Towards multi-order hard X-ray imaging with multilayer zone plates

Multilayer zone plates can be used for holographic imaging without an order-sorting aperture.


Description of datasets
The two dataset files, lineaperture.h5 and holosiemens.h5, contain the raw data (central module of Pilatus 300k detector only) in HDF 5 format. First we describe the HDF 5 layout and metadata structure; in the following subsections, the respective experiments are described and all relevant parameters are stated. In section 2, the holo-STXM experiment and the analysis code is described. See Fig. 1 for a sketch of the experiments and relevant parameters.

File format
Within the HDF 5 container, the data is stored as matrices. Detector data is saved as integer values (unsigned integer, 16 bit) representing single photon counts per pixel; motor positions are encoded as floating point numbers in metre. For details, cf. Tab. 1. Fig. 2 visualises the layout of the three-and four-dimensional data as 2D images taken at 1D and 2D sample positions.

Tungsten line apertures in holography
The dataset lineaperture.h5 contains raw Pilatus 300k images (central module), taken during a horizontal scan of a vertical W line aperture test pattern. The sample was mounted on a piezo stage and scanned by 100 µm in 200 steps, with an accumulation time of 100 ms per point. Encoder values of the piezo axis are also available in the file. The experimental setup is similar to that of Fig. 3 in the main paper, but with the sample placed 1 mm in the defocus of the +1 st focusing order of the MZP, and in a defocus of 2 mm of the coexistent -1 st order.
If the images are played as a video (see file lineaperture.mp4), the vertical lines of the test sample move from the right side to the left side. As can be seen, holographic images on the right part of the detector are much wider and faster than those on the left part. This is attributed to the different focusing orders: Due to a slight detuning of the MZP angles, the +1 st order produces holographic images on the right side of the detector, and -1 st order produces images on the left side. The corresponding virtual pixel sizes are ∆x + ≈ 32 nm, ∆x − ≈ 64 nm, which can be calculated by the Fresnel scaling theorem with magnifications for z 1,+ = 1 mm, z 1,− = 2 mm, z 2 = 5.1 m and a Pilatus pixel size of 172 µm. These pixel sizes are in agreement with the velocity of the holographic images on the detector and the actual real-space movement of the piezo. From this comparison it is concluded that the holographic images in fact are due to the respective focusing orders of the MZP.

Video file of this scan
The file lineaperture.mp4 contains a video of detector images taken during a horizontal scan of the W line aperture sample ("barcode" of several apertures with varying width and distance). The intensity is shown on a logarithmic scale; for the colour bar, cf. Fig. 2. The +1 st and -1 st diffraction orders of the MZP fill the greenish disk, approx. 200 pixel in diameter. In the centre, the primary beam has been blocked by beam stops. The line apertures are scanned horizontally from right to left, in a defocus of 1 mm downstream of the +1 st order focal plane, and accordingly 2 mm downstrean of the -1 st order virtual focus. The corresponding pixel sizes are ∆x + = 64 nm and ∆x − = 32 nm; the step size of the scan is 500 nm with an illumination time of 100 ms. The video is encoded at 25 fps, so it plays at 2.5× nominal speed. In the video, vertical patterns move from the right to the left. These are holographic images from the line aperture. Note that due to a detuning of the MZP, the right hand side (RHS) of the detector is mainly illuminated by the +1 st order, while the left hand side (LHS) is mainly illuminated by the -1 st order of the MZP. As can be seen, the lines in the different parts have different sizes and velocities. An analysis shows on the RHS, the lines are twice as large and twice as fast. The hologram sizes and velocities are in agreement with the two pixel sizes.

Siemens star in holo-STXM
The second dataset, stored in file holosiemens.h5, contains the Pilatus images of a STXM scan. A Siemens star test pattern (500 nm Au on a Si 3 N 4 membrane) has been scanned in two dimensions, with a scan range of 4 × 4 µm 2 and 160 × 160 steps in both directions. The accumulation time was 10 ms, at a constant movement of the horizontal piezo axis (continuous scan). The samples was placed close to the focal plane of the +1 st MZP order, as determined by an optical microscope. The demagnified pixel size of the -1 st order is 32 nm. Also contributions of the ±3 rd focusing order can be identified, but with a very weak signal-to-noise ratio. This dataset can be described as a four dimensional matrix I(x,y; X,Y ) with sample position (x,y) and detector pixels (X,Y ). In the usual STXM sense, the horizontal centre-of-mass I h (x,y) as a function of sample position is defined as the first moment over the detector, or here over a region of interest (ROI): I h (x,y) = X,Y ∈ROI X · I(x,y; X,Y ) X,Y ∈ROI I(x,y; X,Y ) In focal-plane STXM, this is related to the differential phase contrast I h (x,y) ∝ ∂ϕ/∂ x of the sample. We found that for specific ROIs, the images I h (x,y) show the typical behaviour with horizontal edge enhancement and the absence of vertical edges. Other ROIs, on the other hand, produce holographic images; the field of view moves if the ROI is changed, with a pixel "velocity" according to the demagnified pixel size of the -1 st order. In the next section, we describe an analysis programme to calculate the images of Fig. 5 (c,d) in the main paper, using dataset holosiemens.h5.

Description of holo-STXM programme
To visualise the dataset holosiemens.h5 in the described holographic STXM mode, the source codes holosiemens.m (Matlab) and holosiemens.c (ANSI C, needs HDF 5 library) are available. The Matlab script consists of three cells: 1. read in the HDF 5 data set (needs approx. 10 GB of memory); 2. select a region-of-interest on the detector; seven ROIs according to the green (0) and the orange ROIs (1-6) in Fig. 3 are pre-defined; 3. calculate and show the corresponding STXM I h (x,y) image.
With the ROI 0 selected, the STXM image resembles usual differential phase contrast features. Horizontal edges of the Siemens star pattern show alternating positive and negative values; vertical edges remain invisible. Regions of constant phase shift share a common gray value.
But ROIs 1. . . 6 look qualitatively different. Instead of edge enhancement, a holographic image appears. Furthermore, the different ROIs show a different view of the Siemens star. From the feature size (smallest lines and stripes are 50 nm apart), the demagnified pixel size of ≈ 32 nm can be estimated. This correspond to a magnification factor M ≈ 5100, and a defocus distance of z 1 = 1 mm, in full agreement to the hypothesis of a diverging -1 st order illumination by the MZP.
In addition to the Matlab routine, also an ANSI C code programme holosiemens.c is available. Comments how to compile and use the code are included. It has been developed for gcc 4, but should run with all common compilers. The HDF 5 library is needed.
See Fig. 1 for further physical and geometrical parameters of the experiment.

Summary
With this Supplemental Material to our paper entitled "Towards multi-order hard x-ray imaging with multilayer zone plates", experimental raw data of two holographic imaging experiments is made available. To inspire analysis by the holo-STXM method, an analysis code is included. We shortly list the published files: lineaperture 172 µm (square) magnification: ~ 5400 of -1 st order in z 1-= 2f pixel size: ~ 31.7 nm continuous scan