Apparatus for coded aperture X-ray scatter imaging and method therefor

A system and method for producing images of the structure and composition of an object based on measurements of the low-angle x-ray diffraction properties of the object. The imaging system includes a coded aperture that encodes spatial and spectral features onto radiation scattered from image points within the object. The radiation is detected at a two-dimensional array of detectors, whose output is deconvolved and processed to estimate a three-dimensional image having molecular specificity.

FIELD OF THE INVENTION

The present invention relates to imaging in general, and, more particularly, to x-ray scatter imaging.

BACKGROUND OF THE INVENTION

The ability to non-invasively image the molecular composition of an object is desirable in a number of application areas, such as medical imaging, security, structural integrity verification, and homeland defense. While x-ray imaging is the most effective strategy for tomographic imaging in such applications, conventional x-ray systems are not sensitive to molecular composition. X-rays interact with materials via photoelectric absorption, Compton scatter, coherent (Bragg) scatter and fluorescence. Conventional x-ray imaging primarily measures absorption and Compton scatter; however, only coherent scatter and fluorescence are sensitive to molecular or atomic identity.

A traditional x-ray imaging system detects hard and soft materials by the variation in x-ray transmission through an object. More recently, however, imaging systems based on x-ray scattering by the structure of an object have been developed, such as described in U.S. Pat. No. 7,835,495 entitled “System and Method for X-ray Diffraction Imaging,” which discloses a method for x-ray scatter imaging using collimators on each of an array of detector elements. While such approaches give rise to detectors that are sensitive to the direction of x-ray propagation, the use of the collimators severely limits photon efficiency.

Alternative approaches for imaging systems have been developed that employ multiplexed measurements from shaped x-ray beams, such as a fan-shaped beam, to construct x-ray scatter images. Examples of such systems are disclosed in U.S. Pat. No. 7,583,783 entitled “X-ray Computer Tomograph and Method for Examining a Test Piece Using an x-ray Computer Tomograph.” Unfortunately, these approaches require multiple exposures and are relatively poorly conditioned for mathematical image estimation.

Backscatter x-ray systems detect a relatively small amount of radiation that reflects from the object and use it to form an image. These systems are particularly attractive for applications where less-destructive examination is required or where only one side of the target is available for examination. The backscatter pattern is dependent on the properties of the material being interrogated, and is good for imaging a wide range of materials. Backscatter x-ray imaging systems include full-body airport scanners, which are currently being used to detect hidden weapons, tools, liquids, narcotics, currency, etc. As with forward scatter, in backscatter systems that rely on collimators rather than coded apertures only a small percentage of the incident radiation is detected. Backscatter x-ray systems require high-power x-ray sources and/or high-sensitivity detectors in order to provide acceptable resolution and signal-to-noise ratio (SNR). Line-scan systems utilizing a fan beam of radiation to inspect an object and a segmented detector to measure radiation transmitted through the object are able to use a higher portion of available source flux; however, they are generally incapable of producing images from backscattered radiation.

Forward-scattering x-ray scatter imaging systems such as those described in U.S. Pat. No. 7,835,495, employ a primary beam of x-ray radiation that is scanned over an object while radiation from elastic (coherent) scattering is monitored by a fixed-position, energy-resolving detector. The detector is located at a small, fixed angle to the direction of propagation of the primary beam. Information about the crystallographic structure of the material of the scattering object is derived from the resultant scatter spectra. This information can then be compared to known scatter spectra in a library of materials of interest to determine if any such materials are included in the object being scanned.

Unfortunately, scanning x-ray systems capture only a small fraction of the radiation directed at the scanned object and are, therefore, highly inefficient. As a result, in order to produce an output signal having sufficiently high SNR, they require either x-ray sources capable of high power to increase the available radiation at the detector, or long exposure times. In either case, this exposes the scanned object to excessive amounts of x-ray radiation, which can be undesirable in many applications.

In addition, conventional x-ray imaging systems typically employ substantially monochromatic radiation or rely on energy discriminating detectors to improve resolution and signal quality. As a result, the total incident photon flux on the object of interest is limited.

Further, while conventional x-ray diffraction imaging approaches might be suitable for interrogating small-size (<1 cm2) areas, their data acquisition time makes it impractical to scan entire bags or parcels. The size limitation arises, in part, from the fact that while energy resolving detectors can discriminate x-ray diffraction orders from different wavelengths, they are quite expensive—particularly in array sizes necessary for high-speed, high-resolution imaging. Improved “fan beam” tomographic imaging systems offer some improvement in detection efficiency; however, these systems require expensive energy-resolving x-ray detectors and/or low-flux low-bandwidth x-ray sources. Still further, these systems are not well suited for scanning arbitrary objects whose composition can vary over a wide range since detection of a constituent material requires some advance knowledge or suspicion of the presence of that material so that its scattering “fingerprint” can be included in the material library.

Computational x-ray tomography, such as is described in U.S. Pat. No. 7,583,783, has been shown capable of producing images that are also based on measurements of the low-angle x-ray diffraction properties of an object. Such systems typically scan a “pencil beam” of x-ray radiation over a series of locations on the object and use computational processing-over many exposures to acquire a diffraction pattern for each scanned location. These diffraction patterns are used to reconstruct a series of images, which represent the coherent-scatter intensity at a series of scatter angles. Coherent-scatter cross-sections of the object can then be generated for each pixel from the sequence of images to develop a tomographic reconstruction of the object.

