An apparatus and method for directly measuring the depth‐dependent gain and spatial resolution of turbid scintillators

Abstract

Purpose

Turbid (powder or columnar‐structured) scintillators are widely used in indirect flat panel detectors (I‐FPDs) for scientific, industrial, and medical radiography. Light diffusion and absorption within these scintillators is expected to cause depth‐dependent variations in their x ray conversion gain and spatial blur. These variations degrade the detective quantum efficiency of I‐FPDs at all spatial frequencies. Despite their importance, there are currently no established methods for directly measuring scintillator depth effects. This work develops the instrumentation and methods to achieve this capability.

Methods

An ultra‐high‐sensitivity camera was assembled for imaging single x ray interactions in two commercial Gd₂O₂S:Tb (GOS) screens (Lanex Regular and Fast Back, Eastman Kodak Company). X ray interactions were localized to known depths in the screens using a slit beam of parallel synchrotron radiation (32 keV), with beam width (~20 μm) much narrower than the screen thickness. Depth‐localized x ray interaction images were acquired in 30 μm depth‐intervals, and analyzed to measure each scintillator's depth‐dependent average gain $\overline{g}(z)$ and modulation transfer function MTF(z,f). These measurements were used to calculate each screen's expected MTF(f) in an energy‐integrating detector (e.g., I‐FPD). Calculations were compared to presampling MTF measurements made by coupling each screen to a high‐resolution CMOS image sensor (48 μm pixel) and using the slanted‐edge method.

Results

Both $\overline{g}(z)$ and MTF(z,f) continuously increased as interactions occurred closer to each screen's sensor‐coupled surface. The Regular yielded 1351 ± 66 and 2117 ± 54 photons per absorbed x ray (42–66 keV⁻¹) in interactions occurring furthest from and nearest to the image sensor, while the Fast Back yielded 833 ± 22 and 1910 ± 39 photons (26–60 keV⁻¹). At f = 1 mm⁻¹, MTF(z,f) varied between 0.63 and 0.78 in the Regular and 0.30–0.76 in the Fast Back. Calculations of presampling MTF(f) using $\overline{g}(z)$ and MTF(z,f) showed excellent agreement with slanted‐edge measurements.

Conclusions

The developed instrument and method enable direct measurements of the depth‐dependent gain and spatial resolution of turbid scintillators. This knowledge can be used to predict, understand, and potentially improve I‐FPD imaging performance.

1. Introduction

Digital radiography (DR) has replaced screen‐film and computed radiography (CR) as the state‐of‐the‐art in x ray imaging. The predominant technology in DR is the energy‐integrating indirect flat‐panel detector (I‐FPD),¹ which uses a scintillator to convert the energy of x ray interactions into optical photons, which are collected and converted to charge by a pixelated array of photodiodes (e.g., a‐Si:H). The charge image is then readout by a self‐scanned thin‐film transistor (TFT) array to form a digital image. I‐FPDs are now used extensively in scientific, industrial and medical imaging,^{2, 3, 4} and have enabled advanced imaging modalities such as cone‐beam computed tomography (CBCT).⁵

The de facto metric for quantitating and comparing the imaging performance of I‐FPDs is the spatial frequency‐dependent detective quantum efficiency (DQE), given by:

$$\mathrm{DQE}\left(f\right)=\frac{\mathrm{MT}{\mathrm{F}}^2\left(f\right)}{q\mathrm{NNPS}\left(f\right)},$$ (1)

where MTF(f) denotes the detector's modulation transfer function, NNPS(f) denotes its noise power spectrum (normalized by the square of the average detector output), and q denotes the mean x ray input fluence per image exposure.⁶ As the most upstream component in the image detection chain, the properties of the scintillator used in an I‐FPD define the upper limit to its DQE. Consequently, it is critical to understand how scintillator design factors (e.g., material, thickness, optical backing) affect their imaging properties, so that the performance of I‐FPDs can be maximized at low imaging dose.^{7, 8, 9, 10, 11}

The DQE of a turbid scintillator is inherently limited by depth dependence in its response to x rays. As illustrated in Fig. 1, optical photons produced by x ray interactions must escape to an exit surface before detection by an image sensor. The magnitude and spatial spread of these light bursts is expected to vary with x ray interaction depth (i.e., proximity to the image sensor), due to light scattering and absorption within the scintillator. Swank¹² showed how stochastic variation in a scintillator's gain reduces DQE(0) by a scalar:

$$A_s=\frac{m_1^2}{m_0{m}_2},$$ (2)

where m _i represents the i‐th moment of the scintillator's pulse height spectrum. Random gain fluctuations are caused not only by depth dependence in light escaping the scintillator, but also by variations in the energy deposited within the scintillator per absorbed x ray, energy‐dependence in its x ray conversion efficiency (i.e., nonproportionality),¹³ and intrinsic variability in its scintillation processes (i.e., Fano noise).¹⁴

Figure 1.

Depth‐dependent gain and blur in scintillators. (a) A cross‐sectional diagram showing x ray interaction at different depths (z) causing variations in the magnitude and spatial distribution of the light emitted per interaction. (b) Point spread function (PSF) associated with each light burst. [Color figure can be viewed at wileyonlinelibrary.com]

Lubberts showed that depth dependence in a scintillator's spatial blur, that is, MTF(z,f), causes the square of its MTF to decrease more rapidly than its NNPS with increasing spatial frequency. This effect causes a “roll‐off” in the DQE of energy‐integrating detectors, and is known as the “Lubberts effect”.¹⁵ Given some simplifying assumptions (i.e., monoenergetic x rays and local deposition of x ray energy), the Lubberts effect reduces the DQE of a scintillator by a frequency‐dependent scalar:

$$L(f)=\beta \frac{{\left({\int }_0^T\overline{\eta }(z)\overline{g}(z)\mathrm{MTF}(z,f)dz\right)}^2}{{\int }_0^T\overline{\eta }(z)\overline{g}{(z)}^2\mathrm{MTF}{(z,f)}^{2}dz}$$ (3)

where T is the total thickness of the scintillator, $\overline{\eta }(z)$ denotes the mean fraction of x rays that are absorbed in a thin layer of the scintillator at each depth z, $\overline{g}(z)$ is the scintillator's depth‐dependent x ray conversion gain and β is a normalization factor such that L(0) is unity.¹⁶ Together, depth dependence in scintillator gain and blur degrade the imaging performance of I‐FPDs at all spatial frequencies; efforts to push I‐FPD performance limits will require understanding and reducing these effects in future detectors.

