Image quality assessment of a photon counting detector in x-ray projection imaging

Abstract

The recent advancements in the photon counting detection have created a significant growing research interest in the x-ray imaging. It is essential to objectively understand the image quality parameters of a photon counting detector before developing imaging applications. In this work, we have assessed the imaging quality of a cadmium telluride (CdTe) based PCD in projection imaging mode. The detector is 70.4 mm × 6.6 mm dimensions. The detector has a pixel array of 64×4 with a pixel pitch of 1.1 mm×1.65 mm. With each pixel having 4 channels in its corresponding ASIC, this PCD can create three bin images from a single projection. With a microfocus x-ray source, the imaging quality in each bin image was measured in terms of the spatial resolution, noise, and contrast to noise ratio (CNR). We used 70 kV, 50μA, 10 s (0.5mAs) with 0.5mm thick aluminum (Al) filter for the acquisition of each image. The MTF curves indicated that the spatial resolution for the bin-1, bin-2, and bin-3 was almost identical. The NNPS curves indicated that the noise in bin 1 and bin 2 images was almost the same for all frequencies while bin 3 image had relatively less noise. The CNR analyses showed that the bin-1 image had the highest CNR. As the flux was increased from 0.5 to 1 mAs, the number of detected counts also increased that resulted in the CNR increase. Beyond this flux, the pulse pileup occurred due to which multiple counts were read as single that resulted in few detected counts and lower CNR. The knowledge of the spatial resolution, noise, and CNR in terms of energy binning allows the determination and optimization of imaging techniques necessary for various applications.

Introduction

Single photon counting detection technology has shown their value as compared to the charge integrating x-ray detectors [1–8]. For potential applications, such as medical imaging and non-destructive testing, there is growing interest in energy-sensitive photon-counting detectors based on high flux imaging [9–14]. Compared to charge-integrating detectors working in a current mode, photon counting detectors (PCDs) are operated in a pulse mode based on a single event, and each interaction occurred within the detection material can be theoretically processed and registered individually. They can effectively suppress the electronic noise and discriminate the photon energies into various bins depending on the number of channels associated with each pixel. The spectral information offered by these detectors can be exploited to identify the material, quantify K-edge agents and the reduction of radiation dose. Semiconductor-based PCDs directly convert x-ray photons into electrical charges. Silicon (Si, Z = 14) is a typical semiconductor, and homogeneous large Si wafers are readily available, Si has been widely used as a sensor material for PCD. However, the low Z number of Si results in low absorption efficiency for x-rays in the diagnostic range [15]. High absorbing materials with high absorption efficiency such as cadmium telluride (CdTe, Z = 48/52) have been introduced as the sensor material to exploit the high energy x-ray imaging [16–19]. CdTe based crystals directly absorb the incoming x-ray photons and directly convert it into the electrical signals that are read in the ASIC readout stage.

This work aims to objectively investigate the image quality of a CdTe based PCD for x-ray imaging. The PCD has a relatively large pixel size; it can be used in both industrial and medical applications. The parameters that are investigated with three energy windows are the spatial resolution, noise analysis, CNR and its relationship with the detection efficiency.

2. Materials and Methods

2.1. Imaging System

A pixelated photon counting detector (DxRay, Inc. Northridge, CA, USA) composed of 1mm thick CdTe crystals with 70.4 mm × 6.6 mm dimensions. The detector has a pixel array of 64× 4 with a pixel size of 1.1 mm×1.65 mm. Each pixel of the detector has 4 channels in its corresponding application specific integrated circuit (ASIC). In summary, when an incident photon interacts within the CdTe, a cloud of free charge carriers (electron-hole pairs) with an amount proportional to the deposited energy of the incident photon are produced within the semiconductor. These cloud charges are drifted towards the pixelated anode under the influence of the externally applied electrical field. The ASICs transform these charge pulses into voltage pulses through a charge-sensitive preamplifier and a pulse shaper. The voltage pulses are further discriminated using a series of comparators, registered within specific energy ranges or “energy thresholds” and digitally counted. The schematics of the photon counting detector is shown in Fig.1, and the complete details and working of the detector can be found elsewhere [20].

