Statistical analysis in X-ray imaging

Abstract

A method of analyzing a specimen using X-rays, comprising the steps of: Irradiating the specimen with input X-rays; Using a detector to detect a flux of output X-rays emanating from the specimen in response to said irradiation,
which method further comprises the following steps: Using the detector to intercept at least a portion of said flux so as to produce a set {I.sub.j} of pixeled images I.sub.j of at least part of the specimen, whereby the cardinality of the set {I.sub.j} is M>1. For each pixel p.sub.i in each image I.sub.j, determining the accumulated signal strength S.sub.ij, thus producing an associated set of signal strengths {S.sub.ij}. Using the set {S.sub.ij} to calculate the following values: A mean signal strength S per pixel position i; A variance .sup.2.sub.S in S per pixel position i. Using these values S and .sup.2.sub.S to produce a map of mean X-ray photon energy E per pixel.

Claims

1. A method of analyzing a specimen using X-rays: irradiating the specimen with input X-rays; using a detector to detect a flux of output X-rays emanating from the specimen in response to said irradiation; using the detector to intercept at least a portion of said flux so as to produce a set {I.sub.j} of pixeled images I.sub.j of at least part of the specimen, whereby the cardinality of the set {I.sub.j} is M>1; for each pixel pi in each image I.sub.j, determining the accumulated signal strength S.sub.ij, thus producing an associated set of signal strengths {S.sub.ij}; using the set {S.sub.ij} to calculate the following values: a mean signal strength S per pixel position i; and a variance .sub.2s in S per pixel position i; and using these values S and .sup.2.sub.S to produce a map of mean X-ray photon energy E per pixel.

2. A method according to claim 1, wherein said map is produced with the aid of a functional dependence E.sup.2.sub.S/S per pixel position i.

3. A method according to claim 1, wherein the set {I.sub.j} is produced by iteratively repeating a procedure whereby an entire n.sup.th image I.sub.n is captured before proceeding to capture an entire (n+1).sup.th image I.sub.n+1.

4. A method according to claim 1, wherein the set {I.sub.j} is produced by iteratively repeating a procedure whereby, at an n.sup.th pixel position, a plurality M of different detector samples is collected before proceeding to an (n+1).sup.th pixel position.

5. A method according to claim 1, performed as part of an X-ray tomographic imaging procedure.

6. A method according to claim 5, wherein said value of E is used to perform a Beam Hardening correction.

7. A method according to claim 5, wherein said value of E is used to derive values of at least one of the specimen's material density and atomic number per voxel.

8. A charged-particle microscope comprising: a charged-particle source, for producing an irradiating beam of charged particles; a particle-optical column, for directing said beam onto a target so as to produce an X-ray beam; a specimen holder, for holding a specimen to be irradiated by said X-ray beam; and a detector, for detecting a flux of output X-rays emanating from the specimen in response to said irradiation, wherein the charged-particle microscope further comprises a controller that is configured to perform the following actions: using said detector to produce a set {I.sub.j} of pixeled images I.sub.j of at least part of the specimen, whereby the cardinality of the set {I.sub.j} is M>1; for each pixel p.sub.i in each image determining the accumulated signal strength S.sub.ij, thus producing an associated set of signal strengths {S.sub.ij}; using the set {S.sub.ij} to calculate the following values: a mean signal strength S per pixel position i; and a variance .sup.2.sub.S in S per pixel position i; and using these values S and .sup.2.sub.S to produce a map of mean X-ray photon energy E per pixel.

9. A method according to claim 2, wherein the set {I.sub.j} is produced by iteratively repeating a procedure whereby an entire n.sup.th image I.sub.n is captured before proceeding to capture an entire (n+1).sup.th image I.sub.n+1.

10. A method according to claim 2, wherein the set {I.sub.j} is produced by iteratively repeating a procedure whereby, at an n.sup.th pixel position, a plurality M of different detector samples is collected before proceeding to an (n+1).sup.th pixel position.

11. A method according to claim 2, performed as part of an X-ray tomographic imaging procedure.

12. A method according to claim 3, performed as part of an X-ray tomographic imaging procedure.

13. A method according to claim 4, performed as part of an X-ray tomographic imaging procedure.

14. A method according to claim 11, wherein said value of E is used to perform a Beam Hardening correction.

15. A method according to claim 12, wherein said value of E is used to perform a Beam Hardening correction.

16. A method according to claim 13, wherein said value of E is used to perform a Beam Hardening correction.

17. A method according to claim 6, wherein said value of E is used to derive values of at least one of the specimen's material density and atomic number per voxel.

