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We report on the experimental demonstration of a hard x-ray microscopy scheme achieving absorption and phase contrast imaging with a standard laboratory source. The x-ray optical system features two crossed planar waveguides coupled to the primary source. The dual waveguide acts as a secondary micron-sized source, enabling high imaging resolution. Both scanning and full-field imaging modes are demonstrated with the same experimental system, with a resolution of about 2 μm in scanning mode. Examples of absorption, differential phase and retrieved phase depth of thin metal grids and glass micro-spheres are reported as proof of concept of the technique.
© 2014 Optical Society of America
1. Introduction
The production and characterization of hard x-ray nano-beams is opening the way to unprecedented characterization studies in nano and micro technology and nano imaging of biomedical interest [1]. The use of hard x-rays is beneficial where both high resolution and high penetration depths are required. Moreover with x-rays, specimens can be imaged in air, which is very advantageous when imaging in vivo or when a specific sample environment (pressure, temperature etc.) is needed.
Instrumentation advances have enabled the production of smaller and smaller beams of high energy x-rays with a variety of methods [1], which in turn pushed hard x-ray microscopy development and applications at modern synchrotrons [2–5]. Importantly, many interaction mechanisms of x-rays with matter can be simultaneously exploited to obtain imaging contrast. Therefore, the combination of nano and micro focusing with the ability to perform multimodality characterizations is enabling cutting edge results in many multidisciplinary fields of science [6–8].
Synchrotron-based hard x-ray microscopy is built upon earlier advances in soft x-ray microscopy and micro-tomography, enabled by the use of high resolution Fresnel zone plates [9–13] with high efficiency in the soft x-ray spectral range. Synchrotron applications, though impressive, are generally limited by beamline access, high operating costs and the centralised locations of the facilities. Therefore, while synchrotrons are absolutely crucial in establishing new investigation methods, approaches to high resolution x-ray imaging with conventional x-ray sources are necessary as well, to boost the availability and outreach of such techniques.
Pioneering works in x-ray phase contrast imaging with laboratory sources [14–16] demonstrated that by having a sufficiently small x-ray source, with a suitable combination of detectors and sample geometry, high resolution microscopy is absolutely feasible in a laboratory setting. No other optical elements were involved in those studies, thus realizing free space propagation phase contrast imaging. Subsequently other techniques involving the use of x-ray optical elements such as crystals, mirrors or gratings (see e.g. [17–20]) were also implemented with laboratory sources. Those techniques realized absorption, phase and scatter imaging contrast, albeit with moderate resolution.
More recently laboratory-based x-ray microscopes have been realized using microfocus x-ray sources and Fresnel zone plates [21] or specially designed x-ray sources [22]. Also, one-dimensional (1D) phase contrast microscopy using an x-ray waveguide as secondary source, was demonstrated [23].
In this paper we report on the experimental realization of two-dimensional (2D) hard x-ray absorption and phase contrast microscopy, based on a laboratory source equipped with x-ray waveguides (WGs). The WGs are aligned downstream of the primary source, as shown in Fig. 1, realizing a secondary source with micron or sub-micron size. The use of the WGs has several advantages:
- It does not require a specifically designed x-ray source, such as a micro-focus or the like.
- The size of the secondary source depends only on the size of the channel and not on the properties of the primary source [24]. This is the most attractive feature of a WG compared to other focusing optics such as mono or poly-capillaries and compound refractive lenses, for the use with laboratory x-ray sources.
- The secondary source is easily accessible (unlike the primary source that is located behind a beryllium window) therefore offering higher flexibility in adjusting the experimental geometry.
- For the reason above, both scanning and full field microscopy modes can be attained with the same setup, simply by changing the sample-to-WGs distance.
- The propagation of the x-rays along the waveguide provides effective coherence filtering [25].
- The beam from the WGs has a limited divergence and thereby it can be used for quantitative scanning phase imaging as described in the following.
