Abstract:
As described in the methods of the present invention, x-ray photons derived from a microscopic solid-density plasma that is produced by optically focusing a high power laser beam upon a high atomic number target, may be use for phase-contast medical microimaging and also for absorptive microradiography. As described in the methods of the present invention, x-rays derived from a microscopic solid-density plasma are utilized as object illumination sources that are microscopic in at least one direction (so that ultrathin slicebeams and fan-beams are allowed, as are linear arrays of numerous clusterd parallel microbeams). Collimating optical devices of prior art are required.

Description:
FIELD OF THE INVENTION  
         [0001]    This invention relates to systems and methods for using penetrating radiation deflected within an object, to image the internal structure of the object, in particular, of soft-tissue, utilizing an ultrafast laser-produced x-ray source for phase-contrast medical micro-imaging.  
         BACKGROUND OF THE INVENTION  
       A. X-Ray Phase-Contrast Imaging Methods of Prior Art  
         [0002]    X-rays are widely used to study the internal structure of various objects. X-ray imaging is a subject of great international interest because of its capacity for high penetrability into animal soft-tissues, which is related to the short wavelength of x-rays.  
           [0003]    Conventional radiography is based on the detection of differences in x-ray absorption of various details within the object. Typically, absorption patterns differ significantly between a relatively high atomic number (i.e., high-Z) element such as the calcium in bones and the lighter, low atomic number (i.e., low-Z) elements, such as carbon, oxygen, hydrogen and nitrogen, which are the dominant elements in soft-tissues. Another imaging method based on the selective x-ray absorption patterns relative to soft tissue is angiography, which utilizes the high-Z contrast material, iodine, to visualize arterial blood flow patterns in the heart.  
           [0004]    Low-Z elements do not appreciably absorb high energy medical x-rays (which are between 10 KeV and 100 KeV), but rather are mostly transparent to these photons. The difference between absorption of x-rays by soft tissue and bones is the source of contrast in conventional radiography or computed tomography. Unfortunately, at high energies utilized to image deep body tumors, the image contrast of soft-tissues due to absorption decreases markedly.  
           [0005]    Absorptive radiography reveals spatially oriented decreases in detector intensities typically caused by the absorption of x-rays by calcium in bones. However, a complete “energy-wave” profile is characterized mathematically not only by intensity values, but also by wavelength and by phase information, with all three values corresponding (respectively) to the magnitude, frequency and direction of a wave as it propagates (sinusoidally) in a particular direction.  
           [0006]    Phase-contrast imaging is any technique that renders variations in the phase-structure of the object visible. A phase-shift of x-ray photons is induced by slight deviations from their incident path as they traverse through an object, such as animal soft-tissues, which occurs after the photons interact briefly with the atoms in their path. A phase-shift is a type of deflection of the incident beam within a material, which is referred to as “small-angle scattering”. The phase-shift, when adequately large, shifts the intensity of the deflected ray to a different place on the detector, such as an adjacent pixel (in the x- or y-direction). Notably, spatial three-dimensional distortions may be impressed upon the incident wavefront by chemical-biological tissue interfaces within the illuminated object.  
           [0007]    Compared to conventional x-ray absorption imaging techniques, phase-contrast imaging is better suited for delineating soft-tissue structures which do not appreciably absorb x-rays (but which may contain many non-absorptive structural details in the range of between one micron and one millimeter in diameter). Phase-contrast imaging methods are particularly capable of deliniating the microscopic details of the internal structures of non-crystalline objects. Internal structures may produce a measurable deviation in the direction and velocity of the incident photons (because of local variations in the refractive index, plus variations in density and thickness of those structures). For example, x-ray phase-contrast imaging is ideally suited for the detection of (non-absorbing) cancerous tissues when they are still microscopic and are possibly at an earlier stage of carcinogenic development than a larger mass and when they are (presumably), also more treatable.  
           [0008]    To understand phase-contrast imaging, glass, which has a different refractive index than air is considered. Specifically, glass lenses of different shapes and thicknesses cause a beam of light to be deflected to a greater or lesser degree (away from the optical axis). Similar to a glass lens, phase disturbances occur at interfaces between soft-tissue planes that have slightly different refractive indices and thicknesses. Within soft-tissues, incident photons—by undergoing a “lens-like” effect—are refracted by spatially oriented molecular and atomic planes, thereby experiencing a significant shift in phase, corresponding to the change in direction. A phase-shift can also be referred to as a phase-delay, because the deviation in direction of an incident beam in a tissue is due to the temporary slowing of the beam velocity (during its brief interaction with the atoms of a structure of greater refractive index, density or thickness).  
           [0009]    The phase disturbance (within an object) which causes the deflection of the incident beam can be treated as a phase vector oriented perpendicular to the optical axis. The relatively short phase vector and the much longer optical axis vector form the sides of an elongated right triangle. Due to the phase disturbance impressed upon an incident beam, the deflected (phase-shifted) rays can be represented as deviating by a small angle from the incident beams optical axis, thus providing the hypotenuse of this vector triangle.  