Previous investigations have used modeling to study scintillator depth effects. Early work emphasized analytical descriptions of light transport in granular phosphor screens such as Gd₂O₂S:Tb (GOS). For example, Hamaker¹⁷ applied the Kubelka‐Munk theory to describe their x ray conversion efficiency. Later, Swank¹⁸ used solutions to the diffusion equation to approximate the depth dependence in their spatial resolution. More recently, several groups have used Monte Carlo simulation tools such as GEANT4¹⁹ and PENELOPE²⁰ to simulate x ray, electron and light propagation in scintillators. Badano et al.²¹ used this approach to compare depth dependence in the gain and blur of columnar scintillators such as CsI:Tl versus powder screens such as GOS. Sharma et al.²² and others²³ have aimed to validate such simulations by comparing simulation results to MTF and A _s measurements.

Despite a wealth of theoretical knowledge, no methods exist for directly measuring depth effects in the turbid scintillators used in I‐FPDs. The insight provided by modeling approaches can be complemented by the ground truth provided by experimental measurements.

This work describes the instrumentation and method for directly measuring the depth‐dependent gain and spatial resolution of turbid x ray scintillators. In our approach, an ultra‐high‐sensitivity optical camera is used to image light bursts from single x ray interactions in powder GOS screens, which are widely used in I‐FPDs. X ray interaction depth is localized in the screens using a slit beam of parallel synchrotron radiation, and images of the depth‐localized interactions are analyzed to derive each scintillator's depth‐dependent average conversion gain $\overline{g}(z)$ and modulation transfer function MTF(z,f). We refer to this approach as depth‐localized single x ray imaging (SXI). Measurements of $\overline{g}(z)$ and MTF(z,f) are used to calculate each scintillator's MTF(f) as it would be used in an energy‐integrating detector (e.g., an I‐FPD). Finally, these calculations are compared with presampling MTF measurements made using the slanted‐edge method²⁴ to validate SXI results.

2. Materials and methods

Two commercial GOS screens were obtained for SXI experiments. The first sample is Lanex Regular (Eastman Kodak Company), which comprises a mixture of powder GOS and a binder that is coated onto a reflective plastic substrate. The Regular has 170 μm physical thickness and ~60% GOS packing density. The second sample is Lanex Fast Back, which has similar packing density and substrate as the Regular, but a 290 μm thickness. Both scintillators have been used in either prototype or commercial I‐FPDs for medical radiography,^{25, 26, 27} and the Fast Back is commonly used in electronic portal imaging devices (EPIDs) for radiotherapy.^{28, 29}

2.A. Single x ray imaging: instrumentation

The ultra‐high‐sensitivity optical camera used in SXI experiments (Fig. 2) comprises a microchannel plate image intensifier (C9016‐01, Hamamatsu), which is lens‐coupled to an electron multiplying charge‐coupled device (EMCCD) camera (C9100‐13, Hamamatsu). An overview of the imager's specifications is given in Table 1.

Figure 2.

An II‐EMCCD camera was assembled for single x ray imaging experiments. The camera has sufficient sensitivity to image light bursts from x ray interactions in powder GOS (inset left) and columnar CsI:Tl (inset right) scintillators at 32 keV. [Color figure can be viewed at wileyonlinelibrary.com]

Table 1.

II‐EMCCD camera specifications

Image intensifier input	Fiber optic faceplate (FOP)
Image intensifier effective quantum efficiency (GOS)	28.5%
Image intensifier radiant gain	14,000
Relay lens magnification	0.5x
EMCCD quantum efficiency	>95% (550 nm II output)
EMCCD gain	4‐1200
Physical/Effective pixel size	16 μm/32 μm
Bit depth	16 bit
Max frame rate	32 fps

The image intensifier (II) has a fiber optic faceplate (FOP) for its input window, which allows scintillator samples to be directly coupled. The input FOP represents a binary selection stochastic gain stage,³⁰ which on average transmits ~60% of incident visible light, hence the II's effective quantum efficiency (${\overline{\eta }}_{\mathit{eff}}$) is:

$${\overline{\eta }}_{\mathit{eff}}=0.6\left(\frac{{\int }_0^{\infty }\overline{I}\left(\lambda \right){\overline{\eta }}_{\mathit{II}}\left(\lambda \right)d\lambda }{{\int }_0^{\infty }\overline{I}\left(\lambda \right)d\lambda }\right),$$ (4)

where $\overline{I}(\lambda )$ represents the incident light spectrum (e.g., scintillator luminescence) and ${\overline{\eta }}_{\mathit{II}}(\lambda )$ is the II photocathode's wavelength‐dependent quantum efficiency. The II photocathode has 47.5% quantum efficiency to GOS luminescence, which makes ${\overline{\eta }}_{\mathit{eff}}$ = 0.285 in our experiments.

The II has a single stage microchannel plate with a gain of ~14,000. The relay lens (A2098, Hamamatsu) provides 2:1 demagnification which, given the 16 μm pixel pitch of the EMCCD, results in a 32 μm effective pixel pitch in acquired images. The II‐EMCCD is controlled by a host PC to adjust acquisition parameters (e.g., EMCCD gain and frame rate) and capture images. As shown in the inset of Fig. 2, the II‐EMCCD is capable of imaging light bursts from single x ray interactions in GOS and CsI:Tl, at energies below their respective K‐edges (50.2 and 33.2 keV). Sub‐K‐edge imaging eliminates gain and blur variations caused by remote reabsorption of K‐fluorescence, which complicate the evaluation of depth‐dependent phenomena.