Fig. 1 Schematic of the hard x-ray microscope (not to scale). The two crossed WGs, labeled WG1 and WG2 respectively are illuminated by the primary source. WGs and samples are placed in air while a vacuum tube (not shown) is placed between sample and detector to limit x-ray absorption and scattering by air. Two possible samples configurations are shown. In scanning mode the sample is placed very closed to the double WG to exploit the small beam size. In full-field mode the sample is placed farther away from the WGs and the geometrical magnififcation of the setup guarantees high resolution imaging.
The paper is organized as follows: in Sec. 2 the dual WG system is described and the experimental characterization of the x-ray microbeam is reported. In Sec. 3 the experimental results relative to scanning and full-field microscopy in absorption and phase contrast are shown and discussed. The sensitivity of the setup to phase contrast as well as the resolution issues are discussed. The conclusions are drawn in Sec. 4.
2. Micro-beam production with x-ray waveguides
An x-ray waveguide (WG) is an optical element able to confine x-ray beams to sub-micron size [25, 26]. A typical WG for x-rays consists of an air (or vacuum) channel enclosed with x-ray reflecting surfaces. The refractive index of all materials at x-ray wavelengths is usually written as n = 1 − δ + iβ where i is the imaginary unit and both δ and β depend on the x-ray wavelength. Given δ, β > 0, the real part of the refractive index of any material is less than unity, and thereby an effective confinement of x-rays can be performed in a vacuum channel by total external reflection [26].
In reflecting between the two surfaces, x-rays are subject to interference, which produces transverse standing waves inside the cavity [27]. Such standing wave excitations are known as the modes and are only attainable at certain discrete angles below the critical angle . In practice, due to its divergence and wavelength spread, the incoming beam will always excite a partially coherent superposition of modes [28]. On the other hand the propagation along the channel provides confinement and effective coherence filtering of the primary beam [25].
The scheme demonstrated herein uses two planar (1D) WGs aligned in a crossed configuration [29] to spatially confine x-rays in 2D to produce a secondary micron-sized source. The WGs are fabricated with silicon reflecting surfaces and an air gap.
The system schematic is shown in Fig. 1. The primary source of x-rays was a rotating copper anode x-ray generator (Rigaku FR-E+ SuperBright). Tube voltage was set to 45 kV, and tube current to 65 mA. In this way the spectrum of the produced x-rays contains an intense peak at a characteristic energy of 8.05 keV (wavelength λ ≈ 1.54 nm) of the the Kα transition superimposed to the broad bremsstrahlung up to 45 keV (corresponding to a minimum wavelength λ ≈ 0.028 nm). Due to technical reasons, the two WGs used had different widths, 0.5 μm and 2 μm for WG1 and WG2 respectively. The impact of the size difference is discussed later on. A silicon based Medipix 2 detector, with a pixel size of 55 μm, 256 × 256 pixels and chip thickness of 500 μm, was used to detect the x-rays.
The production of the microbeam is demonstrated via Fourier analysis of the far-field diffracted beam from the double WG, measured without the sample. The Fourier transform of the measured far-field intensity I(u) is the auto-correlation function of the field f (x) at the secondary source [29, 30]:
where the symbol ⊗ denotes the convolution product, ℱ the Fourier transform operation and the asterisk indicates complex conjugation. The picture of the diffracted x-ray beam at the detector, located at a distance of 130 cm from the exit of WG2, is shown in Fig. 2(a). The bright elongated spot is the beam from the dual WG, while the halo surrounding it is due to high energy bremsstrahlung photons being transmitted through the silicon cladding. Such halo constitutes a rather constant background (i.e. it does not change for small tilts of the WGs about the optic axis) and thus it has minimal influence on the measurement. The image is taken when both WGs are aligned along the optic axis.Fig. 2 (a) Image of the diffracted beam from the dual WG recorded at the detector position. Both WGs are aligned parallel to the optic axis. (b) Normalized modulus of the autocorrelation function obtained from the intensity in (a). (c) Normalized modulus of the autocorrelation function obtained when both WGs are misaligned (see text). (d) Line pro-files of the modulus of the autocorrelation function in the aligned case, along the horizontal (red) and vertical (black) direction. (e) Line profiles of the modulus of the autocorrelation function in the misaligned case, along the horizontal (red) and vertical (black) direction. (f) Far field spectrum measured with the Medipix2 detector with the waveguide (violet) and without it (blue). The spectra are normalized to their respective maximum value. A shift of the central energy of about 1 keV is observed.
