X-ray phase contrast tomography with a bending magnet source

Transcription

1 REVIEW OF SCIENTIFIC INSTRUMENTS 76, X-ray phase contrast tomography with a bending magnet source A. G. Peele Department of Physics, La Trobe University, 3086, Australia F. De Carlo Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois P. J. McMahon, a B. B. Dhal, and K. A. Nugent School of Physics, University of Melbourne, 3010, Australia Received 2 May 2005; accepted 14 June 2004; published online 3 August 2005 X-ray radiography and x-ray tomography are important tools for noninvasive characterization of materials. Historically, the contrast mechanism used with these techniques has been absorption. However, for any given sample there are x-ray energies for which absorption contrast is poor. Alternatively, when good contrast can be obtained, radiation damage from an excessive dose may become an issue. Consequently, phase-contrast methods have in recent years been implemented at both synchrotron and laboratory facilities. A range of radiographic and tomographic demonstrations have now been made, typically utilizing the coherent flux from an insertion device at a synchrotron or a microfocus laboratory source. In this paper we demonstrate that useful results may be obtained using a bending magnet source at a synchrotron. In particular we show that the same beamline can be used to make and characterize a sample made by x-ray lithographic methods American Institute of Physics. DOI: / I. INTRODUCTION a Now at Maritime Platforms Division, Defence Science and Technology Organisation. Physical variations in a sample placed in a wave field can give rise to contrast modulation in the wave field, which can then be detected using an experimental apparatus. In the case of x-ray imaging, the physical variations so detected have historically been in electron density across the sample, giving rise to absorption contrast. 1 The technique is so successful that x-ray imaging has been a standard tool of medical and materials science for many years. The 1980s saw developments in x-ray microscopy based on the fact that between the carbon K edge 284 ev,4.4 nm and the oxygen K edge 532 ev,2.3 nm water is much less absorbing than biological materials. 2 However, the field has been limited mainly to frozen or dried samples or to other radiation tolerant samples due to the high dose received during the imaging process. 3 The use of high-brilliance sources means that imaging time can be reduced and more samples become accessible. Another approach is to measure the phase variations imposed on the wave field as a result of passing through the sample plane. There are several techniques that have been implemented that allow one to visualize these phase variations. Examples include interferometry, 4 6 Zernike phase contrast, 7 differential interference contrast, 8 segmented detectors, 9 or Shack-Hartmann arrays, 10 and diffractionenhanced imaging. 11 These all require the incorporation of some optical apparatus into the experiment, which can be difficult in the x-ray context. Another way to visualize the phase variations in the wave field relies simply on the evolution of contrast in the intensity of the wave field with propagation. Related approaches have been demonstrated using in-line holography, 12 multiple defocus methods, 13 and Wigner deconvolution methods, 14 while the simpler technique of optics-free propagation was realized only in the latter half of the 1990s Although contrast can be observed, interpreting that contrast in terms of the physical structure in the sample can be difficult. Several methods of inverting the equations governing the propagation of the wave field have now been developed. These include contrast transfer function methods, which require the assumption of a weak object 18 or of a slowly varying phase with a weakly absorbing object, 19 transport of intensity methods, 20 holographic methods, 21 and far- 22 and near- 23 field iterative methods. In this work we will use a variation of the transport of intensity methods suitable for samples that have a single refractive index in a paraxial wave field. 24 The reason for this choice is that it is one of only a few analysis methods that can retrieve a rapidly varying sample phase using only a single intensity measurement. This makes an experiment simpler to perform and matches the types of sample we were testing. The analysis of the various propagation-based phase methods generally proceeds with the assumption that the wave field is fully coherent. However, even with third generation synchrotron or modern microfocus sources, this assumption is far from met. The effect of partial coherence, which for x-ray sources can be closely related to source size and bandwidth, can be thought of as introducing a characteristic length scale over which the average phase information is then retrieved. 25 Similarly, partial coherence can be seen as a low-pass spatial filter that limits the spatial resolution of /2005/76 8 /083707/5/$ , American Institute of Physics

