Phase contrast imaging method

Abstract

A phase contrast imaging (PCI) method in which, instead of using an analyzer grid, detector pixels are grouped and only a part of the total pixels are used to calculate a phase contrast image. In second, third, etc. steps, the pixels which were not used in the previous recalculation are used additionally to recalculate second, third, etc. phase contrast images. Finally the different phase contrast images are fused to result in a full image.

Claims

1. A method for generating at least one of an absorption image, a phase image, or a dark field image of a sample, the method comprising: a) applying a beam of radiation emitted by an x-ray source to a beam splitter grating to split the beam into split beams; b) introducing the sample into the split beams between the beam splitter grating and an x-ray detector; c) measuring a light intensity distribution modulated by the sample with the x-ray detector; and d) computing at least one of an absorption image, a phase image, or a dark field image from different sets of pixels detected by the x-ray detector; wherein the different sets of pixels are obtained by virtually overlaying a pixel matrix read out from the x-ray detector using a virtual mask including ON/OFF locations and by using the pixels that are covered by the ON locations of the virtual mask to populate a first set of the different sets of pixels, and shifting the virtual mask relative to the pixel matrix to obtain additional sets of the different sets of pixels.

2. The method according to claim 1, wherein a position of the beam splitter grating is fixed, and groups of two pixels of the pixels are envisaged and sub-images are calculated by binning values of the two pixels and shifting the virtual mask by one of the pixels.

3. The method according to claim 1, further comprising: moving the beam splitter grating at least once by a given distance parallel to a plane of the x-ray detector and exposing the x-ray detector at each position of the beam splitter grating; wherein steps (c) and (d) are repeated at each of the positions of the beam splitter grating so as to obtain a plurality of absorption images, phase images, or dark field images.

4. The method according to claim 3, further comprising: generating a full phase contrast image by fusing the absorption images, the phase images, or the dark field images, respectively.

5. The method according to claim 1, wherein sets of the different sets of the pixels have translation symmetry.

6. The method according to claim 5, wherein the virtual mask has a pitch of 4 pixels and the beam splitter grating is stationary; and at least one of the absorption image, the phase image, or the dark field image is calculated by shifting the virtual mask 2 times by 1 pixel.

7. The method according to claim 6, further comprising: moving the beam splitter grating to two positions spaced apart by a size of two pixels divided by a magnification M of the beam splitter grating; wherein absorption sub-images, phase sub-images, or dark field sub-images for each of the two positions of the beam splitter grating are calculated by shifting the virtual mask 2 times by 1 pixel for each position of the beam splitter grating.

8. The method according to claim 7, further comprising: fusing the absorption sub-images, the phase sub-images, or the dark field sub-images.

9. The method according to claim 6, further comprising: moving the splitter grating to four positions spaced apart by a size of a pixel divided by a magnification M of the beam splitter grating; and absorption sub-images, phase sub-images, or dark field sub-images are calculated by shifting the virtual mask 2 times by 1 pixel for each position of the beam splitter grating.

10. The method according to claim 5, wherein the virtual mask has a pitch of 2n pixels, in which n is an integer, and the method further comprises: moving the beam splitter grating to n positions which are spaced apart by m pixels divided by a magnification M, in which m is an integer and m<n; and absorption sub-images, phase sub-images, or dark field sub-images are calculated by shifting the virtual mask 2 times by p pixels, in which 1<p<n and p is an integer, for each position of the beam splitter grating.

11. The method according to claim 1, wherein the virtual mask has a pitch of 2 pixels and a 50/50 ON/OFF ratio.

12. The method according to claim 11, further comprising: moving the beam splitter grating to three positions each spaced apart equally; wherein the image generated with the beam splitter grating in a center position of the three positions corresponds to the ON location of the virtual mask.

13. The method according to claim 11, further comprising: moving the beam splitter grating to four positions each spaced apart by ¼ of a pixel pitch; wherein the image generated with the beam splitter in a second position of the four positions corresponds to the ON location of a first virtual mask; and the virtual mask is swopped so that a fourth position of the four positions of the beam splitter grating corresponds to the ON location of a second virtual mask.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a prior art coded aperture set up.

(2) FIG. 2 illustrates a method of capturing a PCI image.

(3) FIG. 3 shows different groupings of detector pixels as used in the context of the present invention.