           [0010]    The phase-shifts experienced by an incident beam can be observed with highest resolution only when employing a highly coherent beam of incident light (to illuminate the object under investigation). Consider a distant star in the perfect vacuum of free space. In that case, the small section of the total spherical wavefront (of light) coming from the star to a small detector on the earth eventually approximates an unperturbed plane-wave, propagating in a manner perpendicular to the optical axis from the star to the earth. For this reason, light coming into our eyes from a distant star is a more highly collimated (i.e., coherent) beam of light than is the light from a nearby candle or campfire (which radiates out from the surface in a full hemisphere). Thus, coherent light (when continuous) can be represented as a train of parallel, unperturbed planar wavefronts, propagating along—and perpendicular to—the optical axis, which may strike an object or detector. A highly coherent beam of light may be produced by synchrotron undulators with x-rays and by lasers (at or near visible frequencies).  
           [0011]    After the incident homogenous (planar) wavefront interacts with the constituent atoms of the specimen, a wrinkle (i.e., a warping) is produced in the formerly perfect plane-wave. The incident plane-waves are converted in the object into a three-dimensionally distorted wavefront, which possesses a phase-shifted profile, thereby producing areas of non-homogenous intensity upon the (two-dimensional) detector. Importantly, refractory disturbances are maximal at interfaces of different refractory surfaces within the object that are oriented parallel to the beam direction (which is the optical axis). Only in a direction parallel to the incident beam, do the edges of “refractory-objects” (which induce the phase-shift) possess maximum physical thickness relative to the beam direction. Thus, to acquire the highest quality phase-contrast image, only tissue interfaces that are oriented parallel to the incident beam can measurably deviate—in a detectable, lens-like fashion—a highly coherent incident plane-wave.  
           [0012]    An incoherent x-ray source used in conventional radiographic imaging is called an x-ray focal-spot and is produced by the collision of an electron beam upon a metal target, such as tungsten. X-rays typically go through an exit aperture soon after the source, but before the object, in order to minimize the resultant beam divergence. Compared to an x-ray beam eminating from a conventional clinical x-ray source, which has a relatively large focal-spot area, a more highly collimated beam of x-rays can be produced from an extremely small size “point-like” source. Only with a microscopic size x-ray focal-spot can the incident beam be spatially quasicoherent (i.e., more-or-less parallel) and be represented as a planar wavefront, propagating perpendicular to the optical axis. To date, x-ray phase-contrast imaging of full size mammographic specimens has only been performed using highly coherent synchrotron x-rays (Arafelli et al).  
           [0013]    High energy photons correspond to shorter wavelength light, such as used in medical x-ray examination. The importance of using high energy x-rays (between 10 KeV and 100 KeV) in medical imaging is generally because the thickness of human anatomy causes an unacceptable amount of attenuation—by absorption—of low energy x-rays and no measurable transmission of the original incident beam. Low energy x-rays (&lt;10 KeV), however, can only be used effectively to measure phase variations in very thin specimens and are of no use for the imaging of gross anatomy.  
           [0014]    Not without significance for the radiographic imaging of microscopic object details, is the fact that x-ray absorption falls off steeply as the wavelength decreases (for objects of diminishing size). This falling-off of absorption-contrast with shorter wavelengths places severe limits upon the minimum size of an object capable of being visualized in clinical radiography. As opposed to absorption-contrast, the phase-contrast produced by using short wavelength medical x-rays—from objects of diminishing size—only falls off gradually.  
           [0015]    In fact, experimentally, the smallest size of an object causing a visible phase-shift, is directly proportional to the shortness of the wavelength of the incident x-rays (provided that the x-rays are coherent). For, example, it has been noted that for 10 Angstrom (1.24 KeV) x-rays, a microscopic carbon fiber of approximately 3 microns produces a full 2p phase-shift and 50% absorption, which are both adequate values for their respective imaging methods. However, if the wavelength is decreased to 1 Angstrom (12.4 KeV), a much larger 3 millimeters carbon fiber is required to produce 50% absorption, while only 30 microns are required to produce a full 2p phase-shift. Thus, only by using both highly coherent short-wavelength x-rays and phase-contrast imaging techniques, can truly microscopic size non-absorbing object details be detected.  
           [0016]    Another source of scattering by soft tissues is incoherent Compton scattering by the constituent atoms of the human body and is different than refraction, where the phase-shift is discrete and predictable.  
           [0017]    Incoherent Compton scattered x-rays are the primary source of radiation exposure by medical personnel and are somewhat chaotically spread out in the plane of the detector, revealing no significant structural information. Narrow field line-scanning and anti-scatter grids (after the object) are methods that can help remove Compton scattered x-rays from contaminating the image with non-informative noise.  
           [0018]    In general, there are three basically different types of x-ray phase-contrast imaging techniques, involving either: 1) holographic interferometry, 2) an analyzer crystal placed after the object, or 3) direct in-line geometry without a crystal analyzer, employing a mathematical processing of intensity information (impinging upon the digital-detector).  