Like x-ray scatter-imaging systems, however, computed x-ray tomography systems do not efficiently utilize the x-ray energy directed at the scanned object. In addition, the need to develop the tomographic model of the object one cross-section at time leads to an undesirable space-time spectral trade-off.

There remains a need, therefore, for an improved imaging system that noninvasively ascertains the structural and molecular composition of three-dimensional objects at high speed and with relatively lower cost and complexity.

SUMMARY OF THE INVENTION

The present invention enables non-invasive, three-dimensional imaging of the structure and molecular composition of an image point of an object in a single snapshot. Embodiments of the present invention are well suited for use applications including luggage scanning, cargo inspection, explosives detection, and medical imaging. Some embodiments of the present invention are particularly well suited for use in imaging objects whose size scale is 10 centimeters or larger.

Embodiments of the present invention include a coded aperture in an optical path that extends from an x-ray source through an object under text and to a detector array. The coded aperture enables multiplexed measurement of scatter angles, spatial, and spectral information from the object. In some embodiments, the coded aperture is located between the object and the detector. In some embodiments, the coded aperture is located between the source and the object.

In embodiments wherein the object is interrogated by a pencil beam x-ray signal, the inclusion of the coded aperture enables instantaneous and simultaneous measurement of scatter angle and object density versus range (i.e., longitudinal position) along the pencil beam without the loss of throughput inherent to the use of collimation filters at the detector elements, as used in the prior art.

It is an aspect of the present invention that the use of a coded aperture having a code that provides suitable orthogonality versus scale rather than translation affords embodiments of the present invention significant advantage over prior-art x-ray imaging systems. In some embodiments, the code is a periodic code, while in other embodiments, the code is a random code. It is a further aspect of the present invention that periodic or random codes can significantly outperform uniformly redundant arrays.

It is another aspect of the present invention that the use of reference structures or coded apertures in combination with decompressive inference enables instantaneous or reduced time estimation of fan beam or volume scatter signatures, especially joint estimation of momentum transfer spectra and spatial structure.

Imagers in accordance with the present invention include a coded aperture that encodes spatial and spectral features of radiation scattered from image points within an object to efficiently use the flux of polychromatic x-ray photons scattered from the object to form a two- or three-dimensional image with molecular specificity. In some embodiments, a pencil beam of x-ray radiation interrogates a line of image points through the object. The coherent scatter properties of the object can be estimated at each image point along the line by acquiring a single irradiance image at a two-dimensional irradiance detector. By scanning the pencil beam over the transverse extent of the object, a complete volumetric molecular image of the object can be estimated.

An illustrative embodiment of the present invention comprises a source of x-ray radiation, a primary aperture, a coded aperture, and a detector array. The primary aperture receives x-ray radiation from the source and provides a pencil beam of radiation, which is directed at an object to be imaged. The pencil-beam radiation is incident on the object along a central axis. As the radiation interacts with the materials of the object, it is scattered along forward directions, whose angles with respect to the central axis depend upon the molecular structure of the materials. The scattered radiation passes through the coded aperture, which acts as a reference structure that modulates the scattered radiation. The modulated radiation is received at the detector, which comprises an array of irradiance detectors. The modulation of the scattered radiation removes its range/angle ambiguity, thus affording an angular sensitivity to each pixel of the detector array.

In some embodiments, relative transverse motion between the pencil beam and the object is enabled such that the entire transverse extent of the object is interrogated.

In some embodiments, a fan beam of x-ray radiation is used instead of the pencil beam. Such embodiments enable an improved temporal resolution, among other advantages. In some embodiments, a cone beam of radiation is used.

An embodiment of the present invention comprises an x-ray scatter imaging system including: a source operable for interrogating an object with a first signal comprising x-ray radiation; a detector operable for detecting a second signal comprising x-ray radiation scattered from the object, the detector including a two-dimensional array of pixels; and a coded aperture operable for modulating the second signal.

DETAILED DESCRIPTION

X-ray diffraction occurs when x-rays scatter elastically from the electrons in an object. Coherence between the scattered x-rays leads to interference effects that give rise to distinct diffraction patterns that can provide insight into the atomic-level structure of the particular material under examination.

X-ray diffraction has been routinely used for many years to determine the structure of crystalline materials in applications such as molecular beam epitaxy (MBE), vapor-phase epitaxy (VPE), and atomic-layer epitaxy (ALE), since the diffraction patterns generated are dependent upon the atomic locations within the crystal. Recently, it has also been directed toward medical applications as well, such as determination of bone-mineral content via measurement of low-angle coherent-scatter x-ray diffraction. An estimation of bone-mineral content at a measurement site within a test sample can be made, for example, by generating scatter diagrams and measuring the angles of peak scatter in a test sample and comparing the results to scatter diagrams for control samples having known proportions of adipose tissue and cortical bone. In order to develop an image of the entire test sample, the sample can be scanned through a focal point using a scanning pattern that interrogates a desired arrangement of measurement sites. Unfortunately, this method makes very inefficient use of the x-rays that hit the object; therefore, undesirably high x-ray doses are required. Further, it has been found that matter density and fat content of the material being examined can introduce errors in the bone-mineral-content measurements.

More recently, coherent-scatter computed tomography (CSCT) using a poly-energetic x-ray beam has been proposed as an improvement to low-angle coherent-scatter x-ray diffraction. CSCT has demonstrated an ability to determine the angular-dependent coherent-scatter cross-section for each pixel in a tomographic slice of an object. CSCT has been shown to be effective for measuring bone-mineral content that is independent of material density and fat content.

