Quantitative image quality evaluation of pixel-binning in a flat-panel detector for x-ray fluoroscopy

X-ray fluoroscopy places stringent design requirements on new flat-panel (FP) detectors, requiring both low-noise electronics and high data transfer rates. Pixel-binning, wherein data from more that one detector pixel are collected simultaneously, not only lowers the data transfer rate but also increases x-ray counts and pixel signal-to-noise ratio (SNR). In this study, we quantitatively assessed image quality of image sequences from four acquisition methods; no-binning and three types of binning; in synthetic images using a clinically relevant task of detecting an extended guidewire in a four-alternative forced-choice paradigm. Binning methods were conventional data-line (D) and gate-line (G) binning, and a novel method in which alternate frames in an image sequence used D and G binning. Two detector orientations placed the data lines either parallel or perpendicular to the guide wire. At a low exposure of 0.6 microR (1.548 x 10(-10) C/kg) per frame, irrespective of detector orientation, D binning with its reduced electronic noise was significantly (p<0.1) better than the other acquisition methods. On average, alternate binning performed better than G binning. At a higher exposure of 4.0 microR (10.32 x 10(-10) C/kg) per frame, with data lines parallel to the guidewire, detection with D binning was significantly (p<0.1) better than G binning. However, with data lines perpendicular to the guidewire, G binning was significantly (p<0.1) better than D binning because the partial area effect was reduced. Alternate binning was the best binning method when results were averaged over both orientations, and it was as good as the best binning method at either orientation. In addition, at low and high exposures, alternate binning gave a temporally fused image with a smooth guidewire, an important image quality feature not assessed in a detection experiment. While at high exposure, detection with no binning was as good, or better, than the best binning method, it might be impractical at fluoroscopy imaging rates. A computational observer model based on signal detection theory successfully fit data and was used to predict effects of similar acquisition methods. Results from this study suggest the use of exposure-dependent detector binning in fluoroscopy that switches between D binning and alternate binning at low and high exposures, respectively.     

Shimming with permanent magnets for the x-ray detector in a hybrid x-ray/ MR system

In this x-ray/MR hybrid system an x-ray flat panel detector is placed under the patient cradle, close to the MR volume of interest (VOI), where the magnetic field strength is approximately 0.5 T. Immersed in this strong field, several electronic components inside the detector become magnetized and create an additional magnetic field that is superimposed on the original field of the MR scanner. Even after linear shimming, the field homogeneity of the MR scanner remains disrupted by the detector. The authors characterize the field due to the detector with the field of two magnetic dipoles and further show that two sets of permanent magnets (NdFeB) can withstand the main magnetic field and compensate for the nonlinear components of the additional field. The ideal number of magnets and their locations are calculated based on a field map measured with the detector in place. Experimental results demonstrate great promise for this technique, which may be useful in many settings where devices with magnetic components need to be placed inside or close to an MR scanner.     

Integrated radiotherapy imaging system (IRIS): design considerations of tumour tracking with linac gantry-mounted diagnostic x-ray systems with flat-panel detectors

The design of an integrated radiotherapy imaging system (IRIS), consisting of gantry mounted diagnostic (kV) x-ray tubes and fast read-out flat-panel amorphous-silicon detectors, has been studied. The system is meant to be capable of three main functions: radiographs for three-dimensional (3D) patient set-up, cone-beam CT and real-time tumour/marker tracking. The goal of the current study is to determine whether one source/panel pair is sufficient for real-time tumour/marker tracking and, if two are needed, the optimal position of each relative to other components and the isocentre. A single gantry-mounted source/imager pair is certainly capable of the first two of the three functions listed above and may also be useful for the third, if combined with prior knowledge of the target's trajectory. This would be necessary because only motion in two dimensions is visible with a single imager/source system. However, with previously collected information about the trajectory, the third coordinate may be derived from the other two with sufficient accuracy to facilitate tracking. This deduction of the third coordinate can only be made if the 3D tumour/marker trajectory is consistent from fraction to fraction. The feasibility of tumour tracking with one source/imager pair has been theoretically examined here using measured lung marker trajectory data for seven patients from multiple treatment fractions. The patients' selection criteria include minimum mean amplitudes of the tumour motions greater than 1 cm peak-to-peak. The marker trajectory for each patient was modelled using the first fraction data. Then for the rest of the data, marker positions were derived from the imager projections at various gantry angles and compared with the measured tumour positions. Our results show that, due to the three dimensionality and irregular trajectory characteristics of tumour motion, on a fraction-to-fraction basis, a 'monoscopic' system (single source/imager) is inadequate for consistent real-time tumour tracking, even with prior knowledge. We found that, among the seven patients studied with peak-to-peak marker motion greater than 1 cm, five cases have mean localization errors greater than 2 mm and two have mean errors greater than 3 mm. Because of this uncertainty associated with a monoscopic system, two source/imager pairs are necessary for robust 3D target localization. Dual orthogonal x-ray source/imager pairs mounted on the linac gantry are chosen for the IRIS. We further studied the placement of the x-ray sources/panel based on the geometric specifications of the Varian 21EX Clinac. The best configuration minimizes the localization error while maintaining a large field of view and avoiding collisions with the floor/ceiling or couch.     