Figure 1.

Schematics of the photon counting detector (PCD) used in this study.

There are two operating modes of the detector, the imaging and spectroscopic modes. In the imaging mode, the pulse height (mV) threshold values corresponding to 4 comparators can be set as any fixed values from 1200 mV to 0 mV. Each pixel of the PCD allows four energy thresholds, and the ASIC records the number of counts that are greater than each threshold and generates four sets of projection data, which is referred to as threshold data. The projection data corresponding to the photons that are of energies between two energy thresholds is referred to as bin image, which is obtained by subtraction of two threshold data sets. Thus, with four threshold data sets, it is possible to get three bin images from a single exposure.

In the spectroscopic mode, the detector sweeps the whole pulse height range from the high pulse height to low pulse height by consecutively reducing the threshold to a preset pulse height step. Information on the energy response calibration, pulse height (mV) - energy (keV) relationship, noise floor determination, and count rate has already been investigated in our previous work on the spectroscopic capabilities of the detector [20,22]. In this work, we are giving an insight into the spatial resolution, noise analysis, and CNR as a function of the x-ray energy and discriminator threshold.

A hybrid micro-focus x-ray tube (Model L9181–06, Hamamatsu Photonics, Japan) is used with a tungsten (W) target and with a focal spot size ranging from to 16 to 50 μm as its output power varies from 10 to 39 W. The tube operates with a tube voltage and tube current ranging from 40–130 kV and 10–300 μA. The complete details and characterizations of the tube can be found elsewhere [21]. In this study, the source to detector distance (SDD) is 50 cm while the three phantoms with thicknesses of 0.3 cm, 2 cm, and 4 cm are placed in contact with the detector, making the geometric magnification (M) approximately to 1. All the evaluations are conducted with a tube voltage of 70 kV while a 0.5 mm thick aluminum (Al) filter was placed at the exit window to block the low energy photons. A 1 cm thick lead (Pb) collimator was used to limit the beam size and reduce the x-ray scattering.

From the previous study [20,22], the relationship between the output pulse height in mV and input energy (keV) is given by the following equation

$$H(mV)=772.8\times e^{0.000919\times E(keV)}-771.9\times e^{-0.02479\times E(keV)}$$ (1)

Accordingly, for 70 kV, the number of counts are recorded until a pulse height range of 700 mV. For imaging, the pulse height range for the four thresholds associated with each pixel of the photon counting detector and the energy bin width window along with the measured pulse height spectrum for the 70-kV beam using the PCD is given in Fig.2. The pulse height spectrum is generated from the differentiation of the spectroscopic (S) curve above the noise floor, and the details can be found elsewhere [23].

Figure 2.

The pulse height spectrum acquired with 70 kV, 50μA in 2 mV threshold step with 10 msec accumulation time for each step. The three energy bin windows are also highlighted along with their corresponding range.

2.2. Spatial Resolution Evaluation

For the quantitative measurement of spatial resolution for each bin image, a 1 mm thick copper (Cu) sheet was utilized to measure the modulation transfer function (MTF). We measured the spatial resolution along the pixel pitch of 1.1 mm as that direction offered a large array of pixels. Due to the large pixel size, the Cu sheet was tilted about 10° angle. With this tilt, all the 4 detector rows $(\text{N}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\tan \text{θ}$}\right.)$ were binned together to create an oversampled ESF. The phantom was scanned at 70kV, 50μA, 5 sec with the 4 threshold settings as mentioned above. With the generated bin images, the oversampled ESF was calculated which was smoothed and differentiated to get the line spread function (LSF) curve. Finally, the MTF curves were obtained from the fast Fourier transform (FFT) of the LSF, and normalization to unity at zero spatial frequency (f) as [24,25],

$$LSF(X)=\frac{ESF(X+\Delta X)-ESF(X)}{\Delta X}$$ (2)

$$MTF(f)=\left|FFT\{LSF(X)\}\right|$$ (3)

