Optimizing illumination for full field imaging at high brilliance hard X-ray synchrotron sources

: A new technique is presented to overcome beam size limitation in full field imaging at high brilliance synchrotron sources using specially designed refractive X-ray optics. These optics defocus the incoming beam in vertical direction and reshape the intensity distribution from a Gaussian to a more desirable top-hat-shaped profile at the same time. With these optics X-ray full-field imaging of extended objects becomes possible without having to stack several scans or applying a cone beam geometry in order to image the entire specimen. For in situ experiments in general and for diffraction limited sources in particular this gain in field of view and the optimization of the intensity distribution is going to be very beneficial.


Introduction
X-ray imaging techniques like tomography are commonly used at lab and at synchrotron sources for example in the fields of material science, medicine or biology [1][2][3][4][5][6][7]. Whereas synchrotron sources offer high brilliance, the beam size in particular in vertical direction is often strongly limited. In addition, the intensity profile of such an undulator source is approximately Gaussian shaped in vertical direction with a FWHM in the range of a few millimeters only [8]. This is a strong limitation for many experiments, in particular full field imaging techniques at 3rd generation synchrotron sources [9,10]. Objects larger than the illuminated field cannot be imaged directly: Image stitching [10] or enlarged cone beam projection [11] have to be applied to overcome this limitation often leading to artefacts in the final reconstructed volume. Time consuming acquisition of several height scans and a more complex image reconstruction are the drawbacks for such full field imaging approaches. In biological studies the additional dose load due to necessarily overlapping fields of view generates problems and often filters are used to reduce the flux at the sample. In particular for in situ and time resolved experiments a stitching of different height step scans is often not possible. One way of overcoming this limitation is to use enlarged cone beam projection. Here, however, a virtual source has to be formed by additional X-ray optics. The alignment is often very time consuming and the reconstruction cannot be performed using the parallel beam geometry approach. Another drawback of a 3rd generation X-ray beam is the typical Gaussian intensity profile, leading to differences in the signal to noise ratio between the high-illumination center region and those regions illuminated by the low-intensity tails. A top-hat like beam profile would therefore be very beneficial for full field imaging techniques in general.
There are plenty of examples of how to adjust the beam profile for a certain purpose in visible light optics [12], nevertheless so far mainly focusing concepts have been transferred to the hard X ray regime. For focusing X-rays at energies above approximately 10 keV refractive X ray optics are used, as for these energies the absorption of the lens materials decreases [13][14][15][16][17]. Using a refractive line focus lens to get an enlarged beam after the focal plane is not a suitable way to enlarge the vertical beam size, as in this case the absorption beam woul At the (KIT/IMT) sion limitat lowing we ies using sy

Optical
The intenti Gaussian b mogeneity redistributi wider areas smaller are The total in in the lens m ld get even wo Institute of M ) we have dev tions for full describe the c ynchrotron mi l design and ion of these n beam intensity (see Fig. 1). ng incoming s and concen as (see Fig. 1 Assuming the width of the requested top-hat distribution is B. In the case of a loss-free, perfect optics, the total intensity I total will stay constant and the top-hat-intensity I top is calculated to be total 0 top . 2 The local focal length f(d) for a ray hitting the entrance aperture in a distance d from the optical axis, is calculated from the intensity distribution of the incoming beam I(d). The ray has to be redirected to a point in the distance a from the optical axis, so the integrated intensities under the Gaussian I total and under the top-hat function I top are equal for all d: The distance a is calculated by including (4) in (5): Let us assume a distance L of the imaging plane from the optics and the incoming rays to be parallel to the optical axis and the length of the optics itself is negligible compared to its distance to the sample plane. Considering the theorem of intersecting lines the local focal length f(d) is given by In Fig. 2 the resulting local focal length f is plotted over the distance d of the incoming ray from the optical axis. Based on these findings, the shape of the required refracting surface of the optics is calculated. For compound refractive lenses (CRLs) with biconcave parabolic lens surfaces the lens geometry can be described by with the minimum radius R of curvature of the parabola, the photon energy dependent decrement of the refractive index δ of the lens material and the focal length f [13]. Eq. (8) is a good approximation for a focal lengths which is large compared to the physical length of th the distanc tens of met timeters on In the c sulting refr surface can face has b perpendicu beam shapi The res optical axis number N o Fig. 3 The res to Fresnelremaining p ments. The ble structur Fresnel-len ous with v material th the intensit he lens [14]. F es between th ter range, whe nly. This limitation however can be overcome by forming K blocks (the three slices in Fig.  4(b)-4(d) form such a block) of a number of P = N/K different lens elements sliced in different ways instead of using N equal Fresnel-lens elements. In Fig. 3 the Fresnelelements (b) to (d) form such a block. The P different slices in such a block differ by the thickness of their innermost zone. The thickness v of the innermost zone of the original Fresnel-element is divided by the number P of different slices in one block. The thickness of the innermost structures of the P different lens elements is m·v/P with m∈ ∩ m≤P. As a consequence, the position of the points where the Fresnel-elements are very thin varies within each block. This leads to a much more homogeneous intensity distribution in the detector plane.