FIG. 1depicts a schematic diagram of a CSCT system in accordance with the prior art. System100comprises x-ray source102, collimator106, blocker120, detector122, and processor128. System100is analogous to CSCT systems described by Westmore, et al. in “Tomographic imaging of the angular-dependent coherent-scatter cross section,”Medical Physics, Vol. 24, pp. 3-10 (1997), and which is incorporated herein by reference.

Object110is positioned so that it is interrogated by pencil beam108along axis112, which exposes object elements114-1and114-2to pencil beam108. It should be noted that object elements114-1and114-2are volumetric portions of object110that has a finite width, height, and depth. Object110is typically positioned, relative to pencil beam108, by a multi-axis stage capable of translation along the x-axis, y-axis, and z-axis and rotation about each of the x-axis and y-axis.

At each of object elements114-1and114-2, a portion of pencil beam108is scattered into transmitted primary beam116and scatter radiation. Specifically, object element114-1scatters the x-ray radiation into scatter radiation118-1at an angle of θ1to axis112, and object element114-2scatters the x-ray radiation into scatter radiation118-2at an angle of θ2to axis112. The specific value of the scatter angle of the scatter radiation from each object point depends on its particular material composition.

Blocker120is placed in the path of transmitted primary beam116to block its transmission to detector122. Typically, blocker120is a lead disc or equivalent.

Each of scatter radiation118-1and118-2is incident on detector122at a point that is based on its scatter angle and distance from detector122. Specifically, scatter radiation118-1is incident on detector122at a point based on scatter angle θ1and distance L1, while scatter radiation118-2is incident on detector122at a point based on scatter angle θ2and distance L2. Collectively, scatter radiation118-1and118-2form scatter image132on detector122. Scatter image132is the collective pattern of scatter radiation118-1and118-2that is incident on detector122. Detector122comprises scintillator124, which converts x-ray energy into visible light, and focal-plane array126. Focal-plane array126is typically a conventional CCD array that receives the visible light from scintillator124.

Detector122provides output signal128, which is based on scatter image132, to processor130. Processor130then forms a diffraction pattern based on output signal128.

Unfortunately, system100has several drawbacks. Since each of object elements114-1and114-2has finite length along the z-axis, and is not necessarily of uniform composition throughout, the diffraction pattern formed from scatter radiation118-1and118-2is affected by the point within the object elements from which it scatters, the material composition at that point, and the angle of incidence of pencil beam108on it. As a result, interrogation of an image point by a pencil beam directed at a single angle results in a lack of clarity about the composition of that image point. For clarity inFIG. 1, scatter radiation118-1and118-2is depicted as a single ray of radiation; however, one skilled in the art will recognize that the scatter radiation is actually incident on detector122at a plurality of points whose incidence pattern is indicative of the constituent materials at its respective object element.

As depicted inFIG. 1, the scatter radiation from more than one object element along axis112can hit detector122at the same point, confounding the measurement results. In order to overcome these limitations, object110is rotated over a range of angles such that pencil beam108intersects each object element at a plurality of beam angles. A typical scan, for example, includes diffraction patterns generated at 64 beam angles at each of 64 object elements within the volume of object110. For 64 object elements and 64 beam angles, this results in the generation of a total of 4096 diffraction patterns. Since the generation of each diffraction pattern requires a significant scan time, the total amount of time to scan object110can become prohibitive.

Further, at each object element and beam angle, processor130receives output signal128from detector122. From this data, processor130reconstructs sixteen tomographic images that display the coherent scatter intensity at sixteen different scatter angles.

It is an aspect of the present invention that the application of coded-aperture snapshot imaging concepts to x-ray scatter imaging can give rise to significant advantages over prior-art x-ray imaging systems. Such coded-aperture x-ray scatter-imaging systems can implement compressive snapshot tomography of pencil, fan, and volume data by encoding separable code structures of diverse range and scatter signals.

The present invention applies compressive tomographic imaging techniques to an imaging system such that range imaging of an object under test is enabled. Compressive tomographic imaging, as used herein, is a technique wherein the radiation emanating from each of a plurality of planes of the object under test is encoded via a coded aperture. The radiation from all of the planes is received simultaneously and object reconstruction strategies are applied to decode each of the planes thereby yielding a “tomographic slice” of the object information. Compressive snapshot imaging, as applied to transverse imaging of the spectral properties of an object field, is described in U.S. Pat. No. 8,149,400 entitled “Coded Aperture Snapshot Spectral Imager and Method Therefor,” which is incorporated herein by reference. It should be noted that, although the present invention employs object reconstruction strategies that are mathematically similar to strategies disclosed in U.S. Pat. No. 8,149,400, reconstruction strategies in accordance with the present invention operate on novel physical structures. In particular, the present invention enables simultaneous range and scatter angle/momentum imaging, range, cross range and scatter, volumetric imaging or volumetric and scatter imaging.

While coded apertures have been applied to two-dimensional x-ray imaging in the past, their application in tomographic systems has been limited. The previous state-of-the-art is illustrated in U.S. Pat. No. 6,392,235, entitled “Coded-aperture System for Planar Imaging of Volumetric Sources,” which discloses a method combining two-dimensional transverse imaging with longitudinal displacement of the coded aperture relative to the target to obtain three-dimensional data. This approach is both mathematically poorly posed and continues the traditional space-time trade-off.

