Patent Publication Number: US-RE48612-E

Title: X-ray interferometric imaging system

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application is a continuation-in-part of U.S. patent application Ser. No. 14/527,523, filed Oct. 29, 2014 and entitled “X-RAY INTERFEROMETRIC IMAGING SYSTEM”, which claims the benefit of U.S. Provisional Patent Application No. 61/898,019, entitled “X-ray Phase Contrast imaging System” and filed on Oct. 31, 2013; 61/901,361, entitled “An X-ray Source Consisting of an Array of Fine Sub-Sources” and filed on Nov. 7, 2013; and 61/981,098 entitled “Two Dimensional Phase Contrast Imaging Apparatus” and filed Apr. 17, 2014, all of which are incorporated herein by reference in their entirety. The present application additionally claims the benefit of U.S. Provisional Patent Application No. 61/987,106, filed on May 1, 2014 and entitled “METHODS OF REDUCING SCATTER RADIATION USING TALBOT EFFECT”; 61/989,743, filed on May 7, 2014 and entitled “Methods of Improving Detector MTF and DQE and Reducing Scatter Background of an X-ray Imaging System Using Coherence Effect”; 61/991,889, filed May 12, 2014 and entitled “Method of Single-Shot Imaging to Obtain Absorption and Differential Phase, and/or Scattering, and/or Phase Contrast Images”; and 61/993,811, filed May 15, 2014 and entitled “Method of Talbot Effect based X-ray Imaging with High Image Contrast and Design of Apparatus Using Such”, all of which are incorporated herein by reference in their entirety. 
    
    
     FIELD OF THE INVENTION 
     The embodiments of the invention disclosed herein relate to interferometric imaging systems using x-rays, and in particular, interferometric imaging systems comprising high-brightness sources of x-rays for generating phase-contrast images. The high brightness x-ray sources may use anodes or targets comprising periodic microstructures of x-ray generating materials embedded in a thermally conducting substrate of low atomic number material. 
     BACKGROUND OF THE INVENTION 
     The initial discovery of x-rays by Röntgen in 1895 [W. C. Röntgen, “Eine Neue Art von Strahlen” (Würzburg Verlag, 1896); “On a New Kind of Rays,” Nature, Vol. 53, pp. 274-276 (Jan. 23, 1896)] occurred when Röntgen was experimenting with electron bombardment of targets in vacuum tubes. The contrast between the absorption from bone containing calcium (atomic number Z=20) and soft tissue containing mostly carbon (Z=6), was immediately apparent because the absorption difference between the two materials at x-ray energies between 5 and 30 keV can differ by a factor of 10 or more, as illustrated in  FIG. 1 . These high energy, short wavelength photons are now routinely used for medical applications and diagnostic evaluations, as well as for security screening, industrial inspection, quality control and failure analysis, and for scientific applications such as crystallography, tomography, x-ray fluorescence analysis and the like. 
     Although x-ray shadowgraphs have become a standard medical diagnostic tool, there are problems with simple absorption contrast imaging. Notably, for tests such as mammograms, variations in biological tissue may result in only a subtle x-ray absorption image contrast, making unambiguous detection of tumors or anomalous tissue difficult. 
     In the past decade, a new kind of x-ray imaging methodology has emerged, based on x-ray phase contrast interferometry. The method relies on the well-known Talbot interference effect, originally observed in 1837 [H. F. Talbot, “Facts relating to optical science No. IV”, Philos. Mag. vol. 9, pp. 401-407, 1836] and fully explained by Lord Rayleigh in 1881 [Lord Rayleigh, “On copying diffraction gratings and some phenomena connected therewith,” Philos. Mag. vol. 11, pp. 196-205 (1881)]. 
     This effect is illustrated in  FIG. 2 . For an absorbing grating G of period p, the diffraction pattern from a monochromatic beam of a wavelength λ with sufficient coherence forms a repeating interference pattern that reconstructs the original grating pattern, (known as a “self-image”) at multiples of a distance known as the Talbot Distance D T . For the case when the incident beam is a plane wave (equivalent to a source located at infinity from the grating G), D T  is given by: 
     
       
         
           
             
               
                 
                   
                     D 
                     T 
                   
                   = 
                   
                     
                       2 
                       ⁢ 
                       
                         p 
                         2 
                       
                     
                     λ 
                   
                 
               
               
                 
                   [ 
                   
                     Eqn 
                     . 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     Between the grating G and the Talbot Distance, other periodic interference patterns emerge as well. The periodicity and the position of the Talbot fringes depend on the transmission properties of the grating G, including amount of phase-shift and percent of absorption, and grating line-to-space (opening) ratio, or duty factor. For example, for a periodic absorption grating, a fringe pattern that reconstructs the original grating pattern with a lateral shift by half the grating period occurs at half the Talbot Distance D T /2, and a fringe pattern with a period of half of the original grating period occurs at one quarter of the Talbot Distance D T /4 and at three quarters of the Talbot Distance 3D T /4, as illustrated in  FIG. 2 . These 2-D interference patterns are sometimes called a “Talbot Carpet” because of the resemblance of these complex patterns to ornate oriental carpets. [Note: this image of an Optical Talbot Carpet in  FIG. 2  is adapted from a file created by Ben Goodman and available at commons.wikimedia.org/wiki/File:Optical_Talbot_Carpet.png.] 
       FIGS. 3 and 4  illustrate a prior art Talbot interferometric comprising a partially coherent source  200  (shown as a microfocus source) of x-rays  288  and a beam splitting grating G 1    210  of period p 1  that establishes a set of Talbot interference fringe patterns  289 . It should be noted that the coherence length of the x-ray source is preferably set to be comparable to or larger than the period p 1  of the beam splitting grating G 1    210 , so that the Talbot interference fringes will have high contrast (Talbot fringes may be well defined if the fringe contrast is, for example, greater than 20%). The beam splitting grating  210  may be an amplitude (also known an absorption or transmission) grating, creating intensity fringes as illustrated in  FIG. 2 , but is more typically a phase grating for efficient use of the illuminating x-rays, introducing periodic phase-shifts to the x-ray pattern that also form periodic Talbot fringes  289 . Henceforth in this application, a transmission grating will be used to describe gratings in which the x-ray transmission through the grating lines is less than 10% and a phase grating will be used to describe gratings in which the phase shift through the grating lines is a fraction (e.g. ½) or odd integer multiple of π. 
     The Talbot fringes  289  are detected using an x-ray detector  290 , preferably with a spatial resolution equal to or better than one third of the Talbot fringe period and having a high x-ray quantum detection efficiency. The detector  290  transforms the x-ray intensity pattern into electronic signals that are transmitted over a connector  291  to an image processing system  295 . When an object is placed in the beam path, the image processing system  295  is used to process the x-ray intensity pattern intensity information  298  to obtain absorption, phase, and scattering contrast images. 
     In practice, the spatial resolution of the detector  290  (such as a flat panel detector, or a charge coupled device (CCD) detector coupled with a scintillator that converts x-rays to visible light) is often on the order of tens of micrometers or larger, and the Talbot fringes  289  may be too fine to detect directly with the detector  290 . In this case, an analyzer grating G 2    220  of period p 2  is often used to produce Moiré fringes. To record a complete set of images, the analyzer grating G 2    220  will be moved in predetermined distances orthogonal to the grating period and relative to the detector to collect multiple interference patterns in a process called “phase-stepping”, or less commonly, rotated at a small angle relative to G 1  to obtain a Moiré pattern in a single-shot image for Fourier analysis. The image(s) are then processed to reconstruct the wavefront and determine the shapes, structures, and composition of the objects that created them. 
     It should also be noted that, instead of physically moving the analyzer grating  220 , the position of the x-ray source may also be displaced to create a translation of the interference images that allows the collection of phase-shift information. This can be accomplished electronically by moving the position of the electron beam that bombards the x-ray generating material that serves as the source for the x-rays [see, for example, H. Miao et al., “Motionless phase stepping in X-ray phase contrast imaging with a compact source”, Proceedings of the National Academy of Sciences, vol. 110(48) pp. 19268-19272, 2013] or by physically moving the x-ray source relative to a fixed position of the analyzer grating  220 . 
     These grating-based x-ray phase-contrast imaging (XPCI) techniques are generally referred to as “grating-based interferometry” (GBI). 
     As illustrated so far, the grating interferometer only produces interference fringes, and the analysis of these fringes will reveal the structure of the already known grating G 1    210  or the wavefront of the illumination beam. However, when an object is introduced in the path of the x-ray beam, variations in the wavefront introduced by the object result in corresponding changes in the pattern of the Talbot interference fringes, generally known as Moiré fringes. Interferometric image reconstruction techniques may then be used to analyze the wavefront and reconstruct images representing the structure of the unknown object. 
     In  FIG. 5 , the prior art Talbot interferometer of  FIGS. 3 and 4  is illustrated being used as an imaging technique for a biological sample, in this case, a mouse  240 -M, placed between the source  200  and the beam splitting grating G 1    210 . The x-rays  288  from the coherent source  200  pass through the mouse  240 -M and the beam splitting grating G 1    210  and create a perturbed set of Talbot fringes  289 -M. The local phase shifts create angular deviations that translate into changes of locally transmitted intensity when analyzed by the analyzer grating G 2    220  and detector  290 . Collecting multiple images from the x-ray detector  290  for situations where the analyzer grating G 2    220  has been displaced by multiple predetermined positions allow a recording of the interference pattern  289 -M. 
     As before, the detector  290  transforms the x-ray intensity pattern into electronic signals that are transmitted over a connector  291  to an image processing system  295  used to produce one or more images  298 -M with absorption, differential phase, phase, and scattering contrast information. Numerical processing of the images, including images collected by the system with and without the object under investigation, can be used to infer the shapes and structure of the objects that created them, including objects such as the mouse  240 -M. The recorded intensity oscillations can be represented by a Fourier series, and with the proper image processing algorithms, differential phase shift and absorption signals can be extracted, and images corresponding to x-ray absorption, phase contrast, and scattering by the object can be synthesized. [See, for example, A. Momose et al., “Demonstration of x-ray Talbot interferometry”, Jpn. J Appl. Phys. vol. 42, pp. L866-L868, 2003; A. Momose, U.S. Pat. No. 7,180,979, issued Feb. 20, 2007; and T. Weitkamp et al. “Hard X-ray phase imaging and tomography with a grating interferometer”, Proc. SPIE vol 5535, pp. 137-142, 2004, and “X-ray phase imaging with a grating interferometer”, Optics Express vol. 13(16), pp. 6296-6304, 2005.] 
     It should be noted that other configurations exist in which the object, such as a mouse  240 -M, can be placed between the beam splitting grating G 1    210 -A and the analyzer grating G 2    220  and detector  290 , as illustrated in  FIG. 6 . Other configurations using various phase and amplitude gratings, or using detector  290  with higher resolution pixels without the analyzer grating  220 , may also be known to those skilled in the art. 
     Aside from imaging the anatomy of mice, clinical applications of phase-contrast x-ray imaging may be found in mammography, where the density of cancerous tissue may have a distinct phase signature from healthy tissue [see, for example, J. Keyriläinen et al., “Phase contrast X-ray imaging of breast”, Acta Radiologica vol. 51 (8) pp. 866-884, 2010], or for bone diseases like osteoporosis or osteoarthritis, in which the angular orientation of the bone structures may be an early indicator of bone disease [see, for example, P. Coan et al., “In vivo x-ray phase contrast analyzer-based imaging for longitudinal osteoarthritis studies in guinea pigs”, Phys. Med. Biol. vol. 55(24), pp. 7649-62, 2010]. 
     However, for the prior art configurations described so far, x-ray power is a problem. An x-ray source with a full-width half maximum diameter S given by 
                   S   ≤     λL     2   ⁢     πp   1                 [     Eqn   .           ⁢   2     ]               
where p 1  is the period of the beam splitting grating G 1    210  and L the distance between the source  200  and the beam splitting grating G 1    210 , is required for the technique to produce high contrast fringes and Moiré patterns. For practical applications and system geometries, this implies a microfocus source. However, electron bombardment of the target also causes heating, and the x-ray power that can be achieved is limited by the maximum total electron power that can fall on the microspot without melting the x-ray generating material. A limited electron power means a limited x-ray power, and the low x-ray flux achievable with typical x-ray targets may lead to unacceptable long exposure times when used, for example, for mammography or other diagnostic tests involving live patients or animals. The total x-ray flux can be increased by distributing higher electron power over a larger area, but then the source becomes less coherent, degrading the image contrast.
 
     Coherent x-rays of higher brightness and sufficient flux can be achieved by using a synchrotron or free-electron laser x-ray source, but these machines may occupy facilities that cover acres of land, and are impractical for use in clinical environments. 
     One innovation that has been shown to enable greater x-ray power employs an additional grating G 0  [see, for example, John F. Clauser, U.S. Pat. No. 5,812,629, issued Sep. 22, 1998]. Such a system is illustrated in  FIG. 7 . In this configuration, a source grating G 0    308  with period p 0 , which is typically an x-ray transmission grating, is used in front of an x-ray source  300 . In this case, the x-ray source may be a high-power extended source with a large incident electron beam area (and not a microfocus source) that produces a higher total flux of x-rays. 
     The x-rays  388  pass through the grating G 0    308  and emerge from the grating apertures as an array of individually spatially coherent (similar to a microfocus source described above) but mutually incoherent sub-sources of illumination for the beam splitting grating G 1 . To ensure that each x-ray sub-source in G 0  contributes constructively to the image-formation process, the geometry of the setup should satisfy the condition: 
                     p   0     =       p   2     ⁢     L   D               [     Eqn   .           ⁢   3     ]               
When the condition is met, the x-rays from the many apertures of G 0  produce the same (overlapping) Talbot interference pattern, and because the various mutually incoherent sources do not interfere with each other, these Talbot patterns will add as intensities. The effect at the detector  290  is therefore to simply increasing the signal (along with it the signal-to-noise ratio) over what a single coherent source can provide.
 
