Single-shot, high sensitivity X-ray phase contrast imaging system based on a Hartmann mask

Significant efforts are currently ongoing in X-Ray imaging to provide multimodal imaging systems, targeting better sensitivity and specificity for both biomedical or non-destructive testing (NDT) applications. X-Ray Phase Contrast Imaging (X-PCI) shows great capability to differentiate elements with similar absorption. For example, in the medical field, knowing the chemical composition of breast microcalcifications would help to differentiate malign and benign tumors. The composition can be determined from the measurement of the phase as the optical index of materials is directly related to the composition. We propose a novel, high-sensitivity X-ray quantitative phase imaging system based on a Hartmann wavefront sensor. The system provides high resolution (20µm without magnification) and high sensitivity (~100 nrad), and is compatible with tomographic experiments using both synchrotron beamlines or laboratory sources. We present here our first X-PCI prototype as well as the first images obtained. We also present an alternative design based on the same approach, providing larger field-of-view at the cost of some trade-off regarding resolution and sensitivity and the first tomographic results obtained with this imaging system.


Introduction
X-ray imaging is an essential tool for non-invasive control of various samples, both for biomedical diagnosis and non-destructive testing.When the absorptions are very similar between two components of a sample, it becomes difficult to differentiate them using X-ray absorption imaging.However, it is still possible to disentangle the components by measuring the induced variations of the phase of the X-ray beam.This is the basic of X-ray Phase Contrast Imaging (X-PCI).For most technics, X-PCI aims at providing clear images of samples that are normally unresolvable with amplitude imaging.However, it is possible to extract more information about the sample by reminding that the phase is linked to the decrement of the real part of the refractive index, called δ, of each component (while the absorption is related to the imaginary part, called β).
Different X-PCI imaging approaches have already been proposed and characterized [1][2][3][4].We propose here a phase imaging system based on a Hartmann mask that will provide quantitative phase images where most existing technics give only qualitative images.

Phase Imaging Principle
Let's consider a plane wave, propagating along the z-direction through a medium with refractive index, n = 1-δ + iβ and wave vector k: When passing through a sample of thickness d, the amplitude of the wave is attenuated by a factor e and the phase is shifted by the quantity δk .The sample modifies locally the wavefront, leading to the local refraction of the wave by an angle α. α corresponds to the local wavefront slope, i.e. the local gradient of the wavefront.
The Hartmann sensor is a device that is commonly used for wavefront sensing [5][6][7][8].It is composed of a grid of regularly spaced holes and a detector placed some distance away.Each hole in the mask generates a bright spot on the camera (Fig. 1a).To determine the wavefront of the incoming wave, two images are needed.The first one is taken without the sample (Fig. 1a).It is a calibration measurement to get the reference position of the spots.The second image is taken with the sample that will locally refract the wave, yielding to local shift of the spots (Fig. 1b).For both images, position and amplitude of each spot are measured.
The ratio of the sample to reference amplitudes gives the absorption of the sample.The difference between the new and the reference positions (∆y in Fig. 1b) is proportional to the angle of refraction (tan(α) =∆y/L), i.e. the 2D gradient of the wavefront relatively to the reference beam.Measurements of local small angular deviations (∆x, ∆y) allow retrieving the angle of refraction (αx and αy) and therefore the 2D gradient of the wavefront.An integration of the wavefront along X and Y directions determines the phase.Therefore, a wavefront sensor generates a phase map.
The main advantages of the Hartmann approach are: 1) 2D images are acquired from one acquisition; 2) single exposure: with only one acquisition, we measure both the absorption and deflection, 3) achromatic: the system is designed to keep high sensitivity over a wide energy range; 4) compatible with tomography.

Small Field of View prototype
The first phase imaging prototype we developed is shown Fig. 2. The system is composed of a Hartmann mask, a scintillator, a relay lens and a CCD camera.The mask is based on an array of holes regularly spaced, drilled on a gold substrate.The incoming X-ray light is diffracted by the holes and propagates up to the scintillator.The scintillator converts X-rays to visible light that is then collected by the relay lens and imaged onto the CCD camera.This first design has been optimized for an energy range of 5 to 25 keV.It provides a field of view of few mm².The spatial sampling is 20µm.The sensor theoretical performances are a dynamic range of +/-60 µrad and a sensitivity of 70 nrad.10th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2020), www.ictconference.com/2020

Larger Field of View Prototype
It is possible to adjust the design parameters of the setup in order to increase the field of view (FoV) up to several centimeters, at the cost of a slight reduction of the sensitivity.
The second prototype, allowing a FoV of few centimeters is presented Fig. 3.A 3*3 cm² mask of holes is positioned in front of a flat panel (Xineos 2329 from Teledyne Dalsa) of dimensions 23*29 cm².In this configuration, the size of the mask is the limiting parameter for the FoV.The system has 2-5 µrad phase sensitivity and 50µm spatial resolution (without magnification).

