A coded aperture microscope for X-ray fluorescence full-field imaging

First results from a 10 µm MURA coded aperture optic for a full-field X-ray fluorescence microscope are presented.


Introduction
Current X-ray microprobe beamlines raster-scan the sample through a focused X-ray beam, and use an energy-resolving point detector to separate the contributions of the various elements at each point on the sample. Although this method has many advantages, it suffers from the need to mechanically move the sample through the beam, which is inevitably rather slow, particularly if the requirement is for 3D tomographic imaging, since this requires two translational scans for each of many rotational positions. An instrument capable of recording an image directly eliminates two of those dimensions, and can replace the rotation with a single translation for tomography (Takeuchi et al. 2009(Takeuchi et al. , 2010. A full-field microscope should collect fluorescence from all points on the sample simultaneously and project them onto an imaging detector. To image elemental contributions we need: (i) An achromatic imaging optical element to magnify the fluorescence signal to match the desired resolution to the detector pixel size.
(ii) A detector which collects energy spectra from each detector pixel. ISSN 1600-5775 In this paper we demonstrate an achromatic imaging system, the coded aperture array. The hyperspectral imaging detector is also under development at Brookhaven National Laboratory, but is the subject of another work.

Modified uniformly redundant arrays
The pinhole camera is the oldest and simplest imaging optic. It suffers from the inverse relationship between light collection efficiency and spatial resolution. The coded aperture array was developed as a way to break that relationship, by using arrays of pinholes in known locations. Even though the resulting image I(x, y) is an overlay of many weak images, it is in principle possible to reconstitute the image mathematically. This became realistic as the era of digital computers arrived.
When the photons generated by an object O(x, y) propagate through the coded aperture mask of binary function M(x, y), the resulting image projected onto the detector is I(x,y), Iðx; yÞ ¼ Oðx; yÞ Mðx; yÞ; with denoting a convolution. Various forms of coded aperture arrays have been demonstrated, with perhaps the most successful being the modified uniformly redundant array (MURA) proposed by Gottesman & Fenimore (1989). It has the advantage of having both high efficiency (50% open area) and a perfect system point spread function (SPSF). This means that the convolution of the MURA mask M(x, y) with its anti-mask H(x, y) is a perfect delta function, Mðx; yÞ Hðx; yÞ ¼ : A MURA mask M(x,y) of order p, a prime number, and its anti-mask H(x, y) are square lattices of size p Â p, with x and y varying from 0 to p À 1 and are defined as 1; if x and y are quadratic residues modulo p; 1; if neither x or y are quadratic residues modulo p; 0; otherwise: The retrieved object is then obtained from the detected image on the detector as O 0 ðx; yÞ ¼ Iðx; yÞ Hðx; yÞ: For this work, we chose to construct MURA masks with a unit pinhole of 10 mm Â 10 mm square, and designed arrays of order 19, 37 and 73. For a given pinhole size, the higher the order of the mask, the bigger the field of view of the system. Fig. 1(a) shows the pattern for order 73. It is usual to tile such structures to increase its useful field of view. Shown in Fig. 1 is the layout of the typical 2 Â 2 tiling that we sent for manufacturing.

Optic fabrication
Looking at the pattern of Fig. 1, it is obvious that the MURA mask is not self-supporting. Previous attempts to use such apertures have been forced to use self-supporting variants. Typically they were made by drilling or etching small holes in sheet metal such that no two holes touched (so-called NTHT structures). Although these experiments have been proven successful (Kulow et al., 2020;Haboub et al., 2014), this involved a significant loss of solid angle, with the open area reducing to at best 25%. We wanted to achieve the theoretical maximum open area of about 50%, so needed a supported structure. A thin layer of silicon nitride is ideally suited for such a support, and this is what we implemented. The optics were fabricated using the LIGA technique (Guckel et al., 1991), at the X-ray lithography facility at CAMD, in Baton Rouge, Louisiana, USA. We prepared lithography masks with all of the patterns listed above, plus other objects which might be of interest (single pinholes, slits and more). Silicon wafers were coated with a 1 mm-thick layer of silicon nitride. One side was patterned with squares matched to the array sizes, and the nitride etched away in those locations. An orientationdependent silicon etch removed the silicon to leave a thin nitride membrane window which is X-ray transparent. On the other side of the wafer, a seed layer of gold was deposited, followed by a deep lithography in a thick photoresist. Following development of the resist, gold was electroplated into the cavities remaining, forming the thick gold aperture structures. Finally the photoresist was removed and the seed layer etched away, leaving free-standing structures. Fig. 2 shows the finished wafer, and Fig. 3 shows electron micrographs of one of the structures thus formed.