     This configuration is called the Talbot-Lau interferometer [see Franz Pfeiffer et al., “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources”, Nature Physics vol. 2, pp. 258-261, 2006; and also Described in U.S. Pat. No. 7,889,838 by Christian David, Franz Pfeiffer and Timm Weitkamp, issued Feb. 15, 2011]. 
       FIGS. 8A-8C  illustrate x-ray images of a live mouse collected using a Talbot-Lau interferometer, as reported by Martin Bech [M. Bech et al., “In-vivo dark-field and phase-contrast x-ray imaging”, Scientific Reports 3, Article number: 3209, 2013,  FIG. 1 ]. The x-ray energy used was 31 keV, and the gratings were fabricated by lithographically etching structures in silicon (Z=14). Absorption gratings G 0  for the source and G 2  for the analyzer were created by additionally coating the patterned silicon with gold (Z=79). 
     All of the images of  FIGS. 8A-8C  were reported as reconstructed from the same set of 5 interferometric images, each collected over an exposure time of 10 seconds. The raw images were Fourier processed and ramp corrected to obtain the three image modalities.  FIG. 8A  illustrates an intensity image based on x-ray attenuation, showing the absorption contrast between the bones and soft tissue.  FIG. 8B  illustrates a phase-contrast image, which clearly identifies soft tissue structures such as the trachea (illustrated with an arrow).  FIG. 8C  illustrates an additional dark-field contrast image due to x-ray scattering from fine features with linear dimensions less than the spatial resolution of the imaging system, which strongly highlights the fur and lungs. 
     Unfortunately, the current art of Talbot-Lau GBIs have many constraints for most practical applications such as clinical imaging, including a requirement that both the source grating G 0  and the analyzer grating G 2  have fine pitches and apertures with large aspect ratios. 
     The requirement for the source grating G 0  is to create fine individual well-separated x-ray sub-sources to minimize the reduction in image contrast due to unwanted transmission of x-rays through the aperture defining structures. However, for a 1:1 line-to-space ratio grating, simple x-ray shadowing dictates that the x-ray transmission through the grating is limited to less than 50%, and is reduced further when the angular shadowing (limiting the angular range of the x-rays from the source to reach the object) is included. Furthermore, the optimal line-to-space ratio for G 0  that reduces the radiation dose to the object (which is important to preclinical and clinical imaging applications) is closer to 3:1 rather than 1:1. In this case, about 75% of the x-rays from the source are blocked due to area shadowing alone, and when gratings with large aspect ratios are used, greater losses occur due to angular shadowing. 
     The requirement for the analyzer grating G 2  is to be able to sample the Talbot interference fringes with sufficient resolution without losing contrast. As a result, both the G 0  and G 2  gratings must have small apertures and be of thickness sufficient to minimize unwanted x-ray transmission, which limits the efficient use of the x-rays from the source. Furthermore, the loss from the analyzer grating G 2  further results in a significantly higher dose (relative to the same system without a G 2  grating) for the object under investigation to produce an image with good characteristics due to multiple exposures for phase-stepping and absorption of x-rays resulting in lower signal-to-noise. When the object under investigation is a live animal or human, higher doses of ionizing radiation are undesirable and generally discouraged. 
     If the aperture dimensions of the grating G 0  are larger, angular collimation can be reduced (although not the area shadowing) so that x-ray transmission is not reduced as severely, but this reduces the spatial coherence length of the x-ray beam downstream from the apertures, and leads a reduction in image contrast. Smaller apertures can increase the possible image contrast and resolution by improving spatial coherence, but decreases the overall number of x-rays in the system, thus requiring longer exposure times. Moreover, with smaller apertures, these fine gratings become more difficult to manufacture. 
     The problem is exacerbated when attempting to use a Talbot-Lau interferometer for higher energy x-rays, which are often desired to obtain sufficient transmission through an object and to reduce radiation dose. In general, as was illustrated in  FIG. 1 , the absorption of x-rays for biological tissue is far lower for x-rays with energy greater than 5 keV, and the use of higher energy x-rays will reduce the absorbed dose of potentially harmful ionizing radiation by orders of magnitude. However, 5 keV photons have a wavelength of 0.248 nm, and 50 keV have a wavelength 10 times smaller (0.0248 nm). Furthermore, building absorbing gratings such as G 0  and G 2  for these higher-energy, shorter-wavelength x-rays can present difficulties, as the thickness of the gratings must increase exponentially to maintain the same absorption factor for higher energy x-rays (the x-ray attenuation length is approximately proportional to E kev   3 ). 
     The preceding problems of Talbot-Lau GBIs using linear gratings, which can be used for collecting interference data in one dimension only, become more severe if one wishes to generate phase-contrast images in two orthogonal directions. This is often required to make the image reconstruction robust and images more understandable, and because features parallel to the grating lines in the 1-D case are typically less accurately measured. One simple approach is to perform XPCI in two orthogonal directions and then subsequently register the two datasets properly. In addition to challenges associated with the imaging and registration processes, this approach may not be practical, especially when used with living subjects who may move or simply become impatient, and who will incur increased dosage (doubled) if the phase stepping must be performed in two directions. Simultaneous two-dimensional XPCI would be desirable, especially if data collection in a single exposure (shot) and at high x-ray energies is possible to reduce exposure times and the absorbed dosage. 
     There is therefore a need for an x-ray interferometric imaging system that offers the resolution and detection capabilities of the Talbot-Lau interferometer, but employing a brighter compact source of x-rays and, ideally, a brighter source of higher energy x-rays, especially one that could provide simultaneous two-dimensional phase-contrast imaging. 
     BRIEF SUMMARY OF THE INVENTION 
     We disclose here an x-ray interferometric imaging system in which the x-ray source comprises a target having a plurality of micro structured x-ray generating materials arranged within a periodic array pattern to form periodic sub-sources of x-rays. The system additionally comprises a beam-splitting grating G 1  that creates a Talbot interference pattern, and an x-ray detector to convert two-dimensional x-ray intensities into electronic signals. 
     If the spatial resolution of the detector is equal to or better than one third of the Talbot fringe period, the detector may record the fringes directly. The system may also comprise a second analyzer grating G 2  that may be placed in front of the detector to form additional interference fringes, and a means to translate the analyzer grating G 2  relative to the detector to create Moiré fringes at the detector. Additionally, the system may comprise a means of translating the phase grating G 1  relative to the analyzer grating G 2 . 
     The x-ray source target comprises a plurality of microstructures of x-ray generating materials (such as molybdenum or tungsten) in close thermal contact with a thermally conducting substrate of a low atomic number material, such as diamond or beryllium. The x-ray generating microstructures may be arranged in a periodic pattern, with each periodic element of the pattern corresponding to a single discrete microstructure or alternatively, with each periodic element of the pattern comprising multiple discrete microstructures. One or more sources of electrons bombard the plurality of x-ray generating materials, which are generally arranged within a periodic array, so that the x-ray generated from each periodic array element serves as an individually coherent sub-source of x-rays of illumination for the beam splitting grating G 1 . In some embodiments, the microstructures have lateral dimensions measured on the order of microns, and with a thickness on the order of one half of the electron penetration depth within the substrate material. In some embodiments, the microstructures are formed in a regular two-dimensional array. 
     The beam splitting grating G 1  may be a phase grating or an absorption grating. The analyzer grating G 2  is generally a transmission grating. Both gratings G 1  and G 2  may be fabricated as lithographically produced microstructures in silicon, and may comprise 1-D structures, 2-D structures, or combinations thereof. 
     A particular advantage of the invention is that high x-ray brightness and large x-ray power may be achieved by using an x-ray target in which the microstructures of a high Z material are in close thermal contact with, or embedded in, a substrate of low Z material and high thermal conductivity, such as beryllium or diamond. The ability of the substrate to draw heat away from the x-ray generating material allows higher electron density and power to be used, generating greater x-ray brightness and power from each of the sub-sources. This results in the creation of individual, well-separated spatially coherent x-ray sub-sources from the high Z material, while the use of a substrate with low Z and low mass density minimizes the production of x-rays from the substrate that can lead to a reduction in image contrast. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a plot of the x-ray absorption of carbon and calcium as a function of x-ray energy. 
         FIG. 2  illustrates a prior art Talbot interference pattern produced by a transmission grating. 
         FIG. 3  illustrates a prior art x-ray grating interference system using a microfocus source. 
         FIG. 4  illustrates a cross section view of the prior art x-ray grating interference system of  FIG. 3 . 
         FIG. 5  illustrates the prior art x-ray grating interference system of  FIG. 3  used to form an x-ray contrast image of a mouse. 
         FIG. 6  illustrates a variation of the prior art x-ray grating interference system of  FIG. 3  used to form an x-ray contrast image of a mouse. 
         FIG. 7  illustrates a prior art Talbot-Lau interferometer being used to form an x-ray contrast image of a mouse. 
         FIG. 8A  illustrates a published x-ray absorption image of a mouse gathered using a prior art Talbot-Lau interference system. 
         FIG. 8B  illustrates a published x-ray phase-contrast image of a mouse gathered using a prior art Talbot-Lau interference system. 
         FIG. 8C  illustrates a published x-ray dark field scattering image of a mouse gathered using a prior art Talbot-Lau interference system. 
         FIG. 9  illustrates a schematic cross-section view of an embodiment of an x-ray interferometric imaging system according to the invention. 
         FIG. 10  illustrates a schematic cross-section view of an embodiment of the invention. 
         FIG. 11  illustrates a perspective view of the embodiment of the invention shown in  FIG. 10 , in which the x-ray target comprises two dimensional periodic array of x-ray generating microstructures. 
         FIG. 12  illustrates a detailed schematic cross-section view of the embodiment of the invention shown in  FIGS. 10 and 11 . 
         FIG. 13  illustrates a perspective view of an embodiment of the invention in which the x-ray target comprises of x-ray generating microstructures in the form of parallel lines. 
         FIG. 14  illustrates a perspective view of an embodiment of the invention in which the object (a mouse) is placed between the gratings G 1  and G 2 . 
         FIG. 15  illustrates a detailed schematic cross-section view of an embodiment of the invention in which a high-resolution detector is used without an analyzer grating. 
         FIG. 16  illustrates a perspective view of an embodiment of the invention in which the object (a mouse) is placed between the grating G 1  and the detector, and the grating G 1  comprises a two-dimensional phase structure. 
         FIG. 17  illustrates a “mesh” 2-D pattern for a beam splitting grating used in some embodiments of the invention. 
         FIG. 18  illustrates a “checkerboard” 2-D pattern for a beam splitting grating used in some embodiments of the invention. 
         FIG. 19  illustrates a perspective view of an embodiment of the invention in which the object (a mouse) is placed between the source and the grating G 1 , and the grating G 1  comprises a two-dimensional phase structure. 
         FIG. 20  illustrates a schematic cross-section view of an embodiment of the invention in which the target is mounted within the vacuum chamber. 
         FIG. 21  illustrates a detailed schematic cross-section view of the embodiment of the invention shown in  FIG. 20 . 
         FIG. 22  illustrates a schematic cross-section view of an embodiment of the invention in which the target is mounted within the vacuum chamber and x-rays are generated using linear accumulation. 
         FIG. 23  illustrates a detailed schematic cross-section view of the embodiment of the invention shown in  FIG. 22 . 
         FIG. 24  illustrates a schematic cross-section view of an embodiment of the invention in which two electron beams bombard the target from both sides. 
         FIG. 25  illustrates a detailed schematic cross-section view of the embodiment of the invention shown in  FIG. 24 . 
         FIG. 26  illustrates a perspective view of a target comprising a grid of embedded rectangular target microstructures on a larger substrate that may be used in some embodiments of the invention. 
         FIG. 27  illustrates a perspective view of a variation of a target comprising a grid of embedded rectangular target microstructures on a larger substrate for use with focused electron beam that may be used in some embodiments of the invention. 
         FIG. 28A  illustrates a perspective view of a target comprising a grid of embedded rectangular target microstructures as used in some embodiments of the invention. 
         FIG. 28B  illustrates a top view of the target of  FIG. 28A . 
         FIG. 28C  illustrates a side/cross-section view of the target of  FIGS. 28A and 28B . 
         FIG. 29A  illustrates a perspective view of a target comprising a set of embedded rectangular target microstructures forming a periodic linear pattern as used in some embodiments of the invention. 
         FIG. 29B  illustrates a top view of the target of  FIG. 29A . 
         FIG. 29C  illustrates a side/cross-section view of the target of  FIGS. 29A and 29B . 
         FIG. 30  illustrates variations in target structure for a target as shown in  FIGS. 28A-C  that may arise from processing variations. 
         FIG. 31  illustrates variations in target structure for a target as shown in  FIGS. 29A-C  that may arise from processing variations. 
         FIG. 32  illustrates a cross-section view of a portion of the target of  FIGS. 28A-C  and/or  FIGS. 29A-C , showing thermal transfer to a thermally conducting substrate under electron beam exposure according to the invention. 
         FIG. 33  illustrates a cross-section view of a variation of the target of  FIGS. 28A-C ,  FIGS. 29A-C  and/or  FIG. 32  comprising a substrate with a thermal cooling channel according to the invention. 
         FIG. 34  illustrates a cross-section view of another variation of the target of  FIGS. 28A-C  and/or  FIGS. 29A-C  comprising an adhesion layer according to the invention. 
         FIG. 35  illustrates a cross-section view of another variation of the target of  FIGS. 28A-C  and/or  FIGS. 29A-C  comprising an electrically conducting overcoat according to the invention. 
         FIG. 36  illustrates a cross-section view of another variation of the target of  FIGS. 28A-C  and/or  FIGS. 29A-C  comprising buried x-ray material according to the invention. 
         FIG. 37  illustrates a cross-section view of another variation of the target of  FIGS. 28A-C  and/or  FIGS. 29A-C  comprising buried x-ray material and a thick thermally and electrically conducting overcoat according to the invention. 
         FIG. 38  illustrates a cross-section view of another variation of the target of  FIGS. 28A-C  and/or  FIGS. 29A-C  comprising an additional blocking structures on the back surface of the substrate, to block the transmission of x-rays produced by the substrate. 
         FIG. 39  illustrates a plot of the x-ray absorption of gold and silicon as a function of x-ray energy. 
         FIG. 40  illustrates a detailed schematic cross-section view for an embodiment of the invention in which an additional antiscattering grating is used. 
         FIG. 41  illustrates a cross-section of the placement of antiscattering gratings within a Talbot interference pattern. 
         FIG. 42  illustrates a schematic cross-section of an anti-scattering grating. 
         FIG. 43  illustrates a detailed schematic cross-section view for an embodiment of the invention in which an additional antiscattering grating is used along with an analyzer grating at the detector. 
         FIG. 44  illustrates a schematic cross-section view for an embodiment of the invention in which the detector elements are aligned with the high intensity portions of the Talbot interference pattern. 
         FIG. 45  illustrates a schematic cross-section view for an embodiment of the invention in which a beamsplitting grating is placed upstream of a detector such that the detector elements are aligned with the high intensity (anti-nodes) of the Talbot interference pattern. 
         FIG. 46  illustrates a schematic cross-section view for an embodiment of the invention comprising both a bright field and dark field detector. 
         FIG. 47  illustrates a schematic cross-section view for an embodiment of the invention comprising both a bright field and dark field detector, in which a scintillator is used to convert x-rays to visible/UV photons. 
         FIG. 48  illustrates a possible structure of an x-ray phase grating according to some embodiments of the invention. 
         FIG. 49  illustrates a possible structure of an x-ray absorption grating according to some embodiments of the invention. 
     