(4) FIG. 4 shows a detector with hexagonal pixels that is particularly suited for diagonal patterning of exposure and detection.

(5) FIG. 5 illustrates an embodiment in which pixels are grouped in a pattern of single horizontal pixel rows. 4 images are taken. For the images taken at grating positions #1 to #3 only the odd [even] columns are used for calculating the phase image. A fourth image is taken with the coded aperture aligned to the even [odd] columns and images #1 and #3 are re-used but now analyzing only the even [odd] columns.

(6) FIG. 6 illustrates phase contrast images calculated from images #1 to #3 and #1; #3& #4 being sorted together to give full information.

(7) FIG. 7 shows grouping of two vertical columns spaced by two pixels. The coded aperture is not moved. Only one single exposure is performed.

(8) FIG. 8 shows a group of two vertical columns spaced by two pixels. The coded aperture is moved once to get the second image. Two exposures are performed. The selection of the sub-images for the second exposure to re-calculate the phase contrast image is done in a similar way as for the first exposure.

(9) FIG. 9 shows a group of two vertical columns spaced by two pixels. The coded aperture is moved three times to get the second; third & fourth image. Four exposures are done. The selection of the sub-images for the second; third & fourth exposure to re-calculate the phase contrast image is done similarly as for the first exposure.

(10) FIG. 10 is an illustration of physical movement and virtual movement.

(11) FIG. 11 shows the geometrical construction of umbra and penumbra for different source and object sizes.

(12) FIG. 12 illustrates an estimation of the intensity distribution after a single pixel.

(13) FIG. 13 is a curve illustrating the impact of the pitch of the coded aperture on the system sensitivity; source size 600 μm FWHM (100% reflects a perfect system without penumbra=point source).

(14) FIG. 14 Illumination (coded aperture) is rotated versus the virtual grating.

(15) FIG. 15 shows an example how to add on PCI; the coded aperture includes an actuator and logic to calibrate position e.g. using x-ray exposures with out patient.

(16) FIG. 16 shows how sub-images are fused to obtain a full PCI image.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(17) FIG. 1 shows the typical setup for a prior art coded aperture PCI in which a physical analyzing grating is used.

(18) A source with a small focus is placed at a distance of typically 1 m to 2 m away from the beam splitter grating or coded aperture. The coded aperture has a grid structure that absorbs a part of the x-ray intensity at regular intervals. Behind the grating downstream to the detector the source beam is split into single beamlets. An analyzer grating blocks a part of the beamlets dependent on relative position of the beamlet and the analyzer grating. The pitch of the beamlet structure (x-ray intensity profile) and the analyzer grating are adapted to the pitch of the detector.

(19) When moving the coded aperture (see FIG. 2) the intensity profile is sampled—typically at three points. For these sampling points the phase contrast image can be calculated by applying the following formula [1].

(20) [1] Hard X-ray dark-field imaging with incoherent sample illumination—Marco Endrizzi, Paul C. Diemoz, Thomas P. Millard, J. Louise Jones, Robert D. Speller, Ian K. Robinson, and Alessandro Olivo; Appl. Phys. Lett. 104, 024106 (2014).

(21) $\{\begin{array}{c}t=\frac{2x_1}{{\Delta }_{\mathrm{MN}}}\sqrt{\frac{n}{D+C}}{I}_2\exp \left[\frac{1}{2^4}\frac{{\left(D-C\right)}^2}{D+C}\right]\\ \Delta x_R=\frac{x_1}{2}\frac{D-C}{D+C}\\ {\sigma }_M^2=\frac{2x_1^2}{D+C}-{\sigma }_N^2\end{array},\mathrm{where}C=-2\ln \left(I_1/I_2\right)\mathrm{and}D=-2\ln \left(I_3/I_2\right).$

(22) The classical absorption x-ray image is denoted as t; Δx.sub.R is the phase image and σ.sub.M the dark field image. I.sub.1 . . . I.sub.3 are the pixel intensity corresponding to the 3 images at different positions of the virtual grating. The index N corresponds to the situation without object and x.sub.1 is the displacement of the virtual grating. A.sub.NM is the resulting amplitude of the system with object (combination of the illumination profile N and the change by the object M).