In contrast, the present invention continues an alternative, natively tomographic approach of multi-dimensional tomographic coding, such as is disclosed in U.S. Pat. No. 7,912,173, entitled “Reference Structures and Reference Structure Enhanced Tomography.” This patent introduces the idea of compressive tomographic imaging, under which prior constraints are combined with measurements to enable estimation of a number of voxels that is greater than the number of measurement. Further, in tomographic systems, it enables estimation of objects embedded in higher dimension than the measurements such as, for example, estimation of two-dimensional, three-dimensional or four-dimensional tomographic volumes from measurements on one-dimensional lines or two-dimensional surfaces. This eliminates or reduces the traditional space-time trade-off. Similar compressive measurement strategies are also disclosed in greater detail in U.S. Pat. Nos. 7,616,306, 7,463,179, 7,463,174, 7,432,843, 7,427,932, and 7,283,231.

It should be noted, however, that none of the methods disclosed in the prior art, including U.S. Pat. Nos. 7,912,173, 7,616,306, 7,463,179, 7,463,174, 7,432,843, 7,427,932, and 7,283,231, enable recovery of range and scatter angle information about one or more object elements, such as enabled by the present invention. As a result, as described below, the present invention affords significant advantage over these methods by providing molecular and/or atomic information of an object element and thus information about the material composition of an object under test.

FIG. 2depicts a schematic diagram of a portion of a coded-aperture x-ray scatter imaging system in accordance with an illustrative embodiment of the present invention. System200comprises source202, primary aperture206, coded aperture218, detector222, processor226, and stage232. System200is analogous to system100, but with the addition of coded aperture210.

FIG. 3depicts operations of a method suitable for generating a three-dimensional estimation of the structure and composition of an object in accordance with the illustrative embodiment of the present invention. Method300begins with operation301, wherein pencil beam208is provided. Systems and methods in accordance with the present invention are disclosed by K. MacCabe, et al., in “Pencil beam coded aperture x-ray scatter imaging,”Optics Express, Vol. 20, (2012), pp. 16310-16320, which is incorporated herein by reference.

Conventional x-ray source202emits poly-energetic x-ray emission204. To improve the specificity with which material can be classified by system200, the spectrum of x-ray emission204is filtered by a tungsten filter to limit it to an energy passband that ranges from approximately 30 keV to the tungsten K-edge of approximately 69.5 keV. After it has been spectrally shaped, x-ray emission204is received by primary aperture206. In some embodiments, the radiation of pencil beam208includes one or more sharp spectral features. It is an aspect of the present invention that the inclusion of sharp spectral features in the output spectrum of source202can enable improved accuracy and resolution for system200.

Primary aperture206is a conventional x-ray spatial filter, such as pinhole aperture, which forms a barrier to x-ray emission204propagating along directions other than those substantially aligned with axis232. As a result, primary aperture206passes only a substantially parallel bundle of x-rays that collectively define pencil beam208. In some embodiments, primary aperture206is other than a pinhole aperture. In some embodiments, primary aperture enables radiation having a shape other than a pencil beam to pass through and proceed toward object110, such as a fan-shaped beam or a cone-shaped beam.

At operation302, pencil beam208is aligned with image point210-i-j, where i is a number within the range of 1 to M, and j is an integer within the range of 1 to N. Image points201-i-jcollectively define a two-dimensional array of image points having M columns along the x-direction and N rows along the y-direction. The values of M and N are based on the cross-sectional area of pencil beam208and the lateral extent of object110along each of the x- and y-direction. The values of M and N are selected to provide a lateral image resolution suitable for the application for which the use of system200is intended.

At operation303, region212-i-jis interrogated with pencil beam208. Pencil beam208interacts with object elements114-1and114-2in region212-i-jto scatter pencil beam208into transmitted primary beam214and scatter radiation216-1and216-2(referred to, collectively, as scatter radiation216), which is scattered in the forward direction (with respect to the propagation of pencil beam208. Scatter radiation216-1and216-2are analogous to scatter radiation116-1and116-2, and scatter at angles within the range of θ1to θ2, respectively, with respect to the transmitted primary beam214, based on the material composition of object elements114-1and114-2, as described above and with respect toFIG. 1.

One skilled in the art will recognize that many more than two scatter radiation signals are generated by the interrogation of region212-i-jwith pencil beam208; however, for the purposes of clarity in this discussion, only two scatter radiation signals (i.e., scatter radiation216-1and216-2) are described.

At operation304, scatter radiation216-1and216-2are encoded with sampling structure defined by the spatial features of coded aperture218to define modulated radiation220-1and220-2, respectively (referred to, collectively, as modulated radiation220).

FIG. 4depicts a schematic drawing of a region of a coded aperture in accordance with the illustrative embodiment of the present invention. Coded aperture218comprises frame402, apertures404, and blocker406. In contrast with previous art, coded aperture218includes a code (i.e., an arrangement of apertures404) that is periodic. As a result, aperture218enables separable estimation of object density and scatter angle versus range (which is encoded as magnification).

Frame402is a lead sheet whose thickness is suitable for blocking transmission of scatter radiation and sufficient mechanical strength to avoid warping or sagging under its own weight when oriented in the x-y plane.

