Comparison of image properties in full-field phase X-ray microscopes based on grating interferometry and Zernike's phase contrast optics

The high penetrating power of X-rays enables us to probe inside of objects non-destructively. One of the most useful applications of this nature is computed tomography (CT), which can visualize three-dimensional internal structures quantitatively by measuring X-ray absorption. The spatial resolution achieved using X-ray imaging techniques has been improved thanks to the development of microscope objective devices working in the X-ray range.^1–5 Although X-ray microscopes can easily achieve 50 nm resolution or higher nowadays, it is difficult to resolve fine structures in soft materials with such a resolution. For example, the absorption of 8-keV X-rays by polyimide 50 nm in thickness is only 0.004%. By contrast, the effect of the X-ray phase shift in soft materials is about three orders of magnitude greater than that of absorption. This implies that contrast enhancement by utilizing the phase shift is promising for high resolution X-ray microscopy applicable to soft materials.

The phase shift can be converted to a detectable intensity change by a phase contrast method. Zernike's phase contrast (ZPC)⁶ is one of the most standard methods used in microscopy. ZPC employs a phase modulator in the back focal plane of the microscope objective that acts only on the wave scattered (or unscattered) by the sample. In the case that the phase shift is much smaller than unity (and the spatial phase variation is mild), the intensity change is proportional to the phase shift.⁷ The phase modulator should provide a phase shift of π/2 or –π/2 to maximize the performance because the phase difference between the scattered and un-scattered waves is π/2. In the X-ray region, since the first development by Schmahl et al.,⁸ ZPC microscopy has been widely applied to the visualization of transparent objects.^9–14 However, in general ZPC, halos, which are the contrast enhancement surrounding large features of the sample, and shade-off, which is the intensity reduction inside the sample features, appear and destroy the quantitativeness (proportionality to the phase shift). These originate from the finite spatial spread of the un-scattered wave and/or the phase modulator in the back focal plane, that is, the image contrast becomes complicated by the loss of phase contrast generation in the low spatial frequency region. This is a practical issue in current ZPC systems, although some software-^7,15 or hardware-based approaches^16–18 to deal with this issue have been proposed.

Two-beam interferometry, where a reference wave is generated and interference with the wave passing through a sample is observed, is another approach to measure phase shifts quantitatively. X-ray imaging microscopes in combination with a two-beam interferometer using various optical devices were reported.¹⁹ Although they provide quantitative phase imaging with a high spatial resolution, strict demands on spatial coherency, requirements of high mechanical stability, and/or generation of too-fine interference fringes limit their practical applications.

Grating interferometry (GI),²⁰ which utilizes self-image generation via the Talbot effect (or the self-imaging effect), is also used as a quantitative method for phase shift measurements. In the Talbot interferometer, which is the standard GI system, scattered waves at different sample positions (but close to the system resolution) interfere, and the derivative of the phase shift can be measured. GI has a great advantage in that an incoherent (laboratory) source can be used by introducing a source grating, which filters out a part of X-rays so that the self-imaging effect does not smear out.²¹ GI is also compatible with full-field X-ray microscopes^22,23 operated with synchrotron radiation. Furthermore, a combination of an X-ray microscope system based on an incoherent X-ray source and a GI system (Lau interferometer²⁴) is possible.²⁵ 

Following Ref. 25, we are aiming at realizing a phase CT microscope system by installing a Lau interferometer in a commercially available X-ray microscope, Xradia 800 Ultra (Carl Zeiss X-ray Microscopy, Inc., Pleasanton, CA, USA), which is already equipped with a ZPC system. Preliminary results have been reported elsewhere.²⁶ In this study, the performances of the GI system and the ZPC system are compared in terms of resolution, phase sensitivity, and quantitativeness.

The Xradia 800 Ultra is designed for Cu-Kα X-rays (8.04 keV). The base components used in absorption-contrast (ABS) observation are an X-ray source (1.2 kW, Cu rotating anode target), a capillary condenser that creates a hollow cone illumination, a Fresnel zone plate (FZP) as a microscope objective, and an imaging detector with 1024 × 1024 pixels. The system is switchable between two magnification modes by exchanging FZPs: large field-of-view (LFOV) mode with 10-fold X-ray magnification (64 nm pixel size at the sample, 65 μm field of view) and high-resolution (HRES) mode with 40-fold X-ray magnification (16 nm pixel size, 16 μm field of view). A ZPC system¹⁴ is provided for both modes by the supplier. A GI system was installed by adding transmission gratings also for both modes. Thus, the developed microscope has six modes (LFOV-ABS, LFOV-ZPC, LFOV-GI, HRES-ABS, HRES-ZPC, and HRES-GI). Figure 1 shows a schematic of the optical layout of the ZPC and GI systems.