2 Peele et al. Rev. Sci. Instrum. 76, the system. 26,27 At a synchrotron source, the main advantage of using an insertion device source instead of a bending magnet source is that more flux is available in a given bandpass for the same source size. However, it can be shown, for a pure phase sample 26,27 and for energies away from absorption edges in the sample, that even for a bandpass as broad as / =0.7 contrast will only be reduced by about a factor of 2 for retrieved spatial frequencies up to an optimal spatial frequency u= 1/2 z given by the wavelength,, and the propagation distance, z. Accordingly, where the bandpass can be broadened sufficiently a bending magnet source may provide similar flux to an insertion device and have similar source size limitations on the resolution. Accordingly, it may be that in an environment where competition for insertion device sources is fierce, a facility established at a bending magnet may still have sufficient functionality to be a useful tool for materials, biological and medical science. We investigated two types of samples using tomographic phase imaging; a naturally occurring biological sample a stinger, probably that of Apis mellifera and some fabricated polymer samples. The fabricated samples were Poly Methyl Methacrylate PMMA components made by the process of x-ray lithography. 28,29 The purpose of our investigation was to demonstrate the following: The utility of bending magnet sources for imaging samples in phase contrast tomography. The technique of broad bandpass imaging at a bend magnet source, with the resulting ability to perform extremely fast data collections. The ability of a single beamline to both make and image a sample. In Sec. II we describe the experimental arrangement and the analysis methods used and in Sec. III we present the results. II. EXPERIMENTAL ARRANGEMENT AND ANALYSIS The experiments were performed at the bend magnet facility 30 at sector 2 of the Advanced Photon Source at Argonne National Laboratory. A mm 2 vertical horizontal beam is delivered with monochromatization from 5 20 kev with a bandwidth of de/e 10 3 via a Kohzu double-crystal monochromator. 31,32 The one-sigma source size is 102 m 35.1 m horizontal vertical with a divergence of 60 rad 2.1 rad horizontal vertical. The sample stage is at a distance of over 50 m from the source. In our experiments the samples were mounted on a goniometer stage with rotation about the vertical axis as well as two orthogonal horizontal axes above the rotary stage and two orthogonal horizontal axes below the rotary stage and one vertical axis translation. The x-ray beam was allowed to pass through the sample and was propagated a distance of 970 mm downstream to a detector. The detector consisted of an approximately 300 m thick cadmium tungstate CdWO 4 scintillator screen imaged via a Zeiss Karl Zeiss, Inc. Microscope Division One Zeiss Drive Thornwood, NY objective 5 neo-fluar, NA=0.15; 4 Achoplan, NA=0.10 coupled by a 1 Tube Lens and connecting tube TABLE I. Sample and experimental parameters. Sample CCD pixel m Energy kev cm 1 PMMA rotor PMMA nozzle Sting Sting 1.33 Pink beam into a CoolSnap CoolSnapfx Roper Scientific, Inc Quakerbridge Rd. Trenton, NJ CCD camera using a region of interest of pixels that were 4.65 m in size. The resulting effective CCD pixel size 1.33 m; 1.66 m slightly oversamples the nominal objective resolution 2.03 m;2.4 m. However, the actual resolution will be worse than this due to parallax and diffusion of the emitted light within the scintillator screen as well as the demagnified source size at the detector. In resolution tests using the 5 objective, the system resolution is found to be 2.7 m. Accordingly, the CCD sampling is actually at something close to the Nyquist requirement of two samples per resolved element. We present here the results for four tomographic measurements. The sample descriptions and experimental parameters are shown in Table I. For each, sample projections between were taken in 0.25 steps. The nonuniform illumination intensity was normalized across the images by dividing through by sample-out images of the beam. These were taken every 20 projections and applied to the