Geometric calibration for a next-generation digital breast tomosynthesis system using virtual line segments

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Purpose In previous work, a theoretical model of the point spread function (PSF) for oblique x‐ray incidence in amorphous selenium (a‐Se) detectors was proposed. The purpose of this paper is to develop a complementary model that includes two additional features. First, the incidence angle and the directionality of ray incidence are calculated at each position, assuming a divergent x‐ray beam geometry. This approach allows the non‐stationarity of the PSF to be modeled. Second, this paper develops a framework that is applicable to a digital system, unlike previous work which did not model the presence of a thin‐film transistor (TFT) array. Methods At each point on the detector, the incidence angle and the ray incidence direction are determined using ray tracing. Based on these calculations, an existing model for the PSF of the x‐ray converter (Med Phys. 1995;22:365‐374) is generalized to a non‐stationary model. The PSF is convolved with the product of two rectangle functions, which model the sampling of the TFT array. The rectangle functions match the detector element (del) size in two dimensions. Results It is shown that the PSF can be calculated in closed form. This solution is used to simulate a digital mammography (DM) system at two x‐ray energies (20 and 40 keV). Based on the divergence of the x‐ray beam, the direction of ray incidence varies with position. Along this direction, the PSF is broader than the reference rect function matching the del size. The broadening is more pronounced with increasing obliquity. At high energy, the PSF deviates more strongly from the reference rect function, indicating that there is more blurring. In addition, the PSF is calculated along the polar angle perpendicular to the ray incidence direction. For this polar angle, the shape of the PSF is dependent upon whether the ray incidence direction is parallel with the sides of the detector. If the ray incidence direction is parallel with either dimension, the PSF is a perfect rectangle function, matching the del size. However, if the ray incidence direction is at an oblique angle relative to the sides of the detector, the PSF is not rectangular. These results illustrate the non‐stationarity of the PSF. Conclusions This paper demonstrates that an existing model of the PSF of a‐Se detectors can be generalized to include the effects of non‐stationarity and digitization. The PSF is determined in closed form. This solution offers the advantage of shorter computation time relative to approaches that use numerical methods. This model is a tool for simulating a‐Se detectors in future work, such as in virtual clinical trials with computational phantoms.

Section: Resultsmentioning

confidence: 99%

Section: A Modeling Parametersmentioning

confidence: 99%

Non‐stationary model of oblique x‐ray incidence in amorphous selenium detectors: I. Point spread function

Acciavatti

Maidment

2019

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“…We model the NGT system with the same acquisition parameters as those described in Part 1 for a digital mammography (DM) image (analogous to the central projection in DBT). To calculate the MTF along any polar angle ( α ), a coordinate transformation can be introduced

f_{x} = f_{r} cos α

f_{y} = f_{r} sin α,

where f r denotes radial frequency.…”

Section: Resultsmentioning

confidence: 99%

“…Ultimately, this model is used to demonstrate the performance advantage of a prototype “next‐generation” tomosynthesis (NGT) system, which we are developing at the University of Pennsylvania . This system is capable of x‐ray source motion with more degrees of freedom than a clinical DBT system.…”

Section: Introductionmentioning

confidence: 99%

“…2 Ultimately, this model is used to demonstrate the performance advantage of a prototype "next-generation" tomosynthesis (NGT) system, which we are developing at the University of Pennsylvania. [11][12][13][14][15][16] This system is capable of xray source motion with more degrees of freedom than a clinical DBT system. Our previous work showed that the NGT system offers an improvement in image quality using the Defrise phantom.…”

Section: Introductionmentioning

confidence: 99%

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Nonstationary model of oblique x‐ray incidence in amorphous selenium detectors: II. Transfer functions

