Characteristic X-ray escape correction in photon-counting detectors
View Patent ↗A method and an apparatus for determining primary and secondary escape probabilities for a large photon-counting detector without pile-up. A model for the detector with no pile-up is formulated and used for spectrum correction in a computed tomography scanner. The method includes computing primary K-escape and secondary K-escape probabilities occurring at a certain depth within the photon-counting detector. Further, a no pile-up model for the photon-counting detector is formulated by determining a response function, based on the computed primary and secondary K-escape probabilities and geometry of the photon-counting detector. The method includes obtaining a measured CT scan of an object and further performs spectrum correction by determining the incident input spectrum based on the response function and the measured spectrum of the large photon-counting detector.
1. A computed-tomography (CT) apparatus, the apparatus comprising:
an X-ray tube configured to radiate X-rays toward an object;
a photon-counting detector configured to capture incident X-ray photons emitted from the X-ray tube; and
processing circuitry configured to
compute a plurality of primary K-escape probabilities and a plurality of secondary K-escape probabilities for the photon-counting detector, wherein computing the primary K-escape probabilities includes computing, for a given energy of an incident photon and a given depth at which a photoelectric interaction occurs, a sum, over a plurality of escape types, of a product of (1) a probability of a K-edge photon being emitted for the given energy when the photoelectric interaction has occurred, and (2) an integral over a solid angle that depends on the given depth;
determine a response function for the photon-counting detector based on the computed primary and secondary K-escape probabilities and a geometry of the photon counting detector;
obtain, from the photon-counting detector, a measured output spectrum corresponding to the incident X-ray photons; and
generate a CT image using the response function and the measured output spectrum.
2. The CT apparatus of claim 1 , wherein the response function includes a first energy portion that contributes to the measured spectrum and is based on a total probability of no escape from the photon-counting detector, and a second energy portion that contributes to the measured spectrum and is based on the plurality of primary and secondary K-escape probabilities from the photon-counting detector.
3. The CT apparatus of claim 2 , wherein the second energy portion further includes a third energy portion that corresponds to energy that escapes from a plurality of surfaces of the photon-counting detector and is lost from the photon-counting detector, and a fourth energy portion that exits the photon-counting detector and enters a neighboring photon-counting detector.
4. The CT apparatus of claim 1 , wherein the primary K-escape probabilities and the secondary K-escape probabilities depend on a depth within the photon-counting detector at which the photoelectric interaction occurs.
5. The CT apparatus of claim 4 , wherein the depth within the photon-counting detector at which the photoelectric interaction occurs corresponds to an incident angle formed between an incident photon that impinges the photon-counting detector and a normal to the surface of the photon-counting detector.
6. The CT apparatus of claim 1 , wherein the measured output spectrum is related to an incident spectrum by the response function.
7. A method for a spectral computed-tomography (CT) scanner, the scanner including an X-ray tube to radiate X-rays toward an object and a photon-counting detector to capture incident X-ray photons emitted from the X-ray tube, the method comprising:
computing a plurality of primary K-escape probabilities and a plurality of secondary K-escape probabilities for the photon-counting detector, wherein computing the primary K-escape probabilities includes computing, for a given energy of an incident photon and a given depth at which a photoelectric interaction occurs, a sum, over a plurality of escape types, of a product of (1) a probability of a K-edge photon being emitted for the given energy when the photoelectric interaction has occurred, and (2) an integral over a solid angle that depends on the given depth;
determining a response function for the photon-counting detector based on the computed primary and secondary K-escape probabilities and a geometry of the photon-counting detector;
obtaining, from the photon-counting detector, a measured output spectrum corresponding to the incident X-ray photons; and
generating a CT image using the response function and the measured output spectrum.
8. The method of claim 7 , wherein the response function includes a first energy portion that contributes to the measured spectrum and is based on a total probability of no escape from the photon-counting detector, and a second energy portion that contributes to the measured spectrum and is based on the plurality of primary and secondary K-escape probabilities from the photon-counting detector.
9. The method of claim 8 , wherein the total probability of no escape is based on a sum of the primary K-escape probabilities and the secondary K-escape probabilities.
10. The method of claim 8 , wherein the second energy portion further includes a third energy portion that corresponds to energy that escapes from a plurality of surfaces of the photon-counting detector and is lost from the photon-counting detector, and a fourth energy portion that exits the photon-counting detector and enters a neighboring photon-counting detector.
11. The method of claim 7 , wherein the measured output spectrum is related to an incident spectrum by the response function.
12. The method of claim 7 , wherein the primary K-escape probabilities and the secondary K-escape probabilities depend on a depth within the photon-counting detector at which the photoelectric interaction occurs.
13. The method of claim 12 , wherein each primary K-escape probability is greater than a corresponding secondary K-escape probability for the depth at which the photoelectric interaction occurred.
14. The method of claim 12 , wherein the primary K-escape and the secondary K-escape probabilities reduce exponentially with increasing depths within the photon-counting detector at which the photoelectric interaction occurs.
15. The method of claim 13 , wherein the depth within the photon-counting detector at which the photoelectric interaction occurs corresponds to an incident angle formed between an incident photon that impinges the photon-counting detector and a normal to the surface of the photon-counting detector.
16. The method of claim 15 , wherein each probability of primary K-escape increases with increasing angle of incidence.
17. A non-transitory computer readable medium having stored thereon a program that when executed by a computer, causes the computer to perform a method for a spectral computed-tomography (CT) scanner including an X-ray tube to radiate X-rays toward an object and a photon-counting detector to capture incident X-ray photons emitted from the X-ray tube, the method comprising:
computing a plurality of primary K-escape probabilities and a plurality of secondary K-escape probabilities for the photon-counting detector, wherein computing the primary K-escape probabilities includes computing, for a given energy of an incident photon and a given depth at which a photoelectric interaction occurs, a sum, over a plurality of escape types, of a product of (1) a probability of a K-edge photon being emitted for the given energy when the photoelectric interaction has occurred, and (2) an integral over a solid angle that depends on the given depth;
determining a response function for the photon-counting detector based on the computed primary and secondary K-escape probabilities and a geometry of the photon-counting detector;
obtaining, from the photon-counting detector, a measured output spectrum corresponding to the incident X-ray photons; and
generating a CT image using the response function and the measured output spectrum.