approximately 560 ± 140 nm.

Conclusions and future work The software approach to correcting image misalignment has enabled submicrometre tomography at a resolution of ∼560 nm to be achieved using relatively modest laboratory equipment. This is a very high resolution for a lab-based point-projection system. Significantly higher resolution in microtomography has only been achieved outside of a synchrotron with more complex zone-plate-based systems (Tkachuk et al., 2006). We have found that the software approach does not work equally well for all data sets and there may well be improvements to be made in the cross-correlation step. Currently the cross-correlation is performed using the standard fast Fourier transform (FFT) based method with only light smoothing to reduce noise in the images. The position of the peak in the cross-correlation map corresponds to the shift between the images; however, the peak can be broad and indistinct for some samples. Further optimization of filtering may improve performance as may alternative correlation functions such as the phase correlation function described

by Tsai et al. (2004). The addition of fiducial markers to the sample may also be helpful in some cases where the sample itself has insufficient high-contrast features for accurate image registration. The software as already noted did not work as well for slow drifts in misalignment as it did for random ‘jitter’ for reasons noted above. Drift comes about primarily from thermal expansion of the stage, target holder and the whole SEM chamber and produces displacements of images parallel to the image plane, which are correlated with time (displacements perpendicular to the image plane produce much smaller effects in the image). Prior correction for this more predictable type of drift by comparison on the first and last images of a 360◦ data set and by correlation methods is likely to reduce the number of iterative cycles required to correct a set of misaligned images. Hardware measures to reduce thermal drift through better ambient temperature control and a modified target stage would also reduce the problem of drift. Acknowledgement The authors would like to thank XRT Ltd for cooperation and encouragement in this work.

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