           [0019]    With holography interferometry, a beam splitter is used to produce two beams of x-rays, with each having a different initial direction and phase. One of the beams does not go through the object and is therefore, a non-scattered plane-wave, which is used as a “reference” wave. With interferometry, the reference wave—which is made to avoid the object—is redirected to the plane of the detector in order to destructively interfere with the phase-shifted “object” wave (which is produced by refractory disturbances within the object). The profile remaining after the superimposition of the two wavefronts (at the detector) reveals structurally important refractive information about the object (with no mathematical processing or digital detectors required absolutely).  
           [0020]    The other x-ray phase-contrast imaging technique (which may employ, but does not require digitization) uses an analyzer crystal after the object. In that case, the reflective Bragg analyzer crystal placed before the object is geometrically aligned within the incident beam, to be more-or-less parallel to the incident beam. Because of this specific geometry, the analyzer crystal possesses a rocking curve which is sensitive to microradian alterations in the direction of the incident beam, which is induced by changes in the refractive index within soft-tissues. Alternatively, a transmissive Laue-type analyzer crystal may be aligned more-or-less perpendicular to the incident beam and may also register refractive changes. In general, the analyzer crystal is used simultaneously as a Compton scatter reduction optic.  
           [0021]    On the other hand, absorption radiography attempts to only utilize the direct beam, which (when not absorbed) is transmitted without deviation through the object and which is called the “zeroth order” spectrum. In this absorption case, the detection of any deviated rays degrade the image quality with an overall bluriness, which translates to reduced contrast. Phase information, however, is present only in the higher spectral orders of the redirected, refraction-modulated, three-dimensional wavefront.  
           [0022]    One variation of analyzer-based x-ray phase-contrast imaging techniques, which is known as diffraction enhanced imaging (i.e., DEI), uses the analyzer crystal as an optical device to delineate the exit beam into two separate refraction and absorption images. In the methods of DEI, by rocking the analyzer crystal into different alignments, these two images are obtained by sequentially filtering out the zeroth spectral order and the higher spectral orders, respectively. The resultant phase-image and an enhanced absorption-image can either be viewed separately or viewed as a single image (after superimposition on a pixel-by-pixel basis). DEI requires a digital detector and computational capabilities.  
           [0023]    The third category of phase-contrast x-ray imaging requires a mathematical algorithm to simulate an phase-image of the object. Image reconstruction is accomplished by virtue of digitally analyzing the phase-shifted wavefront impinging upon the detector. In this quantitative case, the phase image is mathematically separated from the combined (refraction and absorption) signals impinging upon the detector. The method of quantitative phase-contrast x-ray imaging employs an “in-line” optical geometry, with the object placed between a source and the detector and it requires a highly coherent beam of x-rays (such as from a synchrotron).  
           [0024]    As utilized in any phase-contrast imaging method, the deviated rays reaching the detector from the object will have a maximum intensity value located at a different pixel, compared to that “same” ray if it were (hypothetically) otherwise not deviated by the object. Specifically, quantitative phase-contrast x-ray images may be reconstructed indirectly—by performing calculations of the Fresnel-Kirchhoff integral on a pixel-by-pixel basis—using as variables, measurements of non-homogenous detector intensities.  
           [0025]    In all methods of phase-contrast (refractive) imaging, the intensity distribution is greatest near the edges of objects. Thus, the quantitative phase-contrast image of an object may be represented graphically as a uniquely characteristic and dynamically oscillating plot of variable energy distribution. In this manner, lens-like “phase objects” can be visualized (on a Cartesian graph), using orthogonal “object radius-versus-intensity” coordinates, so that each plot for every object may vary distinctly with the shape and size of the object.  
           [0026]    In the quantitative phase-contrast x-ray imaging research of Snigirev et al, variously shaped 10 microns beryllium fibers exhibited distinct features, in addition to the two highly important and dominant maxima, which corresponds to the opposite edges of the fiber. These researchers observed unique shape-dependent graphical object profiles, centrally displaying a moderate-sized split-peak of intensity for a round fiber, a very small maximum central peak for a trapezium fiber and a high maximum central peak for a square fiber. The intensity profiles for the different shaped fibers also vary markedly in the region immediately outside of the dominant maxima. Most significantly, the distance between the dominant maxima are a measure of the object radius.  
           [0027]    Size- and shape-dependent in-line “intensity holograms” have been observed for very small sized glass, boron and lead-filled glass capillaries, for plastic fibers and for various organic materials. Similarly, thick cancerous human tissues have been observed as internally distinct in phase structure from normal tissues. Cancerous tissues appear to have a chaotically disordered microscopic phase-structure, compared to non-cancerous adjacent soft-tissues. Furthermore, by utilizing phase-contrast imaging methods, the deflection of x-rays caused by (surface diffraction from) tumor-associated microscopic crystalline calcium deposits have also been visualized (in thick cancerous specimens).  
