Grating-based x-ray phase-contrast imaging with a multi energy-channel photon-counting pixel detector

Georg Pelzer; Thomas Weber; Gisela Anton; Rafael Ballabriga; Florian Bayer; Michael Campbell; Thomas Gabor; Wilhelm Haas; Florian Horn; Xavi Llopart; Norbert Michel; Uwe Mollenbauer; Jens Rieger; André Ritter; Ina Ritter; Peter Sievers; Stefan Wölfel; Winnie S. Wong; Andrea Zang; Thilo Michel

doi:10.1364/OE.21.025677

1. Introduction

During recent years many potential applications of phase-contrast x-ray imaging have been investigated [1–4]. Using a Talbot-Lau interferometer with a conventional x-ray tube [3, 5] is essential for an application in medical diagnostics, because monochromatic x-ray sources with high intensity and of manageable size are still not available. However, the use of a polychromatic x-ray spectrum results in a loss of quantitative phase information [6] and additional noise received from photons having energies different to the interferometer’s design-energy. The latter results in a reduced contrast-to-noise ratio (CNR) in the differential phase-contrast (DPC) images [7]. This difficulty is not present in grating based phase-contrast imaging setups with monoenergetic X-ray sources, like monochromatized synchrotron beams or like the Compton backscattering X-ray source which has been used by Bech et al. [8] and Schleede et al. [9, 10]. However the complexity of such a setup hinders a broad range use in medical imaging.

We present a method of energy weighting in DPC imaging to improve the CNR. We measure the phase information in 16 energy bins with the energy-resolving detector Dosepix [11]. By taking into account the spectral information about flux and fringe visibility, the relative error of each DPC image pixel can be minimized individually. The CNR in the DPC image can be improved significantly.

2. Methods

The Dosepix detector is a hybrid photon-counting detector that was derived from the Medipix-family [12,13]. The 16×16 pixels of the ASIC are connected with copper-pillars to the 300 μm thick p-in-n silicon sensor with 12 × 16 central pixels of 220 μm size and with 2 × 16 pixels of 55 μm size at two edges. For this study the central pixels were used resulting in a field of view of 2.6 mm × 3.5 mm. Each pixel in the ASIC is equipped with 16 16bit-counters for counting the number of events in 16 energy intervals. A photon interacting in the semiconductor sensor layer releases charge carriers that induce a current pulse in the pixel electrode during their drift towards the electrode. This pulse is amplified and compared to a discriminator threshold in the pixel. The time it exceeds the threshold is a measure of energy deposition. It is measured in the pixel electronics by counting cycles of a clock signal fed to all pixels from the periphery. This time-over-threshold value ToTis then compared to 16 digital thresholds ToT_istored in the pixel. The counter i, which counts the number of events in the time-over-threshold interval [ToT_i, ToT_i₊₁[, is incremented by one if ToT∈ [ToT_i, ToT_i₊₁[. Thus, each pixel measures a spectrum of deposited energies in terms of ToT. The dependence of ToTon energy deposition was determined prior to the measurements by pixel-wise calibration with x-ray fluorescence. The energy resolution resulting from the time-over-threshold method leads to a minimum reasonable width ΔEof the energy channels of about 3 keV. The lowest ToT-threshold was set to 12 keV in order to eliminate the background by K-fluorescence produced in the copper-pillar connections between sensor and pixel electrodes. With the energy intervals (i= 1,...,16) centered at E_i= (13.5 + 3(i− 1)) keV, a 60 kV spectrum suits to the range of the energy channels.

A Talbot-Lau interferometer is utilized to measure the differential phase-shifts imprinted on the x-ray wave field by an object. The phase grating G1 imprints a phase-shift of πon the incident wave with the design energy of 25 keV. A self-image of G1 is reproduced in certain distances, the Talbot distances. The analyzer grating G2 is placed in the third fractional Talbot distance of 15.87 cm. A nickel grating G1 with a period of 4.37 μm is used. The gold G2 grating has a thickness of 80 μm in beam direction and a period p₂= 2.4 μm. The source grating G0 is made of 150 μm thick gold bars with 24.39 μm period. All gratings have an duty cycle of 0.5. The medical x-ray tube is operated at a voltage of 60 kV with 30 mA current on a tungsten anode. The tip of a polymethylacrylate wedge with an opening angle of 84.8deg was positioned in front of half of the detector. The wedge produces a homogeneous differential phase shift over the pixel matrix. With this object in the beam the x-ray waves propagating through the interferometer (in z-direction) are refracted and the Talbot pattern is shifted. By taking images at 8 different G2 x-axis positions over two periods p₂, the periodic intensity pattern is sampled. The exposure time for each image was 6 seconds.

