Methods of calibrating semiconductor radiation detectors using K-edge filters
A set of N standard bin count distributions may be generated by irradiating a test radiation detector system with an X-ray beam attenuated by a respective one of N different K-edge filters for each of the at least one X-ray source energy setting. Energy bins of detectors of a target radiation detector system may be calibrated by generating measured bin count distributions for each calibration setting in which a respective one of the N different K-edge filters attenuates a source X-ray beam. Calibration parameters of the detectors of the target radiation detector system may be adjusted to match each of the measured bin count distributions to a corresponding standard bin count distribution. In addition, energy resolution of the radiation detectors can be measured and calibrated by fitting a portion of the measured X-ray spectrum near a K-edge to a fitting function.
1. A method of measuring an energy resolution of an X-ray radiation detector, comprising:
placing a K-edge filter between an X-ray source and an X-ray radiation detector;
measuring an X-ray spectrum with the K-edge filter in a beam path between the X-ray source and the X-ray radiation detector;
locating at least two points for fitting a region of the measured X-ray spectrum near a K-edge energy of the K-edge filter in the measured X-ray spectrum; and
determining an energy resolution of the X-ray radiation detector by fitting the at least two points to a fitting function that correlates a parameter of the fitting function to obtain a full width at half maximum (FWHM) value of the measured X-ray spectrum.
2. The method of claim 1 , wherein the at least two points comprise points having a respective measured intensity in a range from 5% to 95% of a local maximum intensity of the measured X-ray spectrum in proximity to the K-edge energy of the K-edge filter.
3. The method of claim 2 , wherein the parameter of the fitting function comprises a slope of a line or a curve that fits the at least two points.
4. The method of claim 3 , wherein the energy resolution is a strictly decreasing function of a magnitude of the slope of the line or the curve.
5. The method of claim 1 , wherein:
the at least two points comprise at least three points; and
the region of the measured X-ray spectrum near the K-edge energy of the K-edge filter comprises a portion of the measured X-ray spectrum that extends from a photon energy corresponding to a local maximum intensity of the measured X-ray spectrum to a photon energy corresponding to an intensity of one half of the local maximum intensity of the measured X-ray spectrum.
6. The method of claim 5 , wherein the region of the measured X-ray spectrum near the K-edge energy of the K-edge filter comprises an additional portion of the measured X-ray spectrum that extends from the photon energy corresponding to the intensity of one half of the local maximum intensity of the measured X-ray spectrum to a photon energy that is twice the photon energy corresponding to the intensity of one half of the local maximum intensity of the measured X-ray spectrum less the photon energy corresponding to the local maximum intensity of the measured X-ray spectrum.
7. The method of claim 6 , wherein the fitting function comprises:
a high energy tail component that fits the measured X-ray spectrum above the photon energy corresponding to the intensity of one half of the local maximum intensity of the measured X-ray spectrum; and
a low energy background component that fits the measured X-ray spectrum below the photon energy corresponding to the intensity of one half of the local maximum intensity of the measured X-ray spectrum.
8. The method of claim 7 , wherein the high energy tail component comprises a term that is linearly or non-linearly proportional to a Gaussian function.
9. The method of claim 1 , wherein the fit function y is described as:
y
=
{
N
·
G
,
E
>
E
peak
N
·
(
G
+
exp
(
E
-
E
peak
λ
)
·
(
1
-
G
)
)
,
E
≤
E
peak
}
,
in
which
G
=
exp
(
-
4
·
ln
2
·
(
E
-
E
peak
)
2
FWHM
2
)
,
wherein:
E is the energy of photons within the measured X-ray spectrum;
E peak is the photon energy corresponding to the local maximum intensity of the measured X-ray spectrum;
N is a normalization parameter;
FWHM is a fitting parameter; and
λ, is another fitting parameter.
10. The method of claim 5 , wherein a thickness of the K-edge filter is selected such that the photon energy corresponding to the intensity of one half of the local maximum intensity of the measured X-ray spectrum is within a range from 99% to 101% of the K-edge energy.
11. A method of calibrating a radiation detector system including a plurality of energy bins per each detector, wherein the method comprises:
generating a set of N standard bin count distributions by irradiating a test radiation detector system with an X-ray beam attenuated by a respective one of N different K-edge filters for each of at least one X-ray source energy setting, N being an integer greater than one;
calibrating energy bins of detectors of a target radiation detector system by generating measured bin count distributions for each calibration setting in which a respective one of the N different K-edge filters attenuates a source X-ray beam, wherein calibration parameters of the detectors of the target radiation detector system are adjusted to match each of the measured bin count distributions to a corresponding standard bin count distribution generated with a same one of the N different K-edge filters and a same X-ray source energy setting;
performing the method of claim 1 on each radiation detector within the radiation detector system; and
adjusting electronics parameters for the radiation detector system to a provide an energy resolution within a specification range based on a measured energy resolution obtained by performing the method of claim 1 .