           [0028]    At relatively short object-to-detector distances, quantitative phase-contrast image profiles look totally unique for objects of different shapes. In contrast to the characteristic near-field images mentioned above, at increasingly large object-to-detector distances, the profiles look very much alike.  
         B. Description of a Mathematical Formalism for Quantitative Phase-Contrast Imaging Methods  
         [0029]    The following is a description of a mathematical formalism for quantitative phase-contrast imaging methods which employ a monochromatic and coherent x-ray source, such as from synchrotron radiation. The specific locations within an object causing alterations in the “phase-orientation” of a plane-wave (of penetrating radiation) can be derived mathematically from meaurements of non-homogenous intensity values incident upon the detector.  
           [0030]    The intensity of x-rays incident upon each pixel detector is stated as “the average energy per unit area per unit time” or equivalently as energy density per unit time, measured in watts per meter-squared. The intensity (I) registered upon the detector is proportional (μ) to the magnitude squared of the optical field energy, E(x1, y1), such that Iμ÷E(x1,y1)÷2.  
           [0031]    An equation for the incident optical field energy propagating in the z-direction is: 
             E (x1, y1)=exp[ ikz]*f ( x,y ),  (eq. 1) 
           [0032]    where exp[ikz] is the rapid oscillatory function of the energy field and f(x,y) is the more slowly modulating envelope function, which surrounds the maxima of the oscillatory function. (The asterix, “*”, represents the multiplication sign.) Furthermore, the time-dependent energy field is represented in three-dimensions (over time) by the value of E(x,y,z,t), so that: 
             E ( x,y,z,t )=exp[ ikz]*f ( x,y,z )*exp[− iwt],   (eq. 2) 
           [0033]    (where exp[−iwt] represents the rapidly oscillating time-dependent factor of the propagating wavefront and where w is the angular frequency of the time function).  
           [0034]    Consider the case when using a highly coherent incident plane wave to illuminate an object (i.e., utilizing a beam of negligible divergence from the z-axis), where the paraxial condition is valid. Analogously, consider the case of a spherical incident wavefront, notably with either a very large source-to-object distance or a very large source-to-detector distance. Both coherent situations can be represented mathematically by radiation from a theoretical point source. After pinhole collimation, a coherent beam eminating from such a theoretical point source could be represented as an infintesmally small focal-spot placed at the origin of the optical axis. The origin is at the central zero point (x0,y0) in the source plane where both x0 and y0 are equal to zero. (The source plane is situated perpendicular to the optical axis).  
           [0035]    According to Maxwell&#39;s equation, in free space this coherent radiation is a nearly planar section of a spherical wave and it can be written in the form: 
           E0(x1,y1)=(1 r ) exp{(2 pi/ l)[ r+ ((x1−x0)2/2 r )+((y1−y0)2/2 r )]  (eq. 3) 
           [0036]    where x1, y1 are the coordinates of the image point in the 2-D detector plane, r is the distance between the source and detector planes and l is an x-ray wavelength. Describing a coherent beam of radiation, the small angle approximation is valid when r2&gt;&gt;(x1−x0)2+(y1−y0)2.  
           [0037]    Upon interacting with an object, the plane harmonic wave function (of amplitude, A) will become phase-shifted, and can then be represented as: 
             E ( x,y,z,t )=A exp[ i ( kx+ky+kz+wt+j ),  (eq. 4) 
           [0038]    where k denotes a 3-dimensional x,y,z wave-vector and j denotes the change in phase (i.e., the phase-shift) of the wavefront after its interaction with the object. For example, a phase-shift of a plane-wave—corresponding to the lens-like change in direction of the ray—may be caused by objects, such as a linear fiber (of low optical absorbency) oriented along the y-axis. In that case, when the phase-shift of a wavefront takes place in an x-direction, it is described as j(x). At the same time, the amplitude (A) of the energy field after the non-(x-ray)absorbing object may well remain nearly the same.  
           [0039]    In quantitative phase-contrast imaging methods, the Fresnel-Kirchhoff integral (which is described below in eq. 5), allows for the determination of the general case of a “phase-object”—of thickness, “x”—present within the electric field (which, in turn, is incident upon the detector plane). In this case, the (refractive) object is that which gives rise to the phase disturbance, which is the phase-shift of value, j(x).  
           [0040]    Thus, associated with the phase-shift term due to the object (such as a fiber, oriented in the y-direction), is the term that depends on the thickness of the object, x, so that the value (x,y) represents the dimensions of the coordinates in the object plane (which is parallel to the detector plane). By using measured detector intensities (on a pixel-by-pixel basis), phase-shifts can be used to determine both the size and location of an object in the path of the incident beam.  