Apertures404are openings having a width and height suitable for encoding a spatial code onto scatter radiation216-1and216-2. Apertures404are arranged in an arrangement that is periodic in each of the x- and y-dimensions. Apertures404are formed in frame202using any conventional means, such as milling, drilling, grinding, etching, and the like. In some embodiments, coded aperture218is formed via a conventional molding process, such as injection molding, casting, and the like. In some embodiments, apertures404are periodic in only one of the x- and y-dimensions. In some embodiments, apertures404are not periodic.

The dimensions of frame402and the width, height, number, and spacing of apertures404are matters of design preference and depend upon the application for which system200is intended. For exemplary purposes only, frame402is approximately 25 mm×25 mm and has a thickness of approximately 6 mm and includes a 45×3 array of apertures404. Each of apertures404has a width of approximately 0.45 cm and a height of approximately 7.5 mm.

For an isotropic material, scatter radiation216has circular symmetry about axis112. As a result, the same scatter radiation is available at detector222multiple times. In some embodiments, therefore, coded aperture218includes an aperture pattern that is not circularly symmetric about its center (e.g., a spiral-shaped aperture), which offers an advantage because it enables multiple measurements of the circularly symmetric scatter radiation in a single snapshot.

In some embodiments, coded aperture218includes a mask having a pattern of x-ray absorbing material that covers about 50% of its surface area.

It will be clear to one skilled in the art, after reading this Specification, that the pattern of coded aperture218is a matter of design choice based on the particular class of objects to be scanned.

Blocker406is analogous to blocker120, as described above. Blocker406is a feature located substantially in the center of coded aperture218. When coded aperture218is aligned in system200, blocker406is located so as to block transmitted primary beam214from passing to detector222. The size of blocker406is a matter of design. For exemplary purposes, however, blocker406has a substantially square shape of approximately 0.5 cm per side. In some embodiments, blocker406has a shape other than square.

In some embodiments, coded aperture218includes fine structural features. It is an aspect of the present invention that the resolution of the estimation of the composition (i.e., spatial estimation and momentum transfer) for region212-i-jcan be improved by improving the spatial resolution of the features in the coded aperture.

At operation305, detector222receives modulated image234and provides output signal224. Modulated image234is the collective pattern formed by modulated radiation220-1and220-2(referred to, collectively, as modulated radiation220) as it is incident on detector222.

Detector222is a two dimensional array of amorphous-silicon indirect cesium iodide x-ray detectors230. The lateral extent and position, relative to source202and object110, of detector222is suitable for receiving the complete diffraction pattern of modulated radiation220. For exemplary purposes, detector222is a 40 cm×30 cm element that includes a 2048×1536 array of 0.194 micron-size detectors230. Detector222is located at a distance from source202of approximately 201 cm. In this example, the separation between coded aperture218and detector222is approximately 21 cm. One skilled in the art will recognize, after reading this specification, that amorphous-silicon indirect cesium iodide x-ray detectors represent only one suitable type of detector element suitable for use in detector222. Further, one skilled in the art will recognize that detector222can include any practical number and arrangement of detectors230.

Although system200is a forward-scatter imaging system, it will be clear to one skilled in the art, after reading this Specification, how to specify, make, and use alternative embodiments that image an object based on back-scattered x-ray radiation or side-scattered x-ray radiation.

Further, although the illustrative embodiment comprises a system for forming an image based on modulated scattered x-ray radiation from an object, it will be clear to one skilled in the art, after reading this Specification, how to specify, make, and use alternative embodiments of the present invention that form images based on coded-aperture-modulated radiation other than scattered x-ray radiation, such as modulated fluorescence signals, and the like.

FIG. 5depicts modulated images acquired with an imaging system in accordance with the illustrative embodiment of the present invention. Image500is a modulated image of the modulated radiation obtained from interrogation by pencil beam208of a sample of sodium chloride located at a position approximately 60.2 cm from detector222.

Image502is a modulated image of the modulated radiation obtained from interrogation by pencil beam208of a sample of aluminum located at a position approximately 60.2 cm from detector222.

Image504is a modulated image of the modulated radiation obtained from interrogation by pencil beam208of a sample of sodium chloride located at a position approximately 60.2 cm from detector222and a sample of aluminum located at a position approximately 52.6 cm from detector222.

The insertion of coded aperture218between object110and detector222enables each irradiance pixel of detector222to operate as a radiance pixel. This occurs because coded aperture218makes each irradiance pixel of the detector sensitive to x-rays arriving from only a limited set of ray directions (i.e., imparts angular sensitivity on the pixel).

Irradiance-to-Radiance Conversion Using Pinholes and Coded Apertures

Coded aperture218enables discrimination of scatter radiation emanating from individual object elements114by providing a means of converting irradiance into radiance. The advantages afforded embodiments of the present invention by the inclusion of coded aperture218in an x-ray scatter imaging system can be readily understood by analogy to the operation of a series of measurements made with a pinhole aperture, as provided here.

Source602interrogates object606with pencil beam of x-ray radiation604, which gives rise to scatter radiation612-1,612-2, and612-3from object elements610-1,610-2, and610-3, respectively. Scatter radiation612-1,612-2, and612-3, having strength s1, s2, and s3, respectively, all fall on detection point614-1, which makes discrimination of the radiation from any individual object element difficult, if not impossible.

Pinhole mask618includes pinhole620, which formed in a material suitable for blocking the passage of x-ray radiation.

Pinhole mask618enables independent detection of scatter radiation612-1at detector608by allowing passage of scatter radiation612-1through pinhole616-1but blocking scatter radiation612-2and612-3. As a result, by making a measurement of the irradiance detected at detection point614-1, the strength, s1, of scatter radiation612-1can be directly determined.