Figure 2(b) shows the modulus of the autocorrelation function, calculated using Eq. (1) by fast Fourier transform (FFT) of Fig. 2(a). The exact shape of the autocorrelation function is connected in a non-trivial way to the shape of the field distribution f (x) [30]. Nonetheless |C(x)| is basically single-peaked with weak side lobes extending in the horizontal direction, caused by the relative larger size of WG2. Moreover the central lobe of |C(x)|, measured as the distance between the first minima on either side of the main peak in Fig. 2(d), is 1.1 μm and 4.4 μm in the vertical (WG1) and horizontal (WG2) direction respectively. These values are expected to be about double of the widths of f (x), which is in excellent agreement with the nominal size of the WGs used in the experiment.
A demonstration of the effective x-ray guiding due to multiple reflections in the WGs is the measurement of the modulus of the autocorrelation function when both WGs are misaligned. Such measurement is shown in Fig. 2(c), obtained when the WG1 and WG2 were tilted by 0.1° and 0.015° about the optic axis respectively. In this case clear side peaks appear in the modulus of the autocorrelation function, disconnected from the main peak (see line profile in Fig. 2(e)), implying that higher order modes are being efficiently excited within the WG [26] leading to a structured intensity distribution. This feature shows the WGs are not acting as simple apertures but a multiple x-ray reflection leading to beam confinement is taking place.
A further action of the WGs on the primary beam is noticeable on the x-ray spectrum. Panel (f) in Fig. 2 shows the intensity spectrum as measured by the Medipix2 detector [31]. The spectrum of the primary beam (in the absence of the WGs) is the blue line in the plot. The corresponding spectrum measured after the dual WGs is the violet line. Both spectra have been normalized to their respective maximum intensity for ease of comparison. While the average photon energy of the primary beam is centred around 8 keV as expected, the guided beam has an average energy of about 9 keV. This is the effect of absorption losses occurring in while the x-ray beam is multiple reflected at the interface air-silicon [28] which are higher for the lower energy photons. The WGs act as a high-pass filter, shifting the average energy of the exit beam. The information about the beam energy is important for the quantitative phase retrieval that is shown in the following.
3. Experimental results
The micro-beam may be used in scanning mode, as depicted in Fig. 1. The sample is placed close to the exit of WG2 and raster scanned across the beam in both directions. At each step an image is recorded on the detector and the absorption and the differential phase images of the sample can then be extracted by post-processing. The absorption image is obtained by considering the total transmitted intensity at each step, normalized by the corresponding value measured without the sample. In the scanning absorption mode the resolution is limited by the beam size at the sample position.
The differential phase is proportional to the refraction x-rays undergo when traversing the sample [32]. The refraction angle γx in the x direction is given by
where k = 2π/λ is the wave number, ϕ(x) is the sample induced phase shift as a function of x, Δx is the lateral deviation measured on the detector and z2 is the distance from the sample to detector. We have evaluated Δx = xc − x0 where x0 is the position of the beam in the absence of the sample and xc is the ”centre of intensity” of the measured beam at each position of the scanning sample: where Ii is the intensity measured at the pixel i and xi is the position of such pixel and the sum is extended over the total number of pixels N. A similar procedure is employed to extract the refraction angle γy in the vertical direction.Conversely, in full-field mode, the sample is placed further away from the WG2 exit to allow the beam to diverge and illuminate a large field of view (FOV) at the sample position. In this way the illuminated FOV can be captured in a single exposure. Shortcomings of this approach are that absorption and phase information are both present at the same time in the one image [15], and the resolution is usually worse than in scanning mode. On the other hand no scan is needed and the measurement is much faster and therefore less sensitive to mechanical and stability issues.