    
    
     Note: The illustrations in the Drawings disclosed in this application are typically not shown to scale, and are meant to illustrate the principle of the invention and its function only, and not specific relationships between the microstructures in the target and the various grating periods p 1 , p 2 , p 3 , p 4 , p 5 , and p 6 . Please refer to the descriptions in the text of the Specification for specific details of the dimensions of these objects. 
     DETAILED DESCRIPTIONS OF EMBODIMENTS OF THE INVENTION 
     Descriptions of Various Embodiments of the Invention 
     One embodiment of the invention disclosed herein is an x-ray phase-contrast imaging (XPCI) system as illustrated in  FIG. 9 . The system bears some similarity to the prior art Talbot-Lau interferometer, in that it comprises a beam splitting grating G 1    210  of period p 1  that establishes a Talbot interference pattern, and an x-ray detector  290  typically comprising an array of sensors to convert two-dimensional x-ray intensities into electronic signals. 
     The beam splitting grating G 1    210  may be a phase grating or a transmission grating, and may comprise 1-D periodic patterns (linear gratings), or may comprise more complex 2-D structures such as a grid that is periodic in two orthogonal directions. 
     The system may also comprise an analyzer grating G 2    220  of period p 2  that may be placed in front of the detector to form additional interference fringes, such as Moiré fringes. The system may additionally comprise a means  225  to translate the analyzer grating G 2    220  relative to the detector, and a connector  291  to transmit electronic signals corresponding to the detected x-ray intensity to an image processing system  295  for processing. 
     However, instead of using an extended x-ray source and an additional grating G 0  to create a plurality of x-ray source spots, as was done in the Talbot-Lau system, the embodiments of the present invention use an x-ray source comprising a plurality of x-ray generating sub-sources  108  arranged in a periodic array that generate x-rays  188  from electron beam bombardment, such that each sub-source is individually coherent, but together function as a set of mutually incoherent or partially coherent sub-sources of illumination for the beam splitting grating G 1 . As with the combination of the extended x-ray source and the source grating of the Talbot-Lau interferometer, these sub-sources  108  form the Talbot interference fringe patterns that are created by the beam splitting grating G 1    210  and perturbed by an object  240 -M, and may be recorded by detector  290 . If the spatial resolution of the detector  290  has a spatial resolution equal to or better than one third of the Talbot fringe period, the detector may record the fringes directly. If a lower resolution detector is used, an analyzer grating G 2    220  may also be used to create Moiré fringes, as was described for the Talbot-Lau interferometer. 
     The plurality of discrete x-ray sub-sources can be considerably brighter than the x-ray source of the Talbot-Lau system. Because the source comprises sub-sources that are self-coherent but may be mutually incoherent, there is no need for an attenuating transmission grating G 0  to create an array of sub-sources from an extended x-ray source. 
     A system according to the invention comprising multiple sub-sources in a structured target may be designated a Talbot-ST interferometer. 
       FIGS. 10, 11 and 12  show a more detailed illustration of one embodiment of the invention, in which the array of sub-sources are formed using microstructures of x-ray generating material embedded in a thermally conducting substrate. In this embodiment, an x-ray source  008  illuminates an object  240 -M and a beam-splitting grating G 1    210 , and the interference pattern they form is detected by a detector  290 . 
     For the x-ray source  008 , a high voltage power supply  010  provides electrons through a lead  021  to an electron emitter  011  in a vacuum chamber  002  held to a shielding housing  005  by supports  003 . The electron emitter  011  emits electrons  111  towards a target  100 . The target  100  comprises a substrate  1000  and a region that comprises a periodic array of discrete microstructures  700  comprising x-ray generating material (typically a high Z metallic material such as copper, molybdenum or tungsten) positioned on or embedded or buried in the substrate (typically a low Z material such as beryllium, diamond, silicon carbide). The discrete microstructures  700  may be any number of sizes or shapes, but are generally designed to be periodic arrays of right rectangular prisms with lateral dimensions on the order of microns in size in at least one dimension, such that the emission from each microstructure acts as a sub-source of x-rays with a spatial coherence length that is comparable to or larger than the grating period p 1  at the beam splitting grating G 1    210 . Additionally, the microstructures are preferably of a thickness (as typically measured orthogonal to the target surface) that is on the order of one half of the electron penetration depth within the substrate material. 
     The period p 0  of the microstructures  700  that form the x-ray sub-sources is related to the other geometric parameters in the system by: 
                     p   0     =       p   2     ⁢     L   D               [     Eqn   .           ⁢   4     ]               
where L is the distance from the x-ray sub-sources  700  to the grating G 1    210 , and D is the distance from the grating G 1  to the detector/analyzer grating G 2    220  with period p 2 . In some embodiments, D will be set to be one of the fractional Talbot distances with interference fringes of high contrast (visibility), defined by:
 
                   Contrast   =         I   max     -     I   min           I   max     +     I   min                 [     Eqn   .           ⁢   5     ]               
where I max  and I min  is the intensity peak and valley of the Talbot interference fringes without an object in the beam path, respectively.
 
     For plane wave illumination (i.e. equivalent to the x-ray source being located at infinity) of a beam-splitting grating with a π phase-shift, the distance D is preferably given by: 
                   D   =       D   N     =       N   ⁢           ⁢       p   1   2       8   ⁢   λ         =       N   16     ⁢     D   T                   [     Eqn   .           ⁢   6     ]               
where D N  is the fractional Talbot distance for a plane wave illumination, λ is the mean x-ray wavelength, and N is referred to as a Talbot fractional order. The preferred value of D is dependent on the attenuating or phase shifting properties of the beam-splitting grating G 1 , the line-space ratio of the beam-splitting grating G 1 , and the source-to-grating distance L. For a π phase-shifting grating with a line-to-space ratio of 1:1, an odd integer fractional Talbot order N (N=1, 3, 5 . . . ) is preferred for determining the distance D. For an x-ray source located at a finite distance (e.g. L not infinity), D is increased to:
 
     
       
         
           
             
               
                 
                   D 
                   = 
                   
                     
                       L 
                       × 
                       
                           
                       
                       ⁢ 
                       
                         D 
                         N 
                       
                     
                     
                       L 
                       - 
                       
                         D 
                         N 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Eqn 
                     . 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
     The Talbot fringe period p f  for a given fractional order is given by: 
                     p   f     =       Kp   1     ⁢       L   +   D     L               [     Eqn   .           ⁢   8     ]               
where K is a parameter dependent on the attenuating or phase shifting properties of the beam-splitting grating G 1 . K equals ½ when the beam-splitting grating is a λ phase-shift grating, and equals 1 when the beam splitting grating is a π/2 phase shift grating.
 
     Likewise, the Talbot fringe contrast is improved if a smaller x-ray sub-source size (i.e. more spatially coherent x-rays) is used, and in which the pitch p 1  used for the beam splitting grating G 1  is related to the size of the sub-source a and the distance L between them, satisfying the following requirement: 
                     p   1     &lt;     λL   a             [     Eqn   .           ⁢   9     ]               
where λ is a predetermined x-ray wavelength that will generally correspond to the wavelength of the monochromatic x-rays produced by the corresponding sub-source, or the mean x-ray wavelength for an x-ray sub-source with a broader spectrum.
 
     In the vacuum chamber  002 , electrons  111  bombard the target, and generate heat and x-rays  888  in the microstructures  700 . The material in the substrate  1000  is selected such that it has relatively low energy deposition rate for electrons in comparison to the microstructures of the x-ray generating material, typically by selecting a low Z material for the substrate, and therefore will not generate a significant amount of heat and x-rays. The substrate  1000  material may also be chosen to have a high thermal conductivity, typically larger than 100 W/(m ° C.). The microstructures of the x-ray generating material are also typically embedded within the substrate, i.e. if the microstructures are shaped as rectangular prisms, it is preferred that at least five of the six sides are in close thermal contact with the substrate  1000 , so that heat generated in the microstructures  700  is effectively conducted away into the substrate  1000 . However, targets used in other embodiments may have fewer direct contact surfaces. In general, when the term “embedded” is used in this disclosure, at least half of the surface area of the microstructure will be in close thermal contact with the substrate. 
     The microstructures are typically connected electrically with a lead  022  to the positive terminal of the high voltage source  010  to allow the target to serve as an anode in the electrical system. Alternatively, the target may be grounded while the cathode (electron emitter) is of negative charge, or the target may be connected to a positive terminal while the cathode is grounded, so long as the anode is of relative higher voltage than the cathode. Additionally, in some embodiments, electron optics such as electrostatic lenses or magnetic coils may be placed inside or outside of the vacuum chamber  002  around or near the path of electrons  111  to further direct and focus the electron beam. 
     The target  100  as illustrated may additionally serve as a window in the vacuum chamber  002  so that the x-ray generating material is facing the interior of the vacuum chamber and the electron source, but x-rays  888  are also propagate through the back side of the target  100  towards the beam-splitting grating G 1    210 . In other embodiments, a separate window is used, and additional x-ray filters may also be used 
     Once generated by the source  008 , the x-rays  888  may pass through an optional shutter  230 , an x-ray spectral filter to obtain a desired spectral bandwidth with a desired wavelength, and an object  240 -M to be investigated. The x-rays then diffract off the beam splitting grating G 1    210 , which may additionally be mounted on a substrate  211 , and then fall on the analyzer grating G 2    220 , which may also be mounted on a substrate  221 . The final interference pattern will be detected by an array detector  290  that provides electrical signals corresponding to the x-ray intensity through a connector  291  to an image processing system  295  for analysis. 
     In addition to the x-ray source and interference detection system, means to move the object  240 -M and the various gratings relative to each other, to the detector, and to the source may be used. In  FIG. 10 , the image processing system  295  may also be connected through a network  231  to a means  245  of controlling a stage  244  that sets the position and angle of the object  240 -M, to a means  215  of controlling a mount  214  that sets the position and angle of the beam splitting grating G 1    210 , and to a means  225  of controlling a mount  224  that sets the position and angle of the analyzer grating G 2    220 , as well as a possible connection to the shutter  230  or to a switch  013  for the high voltage supply  010  to allow the x-rays to be moved and modulated (such as being turned on and off). Software run by processors in the image processing system  295  may control the motion of the gratings G 1    210 , G 2    220 , the object  240 -M, and also the x-ray exposure to allow the collection of the multiple images needed to obtain detailed amplitude, differential phase, phase-contrast, and scattering contrast images of the object  240 -M. 
     Additional embodiments may also include controls that allow the electron beam to be moved or modulated. For example, embodiments may be designed that additionally comprise a means of translating the x-ray source anode relative to the analyzer grating G 2 . Additional embodiments that also allow the position and angle of the x-ray detector  290  to be adjusted may also be designed. 
       FIG. 13  illustrates an embodiment of the invention in which the target  100  comprises a substrate  1000  and a plurality of microstructured line sources  701 . These microstructured line sub-sources  701  will typically be a few microns wide in one direction (corresponding to the sub-source size parameter a, generally in the dimension orthogonal to the direction of the lines of the gratings G 1    210  and G 2    220 , which corresponds to the y-direction in  FIG. 13 ) but much longer (e.g. up to 1000 microns or several millimeters) in the direction parallel to the lines (which corresponds to the x-direction in  FIG. 13 ). The pitch of the microstructures  701  as sub-sources as shown in  FIG. 13  is p 0 , and is related to the pitch of the analyzer/detector by Equation 4. 
       FIG. 14  illustrates an embodiment of the invention in which the object  240 -M to be examined is placed between the gratings G 1    210  and the detector  290 . The microstructures  700  of x-ray generating material on the target as illustrated in  FIG. 14  comprise sub-sources arranged in a 2-D periodic array in two orthogonal directions, but may be any periodic array that satisfies the coherence illumination condition of the beam-splitting grating G 1    210 , including a grid, a mesh, a checkerboard, or other periodic structures. 
     If the gratings comprise one-dimensional structures, the microstructures  700  in the source target  100  need only be periodic in the same direction as the 1-D arrays of G 1    210  and G 2    220  (i.e. the lines of microstructures  701  are ideally parallel to the lines of the gratings) but can have arbitrary or non-periodic structure in the perpendicular direction. 
       FIG. 15  additionally illustrates an embodiment of the invention in which the there is no analyzer grating G 2    220 , but instead the detector  299  has a high resolution array G D  with a pixel resolution equal to or better than one third (⅓) of the Talbot fringe period in the direction orthogonal to the grating lines. With this resolution, a single exposure image may be processed to obtain absorption, phase, and scattering contrast images simultaneously. This can be advantageous in that the intensity loss of 50% or more that typically occurs for x-rays passing through G 2    220  is avoided, and the signal reaching the detector and therefore the signal-to-noise ratio is substantially higher. 
     In order to collect the multiple images for the calculation of detailed amplitude, differential phase, phase-contrast, and scattering contrast images for an object  240 -M, the embodiment of  FIG. 15  may additionally comprise a means  255  for translating the detector  290 , not only in the two lateral directions parallel to the plane of the grating G 1 , but also in direction defined along the path of x-ray propagation, to ensure that the detector  299  is placed at the correct multiple of the Talbot distance T D . 
       FIG. 16  illustrates an embodiment of the invention in which the beam splitting grating G 1    210 - 2 D comprises a two-dimensional periodic array, which may be either a transmission or a phase grating. When using a 2-D beam-splitting grating of this type, the patterns may be arranged in any one of a number of periodic patterns, including a mesh, such as the pattern illustrated in  FIG. 17 , or a checkerboard pattern, as illustrated in  FIG. 18 , In these illustrations, clear regions are non-phase shifted regions, while patterned regions represent regions with a relative phase shift. Different, or even opposite relative phase shifts, may also be used in some embodiments, i.e., the clear regions can be phased shifted while the patterned regions are not. 
     For use with an incident x-ray beam with a spectral bandwidth of less than ±15% around the mean energy, a beam splitting grating with a phase shift of π radians and a line-to-space ratio of 1:1 may be preferred. For use with an incident beam with a spectral bandwidth greater than ±15%, a relative phase shift of π/2 radians may be preferred. 
     The beam splitting gratings in some embodiments may have a profile comprising 1-D stripes, such as a Ronchi profile or structures having a rectangular profile. The relative phase shift between the dark and clear stripes is preferably selected to be π or π/2 radians, but may also be any integer multiple or fraction of π. Alternatively, the dark stripes may have low x-ray transmission so that the beam splitting grating is an absorption grating. 
       FIG. 16  illustrates the use of a 2-D beam splitting grating G 1    210 - 2 D in conjunction with a high-resolution detector  299 , as was also shown in  FIG. 15 . To simultaneously obtain a differential phase contrast, phase contrast, absorption, scattering contrast images in two orthogonal directions, the geometric parameters, including the x-ray sub-source size a, the period p 1  of the grating G 1   210 - 2 D and the distance L, need to satisfy the coherence illumination condition of the grating G 1  in both directions. As before, the detector  299  has spatial resolution equal to or better than ⅓ of the Talbot fringe period in the two orthogonal directions in the image plane and is positioned to be aligned with the Talbot fringe pattern. 
     Such embodiments with 2-D patterns on the beam splitting grating G 1    210 - 2 D may also be used with the previously described lower resolution detector  290  in conjunction with a two-dimensional analyzer grating G 2  which may be phase stepped in two directions in any sequence so that the phase information is obtained in both orthogonal directions. Similar to the description of G 1    210 - 2 D above, this 2-D analyzer grating G 2  may be of any periodic structure such as a mesh, a checkerboard, or 2-D array of structures such as circles, triangles, squares, rectangles, etc. 
       FIG. 19  represents an embodiment similar to  FIG. 16 , except that the object  240 -M under examination is now placed between the x-ray source and the beam-splitting grating  210 - 2 D. 
     Note that some of the embodiments are one-dimensional Talbot-Yun interferometers in which absorption, phase, and scattering information is obtained in one direction and incorporate one or more 1-D gratings in combination with a micro structured source target that is periodic in at least in the direction perpendicular to the grating line direction (but may be periodic in other directions as well). Other embodiments are two-dimensional Talbot-ST interferometers in which absorption, phase, and scattering information is obtained in two orthogonal directions (or all three dimensions by performing computed tomography using the 2-D Talbot-Yun setup). 
       FIGS. 20 and 21  illustrate another embodiment of the invention in which the x-ray source  080  comprises a vacuum chamber  020  supported on mounts  030  within an x-ray shielding housing  050 . The source  080  also comprises a target  100  comprising a substrate  1000  and a periodic pattern comprising x-ray sub-sources  700  mounted entirely within the vacuum chamber  020 . As before, this embodiment also comprises a high voltage source  010 , which has a negative terminal connected through a lead  021 -A to an electron emitter  011 -A, while the positive terminal is connected through one or more leads  022  to the microstructures in the target, allowing them to serve as an anode. 
     However, in this embodiment, the surface of the target  100  comprising the periodic array of x-ray sub-sources  700  comprising of x-ray generating material is facing a window  040  mounted in the wall of the vacuum chamber  020 , and the electron emitter  011 -A is aligned to emit a beam of electrons  111 -A onto the surface of the target  100  comprising sub-sources  700  facing the window  040 . 
       FIGS. 22 and 23  illustrate another embodiment of the invention in which the target  100  comprising a substrate  1000  and a periodic pattern comprising x-ray sub-sources  700  mounted entirely within the vacuum chamber  020 . As before, this embodiment also comprises a high voltage source  010 , which has a negative terminal connected through a lead  021 -B to an electron emitter  011 -B, while the positive terminal is connected through one or more leads  022  to the microstructures in the target, allowing them to serve as an anode. 
     However, in this embodiment, the surface of the target  100  comprising the periodic array of x-ray sub-sources  700  comprising x-ray generating material is oriented such that x-rays produced by some of the microstructures propagate towards other microstructures that are also producing x-rays, and a linear accumulation of x-rays  888 -B from a plurality of microstructures  700  emerges from the target. The distance g between the microstructures and microstructures  700  emerges from the target. The distance g between the microstructures and the width w x  in the propagation direction should be small enough such that the emission from the nth microstructure contributing to the accumulated x-rays can be considered as a single sub-source with dimension a of Eqn. 9, i.e.:
 