2.B. II‐EMCCD gain calibration

The conversion gain of a scintillator, that is, the number of optical photons emitted per absorbed x ray, can be estimated from images of single x ray interactions. To achieve this capability, a 532‐nm continuous laser (Compass 215M, Coherent) was used to calibrate the II‐EMCCD's total gain in terms of analog‐to‐digital units (ADUs) per incident photon. As illustrated in Fig. 3(a), the laser light was input to an integrating sphere, then directly coupled to the II's input FOP through an optical fiber. Multiple images of the light emitted by the fiber were acquired with the II‐EMCCD, using identical gain parameters to SXI experiments described in Section 2.C. The images were offset‐corrected and averaged. The pixel values within the averaged light field image [Fig. 3(b)] were then summed, and this quantity was divided by the frame exposure time to determine ${\overline{\nu }}_{\mathit{ADU}}$, which characterized the fiber's average light output in ADUs per second.

Figure 3.

(a) A schematic overview of the II‐EMCCD's gain calibration. Light from a 532 nm continuous laser was passed to an integrating sphere, then to the II's input FOP through an optical fiber. (b) An image of the fiber's output as detected by the II‐EMCCD camera. Images of the fiber were characterized in terms of ADUs/second output by the II‐EMCCD. [Color figure can be viewed at wileyonlinelibrary.com]

Next, ${\overline{\nu }}_{\mathit{ADU}}$ was related to the average rate that photoelectrons were generated at the II photocathode (${\overline{\nu }}_{\mathit{pe}}$) while acquiring the images. The optical fiber was moved from the II's input FOP to the input window of a photomultiplier tube (PMT) assembly (HC124, Hamamatsu), which comprises an R6095 PMT and current‐to‐voltage amplifier. The assembly's output was digitized by an oscilloscope (TDS2024B, Tektronix), with an example illustrated in Fig. 4. These voltage pulses are caused by single photon interactions with the PMT, and are well‐separated temporally to be used for counting.

Figure 4.

Traces of the PMT assembly's output when coupled to the optical fiber. Each voltage pulse corresponds to a detected photon. The rate that pulses exceeded a noise threshold was taken as the photon detection rate ${\overline{\nu }}_{\mathit{pe}}$, which was divided by the PMT's quantum efficiency to determine the fiber's light output rate ${\overline{\nu }}_I$. The dotted line indicates the threshold level used for photon counting measurements. [Color figure can be viewed at wileyonlinelibrary.com]

As shown in Fig. 4, a threshold was defined at a voltage approximately 10 times the standard deviation of the assembly's “dark” signal, and was used to determine the average photon detection rate ${\overline{\nu }}_D$. The average incident photon rate ${\overline{\nu }}_I$, which describes the mean number of photons output by the optical fiber per second, was determined from ${\overline{\nu }}_D$ using:

$${\overline{\nu }}_I=\frac{{\overline{\nu }}_D}{{\overline{\eta }}_{\mathit{PMT}}}$$ (5)

where ${\overline{\eta }}_{\mathit{PMT}}$ denotes the PMT's quantum efficiency to 532 nm light. ${\overline{\nu }}_I$ was related to ${\overline{\nu }}_{\mathit{pe}}$ in the imaging experiments shown in Fig. 3 using:

$${\overline{\nu }}_{\mathit{pe}}={\overline{\nu }}_I{\overline{\eta }}_{\mathit{eff}}.$$ (6)

Finally, ${\overline{\nu }}_{\mathit{ADU}}$ was divided by ${\overline{\nu }}_{\mathit{pe}}$ to derive the constant of proportionality $\overline{\alpha }$, which describes the mean number of ADUs output by the II‐EMCCD per detected optical photon. With $\overline{\alpha }$, the number of photons emitted by a scintillator (N _ph ) can be estimated from a total number of ADUs (N _ADU ) in a light burst image using:

$${\widehat{N}}_{\mathit{ph}}=\frac{N_{\mathit{ADU}}}{\overline{\alpha }{\overline{\eta }}_{\mathit{eff}}}.$$ (7)

2.C. Depth‐localized single x ray imaging: overview

X ray interactions were localized to known depths within the GOS scintillators using the experimental approach shown in Fig. 5. The samples were coupled to the II‐EMCCD and irradiated with a thin, parallel x ray beam in a “side‐on” beam geometry. In side‐on geometry, the beam's trajectory is parallel to the scintillator's substrate and sensor‐coupled surface. As shown in the Fig. 5 inset, the beam's path is isoplanar in the scintillator's thickness dimension z, therefore, the interactions observed by the II‐EMCCD occur at the same nominal depth. Individual events that are well‐separated from each other in acquired images can be analyzed to evaluate the scintillator's depth‐localized gain and optical blur. X ray interaction depth can be adjusted by translating the scintillator with respect to the beam in the z dimension.

Figure 5.

A schematic overview of depth‐localized single x ray imaging experiments. Scintillator samples are mounted to the II‐EMCCD and aligned with respect to a parallel slit beam of synchrotron radiation. (Inset) The sample and beam are aligned in a “side‐on” orientation, in which the beam irradiates the sample at fixed depth z. Single interactions observed by the II‐EMCCD occur at the same nominal depth, and can be analyzed with respect to their magnitude and spatial spread. Dimensions are not drawn to scale. Coordinate conventions defined here (top‐right) are referenced throughout the text. [Color figure can be viewed at wileyonlinelibrary.com]

The XPD beamline of National Synchrotron Light Source II (Brookhaven National Laboratory, Upton, NY, USA) provided a parallel source of 32 keV x rays for depth‐localized SXI. The beam was collimated through a slit to ~20 μm in the z dimension and ~0.5 mm in the x dimension (as drawn in Fig. 5). A high‐aspect‐ratio steel tube was positioned downstream of the slit to reject scattered x‐rays. The GOS samples were pressed in firm contact with the II‐EMCCD, which was mounted to a diffractometer stage. The diffractometer allowed rotation (±0.1° adjustment step) and z translation (1 μm precision) of the sample/camera assembly.

2.D. Depth‐localized single x‐ray imaging: rotational alignment

With side‐on irradiation geometry, errors in the sample's rotational alignment introduce uncertainty in localizing the depth of x ray interaction. To minimize this uncertainty, the sample was aligned using methods briefly described in previous work,³¹ which are explained in more detail here.