           [0041]    By means of a standard Fresnel-Kirchhoff integral, one can express the radiation field incident upon the detector plane in the following form:  
                     E        (     x1   ,   y1     )       =                  1   /         O   ¨          (   iprr0r1   )       _          exp        {       (     2        pi   /   l       )     [     (     r   +                                            (     y1   -   y0     )          2   /   2        r     ]     }     *                              o   ′        dx                 exp        {       (     2        pi   /   l       )     [         (     x   -   x0     )          2   /   2        r0     +                                          (     x   -   x1     )          2   /   2        r1     ]     }     *                              exp              [     ij        (   x   )       ]     ,                   (     eq   .              5     )                               
 
           [0042]    where x1 and y1 are the coordinates of the point on the detector plane and where r0 and r1 are the source-to-object and object-to-detector distances.  
           [0043]    However, for a distinctly non-coherent light source, x0 and y0 (in equation 5) are the coordinates of a much larger size focal-spot in the plane of the source (which define the area of the source). Thus, in equation 5, x0 and y0 do not necessarily represent a theoretical point source (as they do in equation 3 for coherent radiation). Rather, x0 and y0 may also represent the boundary coordinates of a much larger sized focal-spot, which are located at the distances (x0 and y0) from the origin of the source plane.  
           [0044]    In order to calculate the relative intensity distribution upon the image detector, it is convenient to rewrite the equation for the electrical-field (i.e., eq. 5) as follows in the form of eq. 6:  
                 E        (     x1   ,   y1     )       =       E0        (     x1   .   y1     )            [     1   +     c        (   x1   )         ]         ,           (     eq   .              6     )                               
 
           [0045]    where the contrast function, c(x1), directly responsible for the formation of the fiber image takes the form of, c(x1)a, in the following equation (eq 7), so that:  
                     c        (   x1   )       =         c        (   x1   )          a     =                      O   ¨          (   iprr0r1   )       _        exp                   {       (     2        pi   /   l       )     [     (     -     (     x1   -                                                  x0   )          2   /   2        r     ]     }     *                                o   ′        R     -     Rdx                 exp        {       (     2        pi   /   l       )     [         (     x   -   x0     )          2   /   2        r0     +                                            (     x1   -   x     )          2   /   2        r1     ]     }     *                              {       exp        [     ij        (   x   )       ]       -   1     }     ,                   (     eq   .              7     )                               
 
           [0046]    Central to the methods of quantitative phase contrast imaging is the special case for a highly coherent point source, where the object is far from the source (i.e., r0&gt;&gt;r1), so that most particularly, the size of the source (of radius, (x1−x0)) and the distance r0 are not so important mathematically and can be neglected from the standard formula. Only for a coherent x-ray source will the mathematical wave-function in equation 5 accurately characterize (at the detector plane) a two-dimensional energy-field of a phase-shifted (i.e., warped) plane-wave.  
           [0047]    Coherent, planar light waves at x-ray energies can be produced by the effects of numerous synchrotron undulator magnets upon a foreward directed narrow beam of accelerated electrons. As a result, a highly collimated x-ray beam is produced (also in the foreward direction). A synchrotron radiation source size may be quite small, at 100 microns, with a very large source-to-object distance of 50 m and with silicon monochromators to condition the incident beam.  
           [0048]    Notably, for the case of a highly coherent planar incident wavefront—when both r and r0 approach infinity, when r0&gt;&gt;r1 and when both x0 and y0 approach zero—one can use the simplified approximation of the Fresnel-Kirchhoff integral to obtain the phase-shift value, j (x), from the value of c(x1)b, in eq. 8, so that:  
                     c        (   x1   )       =                    c        (   x1   )          b            1   /         O   ¨          (   ipr1   )       _       *                                    o   ′        R     -     Rdx                 exp        {       [       (     2        pi   /   l       )          [       (     x1   -   x     )        2                 2      r1     ]       }     *                                      {       exp        [     ij        (   x   )       ]       -   1     }     ,                   (     eq   .              8     )                               
 
           [0049]    Thus, in the case of a coherent x-ray source, the phase change, j(x), can be obtained by computational methods employing the simplified (i.e., approximated) Fresnel-Kirchhoff integral, where:  
                 E        (     x1   ,   y1     )       =       E0        (     x1   ,   y1     )            [     1   +       c        (   x1   )          b       ]         ,           (     eq   .              9     )                               
 
           [0050]    Because the phase-contrast value, c(x1) is maximum only at interfaces of different refractory surfaces (within the object) that are parallel to the beam direction, the simplified contrast term, c(x1)b, only applies when using a highly parallel, coherent beam of x-rays.  
           [0051]    Consider, for example, a circular fiber in the path of a coherent beam of x-rays having the following maximum value of the phase change, j0 (in which case, j(x)=j0), so that in equation 10: 
           j0=2 pdh/l,   (eq.10) 
           [0052]    where d is the decrement of refraction (that is, the relative change in the refractive index within the object) and h is the maximum thickness of the fiber in the x-direction relative to the incident beam.  