a≥tan θ·(n(g+w x ))  [Eqn. 10]
 
where a is the sub-source dimension that meets the coherence requirements of the system, and θ is one half of the field-of-view angle for the system.
 
     Linear accumulation of x-ray sources as used in this embodiment of the invention is described more fully in the co-pending U.S. patent application entitled X-RAY SOURCES USING LINEAR ACCUMULATION by the inventors of the present invention (U.S. patent application Ser. No. 14/490,672 filed Sep. 19, 2014), which is hereby incorporated by reference in its entirety. Any of the source designs and configurations disclosed in the above referenced co-pending application may be considered for use as a component in any or all of the interferometric imaging systems disclosed herein. 
     Likewise,  FIGS. 24 and 25  illustrate another embodiment of the invention that utilizes linear accumulation of x-rays. In this embodiment, the x-ray source  080  includes a target  2200  comprising a substrate  2210  and a first set of sub-sources  707  and a second set of sub-sources  708  mounted entirely within the vacuum chamber  020 . As before, this embodiment also comprises a high voltage source  010 , but this high voltage source is connected to a junction  010 - 2  that provides high voltage to two electron emitters  011 -D and  011 -E through leads  021 -D and  021 -E, respectively. As shown in  FIGS. 24 and 25 , the first electron emitter  021 -D provides an electron beam  111 -D that bombards the first set of sub-sources  707 , while the second electron emitter  021 -E provides an electron beam  111 -E that bombards the second set of sub-sources  708 . Some of the x-rays  788  generated by the first set of sub-sources  707  and the second set of sub-sources  708  along the x-ray imaging beam axis combine to produce x-rays  2888  from the target  2200  will be augmented by the linear accumulation of x-rays from these two sets of x-ray sub-sources. In some embodiments, the separation between the two sets of sub-sources  707  and  708  may be smaller than 5 mm but larger than the source size in direction perpendicular to a line passing through the center of the two sub-sources. The periods of both the sub-sources  707  and  708  may be selected so that the associated Talbot fringes downstream of the beam splitting grating G 1  substantially overlap. 
     It will also be known to those skilled in the art that other embodiments of the invention comprising an x-ray source in which the target/anode under bombardment by electrons is moved, translated, or rotated to distribute the heat load are also possible. 
     Note: The illustrations of  FIGS. 10 through 25  are not shown to scale, and are meant to illustrate the principle of the invention and not specific relationships between the microstructures  700 , the target  100  and the various grating periods p 1  and p 2 . The microstructures  700 ,  701 ,  707 ,  708  etc. may be on the order of microns in size, while the object under examination  240 -M may be centimeters in size. Likewise, although these are illustrated in which an object with dimensions on the order of centimeters (a mouse) is shown, the techniques described are not limited to such objects, but may be used to examine even larger structures, or microscopic structures as well, as long as a suitable resolution for the detector and other elements of the interferometer are suitably constructed. 
     2. Fabrication of X-Ray Targets 
     Targets such as those to be used in x-ray sources according to the invention disclosed herein have been described in detail in the U.S. patent application entitled STRUCTURED TARGETS FOR X-RAY GENERATION by the inventors of the present invention (U.S. patent application Ser. No. 14/465,816, filed Aug. 21, 2014), which is hereby incorporated by reference in its entirety. Any of the target designs and configurations disclosed in the above referenced co-pending application may be considered for use as a component in any or all of the x-ray sources disclosed herein. 
     As described herein and in the above cited pending patent applications, the target used in the source of x-rays may comprise a periodic array of sub-sources. Each sub-source may be comprised of a single or multiple microstructures of x-ray generating material in thermal contact with, or preferably embedded in, a substrate selected for its thermal conductivity. When the microstructures are in good thermal contact with a substrate having a high thermal conductivity, higher electron current densities may be used to generate x-rays, since the excess heat will be drawn away into the substrate. The higher current densities will give rise to higher x-ray flux, leading to a higher brightness source. As described in the above co-pending patent applications, sources with microstructures of x-ray generating material may have a brightness more than 10 times larger than simpler constructions made from the same materials. Additional configurations in which multiple sub-sources are aligned to contribute x-rays on the same axis can multiply the brightness further through linear accumulation of the x-ray sub-sources. 
     It should also be noted here that, when the word “microstructure” is used herein, it is specifically referring to microstructures comprising x-ray generating material. Other structures, such as the cavities used to form the x-ray microstructures, have dimensions of the same order of magnitude, and might also be considered “microstructures”. As used herein, however, other words, such as “structures”, “cavities”, “holes”, “apertures”, etc. may be used for these structures when they are formed in materials, such as the substrate, that are not selected for their x-ray generating properties. The word “microstructure” will be reserved for structures comprising materials selected for their x-ray generating properties. 
     Likewise, it should be noted that, although the word “microstructure” is used, x-ray generating structures with dimensions smaller than 1 micron, or even as small as nano-scale dimensions (i.e. greater than 10 nm) may also be described by the word “microstructures” as used herein as long as the properties are consistent with the geometric factors for sub-source size and grating pitches set forth in the various embodiments. 
     It should also be noted that here that, when the word “sub-source” is used it may refer to a single microstructure of x-ray generating material, or an ensemble of smaller microstructures that function similarly to a single structure for the purposes of Talbot interferometry. 
     The fabrication of these microstructured targets may follow well known processing steps used for the creation of embedded structures in substrates. If the substrate is a material with high thermal conductivity such as diamond, conventional lithographic patterning, such as focused ion beam lithography or electron beam lithography, using photoresists can produce micron sized structures, which may then be etched into the substrate using processes such as reactive ion etching (RIE). Deposition of the x-ray generating material into the etched structures formed in the substrate may then be carried out using standard deposition processes, such as electroplating, chemical vapor deposition (CVD), atomic layer deposition, or hot pressing. 
     The x-ray generating material used in the target should ideally have good thermal properties, such as a high melting point and high thermal conductivity, in order to allow higher electron power loading on the source to increase x-ray production. The x-ray generating material should additionally be selected for good x-ray production properties, which includes x-ray production efficiency (proportional to its atomic number) and in some cases, it may be desirable to produce a specific spectra of interest, such as a characteristic x-ray spectral line. For these reasons, targets are often fabricated using tungsten, with an atomic number Z=74. Table I lists several materials that are commonly used for x-ray targets, several additional potential target materials (notably useful for specific characteristic lines of interest), and some materials that may be used as substrates for target materials. Melting points, and thermal and electrical conductivities are presented for values near 300° K (27° C.). Most values are cited from the CRC Handbook of Chemistry and Physics, 90 th  ed. [CRC Press, Boca Raton, Fla., 2009]. Other values are cited from various sources found on the Internet. Note that, for some materials Ouch as sapphire for example) thermal conductivities an order of magnitude larger may be possible when cooled to temperatures below that of liquid nitrogen (77° K) [see, for example, Section 2.1.5, Thermal Properties, of E. R. Dobrovinskaya et al., Sapphire: Material, Manufacturing, Applications, Springer Science+Business Media, LLC, 2009]. 
     
       
         
           
               
             
               
                 TABLE I 
               
             
            
               
                   
               
               
                 Various Target and Substrate Materials and Selected Properties. 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Atomic 
                 Melting 
                 Thermal 
                 Electrical 
               
               
                 Material 
                 Number 
                 Point ° C. 
                 Conductivity 
                 Conductivity 
               
               
                 (Elemental Symbol) 
                 Z 
                 (1 atm) 
                 (W/(m ° C.)) 
                 (MS/m) 
               
               
                   
               
            
           
           
               
            
               
                 Common Target Materials: 
               
            
           
           
               
               
               
               
               
            
               
                 Chromium (Cr) 
                 24 
                 1907 
                 93.7 
                 7.9 
               
               
                 Iron (Fe) 
                 26 
                 1538 
                 80.2 
                 10.0 
               
               
                 Cobalt (Co) 
                 27 
                 1495 
                 100 
                 17.9 
               
               
                 Copper (Cu) 
                 29 
                 1085 
                 401 
                 58.0 
               
               
                 Molybdenum (Mo) 
                 42 
                 2623 
                 138 
                 18.1 
               
               
                 Silver (Ag) 
                 47 
                  962 
                 429 
                 61.4 
               
               
                 Tungsten (W) 
                 74 
                 3422 
                 174 
                 18.4 
               
            
           
           
               
            
               
                 Other Possible Target Materials: 
               
            
           
           
               
               
               
               
               
            
               
                 Titanium (Ti) 
                 22 
                 1668 
                 21.9 
                 2.6 
               
               
                 Gallium (Ga) 
                 35 
                   30 
                 40.6 
                 7.4 
               
               
                 Rhodium (Rh) 
                 45 
                 1964 
                 150 
                 23.3 
               
               
                 Indium (In) 
                 49 
                  157 
                 81.6 
                 12.5 
               
               
                 Cesium (Cs) 
                 55 
                   28 
                 35.9 
                 4.8 
               
               
                 Rhenium (Re) 
                 75 
                 3185 
                 47.9 
                 5.8 
               
               
                 Gold (Au) 
                 79 
                 1064 
                 317 
                 44.0 
               
               
                 Lead (Pb) 
                 82 
                  327 
                 35.3 
                 4.7 
               
            
           
           
               
            
               
                 Other Potential Substrate Materials with low atomic number: 
               
            
           
           
               
               
               
               
               
            
               
                 Beryllium (Be) 
                  4 
                 1287 
                 200 
                 26.6 
               
               
                 Carbon (C): Diamond 
                  6 
                 * 
                 2300 
                 10 −19   
               
               
                 Carbon (C): Graphite || 
                  6 
                 * 
                 1950 
                 0.25 
               
               
                 Carbon (C): 
                  6 
                 * 
                 3180 
                 100.0 
               
               
                 Nanotube (SWNT) 
                   
                   
                   
                   
               
               
                 Carbon (C): 
                  6 
                 * 
                 200 
                   
               
               
                 Nanotube (bulk) 
                   
                   
                   
                   
               
               
                 Boron Nitride (BN) 
                 B = 5 
                 ** 
                 20 
                 10 −17   
               
               
                   
                 N = 7 
                   
                   
                   
               
               
                 Silicon (Si) 
                 14 
                 1414 
                 124 
                 1.56 × 10 −9   
               
               
                 Silicon Carbide 
                 Si = 14 
                 2798 
                 0.49 
                 10 −9   
               
               
                 (β-siC) 
                 C = 6 
                   
                   
                   
               
               
                 Sapphire (Al 2 O 3 ) || C 
                 Al = 13 
                 2053 
                 32.5 
                 10 −20   
               
               
                   
                 O = 8 
               
               
                   
               
               
                 * Carbon does not melt at 1 atm; it sublimes at ~3600° C. 
               
