System and method to account for cross-talk among coherent scatter detectors

1. A method to account for cross-talk among a plurality of coherent scatter detectors of a multi-detector inverse fan beam x-ray diffraction imaging (MD-IFB XDI) system, said method comprising:

emitting a plurality of primary beams simultaneously from an x-ray source, each primary beam of the plurality of primary beams is directed to a corresponding convergence point associated with a corresponding coherent scatter detector of the plurality of coherent scatter detectors, each primary beam is configured to interact with an object to produce a scatter radiation;

measuring a diffraction profile X k at each coherent scatter detector D k of the plurality of coherent scatter detectors, each diffraction profile X k comprises a spectrum of a number of photons from the scatter radiation measured by the coherent scatter detector D k , wherein each diffraction X k includes a cross-talk component arising from at least the primary beam directed to the convergence point associated with at least a second of the plurality of coherent scatter detectors D j ;

generating, for each of a plurality of energy levels within the spectrum measured in the diffraction profile X k , a correction factor for the cross-talk component based on the energy level and a scatter angle defined between the primary beam directed to the convergence point associated with the coherent scatter detector D j and a scatter radiation path from that primary beam to the coherent scatter detector D k ; and

correcting each diffraction profile X k corresponding to each coherent scatter detector D k to remove the cross-talk component.

2. A method in accordance with claim 1 , further comprising calculating a plurality of scatter angles by which scatter beams arising from primary beams directed to convergence points for the remaining coherent scatter detectors reaches each coherent scatter detector D k .

3. A method in accordance with claim 1 , further comprising assuming that above a highest energy value, E top , of the spectrum measured in the diffraction profile X k corresponding to a highest momentum transfer value, x top , the cross-talk component is zero.

4. A method in accordance with claim 3 , comprising wherein said generating a correction factor comprises using a momentum transfer x k , wherein:

x

k

=

E

k

hc

·

sin

⁡

(

θ

2

)

wherein E k is the energy level, h is Planck's constant, c is the speed of light and θ is the scatter angle defined between the primary beam directed to the convergence point associated with the coherent scatter detector D j and a scatter radiation path from that primary beam to the coherent scatter detector D k .

5. A method in accordance with claim 3 , wherein said generating a correction factor for each of a plurality of energy levels comprises starting at the energy level designated by E top and successively decrementing the energy level to a next energy level, thereby generating a correction factor at each of the plurality of energy levels for each coherent scatter detector D k using post-correction data from a higher energy level.

6. A method in accordance with claim 5 , further comprising:

setting the correction factor to zero if the momentum transfer x k is greater than or equal to x top ; and

setting the correction factor to the value of the diffraction profile measured at the coherent scatter detector D j evaluated at the momentum transfer value x k if the momentum transfer x k is less than or equal to x top .

7. A method in accordance with claim 6 , wherein said correcting each diffraction profile X k comprises subtracting the correction factor from the value of the diffraction profile X k evaluated at the momentum transfer value x k .

8. A method in accordance with claim 5 , further comprising terminating the correction procedure when the energy level is decremented below a threshold value.

9. A method in accordance with claim 3 , wherein

the x-ray source comprises a multi-focus x-ray source (MFXS) configured to emit radiation sequentially from a plurality of focus points denoted by F 1 , F 2 , . . . F n with a running index i, said method further comprising:

activating each focus point F i in a sequence, each activated focus point F i emits the plurality of primary beams; and

measuring a diffraction profile X k at each coherent scatter detector D k of the plurality of coherent scatter detectors while each focus point F i is activated, wherein said generating a correction factor for each of a plurality of energy levels further comprises looping through of the plurality of focus points.

10. A method in accordance with claim 3 , further comprising:

initializing the correction factor to zero at the momentum transfer value, x top , corresponding to the highest energy value, E top , of the spectrum measured in the diffraction Profile X k .

11. A method in accordance with claim 1 , said at least second coherent scatter detector D j comprises multiple coherent scatter detectors D j with a running index and said generating a correction factor for each of a plurality of energy levels further comprises looping through each scatter detector D j for each energy level.

12. A method in accordance with claim 1 , wherein

said generating a correction factor further comprises the use of a weighting factor defined for the scatter radiation path from the primary beam directed to the convergence point associated with the coherent scatter detector D j to the coherent scatter detector D k .