By making a second measurement of the irradiance detected at detection point614-1with pinhole mask618positioned so that scatter radiation612-2passes through pinhole616-1to detector608but scatter radiation612-1and612-3is blocked, the strength, s2, of scatter radiation612-2is directly measured.

Finally, by positioning pinhole mask618to block scatter radiation612-1and612-2and pinhole616-1but allow scatter radiation612-3to reach detector608, a third measurement of the irradiance detected at detection point614-1provides a direct measurement of the strength, s3, of scatter radiation612-3.

As a result, by making three separate measurements of the irradiance detected by detector608, while knowing the position of pinhole mask618for each measurement and the position of detection point614-1on detector608, the along-beam position and x-ray scatter characteristics of all object elements interrogated with pencil beam604can be determined.

Of course, the example depicted inFIGS. 6A and 6Bshows measurement of only three object points for illustration. In reality, nearly every point along the path of pencil beam604generates other scattered rays at a plurality of angles. All these other scattered x-rays must be detected in order to be able to probe the structure and composition of object606along the entire path of pencil beam604.

FIG. 6Cdepicts a schematic diagram of x-ray imaging system616in operation as a pinhole imaging system.

Detector608detects scatter radiation generated at various points along the path of pencil beam604. This scatter radiation is scattered at angles such that all of their paths go through pinhole620-1and are detected at mutually distinct detection points (i.e., detection points614-2,614-3, and614-4). As a result, the strengths of the x-ray radiation scattered from all object elements that passes through pinhole620-1can be accurately measured by detector608(subject to the resolution of the detector) without mutual interference and without interference from other scattered x-rays that do not go through pinhole620-1.

A complete characterization of all the strengths of all scattered x rays can be obtained through a series of measurements with a series of pinhole masks wherein each mask has a pinhole at a different position. The size of pinhole620-1determines the resolution with which material is probed along the path of pencil beam604and also determines how many positions are required for pinhole620-1are needed for a complete characterization.

Each individual measurement made with pinhole620-1at a particular location yields values of x-ray strengths at those detection points where the path of the scatter radiation is imaged. These values represent the strengths of scatter radiation arriving at detector608at specific angles of incidence selected by the position of the pinhole. A complete series of measurements yields, for each point on detector608, multiple x-ray strength values, one for each possible angle of incidence on the photographic plate. It should be noted that system600, as depicted inFIG. 6A, provides measurements of x-ray irradiance at detector608. In contrast, the inclusion of pinhole mask618converts irradiance measurement into radiance measurement by imparting angular sensitivity into their measurements. As a result, systems616and622provide a measurement of the x-ray radiance at detector608.

One skilled in the art will recognize that each individual measurement requires that object606must be exposed to the x-rays for a time, T, sufficient to achieve an estimate of x-ray strength with a desired accuracy. For N measurements of object606, therefore, the total time required for such a series is equal to N*T. For a measurement of only the strengths of scatter radiation612-1,612-2, and612-3, for example, it is necessary to perform three individual measurements so the total exposure time of object606to x-ray radiation is 3T. It should be noted that measurement accuracy is a function of the total amount of radiation detected during a measurement. As a result, a longer exposure typically yields a more accurate measurement. As the number of measurements required increases, however, the length of time needed for an accurate measurement series can become prohibitive.

FIG. 6Ddepicts a schematic diagram of x-ray imaging system600with an included coded aperture mask. System622comprises system600and aperture plates624-i(where i=1, 2, or 3). System622employs a simplified coded aperture mask that enables a reduction (as compared to that needed for system616) in the total time necessary to determine the scattering characteristics of all object elements interrogated with pencil beam604, with no loss of accuracy.

Each of aperture plates624-iis analogous to pinhole mask618; however, each of aperture plates624-iincludes two pinholes rather than one—pinholes620-2and620-3.

For a first measurement, aperture plate624-1is used. Aperture plate624-1includes pinholes616-2and616-3located in the same positions as pinhole616-1during the first two measurements using system616, as described above. In other words, pinholes616-2and616-3enable both of scatter radiation612-1and612-2to pass through aperture plate624and fall on detection point614, while scatter radiation612-3is blocked. As a result, the irradiance detected at detection point614, d3, is equal to s1+s2.

In similar fashion, for a second measurement, aperture plate624-2is used. Aperture plate624-2includes pinholes616-2and616-3located in the same positions as pinhole616-1during the first and third measurements using system616, as described above. In other words, pinholes616-2and616-3enable both of scatter radiation612-1and612-3to pass through aperture plate624and fall on detection point614, while scatter radiation612-2is blocked. As a result, the irradiance detected at detection point614, d2, is equal to s1+s3.

Finally, for a third measurement, aperture plate624-3is used. Aperture plate624-3includes pinholes616-2and616-3located in the same positions as pinhole616-1during the second and third measurements using system616, as described above. In other words, pinholes616-2and616-3enable both of scatter radiation612-2and612-3to pass through aperture plate624and fall on detection point614, while scatter radiation612-1is blocked. As a result, the irradiance detected at detection point614, d1, is equal to s2+s3.

The results of these three measurements can be used to compute the values of s1, s2, and s3. In particular, through some algebraic manipulations it is found that:

The three measurements can be regarded as equivalent to the direct measurements of object606using pinhole camera system616in that they also yield measurements of s1, s2, and s3, albeit through mathematical manipulations of the measurement results.