2.D.1. Roll alignment

As illustrated in Fig. 6(a), misalignment of the sample's roll (i.e., θ _r ≠ 0°) causes the depth of x ray interactions to vary along the x dimension of the slit beam. Roll misalignment can be identified by an asymmetry in the light field generated by the beam's attenuation within the scintillator. As shown in Fig. 6(b), this asymmetry is most obvious when a part of the beam interacts with the sample's substrate. Because of the substrate's low atomic number and density, this portion of the beam travels further laterally (in the y‐dimension) than the portion directly irradiating the scintillator. X rays interacting with the substrate are more likely to Compton or Rayleigh scatter, and the photons which scatter into the scintillator are observed in acquired images.

Figure 6.

(a) An illustration of sample “roll” θ_r with respect to the beam. At depths near the scintillator substrate, θ_r ≠ 0° causes a portion of the beam to irradiate the substrate, while the rest directly irradiates the scintillator. (b) This causes an asymmetry in the projected light field generated by the beam's attenuation in the sample. The asymmetry can be used to iteratively correct θ_r by noting its direction and extent as the beam is scanned across the scintillator‐substrate interface. The beam's X‐collimation was opened in this image to more clearly demonstrate asymmetry caused by sample roll. [Color figure can be viewed at wileyonlinelibrary.com]

To minimize θ _r , the sample was translated in the z direction until the beam first interacted with the scintillator nearest its substrate. Several images were acquired and averaged to visualize the beam's attenuation profile in the sample [e.g., Fig. 6(b)]. This process was then repeated while z‐translating the sample in 10 μm increments, to observe changes in the beam's attenuation profile as it scanned the substrate‐scintillator interface. As described above, the sample's roll was identified using the direction and extent of asymmetry in the beam's profile as it scanned the interface. The direction of the roll was confirmed by observing similar asymmetry, with the opposite orientation, while scanning the beam across the sensor‐scintillator interface. The sample's roll was then incrementally adjusted, and was considered minimized when the beam's attenuation profile changed rapidly and symmetrically as it scanned through these interfaces.

2.D.2. Pitch alignment

As illustrated in Fig. 7(a), misalignment in the sample's pitch (i.e., θ _p ≠ 0°) causes the depth of x ray interactions to vary along the y‐dimension of acquired images. To minimize this error, θ _p was set to 0° with the following method. The sample was translated in the z direction until the beam entered its approximate center‐of‐depth. Several images were acquired and averaged to visualize the beam's attenuation within the sample. This process was repeated while rotating the diffractometer stage in small‐angle increments above or below the nominal 0° orientation. As shown in Figs. 7(b) and 7(c), the angle with which the beam penetrated the furthest into the sample (along the y‐dimension) was defined as the true 0° pitch.

Figure 7.

(a) An illustration of sample “pitch” θ_p with respect to the incoming beam. (b) The beam's lateral penetration into the sample can be evaluated by inspecting a fixed y‐plane in its projected image. (c) Beam penetration is maximized when θ_p ≈ 0°. [Color figure can be viewed at wileyonlinelibrary.com]

Once rotationally aligned, the sample was translated until x ray interactions were first observed in the scintillator closest to its substrate. This depth was defined as z = 0 μm and approximately 1000 images were acquired. The sample was then translated 30 μm in z, and the process was repeated until the entire thickness of the scintillator was imaged.

2.E. Measuring depth‐dependent gain and blur

Figure 8 shows how depth‐localized images were processed to derive each scintillator's depth‐dependent gain and spatial resolution. As shown in Figs. 8(a) and 8(b), “subimages” of individual x ray interactions were first extracted from their depth‐localized “parent” images using MATLAB's Image Processing Toolbox (MathWorks, Inc., Natick, MA, USA). The subimages were extracted by defining the highest‐valued pixel in each light burst as the interaction's center, and cropping the parent image to a square matrix (61 × 61 pixels) about its position. Each subimage was offset‐corrected, then stored in z‐labeled “stack” with others from the same nominal depth.

Figure 8.

Overview of depth‐dependent gain and blur measurements. (a) Depth‐localized interaction “subimages” are extracted from their “parent” images by cropping a square matrix about the highest‐valued pixel in each event. (b) Subimages are stored in a “stack” with others from the same depth. (c) The magnitudes of the events in a stack are plotted in a histogram as a “depth‐localized pulse height spectrum” (DLPHS). The mean of each DLPHS is converted to numbers of photons to derive the depth‐localized conversion gain. (d) All the events in a stack are summed, then radially averaged to estimate the 2D point spread function of interactions at each depth. Fourier analyses of the 2D PSFs determined MTF(z,f). [Color figure can be viewed at wileyonlinelibrary.com]

Each subimage was summed in 2D to measure the total number of photons in each interaction, using its signal magnitude in ADUs. As shown in Fig. 8(c), the ensemble of these magnitudes for each depth was used to generate a histogram, which we refer to as a depth‐localized pulse height spectrum (DLPHS). Eq. (7) was used to convert the mean of each DLPHS to the number of photons emitted by the scintillator, and measure the depth‐dependent average gain $\overline{g}(z)$.

The same depth‐localized subimages were used to measure MTF(z,f). As shown in Fig. 8(d), the ensemble of subimages collected at each depth were summed, then radially averaged to estimate the scintillator's depth‐dependent point spread function $\widehat{\mathrm{PSF}}\left(x,y,z\right)$. Each $\widehat{\mathrm{PSF}}\left(x,y,z\right)$ was summed in the y‐dimension to compute its corresponding line spread function $\widehat{\mathrm{LSF}}\left(x,z\right)$. Depth‐localized LSFs were Fourier‐transformed, and their magnitudes were used to determine MTF(z,f). Each MTF(z,f) measurement was divided by the II‐EMCCD camera's pixel aperture MTF (32 μm pixel pitch) to correct for discrete sampling blur.