13. A method in accordance with claim 12 , wherein the weighting factor

accounts for at least one of (i) a reduction in solid angle that the coherent scatter detector D k presents to the scatter radiation path and (ii) an increased attenuation associated with the scatter path.

14. A security detection system, comprising:

an x-ray source configured to emit radiation;

a multi-angle primary collimator configured to select from the radiation emitted a plurality of primary beams each directed to a corresponding convergence point of a plurality of convergence points, each primary beam is configured to interact with an object to produce a scatter radiation;

a plurality of coherent scatter detectors each associated with a corresponding one of the plurality of convergence points and each configured to measure a number and an energy of photons from the scatter radiation; and

a processor coupled in electrical communication with each said coherent scatter detector of the plurality of coherent scatter detectors, said processor configured to:

record a diffraction profile X k at each said coherent scatter detector D k of said plurality of coherent scatter detectors, each diffraction profile X k comprises a spectrum of the number of photons from the scatter radiation measured by said coherent scatter detector D k , wherein each diffraction profile X k includes a cross-talk component arising from at least the primary beam directed to the convergence point associated with at least a second of said plurality of coherent scatter detectors D j ;

generate, for each of a plurality of energy levels within the spectrum measured in the diffraction profile X k , a correction factor for the cross-talk component based on the energy level and a scatter angle defined between the primary beam directed to the convergence point associated with said coherent scatter detector D j and a scatter radiation path from that primary beam to said coherent scatter detector D k ; and

correct each diffraction profile X k corresponding to each coherent scatter detector D k to remove the cross-talk component.

15. A security detection system in accordance with claim 14 , wherein said x-ray source comprises a multi-focus x-ray source (MFXS) configured to emit radiation sequentially from a plurality of focus points denoted by F 1 , F 2 , . . . F n with a running index i, and said processor is further configured to:

activate each said focus point F i in a sequence, wherein said multi-angle primary collimator is configured to select from the radiation emitted the plurality of primary beams from said activated focus and

record a diffraction profile X k at each said coherent scatter detector D k of said plurality of coherent scatter detectors while each said focus point F i is activated; and

loop through each diffraction profile X k for each of the plurality of focus points when generating a correction factor for each of the plurality of energy levels.

16. A security detection system in accordance with claim 15 , wherein said at least second coherent scatter detector D j comprises multiple coherent scatter detectors D j with a running index j, and said processor is further configured to loop through each scatter detector D j for each energy level.

17. A security detection system in accordance with claim 14 , wherein said processor is further configured to assume that above a highest energy value E top of the spectrum measured in the diffraction profile X k corresponding to a highest momentum transfer value x top the cross-talk component is zero.

18. A security detection system in accordance with claim 17 , wherein the correction factor is generated using a momentum transfer x k , wherein:

x

k

=

E

k

hc

·

sin

⁡

(

θ

2

)

wherein E k is the energy level, h is Planck's constant, c is the speed of light and θ is the scatter angle defined between the primary beam directed to the convergence point associated with the coherent scatter detector D j and a scatter radiation path from that primary beam to the coherent scatter detector D k .

19. A security detection system in accordance with claim 18 , wherein the correction factor for each of the plurality of energy levels is generated by starting at the energy level designated by E top and successively decrementing the energy level to a next energy level, thereby generating a correction factor for each said coherent scatter detector D k using post-correction data.

20. A security detection system in accordance with claim 19 , wherein said processor is further configured to:

set the correction factor to zero if the momentum transfer x k is greater than or equal to x top ; and

set the correction factor to the value of the diffraction profile measured at said coherent scatter detector D j evaluated at the momentum transfer value x k if the momentum transfer x k is less than or equal to x top .

21. A security detection system in accordance with claim 19 , wherein said processor is further configured to terminate the correction procedure when the energy level is decremented below a threshold energy level value.

22. A security detection system in accordance with claim 18 , wherein said processor is further configured to correct each diffraction profile X k by subtracting the correction factor from the value of the diffraction profile X k evaluated at the momentum transfer value x k .

23. A security detection system in accordance with claim 14 , wherein said processor is further configured to use a weighting factor in generating the correction factor, wherein the weighting factor is defined for the scatter radiation path from the primary beam directed to the convergence point associated with said coherent scatter detector D j to said coherent scatter detector D k .

24. A security detection system in accordance with claim 23 , wherein the weighting factor accounts for at least one of (i) a reduction in solid angle that said coherent scatter detector D k presents to the scatter radiation path and (ii) an increased attenuation associated with the scatter path.