As mentioned above, measurement accuracy is dependent on the total amount of radiation detected during a measurement. As a result, accuracy can also be improved by increasing the strength of the detected radiation. Since the use of aperture plates624-iresults in the combined strength of each of d1, d2, and d3 being twice that of each direct measurement of s1, s2, and s3 made using system600, it is possible to reduce the exposure time for each measurement and still achieve comparable measurement accuracy.

One skilled in the art will recognize, however, that it is possible to drastically reduce measurement time still further by use of decompressive estimation. Each of the measurements s1, s2 and s3 is associated with a unique code position. As discussed above, compressive measurement techniques were disclosed in U.S. Pat. No. 7,616,306 and U.S. Pat. No. 8,149,400, among others. Using such techniques, it is possible to separate images taken simultaneously through a coded aperture by a combination of image priors and local code texture analysis. As a result, and in contrast to a scanned pinhole camera, acceptable image fidelity for irradiance and tomographic imaging can be achieved in as few as one time step. It is also possible to use adaptive-control coded-aperture translation and exposure to significantly reduce image acquisition time and, thus, the duration of exposure of an object to x-ray radiation.

The use of a coded aperture affords embodiments of the present advantage additional advantage with respect to measurement noise. A common type of measurement noise is additive Gaussian noise. If the same exposure time, T, is used for the measurements using pinhole mask618and aperture plates624-i, both sets of measurements are characterized by the same amount of additive Gaussian noise. Those skilled in the art will recognize, however, that the estimates of s1, s2, and s3 obtained from d1, d2, and d3 through equation (1) have a noise variance that is less than the noise variance associated with the direct measurements of 51, s2, and s3 as performed using pinhole mask618. This is because in the measurements using aperture plates624-i, the total amount of signal detected at detector608is twice as much as the total amount of signal that is detected in the direct measurements using pinhole mask618. Each of scatter radiations612-1,612-2, and612-3is measured twice using aperture plates624-i, but only once using pinhole mask618, which compensates for the fact that the scatter radiations are not measured individually.

In addition, nonlinear signal estimation strategies, such as are described by A. Mrozack, et al., in “Coded aperture spectroscopy with denoising through sparsity,”Optics Express, Vol. 20, 2297-2309 (2012), which is incorporated herein by reference, enable improved signal to noise performance from multiplex-coded data even when Poisson noise is dominant. Further, the use of decompressive inference and adaptive, image-based, measurement enables real-time allocation of measurement-integration time to significantly improve the fidelity of a reconstructed image.

Returning now toFIGS. 2-3, at operation306, processor226employs a longitudinal forward model to reconstruct the composition of object110in region212-i-jto classify and locate any objects along axis112. Processor226reconstructs the composition of region212-i-jby estimating its coherent scatter properties based on output signal224, which is based on modulated image234(e.g., as manifested in plots500,502, and/or504), the shape and intensity of pencil beam208, and the aperture pattern of coded aperture218. In some embodiments, spectral filters are included in system200, thereby enabling processor226to further characterize object110based on its spectral characteristics.

The irradiance detected at detector222yields the vector gm=I(rm), where rmis the center of the mthpixel of the detector, and I(r) is the measured irradiance at the mthpixel.

Employing a planar transmission function to model coded aperture218, assuming that pencil beam208can be modeled as a single ray along axis112, a computational longitudinal forward model of object110can be built by expanding the scattering density F(z,k,θ) over a discrete set of voxel basis functions Φ(z,q) (taken to be rectangular in z and q), as:
F(z)=∫ΣfnΦn(z,q)dq(2)
a transformation of the integration variables to (z,q) yields a discrete forward model of the matrix equation g=Hf, where the object vector f has components fnand the matrix H is a “forward matrix” having components:

Hmn=∫ⅆz′z⁢(cos⁢⁢θ2⁢⁢sin⁢θ2)2⁢t2⁡(rm⁡[1-z1z′])⁢∫q⁢ⅆqS(q2⁢⁢sin⁢θ2)⁢Φn⁡(z′,q)(3)
and where the scattering angle θ is represented by:
θ=cos−1(z′/√{square root over (r2m+z′2)})  (4)

An approximate inverse of the matrix H can be computed using numerical methods for the measurements depicted inFIG. 5.

Given a vector, f, of object coefficients as defined by equation (2) above, the irradiance measured by each pixel is given in discrete form by Hf, provided above as g=Hf. Since images500,502, and504also contain background contributions with mean μb, the actual measurements, y, are approximated by the Poisson process as
y˜Poisson(Hf+μb)  (5)
where Poisson(v) is a vector of independent Poisson observations with mean intensities given by the components of v. Given y, H, and a noisy realization of the background b˜Poisson(μb), it is an aspect of the present invention that an accurate estimation of f can be obtained by estimating μbfrom b using a Poisson image denoising algorithm and using the resulting estimate, μ′b, of μbto reconstruct f. The estimate of μ′bis obtained using a maximum penalized likelihood estimation method, which provides:
μ′b≡argmingεΓ(−logP(b|g)+τpen(g)),  (6)
where the Poisson likelihood P(b|g) is given by:

In an algorithm in accordance with the present invention, a multiscale, partition-based estimate is chosen that is the best fit to the data and also is piecewise smooth. The penalization term is proportional to the number of cells in the partition and is enforces the assumption that μbis piecewise smooth.