2.3. Noise Evaluation

The noise properties of radiography image detectors can be characterized according to several different noise sources, such as the quantum noise, the electronic noise, and the fixed pattern noise. The images generated by the photon counting detector has minimum electronic noise; nevertheless, it is critical to evaluate the noise properties of this imaging detector as the quantum noise is always present. The noise energy spectrum and the spatial frequency relationship can be measured as the noise power spectrum (NPS) measured from uniform exposure images. With the normalized NPS (NNPS) by the image expectation, the noise performance of the detector was evaluated.

A 4 cm thick BR12 phantom was used for the calculation of normalized noise power spectrum (NNPS). The noise only images are generated from the difference data by subtracting the image data from two identical scans acquired at 70kV, 50μA, 10 sec with the 4 thresholds. This process of subtraction eliminates the structural noise in the uniform object scans. The 2D digital NNPS is calculated as [26–28]

$$\text{NNPS}(u,v)=\frac{1}{s{(0)}^2}\times {\left|{\text{FFT}}_{\text{2D}}\hspace{0.17em}[I_i(x,y)-\overline{I}]\right|}^2\frac{\Delta \text{x}\hspace{0.17em}\Delta \text{y}}{{\text{N}}_{\text{x}}\hspace{0.17em}{\text{N}}_{\text{y}}}$$ (4)

where S(0)² represents the mean square of the input image, N_x, N_y is the number of pixel elements, and Δ_x, Δ_y are the pixel sizes in each direction. I_i(x, y) is the image indexed with i and Ī is the mean value of the images calculated from the uniform exposure images.

2.4. Contrast to Noise Ratio Evaluation

One of the key parameters for image quality is the contrast to noise ratio (CNR). CNR depends on the number of detected counts by the detector. As the flux increases, the probability of an event (count) being recorded by the detector decreases. Considering a non-paralyzable model of detection, the probability of the counts recorded was measured as P(N_inc τ) is given as [29–32]

$$P(N_{inc}\hspace{0.17em}\tau )=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$(1+N_{inc}\hspace{0.17em}\tau )$}\right.=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$(1+kI\hspace{0.17em}\tau )$}\right.$$ (5)

where the incident count rate (N_inc) is proportional to the tube’s current (I) with k as the constant of proportionality and τ representing the dead time. The probability of recording the counts is dependent on the semiconductor properties which include its purity, x-ray attenuation coefficient and, thickness. The details for estimating the probability under the non-paraylzable model can be found elsewhere [20].

A 2 cm thick wax phantom was used for the analyses of CNR. Two cylindrical holes were drilled in the phantom to simulate two tumors. The first cylindrical had a diameter of 0.8 cm and a drilled depth of 2 cm while the second cylindrical hole had a diameter of 0.5 cm and drilled depth of 1.4 cm, respectively. Under 70 kV, six different flux levels were used to acquire the phantom images by varying the current values as 50, 100, 150, 200, 250 and 300μA and keeping the exposure time as 10 s. Then, the CNR for the 0.8 cm diameter hole for each bin image was calculated as

$$CNR=\frac{\overline{N_T}-\overline{N_B}}{\sigma }$$ (6)

Where $\overline{N_T}$ and $\overline{N_B}$ are the mean number of counts in simulated tumor and background areas and, σ represents the noise in terms of standard deviation of the counts within the tumor and background area.