(23) The state of the art methods are disadvantageous because: an analyzer grating is required, the analyzer grating needs to be adapted to the detector pixels, a high power x-ray source cannot be used and thus long exposure times are required, a part of the dose applied to the patient is not used to gather image information, and thus either the patient is exposed to a high dose or the number of quanta used for the image is low which leads to higher quantum noise.

(24) According to the present invention, instead of using an analyzer grid the detector pixels are grouped in a special manner and only a part of the total pixels are used to calculate the absorption, phase image and dark field image. The recalculation is done by sequentially using the pixels which were not used in the previous sub-image. In this case the required 3 intensities I.sub.1 . . . 3 can be deduced from a single exposure. In a second, third . . . step the coded aperture is moved to calculate additional phase contrast images as well as absorption and dark field images. Finally the different sub-images are fused (see FIG. 16) to result in full resolution images for phase, absorption and dark field.

(25) The grouping of the pixels to form a virtual grating might be one- or two-dimensional.

(26) Different groupings of detector pixels are shown in FIG. 3. (hatched pixels form a group; pixel group sub-structures are marked full black).

(27) The grouping shall not be limited to these examples.

(28) Pixel grouping can be envisaged as if a virtual mask having blocking elements covering pixels that are not used in the calculation of the absorption, phase and dark field images (although the image detector has been exposed and the pixel values are available) and other pixels which are effectively used for the calculation of the absorption, phase and dark field image.

(29) Pixel groups shall preferably have a translation symmetry, i.e. after moving the pixel group by n pixels the pattern shall reproduce (displacement is either in one direction or in two directions; pattern is reproduced either by only moving the groups horizontally OR vertically by n pixels or by moving the pixels horizontally AND vertically by n & m pixels respectively).

(30) The pixel group shall preferably be arranged in a way that the sub-structures do not have direct next neighbors to avoid cross talk.

(31) FIG. 3 shows only line or square substructures but it is also possible to use L-like or open square substructures instead—basically any kind of structure can be used, preferably the structure however fulfills the above requirements.

(32) FIG. 4 shows a detector with hexagonal pixels is particularly suited for diagonal patterning of exposure and detection.

(33) The exposure pattern shall be adapted to the group pattern. In the following one-dimensional vertical grouping is used for explanation but it is obvious that this method can also be applied to one-dimensional horizontal or two-dimensional pattern.

(34) A special case of grouping the pixels in a single row (upper left image in FIG. 3) is explained below:

(35) The x-ray intensity pattern exactly fits to the group pattern (in this case it has a pitch of 2 pixels and a 50/50 on-off ratio).

(36) In total 4 images are taken (always the full pixel matrix is stored). For each image the coded aperture is moved by ¼ of the pitch divided by the magnification M of the coded aperture (in this case ½ of a pixel/M). For the first 3 images only the odd [even] columns are used to reconstruct the phase contrast image. The on-off structure of the pixels form a “virtual” analyzer grating. For the reconstruction of the second phase contrast image the coded aperture is moved to the last position (#4) and the images of position #1 and #3 are re-used but now only even [odd] columns are taken into account.

(37) $M=\frac{Z_{\mathrm{SO}}+Z_{\mathrm{OD}}}{Z_{\mathrm{SO}}}$

(38) As is shown in FIG. 5, pixels are grouped in a pattern of single horizontal pixel rows. 4 images are taken. For the images taken at grating positions #1 to #3 only the odd [even] columns are used for calculating the phase image. A fourth image is taken with the coded aperture aligned to the even [odd] columns and images #1 and #3 are re-used but now analyzing only the even [odd] columns.

(39) This results in two phase contrast images which can be fused to get the full image.

(40) To improve the quality of the re-calculation of the phase, dark field and absorption image the following procedure is possible: Image “#4 without swopping pixel groups” can be used in addition to #1, #2 and #3. For a non-disturbed signal this would give minimum of the transfer function shown in FIG. 2. The additional information can improve the result. Analogously, also the second phase contrast image could be reconstructed based on all four images, after swopping pixel groups.

(41) This embodiment is advantageous over the prior art in that by re-using images #1 and #3 for the second reconstruction the x-ray intensity of the ignored pixels during the first reconstruction is NOT lost. When using a real analyzer grating this power would be simply absorbed by the grating and such would be lost. As this happens downstream the patient this would be dose which is “seen” by the patient but not used for image formation when using an analyzer grating.