Using μ′b, an estimate of f is made according to a generalize maximum likelihood (GML) estimator given by:
{circumflex over (f)}≡argmin{tilde over (f)}(−logP(y|H,{circumflex over (μ)}b,{tilde over (f)})),  (8)
where the GML estimate of f is obtained using a Richardson-Lucy iterative deconvolution method, as described by W. H. Richardson in “Bayesion-based iterative method of image restoration,” in theJournal of the Optical Society of America, Vol. 62, pp. 55-59 (1972), which is incorporated herein by reference.

In addition to the modulation induced by coded aperture218, the diffraction patterns shown inFIG. 5comprise concentric rings, which can be represented over bins in the polar coordinates (ρ, φ). For the purposes of this Specification, including the appended claims, the term “polar downsampling” is defined as representing a diffraction pattern over bins in polar coordinates. It is yet another aspect of the present invention that this polar downsampling can significantly decrease the computational complexity of an algorithm used to reconstruct region212-i-j. This affords embodiments of the present invention advantages over the prior art. Some of the advantages gained by polar downsampling can be evaluated by calculating the number ofandbins needed for an effective reconstruction of the region. As discussed above, and with respect toFIG. 2, detector222is approximately 40 cm×30 cm. The radius values of the concentric rings shown inFIG. 5are within the range of 0-25 cm. The intersection of pencil beam208with the detector plane (i.e., at z=0) defines233radius bins between ρ=2.5 cm and ρ=11.5 cm. The polar angle was similarly segmented over its entire range into 120 bins. As a result, embodiments of the present invention enable a reduction in the required sampling from 2048×1536 to 233×120, significantly simplifying the computation of H.

FIGS. 7A-Ddepict reconstruction results for a sample interrogated by an x-ray pencil beam in accordance with the illustrative embodiment of the present invention. The results depicted in these figures are based on a forward matrix H for the pencil beam system that was calculated by sampling region212-i-jusing rectangular voxels with widths of ⅓ cm in z and 0.3 rad/nm in q. From plots500,502, and504, the coefficient vector f representing the scattering density F(z,q) of the region was estimated using the methods described above.

FIG. 7Adepicts a spatial scattering profile for a first test sample interrogated by a pencil beam of x-ray radiation. Plot700shows the spatial scattering profile, F(z), for a sodium chloride sample as a function of distance, z, from detector218, with the sample placed at a distance of 60.2 cm from the detector (i.e., z=60.2 cm).

FIG. 7Bdepicts a spatial scattering profile for a second test sample interrogated by the pencil beam of x-ray radiation. Plot702shows the spatial scattering profile for an aluminum sample as a function of distance, z, from detector218, with the sample placed at z=60.2 cm.

In each case, the beam penetrated only 1 cm of each sample; however, the spatial extent of the reconstructed objects has a FWHM of about 3 cm. The reconstructions depicted in each of plots702and704are approximately centered at the true object positions, demonstrating the along-beam ranging capability of system200.

FIG. 7Cdepicts a momentum transfer profile for the first test sample. Plot704shows the momentum transfer profile, F(q), for the sodium chloride sample as a function of distance, z, from detector218.

FIG. 7Ddepicts a momentum transfer profile for the second test sample. Plot706shows the momentum transfer profile, F(q), for the aluminum sample as a function of distance, z, from detector218.

The scattering density F(z,q) determined from plots700and702was integrated over a 3 cm region around the expected object position to yield a momentum transfer profile F(q)=F(z,q)dz. Aside from an overall scaling, the exact width of this window was determined to have a minimal effect on the integrated profile. The reconstructed profiles (solid) are shown along with the reference data (dashed) inFIGS. 7C and 7D, respectively, and all plots are normalized to have a maximum value of unity. The two dominant peaks for each material are reconstructed with the correct locations and approximate relative intensities, however reconstruction of the smaller peaks is frustrated by noise in the acquired diffraction patterns. The FWHM of the dominant reconstructed peaks is approximately 1.6 rad/nm.

FIG. 8Adepicts a spatial scattering profile for both the first and second test sample simultaneously interrogated by a pencil beam of x-ray radiation. Plot800shows the spatial scattering profile, F(z), for a sodium chloride sample and aluminum sample as a function of distance, z, from detector218, with the sodium chloride sample placed at a distance of 59.3 cm from the detector and the aluminum sample placed at a distance of 52 cm from the detector.

FIG. 8Bdepicts a momentum transfer profile for the first of two test samples simultaneously interrogated by a pencil beam of x-ray radiation. Plot802shows the momentum transfer profile, F(q), for the sodium chloride sample as a function of distance, z, from detector218.

FIG. 8Cdepicts a momentum transfer profile for the second of two test samples simultaneously interrogated by a pencil beam of x-ray radiation. Plot804shows the momentum transfer profile, F(q), for the aluminum sample as a function of distance, z, from detector218.

From the results shown inFIGS. 7A-Dand8A-C, it can be seen that system200has significant utility for estimating the elastic scattering structure of target samples. Further, by enabling differentiation of x-rays arriving on detector elements230from multiple directions, the present invention enables improved photon efficiency over scatter imaging systems of the prior art.

At operation307, stage232moves object110to index the location of pencil beam on object110. Once pencil beam has been indexed to the next image point210-i-j, operations303through306are repeated to characterize new region212-i-j.

Stage232is a conventional three-axis stage suitable for moving object110through all of regions212.

At operation308, volumetric estimate228is generated based on the collection of characterizations of regions212-i-j.