Purpose: Photon counting x-ray detectors (PCXD) may improve dose-efficiency but are hampered by limited count rate. They generally have imperfect energy response. Multi-layer ("in-depth") detectors have been proposed to enable higher count rates but the potential benefit of the depth information has not been explored. We conducted a simulation study to compare in-depth detectors against single layer detectors composed of common materials. Both photon counting and energy integrating modes were studied. Methods: Polyenergetic transmissions were simulated through 25cm of water and 1cm of calcium. For PCXD composed of Si, GaAs or CdTe a 120kVp spectrum was used. For energy integrating x-ray detectors (EIXD) made from GaAs, CdTe or CsI, spectral imaging was done using 80 and 140kVp and matched dose. Semi-ideal and phenomenological energy response models were used. To compare these detectors, we computed the Cramér-Rao lower bound (CRLB) of the variance of basis material estimates. Results: For PCXDs with perfect energy response, depth data provides no additional information. For PCXDs with imperfect energy response and for EIXDs the improvement can be significant. E.g., for a CdTe PCXD with realistic energy response, depth information can reduce the variance by ~50%. The improvement depends on the x-ray spectrum. For a semi-ideal Si detector and a narrow x-ray spectrum the depth information has minimal advantage. For EIXD, the in-depth detector has consistent variance reduction (15% and 17%~19% for water and calcium, respectively). Conclusions: Depth information is beneficial to spectral imaging for both PCXD and EIXD. The improvement depends critically on the detector energy response.
[1]
R. Carmi,et al.
Material separation with dual-layer CT
,
2005,
IEEE Nuclear Science Symposium Conference Record, 2005.
[2]
J. Schlomka,et al.
Experimental feasibility of multi-energy photon-counting K-edge imaging in pre-clinical computed tomography
,
2008,
Physics in medicine and biology.
[3]
Gisela Anton,et al.
Using the Medipix2 detector for energy weighting
,
2005
.
[4]
Ho Kyung Kim,et al.
Analytic Model of Energy-Absorption Response Functions in Compound X-ray Detector Materials
,
2013,
IEEE Transactions on Medical Imaging.
[5]
E. Roessl,et al.
Cramér–Rao lower bound of basis image noise in multiple-energy x-ray imaging
,
2009,
Physics in medicine and biology.
[6]
M. Danielsson,et al.
Photon-counting spectral computed tomography using silicon strip detectors: a feasibility study
,
2010,
Physics in medicine and biology.
[7]
K. Taguchi,et al.
Vision 20/20: Single photon counting x-ray detectors in medical imaging.
,
2013,
Medical physics.
[8]
N J Pelc,et al.
Depth-segmented detector for x-ray absorptiometry.
,
2000,
Medical physics.
[9]
A. Macovski,et al.
Energy-selective reconstructions in X-ray computerised tomography
,
1976,
Physics in medicine and biology.