corresponding 20 projections to minimize effects of beam instability. In the pink beam mode, no monochromatization was used. The bend magnet source beam was modified by a 0.15 reflection from a chromium mirror and by insertion of 900 m of aluminium filters as well as 400 m beryllium windows. This produces a net spectrum with significant flux between about kev. This had the result of considerably reducing exposure times from the approximately 5 s required for the monochromatic cases. We used an exposure of 20 ms. All of the samples considered here are homogeneous in their composition in the sense that the material has a single refractive index. This makes them amenable to analysis using the following result: 24 T r = 1 ln I 1 I I r /I 0 z k 2 1 +, where T is the retrieved thickness of the sample, r are the transverse coordinates, z is the distance from the sample to the detector plane, I 1 and I represent the inverse and forward Fourier transform operators, k are the Fourier conjugate coordinates to r, I is the measured intensity in the detector plane, I 0 is the uniform intensity of the incident radiation, is the total linear absorption coefficient of the sample, and is the decrement from unity of the real part of the refractive index of the sample. The values of and used in the results shown here are listed in Table I. 33 The thickness can readily be replaced with the phase change through the sample via

3 Bending magnet phase contrast tomography Rev. Sci. Instrum. 76, FIG. 1. Phase contrast image for a lithographically produced PMMA rotor part. The experimental conditions are set out in Table I. Note the fine contrast features from cracking in the part. = 2 T, 2 where is the wavelength of the illuminating radiation. For a nonabsorbing object and away from absorption edges, it has been pointed out 26 that in the regime of validity for the transport of an intensity solution, 19 the detected image is wavelength independent subject to a wavelength scaling factor. This means that for a polychromatic source satisfying the same conditions, the scaling factor can be replaced by a spectrally weighted sum. Equivalently an appropriate effective wavelength can be used in the analysis. 34 Our sting sample was less than 5% absorbing over the polychromatic spectrum used. It also appears to satisfy the strict TIE validity requirements 19 given some ex post facto knowledge of its structure. We assume that the composition of the sting is akin to keratin, in that there is no major absorption edge structure in the polychromatic band used. An effective energy of 16.9± 0.2 kev was found by appropriately varying the energy-dependent terms in Eq. 1 and obtaining a best fit to the retrieved thickness obtained for the monochromatic case. This agrees quite well with simulations of the expected spectrum detected by the scintillator performed using the XOP software, 35,36 which give a peak energy of 18.2 kev. The projected images of the samples were normalized to the incident intensity and the projected thickness was retrieved using Eq. 1. The tomographic reconstruction was performed using the radon backprojection method implemented in the Interactive Development Language. 37 The pixel images were binned into images for faster processing. At this lower resolution, tomographic datasets could be processed using a Pentium IV laptop system in a few hours. It should be noted that at the facility where this data was taken, it would be possible to reconstruct the tomographic datasets in considerably shorter times by implementing the phase retrieval step and inputting the result into the dedicated processing cluster. 30 FIG. 2. a Profile of the thickness calculated using Eq. 1 for the PMMA rotor part. The line along which the thickness is shown is indicated in the inset, which shows a map of the calculated thickness for a side-on view of the rotor. Note that the recovered thickness agrees well with the actual thickness, which is shown in the inset to Fig. 2 b. b The profile of the thickness calculated using Eq. 1 for the PMMA rotor part. The line along which the thickness is shown is indicated in the insert, which shows a map of the calculated thickness for a face-on view of the rotor. Note that the recovered thickness agrees reasonably well with the actual thickness, which is shown in the inset to Fig. 2 a. III. RESULTS Figure 1 shows the phase contrast image for a projection of a rotor part fabricated in PMMA using x-ray lithography also at the 2BM beamline. The part is 1.2 mm wide and 1.1 mm thick with approximately 85 m slots. These features can clearly be seen in phase contrast, as