High-Resolution Three-Dimensional Imaging
with an X-Ray Microscope
J. Lehr
Forschungseinrichtung Röntgenphysik, Georg-August-Universität Göttingen, Geiststraße 11,
D-37073 Göttingen, Germany
Abstract. The Göttingen transmission X-ray microscope (TXM) at BESSY
has been used for threedimensional imaging. As a first test-object sheaths of
the bacteria Leptothrix Ochracea have been visualized. 33 tilted-view images
have been taken at tilt angles between 0 and 160 degrees in steps of 5 degrees.
Before reconstruction the images were flat-field corrected and aligned. The
rotation axis was determined and the images were rotated accordingly. For
tomographic reconstruction a fast MART (Multiplicative Algebraic Reconstruction Technique) algorithm was used. In the recon-structed volume structures of sizes well below 100 nm are made visible.
1 Introduction
The circumstances in X-ray microscopy [1, 2, 4] are know to be well suited for
three-dimensional investigations for several reasons:
• The refractive index for soft X-rays is close to 1 for all substances. Therefore,
scattering reflection at interfaces is negligible and clear images can even be
obtained from thick objects.
• The image-field of the Göttingen X-ray microscope is of the same size as the
thickness of typical objects, i.e. of the order of 10 µm. For typical objects like cells
the three-dimensional structure has to be considered because their lateral dimensions are of the same size as their thickness.
• The attenuation length for soft X-rays in water is also around 10 µm. Hydrated objects of thicknesses around 10 µm have therefore a reasonable transmission.
Whereas the lateral resolution of the X-ray microscope at BESSY is one order of
magnitude smaller than the resolution of visible light microscopes, the depth resolution is of the same size or even larger than for visible light microscopes. The
reason herefore is that todays X-ray objectives have a relatively small aperture in the
range from 0.02 to 0.04 while apertures can be as large as 1.4 in light microscopy.
The focal depth δt of an X-ray microscope is 2.44 drn2/λ. The objective-zoneplate,
which was used for the experiments described below has an outermost structurewidth of 39 nm. For this zoneplate δt is 1.5 µm and the ratio δt:δl is 33:1.
Instead of being a handicap for three-dimensional investigation like in visible
light microscopy, the spatially anisotropic resolution of the X-ray microscope can be
made a virtue when combined with the appropriate reconstruction method. Within
the depth of focus, the image-formation process can be described by a projection
along the optical axis:
I - 72
J. Lehr
I( x, y) = I 0 ( x, y) exp( − ∫ µ ( x, y, z)dz)
(1)
z
Here I(x,y) denotes the image-intensity at the point (x,y), I0(x,y) is the illumination
intensity and ∫zµ(x,y,z)dz is the line integral of the absorption coefficient at (x,y)
along the optical axis.
In X-ray microscopy, depth information can best be obtained from tilted-view
images [5]. This leads to the following approaches: The easiest way, which already
gives a good impression of the threedimensional organization of specimens is, to
take stereo images, which has successfully been demonstrated for the Göttingen Xray microscope at BESSY [6]. In order to get real threedimensional data sets that can
be used for quantitative measurement of surface and volume it is necessary to
implement the method of tomographic reconstruction [7] on the X-ray microscope.
2 Tomographic Reconstruction from TXM-Images
3D-reconstruction from X-ray microscopy images imposes a limited data problem.
This means that 3D data has to be reconstructed from few projections from a limited
tilt-angle. The tilt-angle is limited, because the effective water layer increases with
the tilt angle, if objects are prepared on a flat substrate. For tilt-angles larger than 80
degrees, exposure-times would become too long. Since complete automization of the
image acquisition process at the TXM at BESSY is not yet achieved, the number of
tilted-view images that can be taken in practice is limited. Limited-data
reconstruction techniques [9] that have been tested so far were the ART (algebraic
reconstruction technique) and the MART (multiplicative algrebraic reconstruction
technique) algorithm. Both have proven to suit our needs, where the latter (MART)
shows faster convergence and less artifacts when dealing with few projections.
Tomographic reconstruction is run on an SGI Indigo2 workstation equipped with a
200 MHz MIPS R4400 processor. Reconstruction of a 2563 voxel cube from 33
projections with 2562 pixels takes about 20-40 minutes depending on how many
iterations are calculated.
3 Experimental Results
In a first experiment [10], mineral sheaths of the bacteria Leptothrix Ochracea have
been used as a dry test-object. This bacterium is known as an iron oxygenating
sheath bacterium. It forms long chains of cells held together by a thin tubular sheath
which is enriched by iron [11]. These structures have diameters of several microns
down to a fractional part of 1 µm. As iron is highly absorbing for soft X-rays in the
water window, the contrast is very high and the structures can be visualized
particularly well. The objects were prepared on a fine glass-fiber, which was then
fixed at one end to a tilting stage. 33 TXM-images were taken at angles from -80
degrees to 80 degrees in steps of 5 degrees. The tilt-angle was adjusted manually to a
precision of about ±0.5 degrees. The objective-zoneplate we used has a theoretical
lateral resolution below 50 nm and a focal depth of 1.5 µm at 2.4 nm wavelength.
Figure 1 (bottom) shows a selection of the intensity Data (I(x,y))Θ of the tilted-view
images.
High-Resolution Three-Dimensional Imaging with an X-Ray Microscope
I - 73
Fig. 1. Tilted-view images of mineral sheaths of the bacteria Leptothrix Ochracea (top).
Slices of the reconstructed volume perpendicular to the rotation axis (bottom).
Dark regions in the images correspond to dense object-regions.