3. Results

The energy bin 1 image of the Cu sheet is shown in Fig.3. From the image, one can see that it completely blocks the x-ray resulting in maximum imaging contrast with respect to air and thus provides a good background for measuring the oversampled ESF and LSF curves that are given in Fig.4 (a). The three bin images yielded almost the same MTF curves, and there are no significant differences in the cutoff resolution (10% MTF) as shown in Fig.4 (b). The cutoff resolution is reported to be around 0.35 lp/mm for all the three bin images, thus indicating a sampling efficiency (cutoff resolution/ Nyquist frequency) of about 78%. This cutoff frequency suggests that a 1.4 mm high contrast detail will be detected in all the bin images under these settings. Hence, the spatial resolution of this PCD system is currently limited by its pixel size.

Figure 3.

The energy bin1 image of the copper (Cu) phantom acquired at 70kV, 50μA and 5sec.

Figure 4.

(a) The ESF and LSF curves calculated for the Bin1 image of the Cu sheet acquired at 70kV, 50μA and 5sec (b) The MTF curves showing the comparisons of the three bin images.

The 2D noise image generated from the difference of two bin 1 images is shown im Fig.5(a), and the 2D NNPS calculated from the Bin 1 imaging data is shown in Fig.5(b), and one can see the zero-frequency content or the DC component highlighted by the dotted ROI. It is due to the fact the photon count cannot be negative, and the intensity at the origin in the Fourier domain represents the sum of values of all pixels of the original image. By its very nature, this DC value will fluctuate from image to image based on the stochastic generation of the image data [28].

Figure 5.

(a) The 2D noise image generated from the difference of two bin 1 images; (b) The 2D NNPS for the energy bin1 image highlightimg the DC component.

The 1D NNPS curves are shown in Fig.6 that were calculated from the row averaging along with each bin image. Under these acquisition parameters, the curves indicate that the noise in bin 1 and bin 2 images are almost the same for all frequencies while bin 3 image has relatively less noise. One can expect this kind of trend as the number of counts received in each bin image is different as bin 3 received the least number of photons as demonstrated by the S-curve in Fig.2.

Figure 6.

The 1D NNPS curves generated for the three bin images.

The curve for the probability of count detection as predicted by the non-paralyzable model is given in Fig.7. With increasing photon flux, the probability of detection is decreasing. Under this model, the probability of detection for 50, 100, 150, 200, 250 and 300uA are 0.55, 0.37, 0.28, 0.22, 0.19 and 0.16.

Figure 7.

The probability of count detection as predicted by the non-paralyzable mode under 70 kV.

The bin images of the phantom acquired with 70kV, 50μA, 10s are shown are shown in Fig.8(a) with the simulated tumors highlighted by the dotted ROIs. Here, the total number of counts recorded in Bin 1, Bin 2 and Bin 3 are 14.6×10⁶, 11.2×10⁶ and 4.3×10⁶ respectively. Since the low energy photons are attenuated and absorbed more in the wax phantom’s background, Bin 1 (27–38 kV) has the highest contrast.

Figure 8.

(a) The three bin images of the phantom acquired at 70 kV, 50μA and 10sec showing the simulated tumor highlighted in dotted black ROI. (b) The average profiles across the simulated tumor for the three bin images.

As the photon energies increase, they readily pass through the phantom’s background resulting in a low contrast as seen in Bin 3 (52–71 kV). The average profiles (64×1) calculated across the simulated tumor for the three bin images are shown in Fig.8(b). The profiles highlight the same trend of the varying background attenuation for the wax phantom. Note that the intensities of the background for the three bin images are not uniform and one of the reasons is that the gain for each pixel of the PCD is not the same. By performing the gain adjustment for each pixel of the PCD, we expect the intensities will become uniform.

The CNRs calculated for the three bin images across the large cylindrical hole at six different flux levels are given in table.1. As expected, Bin 1 images yielded the highest CNR values for this acquisition setting. As the photon flux is increased from 0.5 mAs to 1.5 mAs, the number of detected counts also increase that results in CNR increase. Further increase in photon flux causes more spectral distortions due to the pileup effects (peak and tail accumulation). This causes the CNR to decrease as the expected number of incident photons per dead time increases that can be seen in Table.1.