Dynamic pulmonary imaging: performance properties of a digital fluoroscopy system.

The physical characteristics of dynamic pulmonary imaging with digital fluoroscopy, which differ from those in DSA equipment, have been determined. The spectral distributions and mean energies were calculated and corresponding exposures with varying high voltage and copper filtration (60-100 kVp, 0-2.83 mm Cu) were measured. The utilization of 90-100 kVp with a filter consisting of 1.39 mm Cu and 3 mm Al minimized disturbing skeletal artifacts and reduced the radiation exposure by a factor of approximately 5 in comparison with imaging at 60 kVp without copper filtration. Simultaneously, the measured signal decreased by about 25%. The mean energy of this spectrum exceeded that of 140 kVp chest imaging. The dynamic pulmonary imaging method produces logarithmically transformed x-ray transmittance values linearly related (r = -0.999) to water thickness between 7-10.5 cm, which is equivalent to the normal range of the chest in pediatric patients. A good linear correlation (r = 0.933,N = 92) was obtained when the change in transmitted radiation was compared with tidal volume measured in a rabbit model using a pneumotachometer. The results indicate that the method is applicable for quantitative measurements of pulmonary ventilation. Changes in tidal ventilation can be measured with this noninvasive x-ray imaging technique.     

Dual-energy cardiac imaging: an image quality and dose comparison for a flat-panel detector and x-ray image intensifier

This study presents a comparison of dual-energy imaging with an x-ray image intensifier and flat-panel detector for cardiac imaging. It also investigates if the wide dynamic range of the flat-panel detector can improve dual-energy image quality while reducing patient dose. Experimental contrast-to-noise (CNR) measurements were carried out in addition to simulation studies. Patient entrance exposure and system tube loading were also recorded. The studied contrast objects were calcium and iodine. System performance was quantified with a figure-of-merit (FOM) defined as the image CNR(2) over patient entrance exposure. The range of thickness studied was from 10 to 30 cm of Lucite (PMMA). Detector dose was initially set to 140 nGy (16 microR)/frame. The high-energy 120 kVp beam was filtered by an additional 0.8 mm silver filter. Keeping the same filament current, the kVp for the low-energy beam was adjusted as a function of thickness until 140 nGy was achieved. System performance was found to be similar for both systems, with the x-ray image intensifier performing better at lower thicknesses and the flat-panel detector performing better at higher thicknesses. This requirement of fixed detector entrance exposure was then relaxed and the kVp for the low-energy beam was allowed to vary while the mAs of the x-ray tube remained fixed to study changes in dual-energy image quality, patient dose and FOM with the flat-panel detector. It was found that as the kVp for the low-energy beam was reduced, system performance would rise until reaching a maximum while simultaneously lowering patient exposure. Suggested recommendations for optimal dual-energy imaging implementation are also provided.     

Optimization of a flat-panel based real time dual-energy system for cardiac imaging