               
                 ** BN does not melt at 1 atm; it sublimes at ~2973° C. 
               
            
           
         
       
     
       FIG. 26  illustrates a target as may be used in some embodiments of the invention. In this figure, a substrate  1000  has a region  1001  that comprises an array of sub-sources  700  comprising microstructures of x-ray generating material (typically a metallic material), in which the sub-sources are arranged in a regular array of right rectangular prisms. In a vacuum, electrons  111  bombard the target from above, and generate heat and x-rays in the microstructures  700 . The material in the substrate  1000  is selected such that it has relatively low x-ray production (efficiency is proportional to atomic number) and energy deposition rate (stopping power is proportional to density) for electrons in comparison to the x-ray generating microstructure material, and therefore will not generate a significant amount of heat and x-rays. This is typically achieved by selecting a low mass density and low atomic number (Z) material for the substrate. 
     The substrate  1000  material may also be chosen to have a high thermal conductivity, typically larger than 100 W/(m ° C.), and the microstructures are typically embedded within the substrate, i.e. if the microstructures are shaped as rectangular prisms, it is preferred that at least five of the six sides are in close thermal contact with the substrate  1000 , so that heat generated in the microstructures  700  is effectively conducted away into the substrate  1000 . However, targets used in other embodiments may have fewer direct contact surfaces. In general, when the term “embedded” is used in this disclosure, at least half of the surface area of the microstructure will be in close thermal contact with the substrate. 
     Note that the sub-source sizes and dimensions in some embodiments may be constrained by the same limitations as the periodicity p 0  of the grating G 0  in prior art. In other words, the spatial resolution achievable at the object position in the x-ray interferometric imaging systems as shown in  FIGS. 9 through 25  is determined by the overall x-ray source size and the detector resolution, similar to the conditions described in the prior art interferometeric imaging systems, such as the Talbot-Lau system. Therefore, the maximum x-ray source size (width of each microstructure spot) is limited for a given detector resolution and a given imaging geometry as determined by the distance between the source and object and the distance between the object to the detector. 
     The line-to-space ratio of the arrays of sub-sources is a design parameter that should be considered in the design of any system. A large spatial coherence length is inversely proportional to the size of an x-ray source or sub-source. Because the fringe visibility of the Talbot interference fringes increases linearly with the relative ratio of the spatial coherence length of the illuminating x-ray beam to the period of the beam-splitting grating p 1  for a value of the ratio from 0.3 to 1, it is generally preferred to have a small source size. However, the x-ray production is inversely proportional to the area of the sub-source (e.g. a reduction in line width will lead to a decrease of x-ray production). Since the throughput of an imaging system is generally proportional to square of the contrast transfer function and only proportional to the x-ray flux, it is generally preferred to have a line-to-space ration less than 1:1. Some embodiments of the invention may use a line-to-space (i.e. x-ray generating material to substrate material) ratio between 1:5 and 1:2 (i.e. the relative area of the x-ray generating material may range from 20% to 33%). 
     A figure of merit (FOM) that may be helpful for the selection of materials for targets according to this invention is the ratio of x-rays produced by the microstructures to the x-rays produced by the electrons also bombarding the substrate. This figure of merit may be useful for the design of and selection of materials for the targets for the system, and should be taken into consideration in addition to the thermal conductivity of the substrate. As the electron energy deposition rate is proportional to the mass density and the x-ray production efficiency in a material is proportional to its atomic number, this figure of merit may be defined as follows: 
                   FOM   =         Z   2     ×     ρ   2           Z   1     ×     ρ   1                 [     Eqn   .           ⁢   11     ]               
where Z is the atomic number and ρ is the density, and material  1  is the substrate and material  2  is the x-ray generating material.
 
     
       
         
           
               
             
               
                 TABLE II 
               
             
            
               
                   
               
               
                 Figure of Merit for x-ray material/substrate combinations. 
               
            
           
           
               
               
               
            
               
                 Substrate material 
                 Microstructure material 
                 Figure of Merit  
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Material 
                 Atomic # Z 1   
                 Mass density (g/cm 3 )  
                 Material 
                 Atomic  # Z 2   
                 Mass density (g/cm 3 ) 
                 
                   
                     
                       
                         
                           
                             Z 
                             2 
                           
                           × 
                           
                             ρ 
                             2 
                           
                         
                         
                           
                             Z 
                             1 
                           
                           × 
                           
                             ρ 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 SiC 
                 12.55 
                 3.21 
                 Cu 
                 29 
                 8.96 
                 6 
               
               
                 Si 
                 14 
                 2.33 
                 Cu 
                 29 
                 8.96 
                 8 
               
               
                 SiC 
                 12.55 
                 3.21 
                 Mo 
                 42 
                 10.2 
                 11 
               
               
                 Diamond 
                 6 
                 3.5 
                 Cu 
                 29 
                 8.96 
                 12 
               
               
                 Si 
                 14 
                 2.33 
                 Mo 
                 42 
                 10.2 
                 13 
               
               
                 Diamond 
                 6 
                 3.5 
                 Mo 
                 42 
                 10.2 
                 21 
               
               
                 SiC 
                 12.55 
                 3.21 
                 W 
                 74 
                 19.25 
                 35 
               
               
                 Be 
                 4 
                 1.85 
                 Cu 
                 29 
                 8.96 
                 35 
               
               
                 Si 
                 14 
                 2.33 
                 W 
                 74 
                 19.25 
                 44 
               
               
                 Be 
                 4 
                 1.85 
                 Mo 
                 42 
                 10.2 
                 59 
               
               
                 Diamond 
                 6 
                 3.5 
                 W 
                 74 
                 19.25 
                 68 
               
               
                 Be 
                 4 
                 1.85 
                 W 
                 74 
                 19.25 
                 193 
               
               
                   
               
            
           
         
       
     
     A number of microstructures and substrate material combinations are listed below in Table II. Any of the following combinations may be used, but it is preferable that the materials are selected such that the FOM is greater than 12, and that the thermal conductivity of the substrate material is greater than 100 W/(m ° C.) at room temperature. 
       FIG. 27  illustrates another target as may be used in some embodiments of the invention in which the electron beam  111 -F is directed by electrostatic lenses to form a more concentrated, focused spot. For this situation, the target  1100 -F will still comprise a region  1001 -F comprising an array of microstructures  700 -F comprising x-ray material, but the size and dimensions of this region  1001 -F can be matched to regions where electron exposure will occur. In these targets, the “tuning” of the source geometry and the x-ray generating material can be controlled such that the designs mostly limit the amount of heat generated to the micro structured region  1001 -F, while also reducing the design and manufacturing complexity. This may be especially useful when used with electron beams focused to form a micro-spot, or by more intricate systems that form a more complex electron exposure pattern. 
     The depth of penetration of electrons into the material can be estimated by Pott&#39;s Law [P. J. Potts, Electron Probe Microanalysis, Ch. 10 of A Handbook of Silicate Rock Analysis, Springer Netherlands, 1987, p. 336)], which states that the penetration depth x in microns is related to the 10% of the value of the electron energy E 0  in keV raised to the 3/2 power, divided by the density of the material: 
                     x   ⁡     (   µm   )       =     0.1   ×       E   0   1.5     ρ               [     Eqn   .           ⁢   12     ]               
For less dense material, such as a diamond substrate, the penetration depth is much larger than for a material with greater density, such as most materials containing elements used for x-ray generation.
 
     Using this formula, Table III illustrates some of the estimated penetration depths for some common x-ray target materials. 
     
       
         
           
               
             
               
                 TABLE III 
               
             
            
               
                   
               
               
                 Estimates of penetration depth for 60 keV electrons into some materials. 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 Density 
                 Penetration Depth 
               
               
                 Material 
                 Z 
                 (g/cm 3 ) 
                 (μm) 
               
               
                   
               
               
                 Diamond 
                  6 
                 3.5 
                 13.28 
               
               
                 Copper 
                 29 
                  8.96 
                  5.19 
               
               
                 Molybdenum 
                 42 
                 10.28 
                  4.52 
               
               
                 Tungsten 
                 74 
                 19.25 
                  2.41 
               
               
                   
               
            
           
         
       
     
     The majority of characteristic Cu K x-rays are generated within the penetration depth. The electron interactions below that depth typically generate few characteristic K-line x-rays but will contribute to the heat generation, thus resulting in a low thermal gradient along the depth direction. It is therefore preferable in some embodiments to set a maximum thickness for the microstructures in the target in order to limit electron interaction in the material and optimize local thermal gradients. One embodiment of the invention limits the depth of the micro structured x-ray generating material in the target to between one third and two thirds of the electron penetration depth in the substrate at the incident electron energy. In this case, the lower mass density of the substrate leads to a lower energy deposition rate in the substrate material immediately below the x-ray generating material, which in turn leads to a lower temperature in the substrate material below. This results in a higher thermal gradient between the x-ray generating material and the substrate, enhancing heat transfer. The thermal gradient is further enhanced by the high thermal conductivity of the substrate material. 
     For similar reasons, selecting the thickness of the microstructures to be less than one half of the electron penetration depth in the substrate is also generally preferred for efficient generation of bremsstrahlung radiation, because the electrons below that depth have lower energy and thus lower x-ray production efficiency. 
     Note: Other choices for the dimensions of the x-ray generating material may also be used. In targets as used in some embodiments of the invention, the depth of the x-ray material may be selected to be 50% of the electron penetration depth in the substrate. In other embodiments, the depth of the x-ray material may be selected to be 33% of the electron penetration depth in the substrate. In other embodiments, the depth for the microstructures may be selected related to the “continuous slowing down approximation” (CSDA) range for electrons in the material. Other depths may be specified depending on the x-ray spectrum desired and the properties of the selected x-ray material. 
       FIG. 28  illustrates a region  1001  of a target as may be used in some embodiments of the invention that comprises an array of sub-sources  700  with microstructures in the form of right rectangular prisms comprising x-ray generating material arranged in a regular array.  FIG. 28A  presents a perspective view of the sixteen microstructures  700  for this target, while  FIG. 28B  illustrates a top down view of the same region, and  FIG. 28C  presents a side/cross-section view of the same region. (For the term “side/cross-section view” in this disclosure, the view meant is one as if a cross-section of the object had been made, and then viewed from the side towards the cross-sectioned surface. This shows both detail at the point of the cross-section as well as material deeper inside that might be seen from the side, assuming the substrate itself were transparent [which, in the case of diamond, is generally true for visible light].) 
     In these targets, the microstructures have been fabricated such that they are in close thermal contact on five of six sides with the substrate. As illustrated, the top of the microstructures  700  are flush with the surface of the substrate, but other targets in which the microstructure is recessed may be fabricated, and still other targets in which the microstructures present a topographical “bump” relative to the surface of the substrate may also be fabricated. 
     An alternative target as may be used in some embodiments of the invention may have several microstructures of right rectangular prisms simply deposited upon the surface of the substrate. In this case, only the bottom base of the prism would be in thermal contact with the substrate. For a structure comprising the microstructures embedded in the substrate with a side/cross-section view as shown in  FIG. 28C  with depth D z  and lateral dimensions in the plane of the substrate of W x  and W y , the ratio of the total surface area in contact with the substrate for the embedded microstructures vs. deposited microstructures is 
                       A     E   ⁢   m   ⁢   b   ⁢   e   ⁢   d   ⁢   d   ⁢   e   ⁢   d         A   Deposited       =     1   +     2   ⁢   D   ⁢       (     W   +   L     )       (     W   ×   L     )                   [     Eqn   .           ⁢   13     ]               
With a small value for D relative to W and L, the ratio is essentially 1. For larger thicknesses, the ratio becomes larger, and for a cube (D=W=L) in which 5 equal sides are in thermal contact, the ratio is 5. If a cap layer of a material with similar properties as the substrate in terms of mass density and thermal conductivity is used, the ratio may be increased to 6.
 
       FIG. 29  illustrates a region  1001  of a target as may be used in some embodiments of the invention, such as that previously illustrated in  FIG. 13 , that comprises an array of linear sub-sources  701  with microstructures in the form of right rectangular prisms comprising x-ray generating material arranged in a regular array.  FIG. 29A  presents a perspective view of the three microstructures  701  for this target, while  FIG. 29B  illustrates a top down view of the same region, and  FIG. 29C  presents a side/cross-section view of the same region. 
     In this embodiment, the lateral dimensions in the plane of the substrate are a width and length W x  and L y . The effective sub-source size a will correspond to the width W x . 
       FIGS. 30 and 31  illustrate a practical issue that may arise in forming the targets such as those illustrated in  FIGS. 28 and 29 .  FIG. 30  illustrates variations possible with the grid of x-ray generating microstructures  700  as illustrated in  FIG. 28 , and  FIG. 31  illustrates variations possible with the linear x-ray generating microstructures  701  as illustrated in  FIG. 29 . 
     In  FIG. 30 , odd-shaped microstructures  700 -A of other geometric shapes may be formed. Likewise, voids  700 - 0  may also appear where certain structures may be expected. Other deposition processes, for example deposition using pre-formed particles of x-ray generating material may create ensemble clusters of particles  700 -C that, when bombarded with electrons, may still act as x-ray sub-sources similar in function to those that are produced by a uniform structure. Also shown in  FIG. 30  is a microstructure with multiple crystal structures and grain boundaries  700 -G that again may still produce x-rays similar to those that are produced by a uniform structure, but may be considered to comprise an ensemble of microstructures. 
     The effective x-ray sub-source size in all of these situations may be approximated using the size parameter a, even though the microstructures comprise particles that are considerable smaller. 
       FIG. 31  shows examples of ensemble microstructures as may occur when fabricating linear microstructures  701 . If uniform pre-fabricated particles of x-ray generating material are created and coated onto the substrate, an ensemble of particles  703  of x-ray generating material may be formed. In other processes, if non-uniform particles are used, clusters of particles  704 -A and  704 -B may form, in some cases with a non-uniform distribution that may include gaps of voids. In other processes, an ensemble of particles  704  of x-ray generating material may approximate a line source of x-rays. 
     All of these ensembles, when bombarded with electrons, may still act as x-ray sub-sources similar in function to those that are produced by a uniform linear structure. The effective source size in these situations may be approximated using the size parameter a, even though the microstructures comprise particles that are considerable smaller. 
     The heat transfer that may occur under electron bombardment is illustrated with representative arrows in  FIG. 32 , in which the heat generated in sub-sources  700  embedded in a substrate  1000  is conducted out of the microstructures comprising the sub-sources  700  through the bottom and sides (arrows for transfer through the sides out of the plane of the drawing are not shown). The amount of heat transferred per unit time (ΔQ) conducted through a material of area A and thickness d given by: 
                     Δ   ⁢   Q     =       κ   ·   A   ·   ΔT     d             [     Eqn   .           ⁢   14     ]               
where κ is the thermal conductivity in W/(m ° C.) and AT is the temperature difference across thickness d in ° C. Therefore, an increase in surface area A, a decrease in thickness d and an increase in ΔT all lead to a proportional increase in heat transfer.
 