(42) FIG. 6 illustrates that phase contrast images calculated from images #1 to #3 and #1; #3& #4 are sorted together to give full information.

(43) Pixel swopping and thus filling the full image by sorting the two images together is only possible with a virtual analyzer grating. Using a real analyzer grating would require to move this grating additionally.

(44) Obviously the pitch of the coded aperture is twice the pitch of the coded aperture as used in a standard setup (compare FIG. 2). This allows not only a simpler production process of the coded aperture grating but also the use of higher power x-ray tubes (see below).

(45) Grouping of Multiple Pixel Rows:

(46) Grouping multiple pixel rows additionally allows a virtual movement of the analyzer grating. This in turn reduces the number or required images.

(47) There are basically three concepts (the following description is for a virtual grating with a pitch of 4 pixels—it is obvious that this method can be extended to the situations with a pitch of 6; 8 . . . pixels): Use only one position of the coded aperture (no movement)—this will result in reduced resolution and an incomplete transmission (absorption image) as a part of the sample is not illuminated. Use two positions of the coded aperture (one movement)—this will result in reduced resolution and a complete transmission (absorption image) as the full sample is illuminated. Use four positions of the coded aperture (three movements)—this will result in full resolution and a complete transmission (absorption image) as the full sample is illuminated.

(48) FIG. 7 illustrates the first embodiment.

(49) The coded aperture is fixed and one full image is taken. To calculate the phase contrast image two successive columns are ignored for each of the three required sub-images (only the grouped pixels are used). The three sub-images are computed by shifting the group by one pixel. Obviously there is a part of the sample which is not illuminated.

(50) The second embodiment is illustrated in FIG. 8.

(51) In this embodiment the coded aperture is moved by ½ of the pitch divided by the magnification M (in this case 2 pixels/M) for a second exposure. The procedure to get a second phase contrast image is similar to the situation with only one exposure. The two phase images can be sorted together to get a full image—compare FIG. 6. Obviously now the complete sample is illuminated but the resolution is reduced because of the step of the movement of the coded aperture of ½ pitch/M (the maximum resolution would be achieved by moving the aperture by ¼ pitch/M).

(52) The third embodiment is shown in FIG. 9.

(53) In this embodiment the coded aperture is moved three times by ¼ of the virtual analyzer grating pitch divided by the magnification M (in this case 1 pixel/M) for a second; third & fourth exposure. The procedure to get a second; third & fourth phase contrast image is similar to the situation with only one exposure. The four phase images can be sorted together to get a full image—compare FIG. 6—now four instead of two sub-images are computed to get one full image.

(54) Of course this can be extended to larger structures of the virtual grating (6; 8 . . . pixel wide structures) and an increased number of sub-images.

(55) To improve the quality of the re-calculation of the phase, dark field and transmission image the following procedure is possible: Use the information of all 4 images at different physical positions of the coded aperture. Use 4 virtual sampling points for each position of the coded aperture. This improves the quality of the result compared to “classical” PCI.

(56) FIG. 10 is an illustration of physical movement and virtual movement. Compared to “classical” coded aperture PCI additionally a sampling point can be used in the minimum of the undisturbed x-ray profile.

(57) The four sampling points of the real coded aperture & the movement of the virtual analyzer grating offer the advantage that a sampling point in the minimum of the undisturbed x-ray profile can be used (points 2 in FIG. 8a upper right and the two lower images).

(58) Without a sample the signal in the minimum is defined by the penumbra (see below) and the pixel cross talk by scattering in the conversion layer and electron bleeding. This signal can be assumed as a constant offset for a defined set of exposure parameters (tube voltage; tube current; exposure time; filter setting; SID . . . ). The offset can be measured individually for each pixel for a given set of parameters.

(59) With a sample the signal can considerably change (FIG. 10 lower two images) in case of scattering the illumination profile is locally smeared out this causes a large change for the minimum position (FIG. 10: scatter only slightly impacts the other sampling points while the “minimum sampling point” shows a large change). In case of refraction (FIG. 10 bottom, right) there is also a considerable change of the “minimum” sampling point but also of the maximum sampling point.