When the microscope is switched from the ABS (and GI) system to the ZPC system, the condenser is replaced with one dedicated for the ZPC system that provides a hollow cone illumination narrower than that for the ABS system. A phase ring providing 3π/2 phase shift is inserted in the back focal plane of FZP. This produces a negative phase effect that decreases the intensity for phase advance. The X-ray absorption by the phase ring is about 60%, which makes the image contrast higher because only the unscattered wave is attenuated.

The GI system consists of an absorption grating (G0) and a π/2 phase grating (G1). Two G1 gratings designed for the LFOV mode and the HRES mode are switchable, while a common G0 is used only by changing its position depending on mode selection. The image of G0 (G0′) formed by the FZP works as an effective source grating for a Lau interferometer. Consequently, a self-image of G1 is formed and resolved by the imaging detector with a visibility of about 0.6. More details of the design and layout of the gratings were described previously.²⁶ In the GI system, a phase-stepping (or fringe-scanning) measurement²⁷ is performed by acquiring a self-image at every step of a transverse sub-period movement of one of the gratings. As a result, a “twin phase image,” which is a superposition of two sample images of opposite contrast shifted relative to each other, is obtained.²⁸ The shift is caused by the diffraction at G1, that is, each image is formed by the interference between the +1st and the 0th order (or the −1st and the 0th order) of diffraction. The values in the un-overlapped area of the twin phase image represent the phase shift by the sample. The optics of two-beam interferometry are established in the area because the sample is located only in the beam path of the +1st order (or the −1st order) diffraction and the 0th order diffraction works as an empty reference beam. Note that in normal GI, the shift in the twin phase image is smaller than the system spatial resolution, and thus, a differential phase image is observed. Owing to the large distance between G1 and the imaging detector in the presented optical configuration, the resultant image changes to the twin phase image. The twin image cannot be used directly, in particular when the sample is larger than the shift in the twin image. Therefore, retrieval of a single phase image has been reported by a deconvolution process, although the problem of deconvolution artifacts remains unsolved.²⁹ The shift in the twin image could be made larger by introducing narrower pitch gratings (both G0 and G1); however, it would be challenging to fabricate such gratings.

The spatial resolution was investigated using resolution test charts made of gold and polymer (Carl Zeiss X-ray Microscopy, Pleasanton, CA, USA). Each chart has a Siemens star pattern and a logarithmic ruler pattern consisting of lines and spaces with decreasing half-pitch values down to 50 nm. Figure 2 shows images of the gold star pattern (nominal thickness: 700 nm). In the ZPC image, contrast enhancement is observed against the ABS image. The resultant image from the GI system shows the twin feature. In all the images, the 50 nm line and the space pattern can be resolved in all directions. To investigate resolution quantitatively, the Fourier analysis^5,28 of the logarithmic ruler pattern was performed. First, intensity profiles along the ruler pattern were extracted (averaged over 8-pixel-wide for the LFOV mode and 32-pixel wide for the HRES mode) from the images obtained using the six modes of the microscope (Fig. 3). For the GI images, the un-overlapped region in the twin phase image was selected for this purpose. Then, intensity profiles of an empty area of the same length were also obtained. Finally, power spectra (denoised using weighted neighbor averages 10 point wide) of the ruler pattern and the empty area were plotted together against the spatial period measured in half pitch, as shown in Fig. 4. The spatial half period where the power spectrum of the ruler pattern reduces to that of the empty area (red dashed-line) was determined as the spatial resolution limit. This result shows that the spatial resolutions as specified by the X-ray microscope manufacturer are attained for all modes (blue vertical lines), that is, 50 nm for the HRES mode and 150 nm for the LFOV mode (in half period). The 700-nm-thick gold pattern causes 24% absorption and a 1.35 rad phase shift for the Cu-Kα X-ray (8.04 keV). Since the images by the ZPC system in Fig. 4 involve the contribution of absorption, the spatial resolution was confirmed by a polymer ruler pattern, which is typically used as a mold for the gold pattern fabrication (hence the pattern is negative). The absorption and phase shift by the polymer ruler pattern are 0.05% and 0.12 rad (in assumption of poly-methyl methacrylate 700 nm in thickness), respectively. Figure 5 shows images and power spectra obtained for the ZPC system in the same manner as the gold pattern measurements. This result shows that the ZPC system achieves the desired spatial resolution for phase objects as well.