     An alternative embodiment is illustrated in  FIG. 33 , in which the substrate additionally comprises a cooling channel  1200 . Such cooling channels may be a prior art cooling channel, as discussed above, using water or some other cooling fluid to conduct heat away from the substrate, or may be fabricated according to a design adapted to best remove heat from the regions near the embedded microstructures  700 . 
     Other target structures for various embodiments may be understood or devised by those skilled in the art, in which the substrate may, for example, be bonded to a heat sink, such as a copper block, for improved thermal transfer. The copper block may in turn have cooling channels within it to assist in carrying heat away from the block. Alternatively, the substrate may be attached to a thermoelectric cooler, in which a voltage is applied to a specially constructed semiconductor device. In these devices, the flow of current causes one side to cool while the other heats up. Commercially available devices, such as Peltier coolers, can produce a temperature difference of up to 70° C. across the device, but may be limited in their overall capacity to remove large amounts of heat from a heat source. Heat pipes containing a heat transfer fluid that evaporates and condenses, as are used for cooling CPU chips in server farms when compact design is a consideration, may also be used to cool the substrate. 
     Alternatively, the substrate can be attached to a cryogenic cooler, such as a block containing channels for the flow of liquid nitrogen, or be in thermal contact with a reservoir of liquid nitrogen or some other cryogenic substance, such as an antifreeze solution, to provide more extreme cooling. When the substrate comprises a material such as diamond, sapphire, silicon, or silicon carbide, thermal conductivity generally increases with decreasing temperature from room temperature. In such a case, designing the target so that it can withstand cooling to these lower temperatures may be preferred. 
       FIG. 34  illustrates an alternative example of a target that may be used in embodiments of the invention in which the cavities formed in the substrate  1000  are first coated with an adhesion layer  715  (preferably of minimal thickness) before embedding the x-ray generating material that forms the microstructures  700 . Such an adhesion layer may be appropriate in cases where the bond between the x-ray material and the substrate material is weak. The adhesion layer may also act as a buffer layer when the difference between thermal expansion coefficients for the two materials is large. For some choices of materials, the adhesion layer may be replaced or extended (by adding another layer) with a diffusion barrier layer to prevent the diffusion of material from the microstructures into the substrate material (or vice versa). For embodiments in which an adhesion and/or diffusion barrier layer is used, the selection of materials and thicknesses should consider the thermal properties of the layer as well, such that heat flow from the microstructures  700  to the substrate  1000  is not significantly impeded or insulated by the presence of the adhesion layer  715 . 
       FIG. 35  illustrates an alternative example of a target that may be used in an embodiment in which an electrically conducting layer  725  has been added to the surface of the target. When bombarded by electrons, the excess charge needs a path to return to ground for the target to function effectively as an anode. If the target as illustrated in  FIGS. 28 and 29  were to comprise only discrete, unconnected microstructures  700  within an electrically insulating substrate material (such as undoped diamond), under continued electron bombardment, significant charge would build up on the surface. The electrons from the cathode would then not collide with the target with the same energy, or might even be repelled, diminishing the generation of x-rays. 
     This can be addressed by the deposition of a thin layer of conducting material that is preferably of relatively low atomic number, such as aluminum (Al), beryllium (Be), carbon (C), chromium (Cr) or titanium (Ti), that allows electrical conduction from the discrete microstructures  700  to an electrical path  722  that connects to a positive terminal relative to the high voltage supply. This terminal as a practical matter is typically the electrical ground of the system, while the cathode electron source is supplied with a negative high voltage. 
       FIG. 36  illustrates another example of a target that may be used in an embodiment of the invention, in which the sub-sources  702  are embedded deeper, or buried, into the substrate  1000 . Such an embedded microstructure may be further covered by the deposition of an additional layer  1010 , which may be, for example, diamond, providing the same heat transfer properties as the substrate. This allows heat to be conducted away from all sides of the buried sub-source  702 . For such a situation and when the additional layer  1010  does not have sufficient electrical conductivity, it is advisable to provide a path  722  to ground for the electrons incident on the structure, which may be in the form of an embedded conducting layer  726  laid down before the deposition of the additional layer  1010 . In some embodiments, this conducting layer  726  will have a “via”  727 , or a vertical connection, often in the form of a pillar or cylinder, that provides an electrically conducting structure to link the embedded conducting layer  726  to an additional conducting layer  728  on the surface of the target, which in turn is connected to the path  722  to ground, or the high voltage supply. 
       FIG. 37  illustrates another example of a target that may be used in embodiments of the invention, in which the sub-sources  702  are again buried within the substrate. However, in this embodiment, instead of first providing an electrically conducting layer followed by the deposition of an additional cap layer, in this embodiment only a single layer  770  is deposited, selected for a combination of electrical properties and thermally conducting properties. This may be, for example, a deposition of carbon nanotubes (Z=6) oriented vertically relative to the surface, such that they conduct both heat and electrons away from the buried microstructures  702 . This single layer  770  may in turn be connected to a path  722  to ground to allow the target to serve as an anode in the x-ray generation system. Alternatively, the material of the layer  770  may be selected to comprise aluminum (Al), beryllium (Be), chromium (Cr), or copper (Cu). 
       FIG. 38  illustrates another variation of an embodiment, in which additional patterns of blocking material  729  have been deposited on the backside of the target substrate  1000 . If the figure of merit for the selected material combination, as discussed above in Table II, is not large, there may still be significant x-rays generated by the substrate that will reduce contrast in the image. These substrate-generated x-rays can be blocked by a deposition of a suitable material, such as gold, as blocking structures  729 . Gold (Z=79) has a strong x-ray absorption, as illustrated in  FIG. 39 . Processes to deposit these blocking structures may comprise standard deposition processes, and an alignment step may be needed to ensure alignment with the x-ray generating structures on the opposite side. 
     It should be clear to those skilled in the art that although several embodiments have been presented separately in  FIGS. 26-38 , and various processes for their manufacture will be presented later, the elements of these embodiments may be combined with each other, or combined with other commonly known target fabrication methods known in the art. For example, the buried sub-sources  702  of  FIG. 37  may also comprise multiple grains of microstructures, as was illustrated in  FIGS. 30 and 31 . Likewise, the adhesion layer  715  as illustrated in  FIG. 34  may also be applied to fabrication of embedded sub-sources  700  as shown in  FIG. 35 . The separation of these alternatives is for illustration only, and is not meant to be limiting for any particular process. 
     Although the sub-sources illustrated in  FIGS. 26-38  have been shown as regularly spaced patterns with uniform size and shape, a regular pattern of sub-sources having non-uniform size and shape, can also be used in some embodiments of the invention. Additionally, each sub-source within a regular periodic pattern may further be comprised of multiple smaller microstructures of non-uniform sizes and shapes. These smaller microstructures may be non-regular and do not necessarily need to have similar x-ray emission characteristics or strength, so as long as the larger sub-sources that each group of microstructures comprise are periodic in nature. 
     Likewise, although some embodiments have been described with microstructures in, for example, the shape of right rectangular prisms, fabrication processes may create structures that have walls at angles other than 90°, or do not have corners that are exactly right angles, but may be rounded or beveled or undercut, depending on the artifacts of the specific process used. Embodiments in which the microstructures are essentially similar with the shapes described herein will be understood by those skilled in the art to be disclosed, even if process artifacts lead to some deviation from the shapes as illustrated or described. 
     In other embodiments of the system, a periodic attenuating grating G 0  such as are used in the prior art Talbot-Lau interferometers may also be used in conjunction with the source of the invention, so that the x-rays produced by the substrate material surrounding the sub-sources are further attenuated, allowing greater monochromaticity and therefore higher spatial coherence for the source. The apertures of the grating should be coincident with projections of the microstructured x-ray sub-sources, or may, in some embodiments, be placed at a Talbot fractional or integer distance downstream of the source and with the apertures coincident with the source self-images. It is preferable that the grating G 0  is of high atomic number and relatively low aspect ratio, for ease of manufacturability. 
     3. Additional Embodiments 
     3.1. An Additional Absorption Grid 
     Additional embodiments may comprise an additional absorption grid, with features and placement designed to reduce scattered radiation (such as Compton scattering and elastic scattering from fine structures with dimensions substantially smaller than the resolution of an imaging system) that contributes to the background in x-ray imaging and reduction of image contrast in many x-ray imaging techniques, including the various embodiments discussed above or various x-ray absorption imaging techniques. The ratio of the intensity of the scattered radiation to the intensity of the primary radiation used forming the images is particularly significant in imaging examinations where a large quantity of scatter is created, e.g., those involving a large volume of tissue being irradiated and those requiring high energy x-rays, thus limiting the efficacy of disease diagnosis for obese patients or for dense body parts (e.g. craniofacial, dense breast tissue, etc.). Current art in antiscattering grids typically comprise high radiation absorption septa (typically fabricated using high Z materials like lead) interlaced with a medium with high radiation transmission (such as aluminum or fiber material). It is typically specified by the grid ratio (ratio of the height of the structures and the interspacing between them), period, and septum width. Use of an antiscattering grid, however, requires a greater radiation exposure to the patient as a fraction of primary beam is also attenuated by the septa. 
     A common drawback for existing antiscattering grids is that the septa also absorb the useful primary x-rays transmitted through the object, resulting in an undesirable reduction of the image signal and therefore an increased radiation dose to the sample or patient. 
     The embodiments of the invention as previously disclosed above may also be augmented by the use of an antiscattering grid having a pattern of septa determined by specific imaging setup designed to use the Talbot effect. One embodiment of the invention comprises an antiscattering grid positioned between the beam splitting grating G 1  and the detector. The period of the grid spacing and the position may be determined so that the septa are at positions that should be the nodes in the Talbot carpet. The antiscattering grid preferably absorbs the scattered radiation while permitting efficient transmission of the primary radiation, resulting in reduction of background noise and increase in image contrast. The antiscattering grid may comprise simple 1-D structures for the septa, but may also be designed to have 2-D or even 3-D structures tuned to the Talbot interference pattern with which they are intended to be used. 
     An embodiment of the invention incorporating an anti-scattering grid is illustrated in  FIG. 40 . As in the other embodiments illustrated in this disclosure, x-rays  888  are generated from microstructured regions  700  comprising x-ray generating material upon bombardment with an electron beam  111 . The generated x-rays are transmitted through a sample, in this case a mouse  240 -M, and the transmitted x-rays are detected on a detector  290 . However, in passing through the mouse  240 -M, Compton scattering and other undesired scattering phenomena may occur, producing x-rays  889 -C that may propagate at many different angles and reduce the absorption image contrast. 
     The insertion of an anti-scatter grid  420  helps to attenuate the scattered x-rays, while passing the majority of the x-rays that contribute to image formation. Here, the antiscattering grid  420 , designated as G 4 , is positioned at a distance D α  from the beam splitting grating  210 , designated as G 1 . The antiscattering grid  420  will typically comprise a substrate  422  that is made from a material mostly transparent to x-rays (such as aluminum or a carbon fiber material), upon which a number of absorbing structures  424  comprising material that absorbs x-rays, such as gold, tin, platinum, tungsten, tantalum, nickel, lead, copper, gadolinium, or some other high Z material, have been arranged in a periodic manner. The thickness of the absorbing structures  424  is determined by the X-ray imaging energy which is in turn determined by application; for example, for imaging at 40 keV of infants, the thickness of such structures may be on the order of several hundred microns for lead. In some embodiments, the substrate and absorbing structures may both be fabricated from a single wafer or block of high Z material. The space between the absorbing structures  424  may comprise only air, or may have another low Z material deposited therein. In such embodiments, the distance D α  from the beam splitting grating G 1  will be set such that the position is at one of the fractional Talbot distances, i.e. 
                     D   α     =       D   N     =       N   ⁢       p   1   2       8   ⁢   λ         =       N     1   ⁢   6       ⁢     D   T                   [     Eqn   .           ⁢   15     ]               
where D N  is the fractional Talbot distance for a plane wave illumination, λ is the mean x-ray wavelength, and N is referred to as a Talbot fractional order.
 
     The period of the structures in the antiscattering grid may be set to be 
                     p   4     =       Kp   0     ⁢       D   α     L               [     Eqn   .           ⁢   16     ]               
where p 0  is the period of the microstructured source, L the distance between the x-ray sources  700  and the beam splitting grating  210 , and K is a scaling factor which is equal to 1 when the beam-splitting grating introduces a phase shift of π/2, and is equal to ½ when the beam-splitting grating introduces a phase shift of π.
 
     The antiscattering grid may be a 1-D grating, or a 2-D grating, with the periods in the x and y axes corresponding using Eqn. 16 above with the corresponding (e.g., horizontal and vertical) periods in the beam splitting grating. In some embodiments, the absorbing septa will be arranged with an aspect ratio of &gt;5:1, i.e. with features 5 times or more higher than the width of the gap between features, and the normal-incidence transmission of the absorbing regions will be less than 10%. Septa may be designed such that the ratio of the area of the septa to the total area ranges from 20-50%. The position may be controlled by a controller  425  that may allow the antiscattering septa to be aligned with the interference fringes formed by the beam splitting grating  210 . 
     Some scattered x-rays may still propagate at angles and in directions that allow it to be transmitted through the apertures in the antiscattering grid. However, by placing the antiscattering grid such that the absorbing structures are co-positioned with the nodes of the Talbot fringe pattern, nearly 100% of the Talbot fringe pattern may be transmitted, while 50% to 75% or more of the scattered x-rays may be absorbed. In some embodiments, the absorbing structures are not matched to each node but may instead be matched to integer multiples of the nodes. 
     Further reduction in scattered x-rays may be achieved by including a second antiscattering grid. This second grid may be placed at the same Talbot distance in close proximity to the first antiscattering grating, effectively increasing the absorption and aspect ratio of the features, or it may be positioned at another Talbot distance using the same design consideration as discussed in the previous embodiments. 
       FIG. 41  illustrates the placement of two antiscattering grids in the Talbot image of a phase grating. The Talbot pattern as illustrated corresponds to a 1:1 π/2 phase grating, as has been previously presented in references such as “X-Ray Phase Imaging with Talbot Interferometry” by A Momose et al. in BIOMEDICAL MATHEMATICS: Promising Directions in Imaging, Therapy Planning, and Inverse Problems (Medical Physics Publishing, Madison Wis., 2010), pp. 281-320. 
     The x-rays  889  transmitted through a sample enter from the left and fall onto the 1:1 π/2 phase grating  210 . Under spatially coherent illumination, the grating produces a Talbot carpet, as discussed in the previous embodiments. At the third fractional Talbot distance (N=3), an absorption grating  420  is placed and positioned so that the absorbing features, designated by a set of white boxes denoting x-ray blocking material in  FIG. 41 , are aligned with the nodes of the Talbot carpet. At the fifth fractional Talbot distance (N=5), another absorption grating  430  is placed and positioned so that the absorbing features, designated by a set of white boxes denoting x-ray blocking material in  FIG. 41 , are aligned with the nodes of the Talbot carpet. Scattered x-rays  889 -C, illustrated by white arrows, will mostly be blocked by these absorption gratings  420  and  430 , while the intensity of the Talbot pattern remains relatively unchanged. It should be noted that the formation of Talbot carpet as illustrated corresponds to one in which the beam splitting grating is illuminated with x-rays having sufficient spatial coherence. 
     The designs and patterns on the antiscattering grids will correspond to the patterns fabricated into the beam splitting gratings. For example, if the mesh pattern of  FIG. 17  is used as the beam splitting grating G 1 , the antiscattering grid may also be arranged in a mesh pattern. If the checkerboard pattern of  FIG. 18  is used as the beam splitting grating G 1 , the antiscattering grid may also be arranged in a checkerboard pattern. Or, if the checkerboard pattern of  FIG. 18  is rotated 45° to form a diamond pattern, the antiscattering grid may also be arranged in a rotated checkerboard (diamond) pattern. Additional embodiments may further include other periodic structures such as honeycomb structures. 
     The transmission through the antiscattering grid is a function of the aspect ratio and the relative size of the absorbing features. This is illustrated in  FIG. 42 . The height of the grating is given by h g , while the width of the apertures between absorbing structures is w g  and the period of the antiscatter grating is p 4 . Scattered x-rays with a propagation angle θ from normal such that
 
tan(θ)&lt;(w g /h g )  [Eqn. 17]
 
will generally pass through the grid if they happen to not hit one of the absorbing structures end on. Transmission for normal incidence x-rays will be given by the ratio of the area of absorbing and non-absorbing structures. For the case of a 50/50 grid, where p 4 =2w g , the best transmission will be 50%. In this case, the transmission of scatter ration at small scattering angles with respect to the primary radiation is the same as the primary radiation, there is not preferential absorption of the scatter radiation. For scatter radiation with scattering angles greater than
 
θ=tan −1 (w g /h g )  [Eqn. 18]
 
the antiscattering grid preferentially absorbs scatter radiation.
 