2.F. Comparison to MTF(f)

MTF(z,f) does not directly describe the spatial resolution of an energy‐integrating indirect detector (e.g., I‐FPD), which is typically characterized using the presampling MTF(f). An I‐FPD's presampling MTF(f) is the product of its pixel aperture MTF and the energy‐integrated MTF of its scintillator. The latter can be derived from MTF(z,f) using:

$$\mathrm{MT}{\mathrm{F}}_{\mathit{screen}}\left(f\right)=\frac{{\int }_0^T{\int }_0^{E_{max}}\mathrm{MTF}(z,f)S(E)\overline{\eta }(E,z)\overline{g}(E,z)dEdz}{{\int }_0^T{\int }_0^{E_{max}}S(E)\overline{\eta }(E,z)\overline{g}(E,z)dEdz}$$ (8)

where T denotes the total scintillator thickness, S(E) represents the incident x ray spectrum, $\overline{\eta }(E,z)$ denotes the fractional absorption of x rays within the scintillator (for a given energy and depth), and $\overline{g}(E,z)$ is the scintillator's x ray conversion gain. Eq. (8) assumes that x rays deposit their energy locally upon interaction with the scintillator. This is a reasonable assumption at energies below the K‐edge of GOS, where the majority of x ray interactions are photoelectric (92% at 32 keV)³² and fluorescence effects can be neglected.

Accurate measurements of MTF(z,f) and $\overline{g}(z)$ are expected to predict MTF _screen at energies below the K‐edge. To test this hypothesis, the MTFs of the Regular and Fast Back screens were determined by two methods and compared. First, each scintillator was coupled to a CMOS active pixel sensor (Remote RadEye1, Teledyne DALSA) to compose an I‐FPD, and its presampling MTF was measured using a slanted tungsten edge. This measurement was made using an RQA3 beam,³³ which has no x rays above the Gd K‐edge (50.2 keV). The measured presampling MTFs were divided by the sensor's pixel aperture MTF (48 μm pixel pitch) to determine MTF _screen..

Next, Eq. (8) was used to calculate MTF _screen from our measurements of $\overline{g}(z)$ and MTF(z,f) described in Section 2.E. The total thickness of each scintillator was divided into 30 μm “sublayers”, each of which was assigned a depth‐dependent gain and blur as measured using SXI. Boone's TASMIP model³⁴ was used to calculate the RQA3 energy spectrum S(E), which was used to determine the number and energy of x rays absorbed in each sublayer, that is, $\overline{\eta }(E,z)$. The density of GOS was assumed to be 4.39 g/cm³, which corresponds to a 60% packing density.²⁹ As a first‐order approximation, conversion gain was assumed to be proportional to x ray energy.

3. Results

3.A. II‐EMCCD gain calibration

The II‐EMCCD gain calibration results are summarized in Table 2. The total integrated signal in images of the optical fiber was 2.90 × 10⁸ ADU. Each frame's exposure time was 5.00 s, therefore ${\overline{\nu }}_{\mathit{ADU}}$ = 5.80 × 10⁷ ADU/s. PMT measurements of the same fiber detected photons with rate of ${\overline{\nu }}_D$ = 12.37 kHz. According to manufacturer's specifications, the R6095 PMT has a quantum efficiency of 10.6% for 532 nm light, therefore ${\overline{\nu }}_I$ = 1.17 × 10⁵ photons/s. The II photocathode's ${\overline{\eta }}_{\mathit{eff}}$ for 532 nm light is 0.30, which corresponds to ${\overline{\nu }}_{\mathit{pe}}$ = 3.51 × 10⁴ photoelectrons/s at the II‐EMCCD input. Dividing ${\overline{\nu }}_{\mathit{ADU}}$ by ${\overline{\nu }}_{\mathit{pe}}$ yields $\overline{\alpha }$ = 1652 ADU/photoelectron in acquired images. The imager has ${\overline{\eta }}_{\mathit{eff}}$ = 0.285 to GOS emissions, therefore, 5797 ADU corresponded to each optical photon emitted by the Regular and Fast Back samples in images of their light bursts.

Table 2.

Overview of II‐EMCCD gain calibration results

Variable	Value	Quantity
${\overline{\nu }}_{\mathit{ADU}}$	5.80 × 107	ADU/s
${\overline{\nu }}_I$	1.17 × 105	Photons/s
${\overline{\nu }}_{\mathit{pe}}$	3.50 × 104	Photoelectrons/s
$\overline{\alpha }$	1652	ADU/photoelectron
$\left(\frac{\overline{\alpha }}{{\eta }_{\mathit{eff}}}\right)$	5797	ADU/photon

3.B. Depth‐localized single x ray images

Figure 9 shows the contours of $\widehat{\mathrm{PSF}}\left(x,y,z\right)$ measured at depths near the substrate, the center, and the sensor‐coupled surface of the Lanex Regular and Fast Back screens. The magnitude and spatial sharpness of $\widehat{\text{PSF}}$ continuously increased as events occurred closer to each screen's sensor‐coupled surface. On average, the light bursts emitted by the Regular were brighter and sharper than those from the Fast Back, and were less variable with depth.

Figure 9.

Contour plots of the average light bursts versus depth in the (a) Regular and (b) Fast Back. From left to right, plots correspond to the interactions occurring nearest the scintillator's substrate, at its center‐of‐depth, and nearest its sensor‐coupled surface. Contour intervals represent 10% of the maximum pixel value. [Color figure can be viewed at wileyonlinelibrary.com]

3.C. Depth‐dependent gain: $\overline{g}(z)$

Figure 10 shows measurements and curve fits for $\overline{g}(z)$in the Regular and Fast Back screens. The left ordinates have been converted from magnitudes in summed ADU to numbers of optical photons using the calibration results in Section 3.A. The right ordinates have been normalized by the energy deposited in the scintillators per interaction (32 keV). The conversion gain of both scintillators increased with z (i.e., moving from substrate to FOP), as expected. The Lanex Regular emitted 1351–2117 photons (i.e., 42.2–66.2 keV⁻¹) in events occurring furthest from and nearest to the image sensor, respectively. The Fast Back emitted 833–1910 photons per x ray (26.0–59.7 keV⁻¹) between its depth extrema. The Regular had 57% relative variation in its gain versus depth compared to 129% variation in the Fast Back. Parameters for the curves fit to the measurements in Fig. 10 are given in the Appendix.

Figure 10.