Point source
Our first experiments used a microfocus X-ray generator (XRG) which was capable of providing a 10 mm focal spot from a molybdenum anode tube. We used the order 73 MURA to image that focal spot onto a Medipix detector. This detector  has a 256 Â 256 array of photon-counting pixels on a 55 mm pitch. It does not provide energy resolution, but can accept a high photon flux. The resulting image is shown in Fig. 4(a). Since the source is essentially a point source, the recorded image is a smeared shadow of the mask. It was easy to perform the reconstruction using total variation regularized least-squares deconvolution (Chan et al., 2011), and the result is shown in Fig. 4(b).

Extended source
We used the XFP beamline at NSLS-II (Asuru et al., 2019) to demonstrate that the image processing method would also work on extended and fluorescing samples. XFP can operate in a pink beam mode with a partially focused spot of roughly 2 mm Â 2 mm. The optics of the beamline were optimized for low-energy photons, mainly below 20 keV, with the majority of the beam power below 10 keV. We added a 1 mm-thick aluminium filter upstream of our setup to reduce the thermal load this beam would place on any sample. Fig. 5 shows the resultant calculated spectrum.
We chose a gold wire mesh as our sample. The mesh is nominally 25 mm wires woven into a 300 mm-pitch square mesh (Fig. 6). It was placed across a rectangular frame, such that the incident beam only illuminated the mesh and air. The distance d 1 between the object and the mask was 38 mm and     Calculated spectrum of the XFP pink beam with 1 mm-thick aluminium filter.

Figure 6
Optical micrograph of the gold wire mesh with 25 mm wires woven into a 300 mm-pitch square mesh.

Figure 2
The finished silicon wafer prepared using the LIGA technique at the X-ray lithography facility at CAMD. It holds MURA of order 19, 37 and 73 as well as other objects such as single pinholes and slits. the distance d 2 between the mask and the detector was 571 mm. We used the same Medipix detector as the one described in Section 3.1. Given the geometry of the mask and the setup, the theoretical resolution r is calculated to be 14.3 mm as with h the size of the mask pinhole, 10 mm in our case, and Pd the size of the detector pixel which is 55 mm. The first image had the mesh oriented with its wires horizontal and vertical. It was illuminated with a small beam, approximately 200 mm Â 200 mm. The raw data and reconstructed image are shown in Fig. 7. We observed approximately 22.4 mm wire width, which suggests that the actual resolution of the setup is less than 25 mm. The discrepancy in the wire width could easily come from uncertainty in the magnification which will be properly characterized in future measurements.
We then oriented the mesh so that the wires were at roughly 45 to the horizontal, and enlarged the illuminating beam to 600 mm Â 400 mm. The raw data and reconstruction are shown in Fig. 8. The contrast is reduced compared with the image with the smaller beam. We believe that this is due to the increased parasitic scattering from the larger beam, adding a uniform background to the data. This is probably a consequence of our decision to operate close to backscattering, rather than at 90 to the incident beam as is usually done for fluorescence measurements. Nevertheless, the image can be reconstructed successfully. Similarly to the point source, the images of the extended source [Figs. 7(b) and 8(b)] were reconstructed using total variation regularized least-squares deconvolution.

Conclusions
Using the LIGA technique, we fabricated a MURA of order 73 with 10 mm holes and 50% open area, providing the maximum possible throughput for such a system. Using this optic we could reconstruct part of a gold wire mesh of 25 mm wires on a 300 mm pitch. This suggests that we reach a resolution better than 25 mm. The theoretical resolution for our setup is 14.3 mm. In our future work we will carefully characterize the magnification of the system and upgrade our image processing methods as suggested by Kulow et al. (2020). We will also design and fabricate apertures which match more closely the needs of the intended research, and develop a hybrid pixel detector in which each pixel is a spectrometer capable of handling a high rate and providing high-quality spectra.   (a) Raw data on the 256 Â 256 pixels Medipix detector from XFP fluorescence measurement of the gold wire mesh. The beam measured 200 mm Â 200 mm and the mesh was oriented with its wires horizontal and vertical. (b) Retrieved image of the gold wire mesh obtained from using total variation least-squares deconvolution of the detector's raw data.