A simulation study was conducted to evaluate the effects of high-energy beam filtration, dual-gain operation and noise reduction on dual-energy images using a digital flat-panel detector. High-energy beam filtration increases image contrast through greater beam separation and tends to reduce total radiation exposure and dose per image pair. It is also possible to reduce dual-energy image noise by acquiring low and high-energy images at two different detector gains. In addition, dual-energy noise reduction algorithms can further reduce image noise. The cumulative effect of these techniques applied in series was investigated in this study. The contrast from a small thickness of calcium was simulated over a step phantom of tissue equivalent material with a CsI phosphor as the image detector. The dual-energy contrast-to-noise ratio was calculated using values of energy absorption and energy variance. A figure-of-merit (FOM) was calculated from dual-energy contrast-to-noise ratio (CNR) and patient effective dose estimated from values of entrance exposure. Filter atomic numbers in the range of 1-100 were considered with thicknesses ranging from 0-2500 mg/cm2. The simulation examined combinations of the above techniques which maximized the FOM. The application of a filter increased image contrast by as much as 45%. Near maximal increases were seen for filter atomic numbers in the range of 40-60 and 85-100 with masses above 750 mg/cm2. Increasing filter thickness beyond 1000 mg/cm2 increased tube loading without further significant contrast enhancement. No additional FOM improvements were seen with dual gain before or after the application of any noise reduction algorithm. Narrow beam experiments were carried out to verify predictions. The measured FOM increased by more than a factor of 3.5 for a silver filter thickness of 800 microm, equal energy weighting and application of a noise clipping algorithm. The main limitation of dynamic high-energy filtration is increased tube loading. The results of this study can be used to help develop an optimal dual-energy imaging system.     

Fundamental x-ray interaction limits in diagnostic imaging detectors: spatial resolution

The practice of diagnostic x-ray imaging has been transformed with the emergence of digital detector technology. Although digital systems offer many practical advantages over conventional film-based systems, their spatial resolution performance can be a limitation. The authors present a Monte Carlo study to determine fundamental resolution limits caused by x-ray interactions in four converter materials: Amorphous silicon (a-Si), amorphous selenium, cesium iodide, and lead iodide. The "x-ray interaction" modulation transfer function (MTF) was determined for each material and compared in terms of the 50% MTF spatial frequency and Wagner's effective aperture for incident photon energies between 10 and 150 keV and various converter thicknesses. Several conclusions can be drawn from their Monte Carlo study. (i) In low-Z (a-Si) converters, reabsorption of Compton scatter x rays limits spatial resolution with a sharp MTF drop at very low spatial frequencies (< 0.3 cycles/mm), especially above 60 keV; while in high-Z materials, reabsorption of characteristic x rays plays a dominant role, resulting in a mid-frequency (1-5 cycles/mm) MTF drop. (ii) Coherent scatter plays a minor role in the x-ray interaction MTF. (iii) The spread of energy due to secondary electron (e.g., photoelectrons) transport is significant only at very high spatial frequencies. (iv) Unlike the spread of optical light in phosphors, the spread of absorbed energy from x-ray interactions does not significantly degrade spatial resolution as converter thickness is increased. (v) The effective aperture results reported here represent fundamental spatial resolution limits of the materials tested and serve as target benchmarks for the design and development of future digital x-ray detectors.     

Fundamental x-ray interaction limits in diagnostic imaging detectors: frequency-dependent Swank noise

A frequency-dependent x-ray Swank factor based on the "x-ray interaction" modulation transfer function and normalized noise power spectrum is determined from a Monte Carlo analysis. This factor was calculated in four converter materials: amorphous silicon (a-Si), amorphous selenium (a-Se), cesium iodide (CsI), and lead iodide (PbI2) for incident photon energies between 10 and 150 keV and various converter thicknesses. When scaled by the quantum efficiency, the x-ray Swank factor describes the best possible detective quantum efficiency (DQE) a detector can have. As such, this x-ray interaction DQE provides a target performance benchmark. It is expressed as a function of (Fourier-based) spatial frequency and takes into consideration signal and noise correlations introduced by reabsorption of Compton scatter and photoelectric characteristic emissions. It is shown that the x-ray Swank factor is largely insensitive to converter thickness for quantum efficiency values greater than 0.5. Thus, while most of the tabulated values correspond to thick converters with a quantum efficiency of 0.99, they are appropriate to use for many detectors in current use. A simple expression for the x-ray interaction DQE of digital detectors (including noise aliasing) is derived in terms of the quantum efficiency, x-ray Swank factor, detector element size, and fill factor. Good agreement is shown with DQE curves published by other investigators for each converter material, and the conditions required to achieve this ideal performance are discussed. For high-resolution imaging applications, the x-ray Swank factor indicates: (i) a-Si should only be used at low-energy (e.g., mammography); (ii) a-Se has the most promise for any application below 100 keV; and (iii) while quantum efficiency may be increased at energies just above the K edge in CsI and PbI2, this benefit is offset by a substantial drop in the x-ray Swank factor, particularly at high spatial frequencies.     