           [0053]    Importantly, one can determine the phase-contrast parameter, C, as a maximum difference between positive and negative deviations of the intensity values, which represents the edges of objects. One can then make the following estimations for contrast (C), where: 
             C=a j 0,  (eq. 11) 
           [0054]    and where a is a numerical coefficient which is close to unity. Thus, contrast is proportional to the maximum value of the phase-shift, j0, which shows significant values only at interfaces parallel to a highly coherent incident beam.  
           [0055]    Another important consideration preventing the most accurate use of the Fresnel-Kirchoff integral in quantitative phase contrast imaging is the polychromatic nature of collisional x-ray sources, containing a mixture of (extremely broadband) bremstrahlung x-rays and an overlay of characteristic (narrow-bandwidth) x-radiation. Results of calculations using the Fresnel-Kirchhoff integral are notably energy- (i.e., wavelength-) dependent, so that a polychromatic x-ray beam will significantly degrade the phase values derived (from the intensity variations incident upon the detector).  
           [0056]    Monochromators are typically used to adjust the wavelength of a synchrotron radiation beam and are sometimes experimentally used for rotating anode x-ray tubes (to select exclusively the more intense and narrow-bandwidth characteristic k-alpha x-rays). As described in prior art—for purposes of wavelength tunability (of a polychromatic x-ray source)—crystal monochromators are placed before the object, located within the path of the incident beam and tilted at specific angles with the beam-line optical axis. These monochromators may be embodied in either Bragg-Bragg, Laue or Laue-Bragg geometries generally using asymmetrically-cut perfect crystals, such as silicon. Asymmetrically-cut crystal monochromators can also produce a significanty more collimated exit beam.  
           [0057]    Thus, in quantitative phase-contrast imaging methods of prior art, when utilizing a synchrotron x-ray beam that is stringently both monochromatic and coherent, it has been possible to use the simplified Fresnel-Kirchhoff integral for the reconstruction of a high resolution, phase-contrast image of microscopic objects.  
         C. A Description of Blur and Image Resolution as Functions of Contrast and Focal-Spot Size  
         [0058]    An image that shows much detail and has distinct boundaries is often described as being sharp. The presence of blur produces a lack of visual sharpness that is particularly noticeable at the borders and edges within an image. In every imaging process, blur places a definite limit on the amount of detail (i.e., object smallness) that can be visualized. Thus, the direct effect of blur is to reduce the contrast of small objects and features.  
           [0059]    In effect, blur spreads the image of small objects into the surrounding background area. As the image of the object spreads outward due to blur, the contrast and, therefore, visibility are reduced. Thus, for example, the blurred image of a finite-sized circular object is generally not a circle of uniform intensity, but rather is a larger circular image with indistinct boundaries. The image of a blurred line-shaped object would appear as a rectangle.  
           [0060]    Resolution describes the ability of an imaging system to distinguish or separate (i.e., resolve) objects that are close together. The resolving capability of the particular imaging process is determined by the amount of blur.  
           [0061]    Also, for objects to be resolved visually, their separation distance must be increased in proportion to the amount of blur present. The amount of blur in radiographs is generally in the range of 0.15 millimeters to 1.0 millimeters. Only when the amount of blur approaches the dimensions of the object, does the blurring process significantly reduce contrast. In some situations, especially in which small objects already have low inherent contrast (such as connective tissue and small tumors), the blur can significantly effect visibility.  
           [0062]    In terms of blur production, the most significant characteristic of a focal-spot is its size. One can envision x-rays passing through each point of the object from each point (of a larger) focal-spot ultimately diverging and forming a blurred image of the object. In other words, photons eminating from each point in a large focal-spot can cross over the optical axis before the object, so that significant amounts of blur must be produced in such cases.  
           [0063]    The large x-ray source size used in a compact clinical radiographic device is generated from the collision of an electron beam with a metal target and is between 150 microns and 2 millimeters in diameter. In that case, even after the pinhole collimation port (or slit system), the beam still tends to be significantly divergent.  
           [0064]    Theoretically, phase-contrast imaging methods using a large size x-ray source (such as produced by a collisional electron beam) will experience significantly decreased signal-to-noise ratios compared to images taken with highly coherent synchrotron radiation. This degradation of the phase-image, due to large source size, can be visualized mathematically in the source-size variable present in the (numerator of the integated exponent within the) complete Fresnel-Kirchhoff integral (eq. 5). In fact, focal-spot blur due to large source size reduces image resolution in all imaging modalities, however, it is especially deleterious to accurate phase-contrast imaging (because in that case the effect is mathematically non-linear).  
           [0065]    In traditional absorption radiography, the resolving ability of an imaging system is relatively easy to measure and is often used to evaluate system blur, since resolution is inversely proportional to blur. A test object consists of parallel (high-Z metallic) lead strips separated by a distance equal to the width of the strips. Furthermore, the width of the strips (and the separation between them) regularly decrease in size to a small enough value were a particularly small strip can no longer be distinguished from the spaces on either side of it, nor can it be distinguished from the adjacent strip. One line-pair is defined as consisting of one lead strip and the space adjacent to it. The number of line pairs per millimeter visually measurable in such a test object is actually a measure of the spatial frequency of the imaging system. When no blur is present, all the line pair groups of a test object can be resolved visually. As blur is increased, however, resolution is decreased, and only the larger lines (and the comparably larger separation distances between them) are visible.  