For each position xof the analyzer grating G2 the number of detected photons N_iwhich have deposited an energy E∈ [E_i− ΔE/2, E_i+ ΔE/2[ is read out for all 16 energy channels for all pixels with the wedge in the beam. A measurement under the same conditions without the object in the beam gives the number of photons N_0ifor all energy intervals iand each pixel. The differential phases Φ_iin all energy intervals iare calculated by discrete Fourier transformation F_{ν_p}with the base frequency ν_p= 1/p₂. With the notation presented by Engelhardt [14] we define:

Φ_{i} = \arg [ℱ_{ν_{p}} (N_{i} (x))] - \arg [ℱ_{ν_{p}} (N_{0 i} (x))] .

The visibilities V_iare calculated for all energy channels iand all pixels separately as

V_{i} = \frac{{[ℱ_{ν_{p}} (N_{i} (x))]}_{1}}{{[ℱ_{ν_{p}} (N_{i} (x))]}_{0}},

where the indices refer to the zeroth and first amplitude coefficient in the Fourier expansion.

The visibilities with the object V_iand without the object V_0iare calculated.

The weighted DPC-signal in each pixel is calculated as

Φ_{weighting} = \frac{1}{w} \sum_{i} w_{i} Φ_{i}

with the energy weighting factors w_iand w= ∑_iw_i. To increase the image quality the w_ihave to take the signal as well as the expected noise into account. The variance of Φ_idepends on the number of detected photons and the visibility [15, 16]. Combining the independent noise contributions from measurements with and without object we find for the variance of Φ_i:

σ_{Φ_{i}}^{2} = \frac{2}{N_{i} V_{i}^{2}} + \frac{2}{N_{0 i} V_{0 i}^{2}} .

A maximal signal-to-noise ratio (SNR) in each pixel is gained if optimized weighting factors are used. For attenuation based x-ray imaging these have been evaluated by several groups [17–19]. We calculate SNR-optimized weighting factors for the DPC-signal. The SNR²of the measured phase in each individual pixel is given by:

{SNR}^{2} = \frac{{(\sum_{i} w_{i} Φ_{i})}^{2}}{\sum_{i} w_{i}^{2} σ_{Φ_{i}}^{2}} .

With the notation of Giersch et al. [19] we write:

{SNR}^{2} = \frac{{(\vec{a} \cdot \vec{b})}^{2}}{{\vec{b}}^{2}}

but with the vectors a⃗and b⃗having the components

a_{i} = \frac{Φ_{i}}{σ_{Φ_{i}}}

and

b_{i} = w_{i} σ_{Φ_{i}}

adapted to the DPC-signal. For a maximal SNR²a⃗and b⃗should be parallel [19] which leads to

w_{i} \propto \frac{Φ_{i}}{σ_{Φ_{i}}^{2}} .

The values Φ_ican be reduced to their energy dependence [14] of

E_{i}^{- 2}

:

w_{i} \propto \frac{1}{σ_{Φ_{i}}^{2} E_{i}^{2}} .

These weighting factors do not only take the counting statistics but also the visibility into account (see Eq. 4). The maximized SNR in each pixel should then lead to an improved contrast-to-noise ratio (CNR) in the image of Φ_weighted.

3. Results

Figure 1shows the measured average visibility and average count rate dN_0i/dtin the energy channels. The highest visibility is observed in the design-energy’s bin, centered at 25.5 keV. Several energy channels are contributing with high flux but low-visibility to the DPC-image.

Fig. 1 Count rate (circles) and visibility (crosses) measured without object in the 16 energy bins of the Dosepix detector. As expected the visibility peaks at the design energy of 25 keV.

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In Fig. 2the measured DPC-signal Φ(E_i) – averaged over the wedge-covered detector area – in the 16 energy channels is shown. As expected the signal decreases with $E_{i}^{- 2}$ . There are no primary photons with smaller energies than 20 keV in the used spectrum. The drop at the low energies is therefore due to charge sharing between detector pixels, where one photon triggers several pixels. The last energy bin records events with analogue pile-up. Therefore the energy bins from 22.5 keV (i= 4) to 55.5 keV (i= 15) were used for further analysis. The resulting w_ifor one pixel are shown in Fig. 2. It can be seen that mainly photon energies from 21 keV to 30 keV contribute to the image after weighting.

Fig. 2 Differential phase signal averaged in the wedge area [Fig. 3]. The curve with errorbars shows the differential phase like it is obtained in the detector’s energy bins. The energy weighting factors from one arbitrary pixel are shown as stairs.