Compatibility of interventional x-ray and magnetic resonance imaging: feasibility of a closed bore XMR (CBXMR) system

A next-generation interventional guidance system is proposed that will enable intraprocedural access to both x-ray and magnetic resonance imaging (MRI) modalities. This closed bore XMR (CBXMR) system is comprised of a conventional radiographic rotating anode x-ray tube and a direct conversion flat panel detector on a rotating gantry positioned adjacent to the bore of a 1.5 T MRI. To assess the feasibility of such a system, we have investigated the degree of compatibility between the x-ray components and the MRI. For /-->B(ext)/ < 200 G the effect on the radiographic tube motor was negligible regardless of the orientation of -->B(ext) with respect to the motor axis of rotation--the frequency of anode rotation remained within 6% of the 3400 rpm frequency measured at 0 G. For /-->B(ext)/ >2400 G the anode slowed down to below 2400 rpm at all orientations. At intermediate B(ext), the frequency of rotation varied between 2400 and 3200 rpm, showing a strong dependence on orientation, with -->B(ext) perpendicular to the tube axis having a much stronger effect on the rotation frequency than -->B(ext) parallel to the tube axis. In contrast to the effect of -->B(ext) on the induction motor, parallel -->B(ext) had a stronger detrimental effect on the cathode-anode electron beam, whose path was at 16 degrees to the tube axis, than the perpendicular -->B(ext). Parallel -->B(ext) of several hundred Gauss had a defocusing effect on the x-ray focal spot. -->B(ext) perpendicular to the electron beam shifted the beam without significant defocusing. We have determined that the direct conversion flat panel detector (FPD) technology is not intrinsically sensitive to -->B(ext), and that the modifications required to make the proposed FPDs MRI compatible are minimal. The homogeneity of the MRI signal in the normal field of view was not significantly degraded by the presence of these x-ray components in the vicinity of the MRI bore entrance.     

The x-ray light valve: a low-cost digital radiographic imaging system

In recent years new digital x-ray radiographic and fluoroscopic systems based on large-area flat-panel technology have revolutionized our capability of producing x-ray images. However, such imagers are extraordinarily expensive and their rapid image acquisition capability is not required for many applications such as radiography. Here we report a novel approach to achieve a high-quality digital radiographic system at a cost which is only a small fraction of competitive digital technologies. The results demonstrate that our proposed x-ray light valve system has excellent spatial resolution and adequate sensitivity compared to existing technologies.     

Cone-beam computed tomography with a flat-panel imager: magnitude and effects of x-ray scatter

A system for cone-beam computed tomography (CBCT) based on a flat-panel imager (FPI) is used to examine the magnitude and effects of x-ray scatter in FPI-CBCT volume reconstructions. The system is being developed for application in image-guided therapies and has previously demonstrated spatial resolution and soft-tissue visibility comparable or superior to a conventional CT scanner under conditions of low x-ray scatter. For larger objects consistent with imaging of human anatomy (e.g., the pelvis) and for increased cone angle (i.e., larger volumetric reconstructions), however, the effects of x-ray scatter become significant. The magnitude of x-ray scatter with which the FPI-CBCT system must contend is quantified in terms of the scatter-to-primary energy fluence ratio (SPR) and scatter intensity profiles in the detector plane, each measured as a function of object size and cone angle. For large objects and cone angles (e.g., a pelvis imaged with a cone angle of 6 degrees), SPR in excess of 100% is observed. Associated with such levels of x-ray scatter are cup and streak artifacts as well as reduced accuracy in reconstruction values, quantified herein across a range of SPR consistent with the clinical setting. The effect of x-ray scatter on the contrast, noise, and contrast-to-noise ratio (CNR) in FPI-CBCT reconstructions was measured as a function of SPR and compared to predictions of a simple analytical model. The results quantify the degree to which elevated SPR degrades the CNR. For example, FPI-CBCT images of a breast-equivalent insert in water were degraded in CNR by nearly a factor of 2 for SPR ranging from approximately 2% to 120%. The analytical model for CNR provides a quantitative understanding of the relationship between CNR, dose, and spatial resolution and allows knowledgeable selection of the acquisition and reconstruction parameters that, for a given SPR, are required to restore the CNR to values achieved under conditions of low x-ray scatter. For example, for SPR = 100%, the CNR in FPI-CBCT images can be fully restored by: (1) increasing the dose by a factor of 4 (at full spatial resolution); (2) increasing dose and slice thickness by a factor of 2; or (3) increasing slice thickness by a factor of 4 (with no increase in dose). Other reconstruction parameters, such as transaxial resolution length and reconstruction filter, can be similarly adjusted to achieve CNR equal to that obtained in the scatter-free case.     

