Quantitative X-ray phase-contrast microtomography from a compact laser-driven betatron source

X-ray phase-contrast imaging has recently led to a revolution in resolving power and tissue contrast in biomedical imaging, microscopy and materials science. The necessary high spatial coherence is currently provided by either large-scale synchrotron facilities with limited beamtime access or by microfocus X-ray tubes with rather limited flux. X-rays radiated by relativistic electrons driven by well-controlled high-power lasers offer a promising route to a proliferation of this powerful imaging technology. A laser-driven plasma wave accelerates and wiggles electrons, giving rise to a brilliant keV X-ray emission. This so-called betatron radiation is emitted in a collimated beam with excellent spatial coherence and remarkable spectral stability. Here we present a phase-contrast microtomogram of a biological sample using betatron X-rays. Comprehensive source characterization enables the reconstruction of absolute electron densities. Our results suggest that laser-based X-ray technology offers the potential for filling the large performance gap between synchrotron- and current X-ray tube-based sources.

The object of comparison was selected to be a leg -for easier identification distant from any other parts -as indicated by the red arrow in Supplementary Fig. 2. Its outer diameter according to an optical microscope image is approx.140-160 m (see Supplementary Fig. 2).
Supplementary Figure 2: Microscope image of the sample. The red arrow indicates the leg of the object that was used for the comparison. The outer diameter is according to an optical microscope image approx.140-160 m.
Although the single shot X-ray images have a pixel resolution of 6 m (as stated in the main text of the manuscript) the tomogram will suffer additional blurring due to reconstruction method and the angle step size of the data set. We model the overall loss in resolution by introducing a point-spread function (PSF) of the measurement. Its convolution with the ideal object would than resemble our tomographic measurement.
Assuming the PSF to be a 2D Gaussian function in the form of exp 22 (as shown in Supplementary Fig. 3c) the convolution will result in a blurred image with consequently reduced maximum signal for structures smaller or comparable to the PSF.
For 2D Gauss PSF with a FWHM of 36 m the maximum reconstructed density for our test object (insect leg, outer diameter about 150 m and inner diameter about 125 m) will drop to 33% of its absolute value (see Supplementary Fig. 3b).
Supplementary Figure 3: Model of the Point Spread Function. a: Doughnut shape with a step like molecular chitin electron density of 5.2x10 23 cm -3 , an outer and an inner diameter of 150 m and 125 m. b: Convolution of the test object (Fig. 3a ) and a Gaussian PSF (Fig. 3c). A lineout of it (white) is shown in the Supplementary Fig. 5. The color map applies for the Fig. 3 a and b . c: 2D Gauss PSF with a FWHM of 42 m.
The estimate for the FWHM of PSF can be obtained by evaluating the reconstruction of the originally sharp feature. We used the edge of the needle -the holder of our sample -whose blurring effect appears to be 3-4 reconstruction voxels, corresponding to 36 m -48 m.
Returning to our test object one can perform a comparative analysis between the lineout through our convolutional model (white line in the Supplementary Fig. 3b) and a lineout in the corresponding slice within the tomogram (indicated by the red line in Supplementary Fig.  4b). Supplementary Fig. 5 shows this comparison for PSF widths of 24, 36, and 48 m FWHM, i.e. 2,3,4 reconstruction voxels. On the absolute electron density.In order to strengthen the attribute 'quantitative' in our title we have compared the reconstructed electron densities within an insect's leg with a model imitating the structure and density of such profile processed according to imaging and reconstruction properties of our setup.
An insect leg was chosen due to the simplicity of its geometry (a cylindrical shape) and the type of its composition material (mainly chitin). From a scanning electron microscope image of a cross section (of the insect's leg used in the experiments, see Supplementary Fig. 1) it can be seen that most of the inner part is void (due to vacuum desiccation). Furthermore the wall thickness of the cuticle varies between 9-