Lens layout parameters and fabrication
The optics are produced via deep X-ray lithography [19,20] at the KIT synchrotron source. The lens material was chosen to be SU-8 [21], an epoxy based negative resist (type mr-X-50 from mrt, Berlin), processed on a silicon wafer of 525 µm thickness. This lens material has proven to possess a long-term radiation stability at different synchrotron radiation applications up to a deposited dose of 2 MJ/cm 3 [22] and likely above.
The first layout (see Fig. 4) of this type of beam shaping optics was designed and realized for the P05 imaging beamline operated by HZG at the storage ring at PETRA III (DESY, Hamburg Germany) [23,24]. The instrument is optimized for in situ experiments in particular to allow for extended sample environments. The field of view (FoV) however is limited due to the nature of the undulator source: The beam height in vertical direction lies in the range of 1.6 mm to 2 mm FWHM at the sample position while the horizontal beam size is around 7 mm. This is an inherent property of undulator sources and not ideal for full field imaging like radiography and tomography since for many sample systems a larger FoV would be beneficial [23]. Until now computed tomography (CT) images of large samples are scanned with several height steps and the tomograms are stacked afterwards. This is very time consuming when it comes to scan time and data processing time and often leads to artefacts in the reconstructed, stitched volume. In particular for in situ experiments stacking is of course not an option.
To overcome this limitation and allow for scanning larger sample volumes by in situ experiments a novel type of beam enlarging optics was developed. The optics was designed to operate at a photon energy of 24 keV, a source distance of 60 m, and a working distance of 30 m. As the FWHM of the incoming beam was 1.6 mm, a physical entrance aperture of 1.4 mm was chosen. The resulting layout (see Fig. 4) had N = 20 elements in blocks of P = 5 different slices, each with M-1 = 15 segments. The air gap between neighbor elements was chosen to be 150 µm, the minimum thickness of the elements was w = 6 µm, the minimum technically achievable edge rounding radius was 0.5 µm. A proof-of-concept experiment was performed with lens structures of 0.8 mm height. The structures' height was limited to 800 µm by the LIGA fabrication process. For this experiment, two structures were aligned face to face to reach 1.6 mm working width. To cover the full beam width, the structures presented here are going to be stacked and prealigned in the laboratory to cover the full beam width.

Experimental results
A first optical characterization of the optics at the imaging beamline P05 at the storage ring PETRA III, aimed to measure the beam enlargement, the intensity distribution at the detector position as well as the suitability for computed tomography. Figure 5 shows a projection image of the beam with the beam shaping optics installed in the center. The original beam profile (white areas in Fig. 5(a)) is widened to a vertical size of 5.6 mm (grey area in the center part of Fig. 5(a)) by the beam shaping optics as revealed by the intensity profiles ( Fig. 5(b)). For these first tests the optics was placed at a distance of 20 m with respect to the sample. Therefore, the expected widening up to 7 mm could not be realized. The sample to detector distance was 15 mm. In this setup the beam hitting the sample can be assumed to be nearly parallel due to the large optics to sample distance of 20 m. So standard filtered back projection was used for tomographic reconstruction. The horizontal width of the enlarged beam area is 1.6 mm, which results from two beam shaping elements stacked together. Left and right to the enlarged beam one can still recognize the original Gaussian beam with 1.35 mm FWHM. The black stripes in between are due to the two absorbing substrates. In Fig. 5(b) the intensity profile of the enlarged beam (red) is shown in comparison to the nearly Gaussian beam profile (blue). Although the intensity profile is still not perfectly flat, the enlargement of the beam can be seen clearly. The standard deviation of the intensity of the shaped beam profile was about 17 percent of the average intensity. The slight asymmetry of the shaped beam most probably results from the not perfectly Gaussian-shaped incoming beam. The calculated efficiency of the optics was 83%, being the ratio of the integrated intensity of the enlarged beam profile with respect to the integrated intensity of the original Gaussian beam profile. The measured efficiency is 63%. The difference might result from a nonperfect alignment of the micro prisms with respect to the incoming beam. mance of the hin test sampl a CdWO 4 scin n effective pix ental setup is f the CT measurem aping optics to w Distances were: so bility and per mography sca we could not works well an ee Fig. 7(a) larging optics acquisition sch nce on the im geneity of the e is not blurre image resolut of view acqui econstructed s ne for the sam Fig. 7(b) to 7 e spine.
gnienrecennges n spine was at a photon optical mag-3.9 µm line ge in Fig. 6