Measurements and curve fits to the average depth‐dependent gain in the Lanex Regular and Fast Back. Left ordinates denote the total number of photons yielded per 32 keV interaction. Right ordinates are normalized by 32 keV to alternative units of keV⁻¹. The average gain increases as interactions occur closer to the optical sensor. Curve fitting parameters are given in the Appendix. [Color figure can be viewed at wileyonlinelibrary.com]

The error bars shown in Fig. 10 represent 95% confidence intervals for the mean gain measured at each depth. Confidence intervals were computed as 1.96 times the standard error. The relative standard error in each measurement was small (<5%), as each DLPHS had a well‐defined central peak and comprised over 250 interaction subimages. The error bars do not include systematic errors in $\overline{g}(z)$ from converting ADUs to photons, that is, in our estimates of $\overline{\alpha }$ and ${\overline{\eta }}_{\mathit{eff}}$. These variables are uncertain within the tolerances for the absolute quantum efficiency of the II's photocathode, and the PMT assembly used in calibration. Published examples^{35, 36} show that these quantities tend to agree well with manufacturer specifications.

3.D. Depth‐dependent spatial resolution: MTF(z,f)

Figure 11 shows MTF(z,f) measurements in the (a) Regular and (b) Fast Back screens. MTF(z,f) increased with proximity to the sensor‐coupled surface in both samples. The Regular screen had less depth dependence in MTF(z,f) than the Fast Back. For example, MTF(z,f) varied from 0.63 to 0.78 at f = 1 mm⁻¹ in the Regular, while ranging between 0.30 and 0.76 in the Fast Back. These differences correspond to 24% and 153% relative variation in MTF versus depth. MTF(z,f) varied more strongly with depth at higher frequencies. At f = 2 mm⁻¹, MTF(z,f) ranged between 0.31 and 0.55 (77% variation) in the Regular, and 0.06–0.53 (783% variation) in the Fast Back. Measurements near z = 0 in the Fast Back approached a nonzero minimum for f > 2 mm⁻¹. This effect is due to a systematic measurement error which is discussed and corrected in Section 4.B.

Figure 11.

Measurements of MTF(z,f) in the (a) Regular and (b) Fast Back screens. MTF(z,f) increases with z, that is, as x rays interact closer to the sensor‐coupled surface of each screen. [Color figure can be viewed at wileyonlinelibrary.com]

3.E. Presampling MTF(f)

Figure 12 compares slanted‐edge measurements of MTF _screen to calculations made with measured $\overline{g}(z)$ and MTF(z,f). Excellent agreement is observed for both screens. This validates the accuracy of $\overline{g}(z)$ and MTF(z,f) measurements, and confirms that the MTF of an I‐FPD can be understood and predicted from such depth‐dependent information.

Figure 12.

Calculations (lines) and measurements (points) of the Regular and Fast Back MTF_screen at RQA3. Calculations used Eq. (8) with measurements of $\overline{g}(z)$ and MTF(z,f) from depth‐localized SXI. Measurements were made by coupling each screen to a CMOS active pixel sensor and imaging a slanted tungsten edge. [Color figure can be viewed at wileyonlinelibrary.com]

4. Discussion

4.A. Relating $\overline{g}(z)$ to other quantities of interest

Measurements of $\overline{g}(z)$ characterize the average number of photons emitted by a scintillator from single x ray interactions occurring at fixed depth. This quantity depends on inherent properties of the scintillator, namely:

$$\overline{g}(E,z)=E{\overline{G}}_x\overline{\epsilon }\left(z\right),$$ (9)

where E denotes the energy absorbed per x ray interaction, ${\overline{G}}_x$ is the scintillator's intrinsic x ray quantum gain, that if, the average number of photons it produces per unit of absorbed x ray energy, and $\overline{\epsilon }(z)$ denotes the depth‐dependent probability of light escape from the scintillator. Recall that in our experiments, E was fixed at 32 keV. Assuming ${\overline{G}}_x$ is independent of depth, the $\overline{g}(z)$ measurements shown in Fig. 10 are directly proportional to $\overline{\epsilon }(z)$, and thus represent the gain variations due to each scintillator's inherent optical properties.

Measurements of $\overline{g}(z)$ are related, but not directly comparable to conventional x ray sensitivity measurements of I‐FPDs, which quantitate a detector's average signal response per unit entrance exposure. For example, Antonuk et al. and El‐Mohri et al. have shown that I‐FPDs using a Fast Back screen have higher x ray sensitivity than those using a Regular screen at both kilovoltage and megavoltage x ray energies.^{25, 37} While their results may appear to conflict with $\overline{g}(z)$ measurements, we believe they are consistent. The x ray sensitivity of an I‐FPD is proportional to the product of its scintillator's $\overline{g}(E,z)$ and $\overline{\eta }(E,z)$. Although the Fast Back has lower $\overline{g}(z)$ than the Regular, its greater thickness (i.e., mass‐loading) confers higher x ray quantum efficiency at most relevant x ray energies, which we assume underpins its superior x‐ray sensitivity.

4.B. Comparing $\overline{g}(z)$ to published estimates

Our SXI measurements of $\overline{g}(z)$ are consistent with previous estimates that have been made using pulse height spectroscopy (PHS) at similar x ray energies to our experiments. Ginzburg and Dick³⁸ have measured average gains of ${\overline{g}}_{\mathit{PHS}}$ = 35 keV⁻¹ and 28 keV⁻¹ in the Regular and Fast Back screens, respectively. As we have shown in previous work,¹¹ PHS gain measurements are weighted by the number of x rays interacting at each depth within a scintillator, therefore ${\overline{g}}_{\mathit{PHS}}$ is dominated by $\overline{g}(0)$, that is, the gain at depths furthest from the light sensor. We have measured $\overline{g}(0)$ = 42 keV⁻¹ in the Regular and $\overline{g}(0)$ = 26 keV⁻¹ in the Fast Back, which agree reasonably well with their respective PHS measurements of ${\overline{g}}_{\mathit{PHS}}$ = 35 keV⁻¹ and 28 keV⁻¹ _.