Acciavatti

Maidment

2019

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Purpose One limitation of experimental techniques for quantifying resolution and noise in detectors is that the measurement is made in a region‐of‐interest (ROI). With theoretical modeling, these properties can be measured at a point, allowing for quantification of spatial anisotropy. This paper calculates nonstationary transfer functions for amorphous selenium (a‐Se) detectors in breast imaging. We use this model to demonstrate the performance advantage of a “next‐generation” tomosynthesis (NGT) system, which is capable of x‐ray source motion with more degrees of freedom than a clinical tomosynthesis system. Methods Using Swank's formulation, the optical transfer function (OTF) and presampled noise power spectra (NPS) are determined based on the point spread function derived in Part 1. The modulation transfer function (MTF) is found from the normalized modulus of the OTF. To take into account the presence of digitization, the presampled NPS is convolved with a two‐dimensional comb function, for which the period along each direction is the reciprocal of the detector element size. The detective quantum efficiency (DQE) is then determined from combined knowledge of the OTF and NPS. Results First, the model is used to demonstrate the loss of image quality due to oblique x‐ray incidence. The MTF is calculated along various polar angles, corresponding to different orientations of the input frequency. The MTF is independent of the incidence angle if the polar angle is perpendicular to the ray incidence direction. However, along other polar angles, oblique incidence results in MTF degradation at high frequencies. The MTF degradation is most substantial along the ray incidence direction. Unlike the MTF, the normalized NPS (NNPS) is independent of the incidence angle. To measure the relative signal‐to‐noise, the DQE is also calculated. Oblique incidence yields high‐frequency DQE degradation, which is more pronounced than the MTF degradation. This arises because the DQE is proportionate with the square of the MTF. Ultimately, this model is used to evaluate how the image quality varies over the detector area. For various projection images, we calculate the variation in the incidence angle over this area. With the NGT system, the source can be positioned in such a way that this variation is minimized, and hence the DQE exhibits less anisotropy. To achieve this improvement in the image quality, the source needs to have a component of motion in the posteroanterior (PA) direction, which is perpendicular to the conventional direction of source motion in tomosynthesis. Conclusions In a‐Se detectors, the DQE at high frequencies is degraded due to oblique incidence. The DQE degradation is more pronounced than the MTF degradation. This model is used to quantify the spatial variation in DQE over the detector area. The use of PA source motion is a strategy for minimizing this variation and thus improving the image quality.

Line‐based iterative geometric calibration method for a tomosynthesis system

Choi,

Vent,

Acciavatti

et al. 2024

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BackgroundA next generation tomosynthesis (NGT) system, capable of two‐dimensional source motion, detector motion in the perpendicular direction, and magnification tomosynthesis, was constructed to investigate different acquisition geometries. Existing position‐based geometric calibration methods proved ineffective when applied to the NGT geometries.PurposeA line‐based iterative calibration method is developed to perform accurate geometric calibration for the NGT system.MethodsThe proposed method calculates the system geometry through virtual line segments created by pairs of fiducials within a calibration phantom, by minimizing the error between the line equations computed from the true and estimated fiducial projection pairs. It further attempts to correct the 3D fiducial locations based on the initial geometric calibration. The method's performance was assessed via simulation and experimental setups with four distinct NGT geometries: X, T, XZ, and TZ. The X geometry resembles a conventional DBT acquisition along the chest wall. The T geometry forms a “T”‐shaped source path in mediolateral (ML) and posteroanterior (PA) directions. A descending detector motion is added to both X and T geometries to form the XZ and TZ geometries, respectively. Simulation studies were conducted to assess the robustness of the method to geometric perturbations and inaccuracies in fiducial locations. Experimental studies were performed to assess the impact of phantom magnification and the performance of the proposed method for various geometries, compared to the traditional position‐based method. Star patterns were evaluated for both qualitative and quantitative analyses; the Fourier spectral distortions (FSDs) graphs and the contrast transfer function (CTF) were extracted. The limit of spatial resolution (LSR) was measured at 5% modulation of the CTF.ResultsThe proposed method presented is highly robust to geometric perturbation and fiducial inaccuracies. After the line‐based iterative method, the mean distance between the true and estimated fiducial projections was [X, T, XZ, TZ]: [0.01, 0.01, 0.02, 0.01] mm. The impact of phantom magnification was observed; a contact‐mode acquisition of a calibration phantom successfully provided an accurate geometry for 1.85× magnification images of a star pattern, with the X geometry. The FSD graphs for the contact‐mode T geometry acquisition presented evidence of super‐resolution, with the LSR of [0°‐quadrant: 8.57, 90°‐quadrant: 8.47] lp/mm. Finally, a contact‐mode XZ geometry acquisition and a 1.50× magnification TZ geometry acquisition were reconstructed with three calibration methods—position‐based, line‐based, and iterative line‐based. As more advanced methods are applied, the CTF becomes more isotropic, the FSD graphs demonstrate less spectral leakage as super‐resolution is achieved, and the degree of blurring artifacts reduces significantly.ConclusionsThis study introduces a robust calibration method tailored to the unique requirements of advanced tomosynthesis systems. By employing virtual line segments and iterative techniques, we ensure accurate geometric calibration while mitigating the limitations posed by the complex acquisition geometries of the NGT system. Our method's ability to handle various NGT configurations and its tolerance to fiducial misalignment make it a superior choice compared to traditional calibration techniques.