can some small cracks on the surface of the part. The thickness for each tomographic projection was obtained using Eq. 1. The retrieved thickness is shown in the inserts to Fig. 2 for a side-on and face-on projection of the part. The bright band in Fig. 2 a corresponds to the part of the rotor where the projections of the slots do not intrude so that this part of the rotor has a projected thickness equal to the width of the rotor. This can be measured directly from the view in Fig. 2 b.as can be seen in the line plot and the insert plot, the recovered thickness is typically within 10% of the actual value. Conversely, the thickness of the rotor can be measured directly from Fig. 2 a and can be compared with the recovered thickness shown in Fig. 2 b. The recovered thickness is

4 Peele et al. Rev. Sci. Instrum. 76, FIG. 3. Three-dimensional visualizations of the PMMA rotor. Note that even at the coarse resolution at which these datasets are binned the voxel dimension is 6.64 m, the fine crack features observed in Fig. 1 can be seen, and using the 3D dataset can be shown to be confined to the surface of the rotor. typically within 10% of the actual value. However, near sharp edges, such as the edge of the part or the edges of the slots, the recovered thickness deviates more. This is due to the fact that Eq. 1 is valid only when 19 j zu T r 1, 3 1 j=2 j! 1 2 where z is the distance between the sample and the detector and u, which is the Fourier conjugate of r, represents the spatial frequencies in the sample. Near a sharp edge, T becomes large and large spatial frequencies are present so the condition in Eq. 3 is violated. Figure 3 shows some three-dimensional 3D visualizations of the tomographic dataset. The ability of the method as applied at this bending magnet source to image the features in three dimensions is clearly seen. In particular, the cracking seen in the phase contrast image are confirmed to be present as surface cracks only. Figure 4 shows a 3D visualizations of the tomographic dataset for a lithographically fabricated nozzle part. Again, the projected thickness of the sample agrees reasonably well with the actual value. Figure 5 a shows a high resolution and filtered image of the retrieved phase for the sting using the monochromatic beam. This illustrates the detail that can be visualized using these methods. The twin lancets characteristic of the sting 38 FIG. 5. a High resolution phase retrieval of the sting. As an example of how filtering can aid visualization, the retrieved phase has been image processed with an edge enhancement algorithm so that the morphological features in the sting can be seen more readily observed. b Slices through the sting taken from the tomographically reconstructed dataset. Again the resolution is 6.64 m, yet the main features are readily apparent. are clearly seen as is part of the bulb structure at the top of the sting. A 3D visualization is shown in Fig. 5 b. In Fig. 6 the same 3D visualization is shown for the polychromatic beam case. It can be seen that the structures retrieved are the same as for the monochromatic case. However, these images were taken in approximately 1/250th of the exposure time as for the monochromatic case. IV. DISCUSSION We have demonstrated that a bending magnet source can be used to obtain useful phase contrast tomography images, a fact that appears to have been overlooked in the context of phase retrieval. Competition for insertion device sources remains high and there will be many samples that are admirably matched with bend magnet specifications for phase retrieval. Additionally, we have demonstrated a useful diagnostic tool for beamlines that undertake x-ray lithography. Components so machined can be inspected using the same end station with only a relatively small additional investment. Furthermore, the PMMA and SU-8 resists com- FIG. 4. Reconstructed slice of a nozzle part; the dark square is 1 mmin width. Some artifacts of the reconstruction can be seen. FIG. 6. Image showing approximately the same slices as for Fig. 5 b for the experiment using the pink beam to illuminate the sample. It can be seen that the results are approximately the same as for the monochromatic case.