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We also emulate the behavior of an integrating pixel detector by calculating the differential phase via:

\begin{array}{l} Φ_{integrating} & = \arg [ℱ_{ν_{p}} (\sum_{i = 4}^{15} E_{i} N_{i} (x))] \\ - \arg [ℱ_{ν_{p}} (\sum_{i = 4}^{15} E_{i} N_{0 i} (x))] . \end{array}

A photon counting pixel detector with one energy threshold is emulated by calculating:

\begin{array}{l} Φ_{counting} & = \arg [ℱ_{ν_{p}} (\sum_{i = 4}^{15} N_{i} (x))] \\ - \arg [ℱ_{ν_{p}} (\sum_{i = 4}^{15} N_{0 i} (x))] . \end{array}

To compare the image quality, two ROIs were defined as marked in Fig. 3. The CNR of these ROIs was calculated:

CNR = \frac{\bar{Φ_{wedge}} - \bar{Φ_{air}}}{\sqrt{σ_{Φ_{wedge}}^{2} + σ_{Φ_{air}}^{2}}},

where the

\bar{Φ_{wedge}}

and

\bar{Φ_{air}}

are the mean values,

σ_{Φ_{wedge}}^{2}

and

σ_{Φ_{air}}^{2}

the variances of the measured differential-phases inside the ROIs. The CNR values of the DPC images obtained in the energy channels are shown in Fig. 4. The CNR values in the final images gained with energy weighting, counting and integrating are given in table 1.

Fig. 3 Top row: Measured DPC images using integrating-mode (left), counting-mode (middle) and the energy-weighting method (right). From the left to the right an increase of the wedge signal as well as a reduction in noise can be observed. The wedge (top, blue) and air-ROI (bottom, red) are indicated on the left. Bottom row: Histograms of the DPC-signals obtained in the two ROIs. The air-signal is centered at Φ = 0. An increase in the signal difference can be seen. The width of the distributions is reduced with the energy-weighting method, leading to an enhanced CNR.

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Fig. 4 CNR obtained in the 16 energy bins of the Dosepix detector (stairs). The energy bins close to the interferometers design-energy of 25 keV contribute with high CNR to the image.

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Table 1. Overview of the CNR values obtained for different types of data analysis.

View Table

In this experiment the energy-weighted CNR values are larger than that of any single energy bin [Fig. 4] because of the consideration of the full statistics. For integrating-mode emulation a CNR of 18.2 ± 1.8 is observed while the counting-mode performs with an CNR of 22.4 ± 1.8. This advantage of photon-counting detectors is also known from attenuation-based imaging [17].

By applying the proposed weighting-method to the data, the CNR can be increased to 28.8± 1.8. For the CNR²– which is proportional to the dose – an increase of 65.3% compared to a counting detector and 150.4% compared to integrating detector is found. This corresponds to a dose reduction of 39.5% by energy weighting compared to a photon-counting detector. For an energy-integrating detector a reduction of 60.0% in dose is achievable.

The DPC images are shown in Fig. 3. The improvement of image quality with respect to the integrating mode by photon counting and by energy weighting is clearly visible. The distributions of the measured phases among the pixels in the ROIs [cf. Fig. 3] show that the signal difference is increased in Φ_weighting. Additionally the image noise – the width of the distributions – is reduced. Thus, both effects enhance the CNR.

4. Discussion

The improvement obtained with energy weighting depends on several parameters: the x-ray spectrum, the visibility as a function of energy, the detector response and the object. As the weighting factors are determined individually for every pixel, also object properties like attenuation coefficients – leading to beam-hardening – or ultra small angle scattering strength –reducing the visibility – are taken into account in the proposed method for achieving superior CNR in the DPC image. An increase of artifacts due to beam-hardening which might arise due to the individual pixel weighting factors was not observed yet. The signal from low energy photons with their larger phase shifts but also higher dose per photon is weighted higher than the signal from high energy photons. Hence the contrast is increased. It should be mentioned that energy bins have not been optimized so far neither in position nor in width.

5. Conclusion

We have combined the most advanced technologies in x-ray imaging: multi-energy photon-counting and phase contrast imaging. By optimized weighting of energy resolved differential phase contrast measurements with a 16 energy channel pixel detector we have achieved a significant improvement in image quality. Energy-weighting factors for the DPC-signal were derived and optimized towards a maximization of the pixel SNR². Compared to an emulated single-threshold photon-counting detector and an emulated integrating detector we observed an increase in image CNR of 28.6% and 58.2% respectively. The new method was able to reduce the necessary dose compared to an integrating detector by about 60%.

Acknowledgments

This work was funded by the German Ministry for Education and Research (BMBF), project grant No. 13EX1212Bwithin the cluster of excellence Medical Valley EMN. The authors want to thank Dr. Jürgen Mohr and Jan Meiser from the Karlsruhe Institute of Technology and the Karlsruhe Nano Micro Facility (KNMF)for manufacturing the gratings. We acknowledge support by Deutsche Forschungsgemeinschaftand Friedrich-Alexander-Universität Erlangen-Nürnbergwithin the funding programme Open Access Publishing.

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Grating-based x-ray phase-contrast imaging with a multi energy-channel photon-counting pixel detector

Abstract

1. Introduction

2. Methods

3. Results

4. Discussion

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (4)

Tables (1)

Equations (13)

Optics Express

Method	CNR
weighting	28.8 ± 1.8
counting	22.4 ± 1.8
integrating	18.2 ± 1.8