The proof of concept hard x-ray micrographies are shown in Figs. 3 and 4. Scanning measurement were taken with a distance WG2–sample z1 = 15 mm and total distance WG2–detector z1 + z2 = 130 cm and 100×100 data points with a step size of 1 μm in both directions. Full-field data were taken with z1 = 11.2 cm and z1 + z2 = 130 cm. The top part of Fig. 3 shows the measurements of a Ni grid (SPI G1000HS) with nominal thickness of 20 ± 3 μm, nominal period of 25 μm and bar width of 6 μm. A generic grid orientation has been chosen to avoid the special case (attainable only with a square or rectangular grid) of having the sample features parallel to the detector axes. The absorption image is shown in Fig. 3(a) while the refraction images γx and γy are reported in Fig. 3(b) and 3(c) respectively. The difference in the size of the WGs decreases the contrast in γx relative to γy. The beam size at the sample is approximately the same in x and y direction, and therefore the absorption image does not show significant distortion due to possible astigmatism. On the other hand the beam divergence is quite different in the two directions. This causes the sensitivity to the refraction shift to be higher in the direction where the WG with smaller gap is diffracting.
Fig. 3 Experimental results relative to Ni mesh and glass micro-spheres. (a) Absorption image of the Ni mesh. (b) Refraction image γx. (c) Refraction image γy. (d) Unweighted phase map of the Ni mesh.(e) Retrieved projected thickness of the mesh, using the data in (d). (f) Phase map calculated using the weighting operation. (g) Line profiles along the red dashed line marked in (e). (h) Absorption image of the glass micro-spheres. (i) Calculated phase shift of the micro-spheres.
Fig. 4 Images of the Cu mesh. (a) Absorption image. (b) Refraction image γx. (c) Refraction image γy. (d) Unweighted phase map. (e) Phase map after weithing operation. (f) Retrieved projected thickness using the image in (e). (g) Line profile of the absorption image (blue, left axis) and the phase image (red, right axis). (e) Full field image of the same specimen.
The refraction information in both directions can be used to quantitatively estimate the phase shift experienced by the x-ray beam traversing the sample and, because a mono-elemental sample has been used, also the projected thickness t(x, y) = −ϕ(x, y)/(kδ) of such sample [33]. In the x direction:
As shown in [33] the projected thickness can be estimated by computing: In Eq. (5), kx and ky are the coordinates in Fourier space, conjugate to x and y respectively and T(x, y) = ∂t(x, y)/∂x + i∂t(x, y)/∂y.Figures 3(d) and 3(e) show the phase shift and the projected thickness calculated with the method described. The different contrast of the two refraction images produces better contrast in the vertical direction of each image. To partially compensate for this effect we used a weighted combination of the two differential images T′(x, y) = α∂t(x, y)/∂x + i∂t(x, y)/∂y where α = d2/d1 > 1 takes into account the relative divergence of the beam in the two directions, which is inversely proportional to the WG gap size. The phase shift calculated with the weighted superposition is shown in Fig. 3(f). As expected the image looks more balanced and the square mesh appearance is restored. The drawback of this procedure is that the weighting operation amplifies the noisy γx image, making the overall resulting phase map noisier. However, it is worth pointing out the improvement of about three times in the contrast-to-noise ratio (CNR) in the phase image with respect to the absorption image. This is an extremely important feature of a hard x-ray microscopy method aimed at bio-medical applications, where samples are expected to have low absorption, and therefore sensitivity to phase is essential.