5 Bending magnet phase contrast tomography Rev. Sci. Instrum. 76, monly used in x-ray lithography will be amenable to the polychromatic methods discussed above. It is worth questioning whether the resists will demonstrate phase contrast even before they have been developed. In the case of PMMA the mean molecular weight of the polymer drops dramatically, 39 and it is possible that the electron density in the material has changed sufficiently to exhibit phase contrast. Finally we have shown, using an extremely wide bandwidth, that the polychromatic method will work to produce fast phase-retrieved tomographic datasets of a sample. When the sample has an absorption edge in the broad spectrum used then a narrower bandwidth may be required. In such a case monochromation systems with broader bandwidth than crystal monochromaters could be used. For instance, a multilayer monochromater 40 de/e 10 2 has been implemented at the beamline where this data was taken. ACKNOWLEDGMENTS The authors acknowledge Australian Research Council Fellowships AGP: QEII Fellowship, KAN: Federation Fellowship. This work was supported by the Australian Synchrotron Research Program, which is funded by the Commonwealth of Australia under the Major National Research Facilities Program. Use of the Advanced Photon Source was supported by the U.S. DOE., Basic Energy Sciences, Office of Science under Contract No. W Eng-38. We thank R. Barber of MiniFab for providing the rotor sample. 1 W. C. Rontgen, Nature London 53, E. Spiller, Soft X-ray Optics SPIE, Bellingham, 1994, Chap. 12, p D. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation Cambridge University Press, Cambridge, 1999, Chap. 9, p A. Momose, T. Takeda, and Y. Itai, Rev. Sci. Instrum. 66, Y. Kohmura, H. Takano, Y. Suzuki, and T. Ishikawa, Proceedings of the 7th International Conference on X-Ray Microscopy, J. de Physique IV, Vol 104, p. 571, edited by J. Susini, D. Joyeux, and F. Polack EDP Sciences, Les Ulis, F. Beckmann, U. Bonse, F. Busch, and O. Gunnewig, J. Comput. Assist. Tomogr. 21, G. Schmahl, D. Rudolf, and P. Guttman, X-Ray Microscopy II, Vol. 56 of Springer Series in Optical Science, edited by D. Sayre, M. Howells, J. Kirz, and H. Rarback Springer-Verlag, Berlin, 1988, p T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, M. Altissimo, J. Susini, B. Fayard, U. Neuhäusler, S. Cabrini, and F. Polack, in Ref. 5, p J. R. Palmer and G. R. Morrison, Short Wavelength Coherent Radiation, Vol. 11 of OSA Proceedings Series, edited by P. H. Bucksbaum and N. M. Ceglio Optical Society of America, Washington, DC, 1991, p R. G. Lane and M. Tallon, Appl. Opt. 31, D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, C. Jacobsen, M. Howells, J. Kirz, and S. Rothman, J. Opt. Soc. Am. A 7, W. Coene, G. Janssen, M. Op de Beek, and D. Van Dyck, Phys. Rev. Lett. 69, H. N. Chapman, Ultramicroscopy 66, A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, Rev. Sci. Instrum. 66, P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, J. Phys. D 29, S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, Nature London 384, X. Wu and H. Li, J. X-Ray Sci. Technol. 11, L. D. Turner, B. B. Dhal, J. P. Hayes, A. P. Mancuso, K. A. Nugent, D. Paterson, R. E. Scholten, C. Q. Tran, and A. G. Peele, Opt. Express 12, K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, C. Jacobsen, M. Howells, J. Kirz, and S. Rothman, J. Opt. Soc. Am. A 7, J. Miao, P. Charalambous, J. Kirz, and D. Sayre, Nature London 400, L. J. Allen, W. McBride, and M. P. Oxley, Opt. Commun. 233, D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, A. Pogany, and A. W. Stevenson, J. Microsc. 207, A. Pogany, D. Gao, and S. W. Wilkins, Rev. Sci. Instrum. 68, E. W. Becker, W. Ehrfeld, D. Münchmeyer, H. Betz, A. Heuberger, S. Pongratz, W. Glashauser, H. J. Michel, and R. Vonsiemens, Naturwiss. 69, E. W. Becker, W. Ehrfeld, P. Hagmann, A. Maner, and D. Münchmeyer, Microelectron. Eng. 4, Y. Wang, F. De Carlo, D. C. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, Rev. Sci. Instrum. 72, H. R. Lee, B. Lai, W. Yun, D. C. Mancini, and Z. Cai, Proc. SPIE 3149, B. Lai, D. C. Mancini, W. Yun, and E. Gluskin, Proc. SPIE 2880, C. T. Chantler, K. Olsen, R. A. Dragoset, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker 2005, X-ray form factor, attenuation and scattering tables, Version 2.1, 2005; available at ffast. National Institute of Standards and Technology, Gaithersburg, MD. Originally published as C. T. Chantler, J. Phys. Chem. Ref. Data 29, ; 24, P. J. McMahon, B. E. Allman, D. L. Jacobsen, M. Arif, S. A. Werner, and K. A. Nugent, Phys. Rev. Lett. 91, R. J. Dejus and M. S. del Rio, Rev. Sci. Instrum. 67, M. S. del Rio and R. J. Dejus, Proc. SPIE 3448, See, for instance, images at website.lineone.net/~dave.cushman/ stingstructure.html. 39 P. Rai-Choudhury, Handbook of Microlithography, Micromachining and Microfabrication SPIE Press, Bellingham, WA, 1997, Vol. 2, p Y. S. Chu, C. Liu, D. C. Mancini, F. De Carlo, A. T. Macrander, B. Lai, and D. Shu, Rev. Sci. Instrum. 73,