The sensitivity of the GI and ZPC systems was compared by the analysis of the signal-to-noise ratio (SNR) as an indicator of the detectability of phase objects. Images of polystyrene spheres (Polybead^® Polystyrene 2.0, 3.0, and 4.5 μm Microspheres, Polyscience, Inc.) with measured diameters of 1.80 μm, 2.93 μm, and 4.36 μm, whose theoretical maximum absorption/phase shift for Cu-Kα is 0.08%/0.267 rad, 0.13%/0.434 rad, and 0.19%/0.646 rad, respectively, were evaluated. The actual diameters of the spheres were measured from the HRES-GI images. Figures 6 and 7 show images of the spheres and line profiles obtained by the LFOV mode and the HRES mode, respectively. The ZPC images exhibit the halo and shade-off artifacts, whereas the GI images exhibit the twin image effect. The vertical profiles across the center of the spheres were obtained by averaging over about 0.5-μm areas (8 pixels for the LFOV mode and 32 pixels for the HRES mode) horizontally, as indicated by black boxes in the sphere images. For the calculation of SNR, the signal was determined from the maximum and minimum values in the profiles, that is, the contrast enhancement as the difference between maximum and minimum (average of two peaks and two valleys) at the edge of the sphere for ZPC and the maximum phase shift at the center of the sphere for the GI signal. Note that in HRES-GI of Fig. 7(a), a horizontal profile was used because of the overlap, and the average of the absolute values of the maximum and minimum phase shift was used as a signal. Noise was determined as the standard deviation in the empty regions indicated by white boxes in the images. Consequently, the SNRs evaluated are listed in Table I, which demonstrates higher SNRs for the GI system than the ZPC system for the sphere samples. The difference between the GI and ZPC systems is more pronounced for the larger spheres and LFOV mode than for the smaller spheres and HRES mode.

As seen in the ZPC images in Figs. 6 and 7, the values at the center of the spheres observed by the ZPC system are nearly equal to the baseline. This implies that the proportionality to the phase shift is completely lost. When the ZPC system is used for the tomographic measurement, only the sample outline is reconstructed due to the halo and shade-off artifacts. Note that these effects depend on the size and shape of the sample since the ZPC artifacts are caused by suppression of low spatial frequencies (i.e., smaller samples or features exhibit weaker artifacts). However, contrast in a ZPC image would be enhanced for a structure whose size is close to the thickness of the halo. This effect is illustrated by the considerable enhancement in the ZPC power spectra shown in Fig. 4, and the enhanced contrast of small dust particles is seen between spheres [e.g., in Fig. 6(b)]. By contrast, the phase shift measured by the GI system is consistent with the theoretical values shown as the red dashed lines in Figs. 6 and 7 [except for Fig. 7(a)], which were calculated using the refractive index of polystyrene, 1–3.636 × 10⁻⁶, for the Cu-Kα X-ray. When a reliable procedure is developed for producing a single phase image from the twin phase image, phase tomography is attainable to visualize inner structures as a map of the refractive index, which is approximately proportional to the electron density or mass density.

A full-field X-ray microscope having two different phase-contrast modes has been implemented with a laboratory X-ray source. In addition to the ZPC system that highlights boundary features, the GI system installed in the microscope has added a function for the quantitative phase measurement. It was shown that both the ZPC and GI systems preserve the original spatial resolution. The signal-to-noise ratios of images obtained from identical polymer spheres show that the GI system has superior sensitivity, particularly in the LFOV mode, to the ZPC system. Quantitativeness in the phase measurements by the GI system was also demonstrated. However, the GI system yields a twin phase image, which needs to be converted to a single phase image for phase tomography. After overcoming this issue by developing sophisticated (e.g., iterative) deconvolution procedures, the GI system can be applied to phase tomography in near future.

This work was supported by JST ERATO (Grant No. JPMJER1403).