     In some embodiments, the antiscattering grid may be used in addition to an analyzer grating G 2  for the detector. Such an embodiment is illustrated in  FIG. 43 . Using such a configuration, multiple embodiments of the invention enable one to obtain additional information about the sample. 
     The embodiment as illustrated in  FIG. 43  comprises an x-ray source  002  with microstructured periodic array sub-sources as disclosed in various embodiments, a beam splitting grating G 1    210 , an antiscattering grid G 4    420 , and a detector  290 , without the analyzer grating G 2 . In absence of the beam splitting grating  210  and the antiscattering grid  420 , this imaging system is similar to most conventional x-ray imaging systems, except for the microstructured x-ray source  002 , which is usually an extended x-ray source. The current art of antiscattering grid is ineffective for absorbing scattered radiation with small scattering angles with respect to the primary radiation because it has a significant fraction of the area that are transparent to both the scatter radiation and primary radiation. This becomes particularly significant for observing subjects such as babies or uncompressed breasts, in which scattering such as Compton scattering can be 5× greater than the signal carrying absorption contrast information. According to embodiments of the invention, scattered radiation can be preferentially absorbed by placing the antiscattering grid at one of the fractional Talbot distances and positioning the absorbing features at the nodes of the corresponding Talbot carpet. This embodiment is particularly important for imaging objects having large volume using high energy x-rays, such as clinical x-ray imaging and security inspection. 
     According to another embodiment of the invention, a dark-field image may be recorded by the detector  290  without the analyzer grating  220  by placing the antiscattering grid  420  at one of the fractional Talbot distances and positioning the absorbing features at the antinodes (or integer multiples of the antinodes) of the corresponding Talbot carpet. Another dark-field image can be recorded by the detector  290  without the absorption grid  420  but with the analyzer grating  220  aligned so that its absorbing parts are aligned to the antinodes of the Talbot carpet. Because two different dark-field images are obtained at different distances from the beam splitting grating  210 , they will contain different spatial information about the object. 
     According to another embodiment of the invention, by placing an antiscattering grid at one of the fractional Talbot distances and positioning its absorbing features at the nodes of the corresponding Talbot carpet, several established phase contrast imaging techniques usually done without the antiscattering grid can be used, including differential phase contrast imaging, phase stepping to obtain simultaneous phase, absorption, and scattering images, and imaging using a high spatial resolution detector without phase stepping. 
     3.2. Detector MTF and DQE 
     Variations in the detector configuration and positioning may also contribute to improvements in the signal-to-noise ratio for x-ray systems constructed according to the invention. The figures of merit that may be impacted by the selection of detector properties are the modulation transfer function (MTF) and the detection quantum efficiency (DQE). 
     The presence of Compton scattering, as described above, may contribute to the degradation of these figures of merit. However, other factors may also impact MTF and DQE. The achievable MTF and DQE of a detector depend on different physical processes. The intrinsic physical processes to all x-ray array detectors include the interaction (traveling) range of the photoelectrons produced by the ionizing radiation, production of secondary x-ray fluorescence produced by the ionization/de-excitation of atoms in the detector sensing material by the incident x-rays, and parallax blurring resulting from the finite thickness of the sensing material at oblique incidence angles with respect to the surface normal. Reabsorption of Compton scattered radiation and secondary fluorescence x-rays by the materials of the detector can also contribute to the reduction of MTF and DQE, but this contribution is usually negligible. 
     Additional processes in actual detectors may also contribute to the reduction of MTF and DQE. For direct conversion digital array detectors (such as amorphous selenium-photoconductor-based flat panel detector), lateral diffusion of charge carriers may contribute to the reduction of MTF ad DQE. For indirect conversion digital array detectors comprising a layer of a phosphor material (such as Gd 2 O 2 S) ora scintillator material (such as column-grown CsI fibers), light spread due to scattering can contribute significantly to the reduction of the MTF and DQE in the detector. 
     For all digital array detectors, the fill factor (the percent of the effective detection area) will also contribute to the reduction of MTF and DQE, which can be especially problematic with small detector pixels. For all the factors contributing to the reduction of MTF and DQE, these effects get worse with increasing detector resolution (smaller pixels), and may lead to many design compromises and tradeoffs, including: the compromise between scintillator/phosphor thickness (and, therefore, its quantum detection efficiency); spatial resolution limitations due to light scattering induced image blurring; and considerations and trade-offs between improving resolution (smaller pixels) with detector parameters such as fill factor, material mass density (to which the photoelectron range is inversely proportional), and the elemental composition of the detector sensing material which determines the range of the characteristic fluorescence x-rays. 
     Most of the detrimental factors to MTF and DQE make a maximum contribution when the radiation is incident near or at the edges of the detector pixels. Thus an improvement in MTF and DQE may be achieved if all the incident radiation is directed to be incident at the center of the detector pixels. 
     Commonly deployed position-sensitive detectors do not have intrinsic angle sensing/rejection capability. Scattered radiation (including small-angle scattering by fine structures in the object as well as Compton scattering) is part of the undesirable image background, producing “counts” in the detector that are indistinguishable from the “counts” due to the desired radiation. 
     Therefore, the use of a system comprising a detector that rejects or reduces the scattered radiation can increase the image contrast and the DQE of the system. 
     3.3. Embodiments with a Modified Detector 
     As discussed above, the scattered radiation may be blocked by placing an absorption grid or grating aligned such that the absorption regions correspond to the dark Talbot fringes. 
     Likewise, it is also possible to select the detector grid spacing and positioning so that the centers of the rows (and/or columns) are aligned with the centers of the anti-nodes of the Talbot fringes, such that the area between sensor pixels (which by definition is made to be transparent to the incident x-rays) correspond to the position of the nodes of the Talbot carpet. By using a detector with such a spacing and alignment, the scattered x-rays that would normally be absorbed by the detector are not absorbed. As a consequence, the noise associated with them in the sensor pixels due to photoelectrons, reabsorption of secondary fluorescence x-rays, and Compton scattering, will be absent, and the signal-to-noise ratio is improved. 
       FIG. 44  illustrates a system in which the detector is so arranged. As in previous embodiments, the x-rays  888  generated by a source comprising a plurality of microstructured sub-sources  700  arranged in a regular pattern (i.e. a set of lines or an array) generate x-rays that propagate through an object to be examined  240 -M and fall onto a beam-splitting grating  210 -D. The beam-splitting grating is generally a one- or two-dimensional phase-shifting grating, with spacing and period p 1  of the grating having a relationship to the spacing of the sub-sources as described in Eqn. 9 above. The Talbot pattern as illustrated corresponds to a beam splitting grating  210 -D having a 1:1 π/2 phase shifting pattern, as illustrated in, for example, “X-Ray Phase Imaging with Single Phase Grating” by Y Takeda et al., Jpn. J. Appl. Phys. vol. 46, 2007, pp. L89-L91. 
     A detector comprising various sensor pixels  290 -BP connected electronic backplane  290 -B produces signals related to the number of x-rays detected, and that signal passes through a connector  291  to a data processing system  295  for analysis. The detector is positioned at one of the fractional Talbot distances, i.e. 
                     D   5     =       D   N     =         N   5     ⁢       p   1   2       8   ⁢   λ         =         N   5       1   ⁢   6       ⁢     D   T                   [     Eqn   .           ⁢   19     ]               
where D N  is the fractional Talbot distance for a plane wave illumination, λ is the mean x-ray wavelength, and N 5  is the Talbot fractional order (N=1, 2, 3, . . . ) at which the detector is placed.
 
     The spacing p 5  of the sensor pixels is then selected to correspond to the Talbot spacing for the corresponding beam-splitting grating G 1 . The relationship is given by: 
                     p   5     =       Kp   0     ⁢       D   5     L               [     Eqn   .           ⁢   20     ]               
where p 0  is the period of the microstructured source, L the distance between the x-ray sources  700  and the diffraction grating  210 -D, and K is a scaling factor which is equal to 1 when the beam-splitting grating introduces a phase shift of π/2, and is equal to ½ when the beam-splitting grating introduces a phase shift of π.
 
       FIG. 45  illustrates another embodiment in which the grating  210 -D is used to produce a Talbot interference pattern. The detector  290 -B-L comprises pixels  290 -BP-L in which the majority of the area of the detector comprises pixels, with only a small gap between pixels. The detector  290 -B-L is placed at a predetermined Talbot distance (fractional or odd integer) such that the antinodes (regions of constructive interference) of the Talbot pattern is incident on or near the center of each detector pixel  290 -BP-L. Thus the detector has a periodicity that corresponds to the period of the Talbot pattern. Such a grating and detector scheme may be used with the microstructured source previously mentioned, or with any other source with sufficient lateral coherence, such as a microfocus source. 
     The designs and patterns on the detector grids will correspond to the patterns fabricated into the beam splitting gratings. For example, if the checkerboard pattern of  FIG. 18  is used as the beam splitting grating G 1 , the detector grid may also be arranged in a checkerboard pattern. Or, if the mesh pattern of  FIG. 17  is used as the beam splitting grating G 1 , the detector grid may also be arranged in a mesh pattern. If the checkerboard pattern of  FIG. 18  is rotated 45° to form a diamond pattern, the detector grid may also be arranged in a rotated checkerboard (diamond) pattern. 
     3.4. “Single Shot” Talbot Techniques 
     Existing x-ray imaging systems for clinical, security inspection, and nondestructive test use primarily absorption contrast (difference in attenuation between neighboring features). It has been long recognized that x-ray phase contrast (difference in phase shift between neighboring features) can be significantly larger than absorption contrast for most materials at high energy x-rays, especially for low Z materials. Recently, scattering contrast (difference in small angle scattering strength between neighboring features) has been recognized for imaging sub-resolution features within an imaging resolution element (such as pores and fine structures of dimension less than the imaging resolution). It is highly desirable to be able to simultaneously obtain in a single shot (exposure) an absorption contrast image in combination with at least one of a differential phase contrast image, phase contrast image, or scattering contrast image. 
     Several researchers have developed single-shot x-ray phase contrast imaging techniques that use beam splitting gratings and an analyzer grating slightly rotated with respect to the beam splitting grating, and then using a Fourier transform image analysis technique to arrive at a phase contrast image. The drawback of this technique is that the image spatial resolution is substantially compromised. Additional developments include further variants of single-shot techniques [see, for example, H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of X-ray scattering—initial results,” IEEE Trans. Med. Imaging vol. 27(8), 997-1002 (2008); and H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology vol. 251(3), 910-918 (2009)], which they called the “spatial harmonic method”. In these references, a single projection image containing a transmission grating (grid) will have several distinct harmonic peaks in the spatial frequency domain. Inverse Fourier transformation of these peaks results in harmonic images. The relative weight between absorption and diffraction-caused attenuations differs among these images, and therefore provide sufficient information to extract separate absorption and diffraction images. Raw images obtained by both single-shot techniques do not contain separate absorption and dark-field (scattering) images, and require image analysis to obtain images from different contrast mechanisms. 
     3.5. Embodiments with Two Modified Detectors (for “Single Shot” Techniques) 
     In other embodiments of the invention, a system with two detectors, one positioned at one of the fractional Talbot distances and aligned with its grid (active pixels), spacing (transparent areas between the active pixels) and positioning so that the centers of the rows (and/or columns) are aligned with the centers of the antinodes of the Talbot fringes, while the other positioned at another one of the fractional Talbot distance downstream of the first detector and aligned with its grid (active pixels), spacing (areas between the active pixels, preferably transparent) and positioning so that the centers of the rows (and/or columns) are aligned with the centers of the nodes of the Talbot fringes. By using a pair of detectors with such a spacing and alignment, both the absorption and the scattering (dark-field) images may be collected at the same time, in a “single shot”. In some embodiments, the positions of the two detectors can be reversed, but the spacing between the active pixels of the upstream detector in this case should still be sufficiently transparent to x-rays. 
       FIG. 46  illustrates a system in which a pair of detector is so arranged. As in previous embodiments, the x-rays  888  generated by a source comprising a plurality of microstructured sub-sources  700  arranged in a regular pattern (i.e. a set of lines or an array) generate x-rays that propagate through an object to be examined  240 -M and fall onto a beam-splitting grating  210 -D. The beam-splitting grating is generally a one- or two-dimensional phase-shifting grating, with spacing and period p 1  of the grating having a relationship to the spacing of the sub-sources as described in Eqn. 9 above. 
     One detector comprising various sensor pixels  290 -BP connected electronic backplane  290 -B produces signals related to the number of x-rays detected, and that signal passes through a connector  291  to a data processing system  295  for analysis. As above, the detector is positioned at one of the fractional Talbot distances, i.e. 
                     D   5     =       D   N     =         N   5     ⁢       p   1   2       8   ⁢   λ         =         N   5       1   ⁢   6       ⁢     D   T                   [     Eqn   .           ⁢   21     ]               
where D N  is the fractional Talbot distance for a plane wave illumination, λ is the mean x-ray wavelength, and N 5  is the Talbot fractional order (N=1, 2, 3, . . . ) at which the first detector is placed. The active pixels (indicated by the hatched boxes) of the detector  290 -BP are aligned with the antinodes of the corresponding Talbot carpet. The areas between the active pixels are preferably transparent, but not necessary.
 