18. A method according to claim 14, wherein said value of E is used to derive values of at least one of the specimen's material density and atomic number per voxel.

19. A method according to claim 15, wherein said value of E is used to derive values of at least one of the specimen's material density and atomic number per voxel.

20. A method according to claim 16, wherein said value of E is used to derive values of at least one of the specimen's material density.

Description

(1) The invention will now be elucidated in more detail on the basis of exemplary embodiments and the accompanying schematic drawings, in which:

(2) FIG. 1A renders an elevational view of a charged-particle microscope that can be used in conjunction with the current invention.

(3) FIG. 1B illustrates an in situ CT module that can be used in a CPM.

(4) In the FIGURES, where pertinent, corresponding parts may be indicated using corresponding reference symbols. It should be noted that, in general, the Figures are not to scale.

Embodiment 1

(5) FIG. 1A is a highly schematic depiction of an embodiment of a CPM 1 that can be used in conjunction with the present invention; more specifically, it shows an embodiment of a SEMthough, in the present context, it could just as validly be an ion-based microscope, for example, or a TEM, for instance. The microscope 1 comprises a particle-optical column/illuminator 3, which produces a beam 5 of charged particles (in this case, an electron beam) that propagates along a particle-optical axis 5. The particle-optical column 3 is mounted on a vacuum chamber 7, which comprises a specimen holder 9 and associated stage/actuator 11 for holding/positioning a specimen 13. The vacuum chamber 7 is evacuated using vacuum pumps (not depicted). With the aid of voltage source 15, the specimen holder 9, or at least the specimen 13, may, if desired, be biased (floated) to an electrical potential with respect to ground.

(6) The particle-optical column 3 comprises an electron source 17 (such as a Schottky emitter), (electrostatic/magnetic) lenses 19, 21 (in general, more complex in structure than the schematic depiction here) to focus the electron beam 5 onto the specimen 13, and a deflection unit 23 to perform beam deflection/scanning of the beam 5. When the beam 5 impinges on/is scanned across the specimen 13, it will precipitate emission of various types of stimulated radiation, such as backscattered electrons, secondary electrons, X-rays and cathodoluminescence (infra-red, visible and/or ultra-violet photons); one or more of these radiation types can then be sensed/recorded using one or more detectors, which may form an image, spectrum, diffractogram, etc., typically by assembling a map (or matrix) of detector output as a function of scan position on the specimen. The present FIGURE shows two such detectors, 25, 27, which may, for example, be embodied as follows: Detector 25 may, for example, be an electron detector (such as an Solid State Photo-Multiplier or Everhart-Thornley detector), a (cathodoluminescence) light detector (such as a photodiode), or an X-ray detector (such as an SDD or Si(Li) sensor). Detector 27 is a segmented electron detector, comprising a plurality of independent detection segments (e.g. quadrants) disposed about a central aperture 29 (allowing passage of the beam 5). Such a detector can, for example, be used to investigate (the angular dependence of) a flux of output (secondary or backscattered) electrons emerging from the specimen 13.
These are just examples, and the skilled artisan will understand that other detector types, numbers and geometries/configurations are possible.

(7) The microscope 1 further comprises a controller/computer processing unit 31 for controlling inter alia the lenses 19 and 21, the deflection unit 23, and detectors 25, 27, and displaying information gathered from the detectors 25, 27 on a display unit 33 (such as a flat panel display); such control occurs via control lines (buses) 31. The controller 31 (or another controller) can additionally be used to perform various mathematical processing, such as combining, integrating, subtracting, false colouring, edge enhancing, and other processing known to the skilled artisan. In addition, automated recognition processes (e.g. as used for particle analysis) may be included in such processing.

(8) Also depicted is a vacuum port 7, which may be opened so as to introduce/remove items (components, specimens) to/from the interior of vacuum chamber 7, or onto which, for example, an ancillary device/module may be mounted (not depicted). A microscope 1 may comprise a plurality of such ports 7, if desired.

(9) In the context of performing X-ray tomography, the microscope 1 can also comprise an in situ CT module 7 as shown in FIG. 1B. In this FIGURE, the CPM's specimen holder 9 has been provided with a standalone metal target 13, which is positioned (using actuator 11) so that electron beam 5 impinges upon it, thus producing X-rays in a variety of directions. The FIGURE shows a beam B of such X-rays that propagate to one side from target 13 (effective source Sx) into module 7, where they pass through a specimen S and impinge upon a detector D. The specimen S is mounted on a stage apparatus A that allows the specimen S to be positioned/moved (typically translated and rotated) relative to the source Sx. Such a CT module 7 may be permanently present (ab initio) in the vacuum enclosure 7, or it may be an add-on module that can be mounted (post-manufacture of the CPM 1) on/within a spare vacuum port 7, for example.