Blurring artifacts in megavoltage radiography with a flat-panel imaging system: comparison of Monte Carlo simulations with measurements

Originally designed for use at medical-imaging x-ray energies, imaging systems comprising scintillating screens and amorphous Si detectors are also used at the megavoltage photon energies typical of portal imaging and industrial radiography. While image blur at medical-imaging x-ray energies is strongly influenced both by K-shell fluorescence and by the transport of optical photons within the scintillator layer, at higher photon energies the image blur is dominated by radiation scattered from the detector housing and internal support structures. We use Monte Carlo methods to study the blurring in a notional detector: a series of semi-infinite layers with material compositions, thicknesses, and densities similar to those of a commercially available flat-panel amorphous Si detector system comprising a protective housing, a gadolinium oxysulfide scintillator screen, and associated electronics. We find that the image blurring, as described by a point-spread function (PSF), has three length scales. The first component, with a submillimeter length scale, arises from electron scatter within the scintillator and detection electronics. The second component, with a millimeter-to-centimeter length scale, arises from electrons produced in the front cover of the detector. The third component, with a length scale of tens of centimeters, arises from photon scatter by the back cover of the detector. The relative contributions of each of these components to the overall PSF vary with incident photon energy. We present an algorithm that includes the energy-dependent sensitivity and energy-dependent PSF within a ray-tracing formalism. We find quantitative agreement (approximately 2%) between predicted radiographs with radiographs of copper step wedges, taken with a 9 MV bremsstrahlung source and a commercially available flat-panel system. The measured radiographs show the blurring artifacts expected from both the millimeter-scale electron transport and from the tens-of-centimeters length scale arising from the scattered photon transport. Calculations indicate that neglect of the energy-dependent blurring would lead to discrepancies in the apparent transmission of these wedges of the order of 9%.     

Spektr: a computational tool for x-ray spectral analysis and imaging system optimization

A set of computational tools are presented that allow convenient calculation of x-ray spectra, selection of elemental and compound filters, and calculation of beam quality characteristics, such as half-value layer, mR/mAs, and fluence per unit exposure. The TASMIP model of Boone and Seibert is adapted to a library of high-level language (Matlab) functions and shown to agree with experimental measurements across a wide range of kVp and beam filtration. Modeling of beam filtration is facilitated by a convenient, extensible database of mass and mass-energy attenuation coefficients compiled from the National Institute of Standards and Technology. The functions and database were integrated in a graphical user interface and made available online at http:// www.aip.org/epaps/epaps.html. The functionality of the toolset and potential for investigation of imaging system optimization was illustrated in theoretical calculations of imaging performance across a broad range of kVp, filter material type, and filter thickness for direct and indirect-detection flat-panel imagers. The calculations reveal a number of nontrivial effects in the energy response of such detectors that may not have been guessed from simple K-edge filter techniques, and point to a variety of compelling hypotheses regarding choice of beam filtration that warrant future investigation.     

Time-domain finite-difference/finite-element hybrid simulations of radio frequency coils in magnetic resonance imaging

A hybrid method that combines the finite-difference time-domain (FDTD) method and the finite-element time-domain (FETD) method is presented for simulating radio-frequency (RF) coils in magnetic resonance imaging. This method applies a high-fidelity FETD method to RF coils, while the human body is modeled with a low-cost FDTD method. Since the FDTD and the FETD methods are applied simultaneously, the dynamic interaction between RF coils and the human body is fully accounted for. In order to simplify the treatment of the highly irregular FDTD/FETD interface, composite elements are proposed. Two examples are provided to demonstrate the validity and effectiveness of the hybrid method in high-field receive-and-transmit coil design. This approach is also applicable to general bio-electromagnetic simulations.     

Study of increased radiation when an x-ray tube is placed in a strong magnetic field