Table 1.

CNR comparison among the three energy bin images with various photon flux.

	0.5mAs	1mAs	1.5mAs	2mAs	2.5mAs	3 mAs
Bin 1	3.02	3.31	3.5	3.16	2.98	2.91
Bin 2	2.52	2.75	2.91	2.69	2.49	2.39
Bin 3	1.7	1.91	2.06	1.86	1.61	1.42

Discussion and Conclusions

In this study, we characterized the imaging quality performance of a pixelated photon counting detector in projection imaging mode for the three bin images. Using a high contrast copper (Cu) edge, we measured the MTF curves. The MTF curves indicated that the spatial resolution for the bin-1, bin-2, and bin-3 was almost identical. Yu et al. report similar results for their 0.9mm×0.9mm PCD based CT system [33]. However, Koenig et al showed with their small pixel (0.055 mm ×0.055 mm) PCD based system that with the charge sharing and K-escape, a charge cloud dedicated to one pixel may well be detected by the neighboring pixels, which results in the intrinsic blurring that results in the loss of spatial resolution [34]. The spatial resolution here does not degrade which suggests that the charge cloud does not exceed the pixel size. The microfocus that we used has a little impact on the spatial resolution as the detector pixel size is large than the potential focal spot blurring that would be introduced by the microfocus tube. The microfocus source was readily available in our lab to conduct this study. If a large focal spot (300μm) tube was to be utilized, we expect that the spatial resolution would remain moreover the same. Note that MTF reported here is exclusive to this system that majorly includes the microfocus x-ray source and the PCD. In addition to the PCD pixel pitch, MTF measurements are highly dependent on other factors such as source focal spot size, geometric alignment, and stability of the optical stage. The microfocus source results in minimum focal spot blurring. To get accurate measurements, the source and the PCD were installed on a stable optical rail, the copper (Cu) edge was perfectly aligned with focus spot of the source, and a high precision optical stage was used to image the edge.

The NNPS curves indicated that the noise in bin 1 and bin 2 images were almost the same for all frequencies while bin 3 image had relatively less noise as the photon count was significantly less as compared to the other two bin images. If the acquisition parameters were to be changed, e.g., different threshold levels, kV and different filtration, the noise level in each bin would be different. The CNR analyses showed that the bin-1 image had the highest CNR. As the tube current was increased from 50 μA to 150 μA, the number of detected counts also increased that resulted in the CNR increase. The output count rate reached the maximum for the 1.5mAs (150μA×10s) flux. Beyond this flux, the pulse pile-up and deadtime losses start to dominate, and it results in few detected counts which lower CNR. Several techniques can be used to limit the spectral distortions caused by the charge sharing and pulse pileup to use the PCD based systems effectively [35–38].

Due to the limited number of pixels available along the direction of 1.65 mm pitch, we were limited in measuring the MTF and NNPS with a pixel pitch of 1.1 mm as that direction offered more pixels. As compared to thin silicon (Si), the thick CdTe based PCD is more susceptible to the harmful effects of radiation which may lead to damage in the detectors and to the associated readout electronics. The CdTe detectors are manufactured by simply depositing metal contacts onto the semiconductor surface. One limitation of the thick CdTe detector is that the radiation induced positive charge accumulates at the AlN-CdTe interface which can reduce the interpixel resistance, increase the cross talk among the pixels and increase leakage current [39–41].

This study provides insight into characterizing the image quality of a photon counting detector. The knowledge of the spatial resolution, noise, and CNR in terms of energy binning allows the determination and optimization of imaging techniques necessary for various applications.

Highlights.

• Imaging quality of a CdTe based photon counting detector was assessed.

• With a microfocus x-ray source, spatial resolution, noise and CNR were measured.

• The spatial resolution for bin-1, bin-2 and bin-3 images were almost identical.

• The CNR analyses showed that the bin-1 image had the highest CNR.