Wickersheim et al. and Ludwig et al. have estimated ${\overline{G}}_x$ to be between 65 and 78 keV⁻¹ in GOS.^{39, 40} Our measurements show that interactions occurring nearest the sensor‐coupled surface of each screen (i.e., z → T) have average gains of 66.2 keV⁻¹ (Regular) and 59.7 keV⁻¹ (Fast Back), which approach this intrinsic limit. This comparison indicates that a large fraction of the light generated in such interactions is collected in both screens. In our measurements, $\overline{g}(z)$ does not approach the same value for z → T in the two scintillators. Physical differences between the two screens could be examined to better understand this result. For example, the Fast Back is thicker than the Regular, and has larger phosphor grain size. Because scintillation light is emitted isotropically, optical photons can potentially traverse a longer path length before collection in a thicker screen than in a thinner one (when comparing events occurring at a given distance from the optical sensor). If the optical backing, light scattering, and absorption properties of the two screens are the same, or similar enough, the photons which travel a greater distance in the thick screen will have a higher probability of being absorbed and less light will be collected.^{9, 18} Our result is consistent with this possibility. On the other hand, one may expect optical photons propagating in the Fast Back to experience fewer scattering events (per unit path length) than in the Regular, due to its larger grain size. This could result in less overall light absorption in the Fast Back. Another possibility is that the two screens have slight differences in their volumetric packing density, which would also affect the number of scattering events per unit path length.²³

It is difficult to attribute differences in $\overline{g}(z)$ to a single a parameter (e.g., scintillator thickness, grain size, packing density), because each factor plays a role in determining the scintillator's optical properties. Although it is outside the scope of this work, depth‐resolved SXI could be used to directly measure $\overline{g}(z)$ in a set of samples that systematically control for these variables. This information has not been available in the past, but could improve current understanding of powder screen optics, particularly through comparisons to analytical models such as those proposed by Swank,¹⁸ or optical Monte Carlo simulations such as those described by Badano et al., Liaparinos et al., and Lim et al.^{21, 23, 41}

4.C. MTF(z,f) considerations and corrections

The exact spatial location of each x ray interaction is unknown in SXI experiments. Recall that while extracting light burst subimages from their parent images, the highest‐valued pixel in each subimage was assumed to be centered on the point of interaction [i.e., the origin of $\widehat{\mathrm{PSF}}\left(x,y,z\right)$]. While this may be a reasonable approximation, this assumption introduces bias toward overestimating the central pixel value of $\widehat{\mathrm{PSF}}\left(x,y,z\right)$. The overestimation, in turn, can cause MTF(z,f) measurements to approach a nonzero minimum at higher frequencies [e.g., in Fig. 11 (b)]. This effect can be demonstrated using the following example calculations.

Consider that the LSF of photons emitted from a scintillator (from a thin layer at fixed depth) is known exactly, and that the emission is isotropic, that is, the LSF describes the probability density function of photons detected along any radius from the point of each x ray interaction. For simplicity, assume that the scintillator emits a fixed number of photons per absorbed x ray, which are detected by an ideal light sensor (100% detection efficiency, no spatial blur) at the scintillator's output surface, z = T. If the light sensor is pixelated, 2D light burst images can be simulated by random sampling of the LSF to determine each photon's x‐ and y‐coordinates, then spatially binning the results in pixels of a given size. We will use this approach to generate subimages from an example “ground truth” LSF, then show how knowledge of each interaction's location affects SXI measurements of the LSF as described in Section 2.E.

First consider the ideal case where the exact position of each x ray interaction is known, and each subimage is centered about its location. As shown in Figs. 13(a) and 13(b), the “ground truth” LSF can be accurately measured by summing multiple light burst subimages, averaging them radially, then summing $\widehat{\mathrm{PSF}}\left(x,y,z\right)$ in one dimension. As shown in Fig. 13(c), the measured MTF also agrees well with the ground truth, despite deterministic blur introduced by the pixelated light sensor. This is because the scintillator's MTF approaches zero far below the Nyquist frequency of the light sensor (15.625 mm⁻¹, matched to our experiments), hence undersampling is negligible.

Figure 13.

(a) Subimages generated from an example “ground truth” LSF, in the ideal case that the position of each x ray interaction is known and each subimage is centered on its location. The pixel pitch is matched to the II‐EMCCD camera's (32 μm) used in SXI experiments. (b) Comparisons between the resulting LSFs “measured” using methods described in Section 2.E., and the “ground truth” used to generate the subimages. (c) Comparisons between the “measured” MTFs and “ground truth”. [Color figure can be viewed at wileyonlinelibrary.com]

Next, consider the same generated subimages in the “experimental” case, where the position of each interaction is unknown. Figure 14(a) shows how centering each light burst subimage about its highest‐valued pixel can introduce a spatial error in such measurements. As shown in Fig. 14(b), this error can accumulate when averaging multiple event subimages and slightly overestimate the central value of the measured LSF compared to “ground truth”. Figure 14(c) shows that the MTF corresponding to the distorted LSF approaches a nonzero minimum at higher frequencies.

Figure 14.

(a) Interaction subimages generated from an example “ground truth” LSF, processed the same as GOS experimental data, where each light burst is assumed to be centered about its highest‐valued pixel. This assumption can fail (inset) and introduce a small spatial error in each measurement. (b) The central pixel value of the “measured” LSF is slightly overestimated due to this assumption. (c) The measured MTF approaches nonzero minimum at higher frequencies due to this overestimation. [Color figure can be viewed at wileyonlinelibrary.com]

In our experiments with GOS, we observed that distortion of the LSF center was most evident when the optical photons of an interaction were distributed over a large area, for example, ~61 × 61 pixels at depths near z = 0 in the Fast Back. Under these conditions, the average number of photons incident on each pixel was low, and both photon shot‐noise and statistical fluctuations in the II‐EMCCD's gain⁴² caused further uncertainty in determining each event's true central position.

We have shown that practical limitations in estimating each interaction's location using a “highest‐valued‐pixel” approach introduce small bias errors in the MTF(z,f) measurements at high frequencies. To correct for these errors, Regular and Fast Back data were fit to a first‐order exponential function:

$$\mathrm{MTF}(z,f)=A(f)e^{B(f)z},$$ (10)

where A(f) and B(f) were frequency‐dependent fitting parameters given in the Appendix. The form of Eq. (10) was derived empirically but has also been motivated physically by Swank.¹⁸ As shown in Fig. 15, Eq. (10) accurately represents MTF(z,f) measurements at frequencies, where there is no apparent distortion (e.g., f < 2 mm⁻¹ in the Fast Back), and constrains MTF(z,f) to vary monotonically with respect to frequency and depth. Corrected MTF(z,f) data for the Regular and Fast Back are shown in Fig. 16, and can be compared to their direct measurements shown in Fig. 11. Their comparison shows that the shape and magnitude of the direct measurements are preserved, while nonzero minima in the results are removed.