Results and Discussion
To demonstrate the interest of the Hartmann approach for phase imaging, we first used 120µm diameter nylon fibers as phase objects and a hex key as absorption object (Fig. 4a).The small FoV system was placed at 60cm away from an Excillum Metaljet high brilliance microfocus X-ray source, having a K-α emission around 9 keV.The sample was placed between the source and the system, at roughly 30cm from the Hartmann mask.The raw image is presented on Fig. 4b, with a zoom (Fig. 4c) that shows the bright spots.10th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2020), www.ictconference.com/2020Figure 6 presents results obtained with the second prototype (Fig. 3), allowing a larger FoV.The experimental set-up is composed of the Excillum Metaljet high brilliance microfocus X-ray source, the Hartmann mask and the Flat panel Xineos 2329 (Teledyne Dalsa).
We used two Eppendorf tubes, one filled with immersion oil for microscope and the other one with water (Fig. 6a).The mask was placed at 50cm from the microfocus X-ray source.The samples were placed between the source and the mask, at~1cm from the mask.The raw image and a zoom are presented Fig. 6b-c.The position and amplitude of each spot were calculated on the images taken with and without the tubes.The ratio of the amplitudes gives the absorption of the sample (Fig. 7a) and the difference of position is proportional to the deflection generated by the sample (Fig. 7b).We can clearly observe deflections in the X direction up to +/-6µrad and absorption of roughly 25% for the oil and 35% for the water (Fig. 7c-d).The noise level is ~1µrad P-V.

First Steps toward tomography
We performed a first tomographic experiment on a reference sample composed of three tubes: one was a tube of carbon (1.5mm in diameter), one was a tube of PMMA (2mm in diameter) and the third one was a 2mm diameter polycarbonate tube filled with 150µm spheres of soda lime glass (Fig. 8a).The sample was situated at 22 cm from the Excillum microfocus X-ray source.The large FoV Hartmann mask was located at a distance of ~44 cm from the source.In this optical configuration, the theoretical spatial resolution on the sample was about 25µm with 1.5 cm of field of view.Images were acquired with the Xineos 2329 flat panel.400 projections were taken.The image on Fig. 8b represents a 2D absorption image (similar to Fig. 7a).Around 9 keV, PMMA and carbon have similar absorption, and thus are not that easy to distinguish with conventional absorption images.
(a) (b) From the 400 projections, 3D tomographic reconstruction was performed.For each projection, the absorption and deflection images were obtained (similar to Figs. 7a-c) and then combined.The resulting absorption image is presented on Fig. 9  10th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2020), www.ictconference.com/2020

Conclusion
Imagine Optic explored the ability of wavefront sensors to perform X-ray phase imaging associated with user-friendly software.The first prototype, with its small field of view (few mm 2 ) and high sensitivity (100 nrad) is compatible with small low-density object imaging.The second prototype has several cm 2 of field of view and 2-5µrad of sensitivity depending on the designs.Further characterization and optimization of the imaging systems are conducted.
As a conclusion, the main advantages of the Hartmann approach are: 1) 2D images are acquired from one acquisition; 2) the determination of absorption and phase from only one acquisition; 3) achromaticity; 4) compatible with tomography (as illustrated by Figs.9-10).Therefore, our approach provides a simple alternative to already proposed X-PCI methods, either based on costly optical elements such as gratings or requiring the acquisition of multiple images to provide a single X-PCI image.Moreover, our system demonstrated its ability to provide quantitative phase images.

Figure 1 .
Figure 1.Schematic description of a Hartmann wavefront sensor.a) The reference wave (without sample) creates sub-images on the detector.b) When passing through a sample, the wavefront is modified, resulting in a displacement (∆y) of the sub-images on the detector.α is the angle of refraction.

Figure 2 .
Figure 2. Picture of the first phase imaging prototype.The system is 50 cm long.

Figure 3 :
Figure 3: The phase imaging system based on a Hartmann mask and a flat panel.

Figure 4 :
Figure 4: a) Sample composed of two crossing nylon fibers and a hex key as an absorption object; b) Raw image where the nylon fibers cross; the black part on the right corresponds to the hex key; c) zoom on the raw image to illustrate the bright spots

Figure 6 :
Figure 6: a) Picture of the two Eppendorf tubes in front of the mask; b) raw image c) zoom on the raw image

Figure 7 :
Figure 7: The sample with oil is on the left, the one with water on the right.a) Intensity map (from 0 to 40%); b) and corresponding profile along the yellow line (cyan) and the mean around the yellow line (in blue).c) Deflection along X (from -5 to 5µrad) and d) corresponding profile.

Figure 8 :
Figure 8: (a) Picture of the tubes used for the 9keV tomography experiment.One was a tube made of carbon (1.5mm in diameter), one was a tube of PMMA (2mm in diameter) and the third one is a 2mm diameter polycarbonate tube filled with 150µm spheres of

Figure 9 :
Figure 9: Absorption 3D image: axial view on the 3 tubes (a) and coronal view (b) of the tube filled with micro-spheres.