The images are background-corrected and normalized to I0(x,y)=1. Before reconstruction the images were aligned and the rotation axis was determined by tracing
characteristic points in the object. Already by animating the sequence of tilted-view
images a good qualitative impression of the three-dimensional morphology of the
object can be obtained. For quantitative measurement however three-dimensional
reconstruction of the objects density-values has to be done. The values of the
reconstructed volume correspond to µ·∆s, where ∆s is the edge-length of a voxel.
Figure 1 (top) shows slices of the reconstructed volume perpendicular to the
rotation axis. In the reconstructed volume structures of sizes well below 100 nm have
been made visible. A more illustrative representation of the object can be obtained
by volume-rendering or surface-rendering of an isosurface (Fig. 2). In the case of the
objective-zoneplate we used for the experiments presented here, the condition for
using (1) to describe the image formation process is not strictly fulfilled, since the
diameter of the reconstructed volume is larger than the depth of focus. But as the
results show, our reconstruction-algorithm seems to be quite tolerant to this small
error.
I - 74
J. Lehr
4 New Possibilities with 3D X-Ray Microscopy
This technique gives access to a wide range of new types of X-ray microscopy investigations. It is now possible to get quantitative data for surface and volume of
objects and distances in objects can be measured. Since we reconstruct the linear
absorption coefficient µ(x,y,z) of the object, the densities of structures can be determined if their chemical composition is known. This can for example be used to
measure the chemical concentration in pecial cell features, if their chemical composition is known from other methods. For our test-object, the calculated absorption
coefficients correspond quite well to the values we expect when assuming that the
structures are composed of hydrated Fe2O3 with densities around 3 gcm-3 [11, 12].
Fig. 2. Stereo-pairs of an isosurface-rendering of the reconstructed volume.
High-Resolution Three-Dimensional Imaging with an X-Ray Microscope
I - 75
5 Outlook
To make this method more easily accessible for X-ray microscopy users, several improvements have to be made, mainly concerning the automization of the image
acquisition process and the object preparation. For alignment of the image data and
determination of the rotation axis up to now we use an interactive method which is
based on visual estimation of characteristic points and the sinograms of the projection data. The automization of this process will also be subject of future investigations.
Any method for three-dimensional reconstruction requires that many images of
the same object have to be taken. For wet biological specimens at room temperature
this means that the dose applied to an object will introduce structural changes in the
object [13]. It will therefore be vital to combine the method described above with the
cryo fixation method. For two-dimensional imaging of biological specimen this
method has already been implemented on the X-ray microscope at BESSY [8].
Acknowledgements
The author wishes to thank Prof. Dr. G. Schmahl for his continuous support and
encouragement and Dr. P. Guttmann for his help at BESSY. For the surfacerendering, a graphics program from Lab. DyOGen, Université Joseph Fourier,
Grenoble was used. This work has been funded by the German Bundesministerium
für Wissenschaft, Bildung, Forschung und Technologie (BMBF) under contract
number 05644 MGA and by the PROCOPE exchange program.
References
1
G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider,
C. David, M. Diehl and T. Wilhein: X-Ray Microscopy Studies. Optik 93,
pp. 95–102, (1993).
2
G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme and G.
Schneider: Röntgenmikroskopie. Naturwissenschaften 83, (1996), pp. 61–70.
3
V .V. Aristov and A.I.Erko (eds.): X-Ray Microscopy IV. Proceedings of the 4th International Conference, September 20-24, 1993. Chernogolovka, Russia,
1994.
4
Niemann, G. Schneider, P. Guttmann, D. Rudolph and G. Schmahl: The New
Göttingen X-Ray Microscope with Object Holder in Air for Wet Specimens. in:
[3] pp. 66–75.
5
W.S. Haddad, I. McNulty, J.E.Trebes, E.H. Anderson, R.A. Levesque, L. Yang.
Ultrahigh-Resolution X-ray Tomography. Sciene, vol. 266, 18 Nov. (1994),
pp. 1213–1215.
6
J. Lehr: 3D X-Ray Microsopy: High-Resolution Stereo-Imaging with the
Göttingen X-Ray Microscope at BESSY. Zoological Studies 34, Supplement
(1995), pp. 137–138.
I - 76
J. Lehr
7
Rosenfeld and A.C. Kak: Digital Picture Processing. Academic press (1982).
second edition, volume 1, pp. 353–430.
8
Schneider, B. Niemann, P. Guttmann, D. Rudolph and G. Schmahl: Cryo X-Ray
Microscopy. Synchrotron Radiation News, vol. 8, No. 3 (1995).
9
D. Verhoeven: Limited-data-computed tomography algorithms for the physical
sciences. Applied Optics, vol. 32, No. 20, 10 July (1993), pp. 3736–3754.
10 Lehr : 3D X-Ray Microscopy : High-Resolution Tomographic Imaging
of Mineral Sheaths of Bacteria Leptothrix Ochracea. Optik. (in press)
11 Thieme, T. Wilhein, P. Guttmann, J. Niemeyer, K.-H. Jacob, S. Dietrich: Direct
Visualization of Iron and Manganese Accumulating Microorganisms by X-Ray
Microscopy. in: [3], pp.152–156.
12 T. Wilhein: Gedünnte CCDs: Charakterisierung und Anwendungen im Bereich
weicher Röntgenstrahlung. Verlag Shaker, Dissertation Universität Göttingen,
(1994).
13 R.C. Weast (ed.): CRC Handbook of Chemistry and Physics. CRC Press, Boca
Raton, Florida (1988).
14 G. Schneider: Investigations of Soft X-Radiation Induced Structural Changes in
Wet Biological Objects. in: [Aristov V.V, A.I.Erko (eds.), 1994], pp. 181–195.