           [0066]    Analogously, the contrast between the smaller visual details in a medical image is also reduced by elevated levels of blur. In order to form an unblurred image of the object, the x-ray imaging system must be able to produce sufficient visual contrast for all of the spatial frequencies contained in the object. If some of the frequency components are lost in the imaging process, the image will not be a true representation of the object.  
           [0067]    A graphical curve representing a plot of “relative contrast versus number of line pairs visualized per millimeter ” is designated a contrast transfer function (CTF), which shows the ability of the imaging system to transfer contrast of objects of different sizes in the presence of blur. The number of line-pairs visualized in the image is also a measure of the spatial frequency observed in the object. The typical CTF curve associated with a focal-spot blur has a specific point at which the contrast becomes zero (just below the size of the smallest object detail visualized). This is commonly referred to as the disappearence frequency and represents the resolution limit, or resolving ability of the system.  
           [0068]    The graphical plot of a modulation transfer function (MTF) is similar to the CTF plot in many respects. One primary difference, however, is that while the CTF describes the system&#39;s ability to image line pairs, the MTF describes the ability to image sine-wave shapes of relative intensities, or spatial frequencies. Rather than represent the limit of visual resolution in terms of lines and spaces, as used in the CTF, the MTF illustrates contrast in terms of peaks and valleys of relative intensities.  
           [0069]    Similar to the CTF curve, the decreasing size of detail visualized in a test object has a point on the negatively sloped MTF curve where the degree of contrast falls to zero. The spatial dissapearence frequency is the point where the minimum size of the detail capable of being visualized reaches a limit and where blur tends to irreparably degrade the quality of the image. Importantly, a very small focal-spot produces an absorption image that has a spatial disappearence frequency (i.e., the maximum number of line-pairs per millimeter capable of being visualized) at a much smaller size of object detail than that of an image produced by a conventional large radiographic focal-spot. absorption radiography this phenomenon can be represented mathematically, where the focal-spot blur value (Bf) in the detector plane with respect to an object of finite size is given by: 
           Bf=Focal-Spot Size*Object-to-Receptor Distance=F* (ORD/FRD), Focal Spot-to-Receptor Distance  (eq. 12) 
           [0070]    where F is the dimension of the focal-spot. If the object is in direct contact with the receptor (ORD/FRD=0), the focal-spot blur will tend to vanish. Importantly, in the case when the object is not in contact with the detector, only a microscopic x-ray focal point will produce an image with markedly decreased blur at the edges of very small object details.  
         D. Microscopic Laser-Produced X-Ray Sources and Laser-Based X-Ray Imaging of Prior Arts  
         [0071]    The recent advent of high-intensity, ultrafast (femtosecond-pulsed) lasers has allowed for their use in the collisional generation of x-rays from metal and non-metal targets. Termed “chirped pulsed amplification”, an ultrafast, periodic and high-power (terawatt) laser pulse can be used to create an extremely rapid acceleration of electrons initially within a 10 microns diameter area of a metal target. Ultimately, x-rays are produced from within a microscopic ionized plasma at the target surface (which is less than 50 microns in diameter). The ultrafast, relativistic acceleration of the electrons within the target happens so rapidly—within intervals of several picoseconds—that the plasma remains in a solid density. The microscopic focal-spot area of a laser-plasma x-ray source is, on average, two orders of magnitude smaller than a focal-spot typically produced from an electron beam used for medical imaging (which range in diameter from 150 microns to 2 millimeters).  
           [0072]    Notably, as represented by the MTF curve in Kroll et al, the contrast for a typical mammographic focal-spot (of 500 microns in diameter) was nearly undetectable for the same size spatial frequency where, remarkably, the contrast from a microscopic size laser-produced x-ray source (of 50 microns in diameter) remained nearly undiminished. Moreover, the minimum reported size of a laser-produced x-ray focal-spot observed to date has been 3 microns in diameter, generated from an smaller laser-produced focal-spot of 1 micron in diameter.  
           [0073]    In the case of absorptive radiography, one can also see from eq. 12, that by using a microscopic x-ray source, the blur value (Bf) is linearly reduced in comparison to the blur value produced from (a two orders of magnitude) larger area conventional clinical x-ray source. Importantly, the requirement for a microscopic x-ray focal-spot is especially stringent in phase-contrast imaging, where the mathematical relation between focal-spot size and contrast resolution for a microscopic non-absorbing object is non-linear (as described in the numerator of the integrated exponent in the Fresnel-Kirchhoff integral, eq. 5).  