     As above, the spacing p 5  of the sensor pixels is then selected to correspond to the Talbot spacing for the corresponding beam-splitting grating G 1 . The relationship is given by 
                     p   5     =       Kp   0     ⁢       D   5     L               [     Eqn   .           ⁢   22     ]               
where p 0  is the period of the microstructured source, L the distance between the x-ray sources  700  and the diffraction grating  210 -D, and K is a scaling factor which is equal to 1 when the beam-splitting grating introduces a phase shift of π/2, and is equal to ½ when the beam-splitting grating introduces a phase shift of π.
 
     However, in this embodiment, the system also comprises a second detector comprising various sensor pixels  290 -DP connected electronic backplane  290 -D that produces signals related to the number of x-rays detected for the dark field, and that signal passes through a connector  291 -D to a data processing system  295  for analysis. As above, the detector is positioned at one of the fractional Talbot distances, i.e. 
                     D   6     =       D   N     =         N   6     ⁢       p   1   2       8   ⁢   λ         =         N   6       1   ⁢   6       ⁢     D   T                   [     Eqn   .           ⁢   23     ]               
where D N  is the fractional Talbot distance for a plane wave illumination, λ is the mean x-ray wavelength, and N 6  is the Talbot fractional order (N=1, 2, 3, . . . ) at which the second detector is placed. The active pixels (indicated by the hatched boxes) of the detector  290 -DP are aligned with the nodes of the corresponding Talbot carpet. The areas between the active pixels need to be sufficiently transparent to x-rays.
 
     As above, the spacing p 6  of the sensor pixels of the second detector is then selected to correspond to the Talbot spacing for the corresponding beam-splitting grating G 1 . The relationship is given by 
                     p   6     =       Kp   0     ⁢       D   6     L               [     Eqn   .           ⁢   24     ]               
where p 0  is the period of the microstructured source, L the distance between the x-ray sources  700  and the diffraction grating  210 -D, and K is a scaling factor which is equal to 1 when the beam-splitting grating introduces a phase shift of π/2, and is equal to ½ when the beam-splitting grating introduces a phase shift of π.
 
     The designs and patterns on the detector grids will correspond to the patterns fabricated into the beam splitting gratings. For example, if the checkerboard pattern of  FIG. 18  is used as the beam splitting grating G 1 , the detector grids may also be arranged in a checkerboard pattern. Or, if the mesh pattern of  FIG. 17  is used as the beam splitting grating G 1 , the detector grids may also be arranged in a mesh pattern. If the checkerboard pattern of  FIG. 18  is rotated 45° to form a diamond pattern, the detector grids may also be arranged in a rotated checkerboard (diamond) pattern. 
     With this arrangement, the partially transmitting second detector  290 -DP records a dark-field x-ray image due to a combination of scattering contrast (x-rays scattered by small-angle scattering by sub-resolution features) and/or refraction (phase) contrast from sharp features with a large phase gradient, while the first (image) detector  290 -BP records an image with a combination of an absorption contrast image and/or a refraction (phase) contrast image from features with a small phase gradient. Alternatively, a partially transmitting grating with reverse property from the preceding partially transmitting grating can be used. In this configuration, the images recorded by the partially transmitting detector and the image detector are reversed compared to the preceding detector arrangement. 
     The ratio of half of the period of the Talbot interference fringe or pattern to the fractional Talbot distance provides a first angular measure which can be used as an approximate measure for substantial presence of scattered/refracted x-rays in the nodes of the Talbot fringes or pattern. By selecting the Talbot fractional orders for the placement of the partially transmitting detector and the main detector and geometric parameters of the beam splitting grating period, distances between the source, beam splitting grating, and x-ray wavelength, one can optimize sub-resolution feature sizes or desired phase gradient of large features for preferentially higher contrast imaging. 
     An alternative embodiment of a two detector “single shot” system is illustrated in  FIG. 47 . Here, the bright Talbot Fringes  889 -B and dark Talbot regions  889 -D are illustrated as propagating away from a beam splitting phase grating with period p 1 . At a suitable distance away, typically at a multiple of the fractional Talbot distance, a detector  290 -DS comprising a scintillator  260  and additionally a reflective coating  270  is placed. The reflective coating is such that the visible light  988  generated when the scintillator absorbs x-rays and emits visible or near UV light is reflected to the scintillator. The detector  290 -DS detects the x-rays that are transmitted through the scintillator  260  and the reflector  270 , and may additionally comprise sensor pixels  290 -DPS that are placed at in a regular array with period p 6  such that their positions will correspond to the nodes of the Talbot pattern. This detector  290 -DS may in turn produce signals related to the number of x-rays detected in the nodes due to scattering by features with dimensions smaller than the resolution element of the imaging system, and these signals pass through a connector  291 -D to a data processing system  295  for analysis. 
     The scintillator  260  may also be coated in a 1-D or 2-D pattern, so that visible or near UV photons are generated only in regions corresponding to high x-ray intensity (i.e. the antinodes of the Talbot fringes). 
     The system also comprises a beamsplitter  280  that transmits x-rays but reflects visible and/or UV Photons, and a visible/UV imaging system  380  (e.g. a lens or a microscope objective) that forms an image of the bright field portions of the Talbot interference pattern. The visible/UV photons  998  emitted by the scintillator reflect off this beamsplitter, and the reflected visible/UV photons  988 -R are formed into an image by the visible/UV imaging system onto a bright field detector  290 -BS. The visible/UV detector may have a uniform array of pixels, or may have selected regions with a period p 5  with positions arranged to correspond to the images of the bright field portions of the Talbot pattern. The visible/UV detector  290 -BS produces signals related to the number of x-rays detected in the antinodes of the Talbot fringes, and that signal passes through a connector  291 -B to a data processing system  295  for analysis. 
     In this manner, both bright field and dark field information are gathered in parallel, without the detectors blocking each other, as may be the case for the pair of detectors as was shown in  FIG. 46 . 
     4. Fabrication of Gratings 
     Fabrication of the gratings used in embodiments of the invention may be made using known prior art fabrication processes such as those previously described by Christian David [C. David et al., “Fabrication of diffraction gratings for hard x-ray phase contrast imaging”, Microelectron. Eng. 84, 1172-1177, 2007]. 
     Gratings for x-rays may be fabricated using silicon substrates, with etched changes in topography to induce phase changes and depositions of a higher Z material, such as gold (Au, Z=79), to induce absorption changes. The x-ray absorption properties for gold and silicon are illustrated in  FIG. 39 . 
     As shown in  FIG. 48 , a periodic pattern  3010  may be etched into a silicon substrate  3000  to create a structure which introduces a periodic phase shift for x-rays falling at normal incidence. The phase shift depends on the etch depth, with a phase-shift of π radians for normal incidence x-rays achieved when the following condition is met: 
     
       
         
           
             
               
                 
                   
                     d 
                     etch 
                   
                   = 
                   
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         λ 
                         
                            
                           
                             n 
                             - 
                             1 
                           
                            
                         
                       
                     
                     = 
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         λ 
                         δ 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Eqn 
                     . 
                     
                         
                     
                     ⁢ 
                     25 
                   
                   ] 
                 
               
             
           
         
       
     
     Values for δ for silicon at several x-ray energies, along with the depth etched structures need to a phase-shift of π radians are shown in Table IV. 
     A typical grating fabrication process comprises coating a &lt;110&gt; oriented silicon wafer with a photoresist, and patterning the resist using conventional photolithography, focused ion beam lithography, or electron beam lithography. The silicon then undergoes an etching process such as wet etching in, for example, a potassium hydroxide (KOH) solution, or reactive ion etching (RIE), with the etching selectively occurring only for portions of the silicon not masked by the resist. The etch depth may be controlled by adjusting the time of the etch process. Other variations of the etching process will be known to those skilled in the art of semiconductor processing and manufacturing. 
     
       
         
           
               
             
               
                 TABLE IV 
               
             
            
               
                   
               
               
                 Etch depth for Silicon phase shift of π radians. 
               
            
           
           
               
               
               
               
               
            
               
                   
                 X-ray  
                 Wavelength 
                   
                 π phase shift 
               
               
                   
                 Energy (keV) 
                 λ (nm) 
                 δ 
                 depth (μm) 
               
               
                   
               
               
                   
                  3.0 
                 0.413  
                 5.43E−05 
                   3.81 
               
               
                   
                  5.0 
                 0.248  
                 1.98E−05 
                   6.26 
               
               
                   
                    8.048 
                 0.154  
                 7.58E−06 
                  10.17 
               
               
                   
                 (Cu Kα) 
                   
                   
                   
               
               
                   
                 10.0 
                 0.124  
                 4.89E−06 
                  12.69 
               
               
                   
                  17.48 
                 0.0709 
                 1.59E−06 
                  22.36 
               
               
                   
                 (Mo Kα) 
                   
                   
                   
               
               
                   
                 30.0 
                 0.0413 
                 5.36E−07 
                  38.52 
               
               
                   
                 50.0 
                 0.0248 
                 1.93E−07 
                  64.31 
               
               
                   
                  59.39 
                 0.0209 
                 1.37E−07 
                  76.32 
               
               
                   
                 (W Kα) 
                   
                   
                   
               
               
                   
                 100.0  
                 0.0124 
                 4.82E−08 
                 128.74 
               
               
                   
               
            
           
         
       
     
     Absorption gratings such as those used for G 2  may be fabricated by initially creating a silicon phase grating, as described above, and then depositing an x-ray absorbing material, such as gold, into the grooves already patterned in the silicon. This is illustrated in  FIG. 49 , in which an amount of x-ray absorbing material  3030  such as gold has filled the grooves created in a silicon substrate  3000 . One process for the deposition of gold into the silicon grooves involves a standard electroplating processes. To ensure that gold is only deposited into the grooves, a sacrificial layer of aluminum may initially be deposited at an angle, and a seed layer ˜50 nm thick comprising Chromium (Cr) and gold (Au) are then deposited. A phosphoric acid treatment removes all the material deposited on the tops of the silicon structures, leaving seed material only in the bottom of the grooves in the silicon. Standard electroplating may follow, with growth of gold occurring only onto the deposited seed layers. Deposition of gold at hundreds of microns can create absorption gratings with a transmission modulation of 75% or more. Absorption will, however, depend on the x-ray energy and the absorption coefficient for the material, as was illustrated in  FIGS. 1 and 39 . Other methods for making x-ray absorption gratings will be known to those skilled in the art. 
     For some applications and for certain x-ray wavelengths, crystal gratings may also be used. 
     It should be noted that the antiscattering grids or gratings disclosed with these embodiments of the invention can be fabricated using any number of lithographic pattering techniques known to those skilled in the art as well. 
     5.0 Detector Properties 
     The detector may be any one of a number of detectors used to form x-ray images. One type of commonly used x-ray detector comprises a fluorescent screen or scintillator, such as one comprising a layer of cesium iodide (CsI), thallium doped CsI, yttrium aluminium garnet (YAG) or gadolinium sulfoxylate (GOS), that emits visible photons when exposed to x-rays. The visible photons are then detected by an electronic sensor that converts visible intensity into electronic signals, often with the additional formation of a relay image using visible optics that enlarge and magnify the intensity pattern of the photons emitted by the fluorescent screen. With the relay optics, the electronic detector need not comprise a high resolution sensor itself, and inexpensive commercial CCD detectors or complementary metal-oxide-semiconductor (CMOS) sensor arrays with, for example, 1024×1024 pixels, each 24 μm×24 μm square, may be used. 
     Commercial flat panel digital x-ray sensors in which a layer of scintillator material is placed in close proximity to (or even coated onto) an array of conventional optical image sensors are manufactured by, for example, Varian Inc. of Palo Alto, Calif. and General Electric, Inc. of Billerica, Mass. Other configurations of image sensors may be known to those skilled in the art. In embodiments in which a G2 analyzer grating is used, it is preferable to use highly efficient, fast read-out detectors such as flat panel detectors, used for medical and industrial uses. For many applications, using a flat panel detector with a resolution larger than 20 microns will require that an analyzer grating G 2  with a period equal to the Talbot fringe period be placed in the x-ray beam path before the detector. 
     A second approach is to use an electronic sensor that directly creates an electrical signal in response to the absorption of x-rays, by, for example, the creation of direct electron-hole pairs in amorphous selenium (a-Se). These are then converted into electronic signals using an array of thin-film transistors (TFTs). Such direct flat panel detectors (FPDs) such as the Safire FPD of Shimadzu Corp. of Kyoto, Japan, are commercially available. 
     6.0. Variations 
     Embodiments may further comprise other components typically included in Talbot interferometer, including spectral filters to obtain a desired x-ray energy bandwidth and positioning control systems for all the various components of the system. 
     It should be noted that certain terms used within this disclosure will be well known to those skilled in the art, such as grids or gratings. In the descriptions here, grids and gratings are terms that may be used interchangeably, and are not meant to be restrictive to a particular grid, period, or pattern. 
     Likewise, it should be noted that certain terms used within this disclosure will be well known to those skilled in the art, such as Talbot fringes, interference patterns, or “carpets”. In the descriptions here, interference patterns, fringes, or “carpets” are terms that may be used interchangeably, and are not meant to be restrictive to any particular intensity pattern. 
     Likewise, it should be noted that certain terms used within this disclosure will be well known to those skilled in the art, such as septa for the absorbing structures of antiscattering grids. In the descriptions here, septa or septum or structure are terms that may be used interchangeably in reference to the absorbing structures of the antiscattering grid, and are not meant to be restrictive to any particular ratio of height to width, or to imply a solely one-dimensional geometry. 
     With this application, several embodiments of the invention, including the best mode contemplated by the inventors, have been disclosed. It will be recognized that, while specific embodiments may be presented, elements discussed in detail only for some embodiments may also be applied to others. 
     While specific materials, designs, configurations and fabrication steps have been set forth to describe this invention and the preferred embodiments, such descriptions are not intended to be limiting. Modifications and changes may be apparent to those skilled in the art, and it is intended that this invention be limited only by the scope of the appended claims.