The projected thickness map in Fig. 3(e) appears to underestimate the actual grid thickness. Two factors affect the retrieved value of the grid thickness. Firstly, because the mesh features are comparable with the system resolution, a smoothing of the retrieved thickness will decrease the estimated thickness value. Secondly, as discussed before, the poor sensitivity on the refraction in the horizontal direction has an effect on the subsequent evaluation of the projected thickness. A possible calibration procedure would consist in measuring a sample of known composition and thickness, but with features much larger than the resolution. This would allow the phase sensitivity and the resolution to be decoupled and the actual phase sensitivity to be estimated.
A further example of the capabilities of the microscope is reported in Figs. 3(h) and 3(f), showing respectively the absorption and phase images of glass micro-spheres (Whitehouse Scientific) with nominal size in the range 3–30 μm. This example shows the ability of our system to distinguish isolated micro-objects with a refractive index that, unlike the metal grid, is similar to those of biological material.
A comparison of results obtained in scanning and full-field mode is shown in Fig. 4. In this case a Cu grid (SPI G1000HS) is imaged, with the same nominal parameters as the Ni grid presented in Fig. 3. Absorption and refraction images are reported in the panels (a), (b) and (c). Cu displays stronger absorption and phase shift with respect to Ni, therefore the estimation of the phase shift and projected thickness is more reliable than the one presented before. The unweighted phase map is shown in the panel (d). The same weighting procedure applied to this measurement is able to restore both orthogonal bars very satisfactorily (Figs. 4(e) and 4(f)). The plot in panel (g) shows the line profiles of the absorption image (blue) and the phase image (red) respectively. This represents another confirmation that, even with a relatively strongly absorbing specimen, phase image guarantees a CNR improvement.
The high contrast measured with the Cu grid enables a reliable estimation of the resolution. From the slope measured at the edges of the grid bars (see Figs. 3(d) and 3(g)), 2 μm resolution can be estimated, with resolution slightly better in the vertical direction (thanks to the better CNR). This value approximately corresponds to the estimated beam size at the sample position, which ultimately motivated the choice of 1 μm step size for the raster scans.
Finally the full-field image of the same grid is displayed in Fig. 4(h). In full-field mode two parameters affect both the resolution and FOV of the image: the beam size at the sample position and the magnification. Physical constraints of the system fixed the maximum distance z1 + z2 from the WG2 to the detector, though z1 could still be adjusted. Increasing z1 is decreasing the magnification and increasing the beam size on the sample, resulting in a larger FOV but lower resolution. By decreasing z1 the FOV is reduced and so the full-field mode cannot be effectively realized. The consequence is that the typical resolution in full-field mode is worse than in scanning.
The lower resolution of the image in Fig. 4(h) is evident, nevertheless, by avoiding the scan, the exposure time for the whole image has been much reduced. The exposure time for the scanning measurement was 5 s per point (and 100×100 data points), while the full-field image has been acquired with 100 s integration time.
4. Conclusions
In conclusion, we have shown the experimental realization of hard x-ray microscopy with a laboratory source equipped with hard x-ray waveguides. The setup is able to detect absorption and differential phase contrast in scanning mode and the setup can be switched from scanning to full-field mode with minimal changes. Metal grids and glass micro-spheres have been imaged as proof of concept to demonstrate the capabilities of the technique. Quantitative absorption, refraction and phase imaging is demonstrated with the acquired data.
Further improvements will comprise the use of two waveguides with the same (or very similar) size to produce the same divergence in both directions, and the installation of preliminary focusing optics, before the waveguides, to improve the output photon flux and therefore enable the use of smaller (sub-500 nm) waveguides for microscopy. In addition, reflective optics for pre-focusing would act as low-pass filter for the incoming x-rays, thus greatly reducing the background of high energy x-ray photons on the measured images.
Acknowledgments
D.P. and K.S.M. gratefully acknowledge funding from the Australian Research Council through the DECRA scheme. The Medipix2 detector used for the measurement has been acquired thanks to a Faculty of Science (Monash University) equipment grant. The WGs used in this work were fabricated by S. Kandasamy at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF). The micro-spheres measured for this report have been kindly provided by M. Kitchen.
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