BL29XUL: High-resolution Imaging of a Nanostructure
Material by Focused X-ray Ptychography
Yukio Takahashi(Osaka Univ., RIKEN) and Nicolas Burdet (RIKEN)

Abstract
Coherent X-ray diffraction imaging (CXDI) is a lensless imaging technique based oncoherent diffraction and phase retrieval calculation, which can achieve a high spatial
resolution beyond that of conventional X-ray microscopes employing lenses. X-rayptychography is a method of CXDI for reconstructing extended objects, in which aprobe is scanned across the sample and the diffraction pattern is observed at each beam
position. The spatial resolution of CXDI is limited, in principle, only by the x-ray
wavelength and the largest scattering angle recorded. The use of highly focused
incident X-ray beams is effective for collecting high angle diffraction data at a highsignal-to-noise ratio. The participants will measure multiple coherent X-ray diffraction
pattern from a nanostructure material using high-intense X-rays focused by
Kirkpatrick-Baez (KB) mirrors. Finally, we will demonstrate an image reconstruction
from the diffraction patterns using phase retrieval calculation. During the practicalcourse the participants will learn how a coherent beam is produced from incoherent
radiation, thus how to focus it with KB mirrors and finally how to detect and invert thecoherent diffraction radiation to produce a quantitative image of the sample.
Practice
1. Introduction of beamline
The beam line BL29XUL equips a SPring-8 standard in-vacuum undulator, transportchannel as long as 1 km and four tandem experimental stations. Figure 1 shows theoverall view of BL29XUL. The first experimental hutch (EH1) is placed at 52 m fromthe source, the second (EH2) is 60.2 m, the third (EH3) is 98 m, and the fourth (EH4)
is 987 m. BL29XUL produces X-ray over a wide range of energy range (4.9- 18.7 keV )thanks to both the variable gap of the in-vacuum undulator and the scanning angle ofthe Si(111) monochromator. The energy resolution is approximately 1.3×10-4. In thepractice, we will use 6.500keV monochromatic X-ray beam (wavelength λ = 0.1907
nm). In EH1, a slit is located, which produces virtual light source. In EH3, KB mirrors,a sample chamber, and CCD are located as shown in Fig. 3. In order to illuminate fullcoherent X-rays to the KB mirrors, the slit size is adjusted to 10×10 µm2. The X-ray
beam is transported through the vacuum pipe to EH3.

Fig. 1 Overall view of BL29XUL.

Fig. 2 Photograph of apparatus for coherent X-ray diffraction measurements in EH3of BL29XUL

2. Alignment of the KB mirrors
KB mirrors, which consist of two elliptical mirrors as shown in Fig. 3, are an X-ray
focusing device. Table 1 shows a summary of the parameters of the KB mirrors for thepractice. The KB mirrors can produce the focused X-ray beam of ~500×500 nm2 insize at 6.5 keV. In the alignment of the KB mirrors, the glancing angles are precisely
adjusted by the combined system of flexure hinges and a linear actuator. The intensity
profile on the focal plane is measured by the wire scanning method.

TABLE 1. Parameters of the KB mirrors
First mirror
Second mirror
Central glancing angle (mrad)
3.5
3.15315284
Acceptance width (µm)
Focal length (mm)1000895

Fig. 3 Schematic illustration of KB mirrors (H. Mimura et al., JJAP 44, L539-L542(2005), Fig. 3, ©2005 The Japan Society of Applied Physics)

3. Observation of the sample by optical microscope
The sample is a test object with artificial nanostructures. Figure 4 shows the SEM
image of the sample. The 200-nm-thick Pt film is deposited on the 1-µm-thick SiN
membrane chip. The SPring-8 logo is fabricated in the Pt film on the membrane using
a focused ion beam. In the practice, the test object is observed by optical microscope,in order to measure the distance between the logo and the edge of the window of themembrane.

Fig. 4 Scanning electron microscope image of the sample.
4. Measurement of ptychographic diffraction patterns of the sample
The sample is mounted on the stage inside the chamber. By monitoring the X-ray
intensities penetrating the sample, the sample is aligned on the focal position. Figure 5
shows the schematic layout of the coherent diffraction pattern measurement of thesample. The sample is illuminated in 10×10 overlapping fields of view that is spacedby 300 nm. The sample position is precisely controlled by using piezo stages withcapacitive sensors. Coherent forward diffraction patterns are recorded using an X-ray
direct-detection CCD. The X-ray exposure time at each position is ∼1 s.

Fig.5 Schematic illustraion of foucsed X-ray ptychography.

5. Data analysis
Finally, we will demonstrate an image reconstruction from the collected diffraction
patterns using a phase retrieval algorithm called the Ptychographic Iterative Engine(PIE) which sequentially generates sub-images that agree with the measurements. Itsprocedure for data analysis is detailed here:
1. A current object transmission function from a shifted position ‫ܚ‬௝ becomes after
multiplication with a localized probe function:
Then, this complex function evolves (or propagates) to the far field by use of acomputational FFT:
(1)
2. Next, the modulus constraint is applied while preserving the computed phase:(2)
3. The inverse Fourier transform ofturn used to estimate a new object:updates the current view which is in(3)4. The above steps are repeated for each of the j diversity images all over the positionsrj to update for the object field. Completion is realized after n iterations, with one
iteration being interpreted as one pass over all scan positions (The PIE scheme issummarized in Fig. 6 ).
The overlap constraint between positions implies a multiple update of the different
field realizations within a single iteration, and thus dramatically increases the successof converging efficiently to a unique solution. Obviously, the relative strength of theoverlapping constrained illumination is the ingredient that favors the convergence ofthe calculation.

Fig.6 Schematic representation of Ptychographic Iterative Engine.