(60) In general introducing a 4th sampling point will increase the quality of the recalculated phase and dark field image. As this is only connected with a virtual movement of the analyzer grating it is no additional effort to introduce this 4th point. In total 4×4 sampling points are used to reconstruct the complete image.

(61) Obviously again the x-ray power is used more effectively compared to a real analyzer grating which just absorbs. The ignored columns are used to calculate the single phase contrast images. Thus almost all x-ray power passing through the patient is used to generate the image which can reduce the total patient dose considerably—most likely by 30%.

(62) Even though the above explanation is given for a special grouping of the pixels it is obvious that other groupings will give a similar result. E.g. use 3 columns and ignore 3 or use a 2D pattern and perform the procedure in 2D instead of 1D (requires also a movement of the coded aperture in 2D).

(63) Besides the fact that no analyzer grating and thus no adjustment of the grating is required this method also allows to use high power x-ray sources (also called “low brilliance” sources). This can be achieved as the pitch of the virtual grating can be considerably larger than the pitch of the real grating. There is no loss in resolution as the virtual grating can be moved virtually relative to the detector (which typically is not done for a real grating—would require an additional actuator and time) and the coded aperture is moved mechanically (all possible combinations of the real and the virtual positions are used to recalculate the full image).

(64) The reason why a larger source can be used becomes clear when the umbra and penumbra of an object are considered for different object sizes and different source sizes:

(65) The ratio between umbra and penumbra becomes smaller with increasing source size (FIG. 11 middle and right image) or decreasing object size (FIG. 11 middle and left image).

(66) For a grating the absorbing object is repeated and thus the light intensity of neighboring apertures is superimposed. In case the penumbra is larger than the umbra the modulation depth of the resulting light intensity distribution is very low. The coded aperture only absorbs light without generating a varying intensity profile and thus phase contrast imaging would not be possible.

(67) To get a better estimation of the modulation of the intensity field equations from the following publication can be used:

(68) The relationship between wave and geometrical optics models of coded aperture type x-ray phase contrast imaging systems.

(69) Peter R. T. Munro, Konstantin Ignatyev, Robert D. Speller and Alessandro Olivo, 1 Mar. 2010/Vol. 18, No. 5/OPTICS EXPRESS 4103.

(70) The estimation of the intensity distribution after a single pixel is illustrated in FIG. 12.

(71) Using the equation of FIG. 12, it is possible to calculate the sensitivity of the system for displacement of the coded aperture. This sensitivity is also important for the re-calculation of the phase contrast image—the higher the better. The approach of coded aperture PCI relies on a change of propagation direction resulting in a local displacement of some beamlets and/or beam broadening of single beamlets—this displacement/broadening must be measured.

(72) The graph shown in FIG. 13 shows an example for typical values of a PCI system (zSO=2 m; zOD=1 m). The source size is chosen to be 600 μm—this is a typical value for the small focus of a standard tube. With such a spot size >20 kW of tube power is possible.

(73) For a detector with a pixel size of 150 μm the classical absorbing analyzer grating pitch must be 100 μm (using the geometry as described above). For a virtual grating with a grouping of two neighboring columns a pitch of 400 μm can be used which increases the sensitivity drastically (53% instead of ˜1%).

(74) Furthermore the virtual grating can be rotated versus the coded aperture to generate a Moiré effect. This allows single shot PCI without moving the coded aperture for the cost of resolution.

(75) FIG. 14 shows an embodiment in which the illumination (coded aperture) is rotated versus the virtual grating.

(76) The angle of rotation is given by the pitch p of the virtual grating in units of pixels and by the number # of required images.

(77) The advantageous of the method of the present invention can be summarized as follows: No real grating required—lower cost and lower complexity No adjustment of analyzer grating required—this is a complex process as there are no direct figures which can be used (a microscope will also not help as the pixel boundaries are not visible)

(78) Further advantages are: Standard low brilliance x-ray sources can be used—this allows short exposure times as tube power can be high (>20 times; comparing the grouping of two columns with the usage of an absorbing analyzer grating). Due to the lower complexity the additional components for PCI can be removed to allow general radiography exposures or inserted into a standard x-ray system to add PCI capabilities—this is also connected with advantage #3 as a standard tube can be used

(79) FIG. 15 is an example of a way to add-on PCI; the coded aperture includes an actuator and logic to calibrate position of the coded aperture e.g. using x-ray exposures without patient.