When a fixed anode x-ray tube is placed in a magnetic field (B) that is parallel to the anode-cathode axis, the x-ray exposure increases with increasing B. It was hypothesized that the increase was caused by backscattered electrons which were constrained by B and reaccelerated by the electric field onto the x-ray tube target. We performed computer simulations and physical experiments to study the behavior of the backscattered electrons in a magnetic field, and their effects on the radiation output, x-ray spectrum, and off-focal radiation. A Monte Carlo program (EGS4) was used to generate the combined energy and angular distribution of the backscattered electrons. The electron trajectories were traced and their landing locations back on the anode were calculated. Radiation emission from each point was modeled with published data (IPEM Report 78), and thus the exposure rate and x-ray spectrum with the contribution of backscattered electrons could be predicted. The point spread function for a pencil beam of electrons was generated and then convolved with the density map of primary electrons incident on the anode as simulated with a finite element program (Opera-3d, Vector Fields, UK). The total spatial distribution of x-ray emission could then be calculated. Simulations showed that for an x-ray tube working at 65 kV, about 54% of the electrons incident on the target were backscattered. In a magnetic field of 0.5 T, although the exposure would be increased by 33%, only a small fraction of the backscattered electrons landed within the focal spot area. The x-ray spectrum was slightly shifted to lower energies and the half value layer (HVL) was reduced by about 6%. Measurements of the exposure rate, half value layer and focal spot distribution were acquired as functions of B. Good agreement was observed between experimental data and simulation results. The wide spatial distribution of secondary x-ray emission can degrade the MTF of the x-ray system at low spatial frequencies for B < 0.5 T.     

Investigation of electron trajectories of an x-ray tube in magnetic fields of MR scanners

A hybrid x-ray/MR system combining an x-ray fluoroscopic system and an open-bore magnetic resonance (MR) system offers advantages from both powerful imaging modalities and thus can benefit numerous image-guided interventional procedures. In our hybrid system configurations, the x-ray tube and detector are placed in the MR magnet and therefore experience a strong magnetic field. The electron beam inside the x-ray tube can be deflected by a misaligned magnetic field, which may damage the tube. Understanding the deflection process is crucial to predicting the electron beam deflection and avoiding potential damage to the x-ray tube. For this purpose, the motion of an electron in combined electric (E) and magnetic (B) fields was analyzed theoretically to provide general solutions that can be applied to different geometries. For two specific cases, a slightly misaligned strong field and a perpendicular weak field, computer simulations were performed with a finite-element method program. In addition, experiments were conducted using an open MRI magnet and an inserted electromagnet to quantitatively verify the relationship between the deflections and the field misalignment. In a strong (B > E/c; c: speed of light) and slightly misaligned magnetic field, the deflection in the plane of E and B caused by electrons following the magnetic field lines is the dominant component compared to the deflection in the E X B direction due to the drift of electrons. In a weak magnetic field (B < or = E/c), the main deflection is in the E x B direction and is caused by the perpendicular component of the magnetic field.     

Signal and noise transfer properties of photoelectric interactions in diagnostic x-ray imaging detectors

Image quality in diagnostic x-ray imaging is ultimately limited by the statistical properties governing how, and where, x-ray energy is deposited in a detector. This in turn depends on the physics of the underlying x-ray interactions. In the diagnostic energy range (10-100 keV), most of the energy deposited in a detector is through photoelectric interactions. We present a theoretical model of the photoelectric effect that specifically addresses the statistical nature of energy absorption by photoelectrons, K and L characteristic x rays, and Auger electrons. A cascaded-systems approach is used that employs a complex structure of parallel cascades to describe signal and noise transfer through the photoelectric effect in terms of the modulation transfer function, Wiener noise power spectrum, and detective quantum efficiency (DQE). The model was evaluated by comparing results with Monte Carlo calculations for x-ray converters based on amorphous selenium (a-Se) and lead (Pb), representing both low and high-Z materials. When electron transport considerations can be neglected, excellent agreement (within 3%) is obtained for each metric over the entire diagnostic energy range in both a-Se and Pb detectors up to 30 cycles/mm, the highest frequency tested. The cascaded model overstates the DQE when the electron range cannot be ignored. This occurs at approximately two cycles/mm in a-Se at an incident photon energy of 80 keV, whereas in Pb, excellent agreement is obtained for the DQE over the entire diagnostic energy range. However, within the context of mammography (20 keV) and micro-computed tomography (40 keV), the effects of electron transport on the DQE are negligible compared to fluorescence reabsorption, which can lead to decreases of up to 30% and 20% in a-Se and Pb, respectively, at 20 keV; and 10% and 5%, respectively, at 40 keV. It is shown that when Swank noise is identified in a Fourier model, the Swank factor must be frequency dependent. This factor decreases quickly with frequency, and in the case of a-Se and Pb, decreases by up to a factor of 3 at five cycles/mm immediately above the K edge. The frequency-dependent Swank factor is also equivalent to what we call the "photoelectric DQE," which describes signal and noise transfer through photoelectric interactions.