Figure 15.

MTF(z,f) measurements and first‐order exponential function [Eq. (10)] fits for the Fast Back screen. Curve fitting was used to correct for measurement bias at higher frequencies. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 16.

MTF(z,f) for the (a) Regular and (b) Fast Back screen, corrected by first‐order exponential fits to MTF(z,f). [Color figure can be viewed at wileyonlinelibrary.com]

The spatial resolution of the II‐EMCCD camera should be considered when interpreting measurements of MTF(z,f). As specified by the manufacturer, the FOP input window of the II has a numerical aperture of 1 and a fiber pitch of 6 μm. Because the fiber pitch is smaller than the highest frequency components of the light bursts emitted by GOS, we assume the FOP contributes negligible blur at the frequencies of interest in SXI experiments (f < 5 mm⁻¹). The limiting resolutions of the II and relay lens also exceed these frequencies of interest, and the Nyquist frequency of the imager is large in comparison (15.625 mm⁻¹). Imperfections in experimental setup (e.g., relay lens focus, and scintillator coupling to the II) can cause additional blur in the measurements, however, these effects were not considered here.

4.D. Applying depth‐localized SXI to other scintillators

Depth‐localized SXI can be applied to study other scintillators considered for use in I‐FPDs, preferably with x ray energy fixed below the scintillator's K‐edge to facilitate data analysis. In this work, all measurements were performed below the K‐edge of Gd (50.2 keV) to eliminate remote reabsorption of its K‐fluorescence, which complicates depth localization. A suitable beam for depth localized SXI would have energy that approaches, but does not exceed the scintillator's K‐edge. Such a beam would simultaneously maximize the light yielded by the scintillator per absorbed x ray, which is desirable for improving SXI signal‐to‐noise ratio, while avoiding undesirable fluorescence effects.

Preliminary work by our group has used SXI to evaluate $\overline{g}(z)$ and MTF(z,f) in columnar CsI:Tl scintillators, which are also widely used in I‐FPDs.^{31, 42} These investigations observed less depth dependence in the x ray conversion gain and MTF of CsI:Tl compared to powder GOS. The results show that optical Swank noise and the Lubberts effect degrade the x ray imaging performance of CsI:Tl less than GOS.

Conclusions

This work described the construction, calibration and use of a single x ray photon imaging system for directly measuring the depth‐dependent gain $\overline{g}(z)$ and spatial resolution MTF(z,f) of turbid x ray scintillators. The system was used to directly measure $\overline{g}(z)$ and MTF(z,f) in the Lanex Regular and Fast Back powder GOS scintillators at 32 keV. In both screens, $\overline{g}(z)$and MTF(z,f) continuously increased as interactions occurred closer to the scintillator's sensor‐coupled surface. The Fast Back had greater depth dependence in $\overline{g}(z)$ and MTF(z,f) than the Regular. Measurements of $\overline{g}(z)$ and MTF(z,f) accurately predicted each scintillator's MTF(f) in an energy‐integrating detector (i.e. I‐FPD). This result validated $\overline{g}(z)$ and MTF(z,f) measurements and demonstrated how knowledge of scintillator depth effects can be used to understand I‐FPD imaging performance.

Conflicts of interest

The authors have no conflicts to disclose.

Appendix 1.

1.1. Curve fits to depth‐dependent gain and mtf measurements

Fits to depth‐dependent gain and MTF measurements for the Lanex Regular and Fast Back are provided here to facilitate their use for readers and future studies. The measurements of $\overline{g}(z)$ shown in Fig. 10 were fit using a third degree polynomial:

$$\overline{g}(z)=p_1{z}^3+p_2{z}^2+p_{3}z+p_4.$$ (A1)

Fitting parameters p ₁ through p ₄ are given for both screens in Table A1.

Table 3.

Third degree polynomial fitting parameters for $\overline{g}(z)$ measurements in the Lanex Regular and Fast Back screens

	p 1	p 2	p 3	p 4
Regular	−1.37E‐04	2.81E‐02	4.03E+00	1.32E+03
Fast Back	−4.59E‐05	1.59E‐02	3.12E+00	7.87E+02

MTF(z,f) measurements were fit to a first‐order exponential function [Eq. (10)] as described in Section 4.C. Each scintillator's fitting parameters A(f) and B(f) can be approximated by 7‐th degree polynomials:

$$\begin{array}{cc}\hfill A(f)=& a_1{f}^7+a_2{f}^6+a_3{f}^5+a_4{f}^4+a_5{f}^3\hfill \\ & +a_6{f}^2+a_{7}f+a_8,\hfill \end{array}$$ (A2)

$$\begin{array}{cc}\hfill B(f)=& b_1{f}^7+b_2{f}^6+b_3{f}^5+b_4{f}^4+b_5{f}^3\hfill \\ & +b_6{f}^2+b_{7}f+b_8.\hfill \end{array}$$ (A3)

Tables A2 and A3 provide parameters for calculating each scintillator's A(f) and B(f), respectively.

Table 4.

Fitting parameters for A(f) in the Regular and Fast Back, which can be used in Eq. (10) to compute fits to MTF(z,f) measurements

	Regular	Fast back
a 1	5.40E‐04	1.97E‐03
a 2	−1.09E‐02	−3.84E‐02
a 3	8.97E‐02	3.01E‐01
a 4	−3.86E‐01	−1.20E+00
a 5	9.07E‐01	2.49E+00
a 6	−1.02E+00	−2.28E+00
a 7	1.58E‐02	2.04E‐02
a 8	1.00E+00	1.01E+00

Table 5.

Fitting parameters for B(f) in the Regular and Fast Back, which can be used in Eq. (10) to compute fits to MTF(z,f) measurements

	Regular	Fast back
b 1	9.92E‐09	4.50E‐06
b 2	3.44E‐06	−6.34E‐05
b 3	−6.21E‐05	2.84E‐04
b 4	4.50E‐04	−1.55E‐04
b 5	−1.73E‐03	−2.31E‐03
b 6	3.48E‐03	6.28E‐03
b 7	−4.15E‐04	−5.99E‐04
b 8	9.86E‐06	5.97E‐06