(10) In the specific context of the current invention, the controller 31 and/or a dedicated separate processing unit (not shown) can be used to perform the following actions: Using detector D to produce a set {I.sub.j} of pixeled X-ray images I.sub.j of at least part of the specimen S, whereby the cardinality of the set {I.sub.j} is M>1. As set forth above, this may, for example be done: On a pixel-by-pixel basis, whereby M samples of the X-ray flux are measured in succession at a given position on the specimen S before moving the beam B onto a next position on the specimen S; or On an image-by-image basis, whereby an entire scan of (said part of) the specimen S is made by beam B, leading to creation of a whole image l.sub.o and this procedure is performed a total of M times in succession. For each pixel p.sub.i in each image I.sub.j, determining the accumulated signal strength S.sub.ij, thus producing an associated set of signal strengths {S.sub.ij}. Using the set {S.sub.ij} to calculate the following values: An average signal strength S per pixel position i; A variance .sup.2.sub.S in S per pixel position i. Using these values S and .sup.2.sub.S (as input to equation (3a), for example), to produce a map of mean X-ray photon energy E per pixel.

(11) It should be noted that many refinements and alternatives of such a set-up will be known to the skilled artisan, including, but not limited to: The use of dual beamsfor example an electron beam 5 for imaging and an ion beam for machining (or, in some cases, imaging) the specimen S; The use of a controlled environment at the specimen Sfor example, maintaining a pressure of several mbar (as used in a so-called Environmental SEM) or by admitting gases, such as etching or precursor gases,
etc.

Embodiment 2

(12) An example will now be given as to how the present invention can be used to perform a correction for Beam Hardening effects: (A) Perform an averaging operation on the set {I.sub.j} of pixeled images to produce a mean image. (B) Compile an E-map as set forth above. (C) From the mean image resulting from step (A), construct a normal tomogram. This tomogram will be subject to Beam Hardening effects. (D) From the E-map resulting from step (B), construct an energy-shift tomogram T.sub.. This tomogram effectively indicates how much the mean energy will shift per ray going through a particular point. (E) Compute a mean X-ray energy E.sub.m along a given ray direction (s) by calculating an integral using source mean energy E.sub.o as an initial condition:
E.sub.m=E.sub.o+T.sub.66ds (F) A generally accepted model for attenuation (p) is the Alvarez model:
(E)K.sub.1Z.sup.3/E.sup.3+K.sub.2(5) in which: K.sub.1 and K.sub.2 are material constants, is material density, Z denotes atomic number, and E is energy; Certain simplifications have been introduced, such as assuming that the so-called Klein-Nishina function is constant in the energy band in question (reasonable in a typical micro-CT energy range, say below 150 keV). Constants K.sub.1 and K.sub.2 can be estimated for a given class of materials based on tabulated values for attenuation versus energy, but, as will transpire below, this is not necessary in the current context. It is seen from this relation that: For high energies, attenuation is independent of energy; For low energies, attenuation is approximately proportional to 1/E.sup.3. If one assumes the same model to hold for mean energy E.sub.m (see point (E) above), and if one concentrates on a low-energy band (e.g. below 80 keV) in which one can assume the second term to be approximately zero, then one can derive a corrected X-ray attenuation expression:
(E.sub.m)=(E)(E.sub.m/E.sub.o).sup.3. This allows construction of a set of simulated projections in which, for each ray direction, one uses an X-ray attenuation map initially reconstructed from measured projection data, but subsequently corrected using the inventive E-map along the ray direction in question. These simulated projections can then be used in a normal tomographic reconstruction to obtain a tomogram with greatly reduced (ideally zero) Beam Hardening effects. (G) If desired, at least one of Z and p can be derived from expression (5), using values of K.sub.1, K.sub.2 obtained from a calibration series and/or tabulated references.

Embodiment 3

(13) As an alternative to the approach set forth in Embodiment 2, one can consider the inventive E-map as an energy-weighted spectrum (more strictly: .sup.2.sub.S can be regarded as an energy-weighted image, with E.sup.2.sub.SS). In conjunction with one of the images in the set {I.sub.j} (or a mean image as referred to in (A) above), one now has two inputs into a dual-energy reconstruction algorithm. In this case, the E-map is effectively a normal image that has been skewed to higher energies. Some additional information on dual-energy reconstruction algorithms can, for example, be gleaned from the following sources: www.aapm.org/meetings/amos2/pdf/42-11941-4304-839.pdf engineering.purdue.edu/-bouman/publications/pdf/CT-2012-Ruoqiao.pdf