           [0074]    X-rays produced from ultrafast lasers have also been exploited for imaging in ways that are not related to its microscopic focal-spot size, but rather, are dependent upon the temporal qualities of the ultrafast x-ray source. Specifically, laser-produced x-rays have been used for time-gated imaging techniques. Because the x-rays from a laser-driven source can have a duration that is relatively short (less than one picosecond) with respect to the transit time through the sample (approximately one nanosecond), it is possible to eliminate the effects of scattered photons by temporal discrimination. When compared with ballistic photons, scattered photons travel a longer path through the object and thus, experience a longer delay upon reaching the same location at the detector. Scattered photons that reach a detector will decrease the absorption-contrast signal, and at the same time, increase the noise in the image.  
           [0075]    If one uses a detector which may be turned off rapidly after the arrival of the ballistic photons, then the scattered photons may be removed from the image. Relatively simple microchannel plate (MCP) detectors with gate times as short as 50 picoseconds have been developed. Time-gated detectors register only non-scattered, ballistic photons that are unperturbed during their transit through the sample. Because time-gated detectors allow for the removal of scattered radiation from the (absorption) image, the result of their use in radiography is a marked improvement of image quality and a potential reduction of patient exposure.  
           [0076]    In the quantitative phase-contrast imaging system developed by Arfelli et al (which is based on an in-line optical geometry), a scintillation screen was used after the object, near the detector, to amplify the signal reaching the detector. In that case, the addition of a scintillation screen allowed for the low dose, high resolution imaging of both mammographic phantoms and thick cancerous human breast tissue.  
           [0077]    The total average power generated by a compact (i.e., table-top) terawatt-power, laser-produced x-ray source is very soon expected to be increased by two orders of magnitude, when the repetition-rate of the laser pulse will be increased from 10 Hertz to one-thousand Hertz. Importantly, the total average power of a microscopic laser-produced x-ray source can also be increased by optically focusing the laser into a microscopically narrow, but highly elongated, ultrafine focal-line.  
         SUMMARY OF THE INVENTION  
         [0078]    The present invention describes methods of phase-contrast imaging of the internal structures of objects using a quasimonochromatized and coherent x-ray beam, that is created from an ultrafast laser-produced x-ray source, comprising a microscopic plasma that is produced when a high-power laser is focused upon a high atomic number target. As described in the methods of the present invention, a laser-produced x-ray beam is specified for quantitative phase-contrast imaging techniques intended for medical purposes and for the non-destructive testing of industrial materials, employing an “in-line” optical geometry, with the object placed directly between the source and the detector. Utilized in the methods of the present invention, are collimating monochromators of prior art placed between the source and the object, which may be embodied in x-ray-reflective Bragg geometries, using asymmetrically-cut perfect crystals of silicon or pyrolytic graphite. Microcapillary x-ray lenses or microchannel plates may also be used as initial collimating devices. When employed together, elongated focal-lines and collimating optics can produce microscopically narrow, high brightness slice-beams and fan-beams for either slot-scanning or tomography. It is known that pixel-by-pixel calculations of the Fresnel-Kirchhoff integral can be utilized to locate an object in the path of an incident beam, using as variables, intensity values incident upon the detector. Described in the present invention is the use of the simplified, i.e., approximated, Fresnel-Kirchhoff integral for quantitative phase-contrast x-ray imaging methods, that utilizes a coherent x-ray beam generated from a laser-produced plasma that is used in conjunction with collimating optics, provided that the source is microscopic in at least one direction in the plane of the target. As a consequence of using a quasimonochromatic and highly-coherent laser-produced x-ray beam, the approximated Fresnel-Kirchhoff integral can be used to mathematically reconstruct a high-resolution refraction-based quantitative phase-contrast image of an object or its interior. Additionally, as described in the methods of the present invention, a laser-produced plasma x-ray source that is microscopic in at least one direction in the plane of the target, if used in conjunction with the appropriate collimating optics, may be applied to non-quantitative phase-contrast imaging techniques, producing either an analog in-line image or alternatively, utilizing either an analyzer crystal after the object or specifying interferometric holography. Finally, as described in the methods of the present invention, a laser-produced plasma x-ray source that is microscopic in at least one direction in the plane of the target, if used in conjunction with the appropriate collimating optics, may produce either a slice-beam or a fan-beam with utility for absorptive radiography and computed tomography. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0079]    Previously, neither an electron beam-produced nor a laser-produced collisional x-ray source could generate the necessary amounts of highly coherent x-ray flux that are needed to rapidly acquire—in a clinically-appropriate time interval—a phase-contrast image of the internal structure of a thick object, such as the human anatomy. Thus, it is unexpected and surprising that an ultrafast laser-produced x-ray source can be utilized—in a novel and advantageous fashion—for (non-absorptive) phase-contrast imaging techniques, specifically by virtue of its possessing at least one microscopic dimension (that is perpendicular to the optical axis).  
         [0080]    As described in the methods of the present invention, the preference for a small source size in phase-contrast imaging can be addressed with laser-produced x-rays eminating from an extremely small size, microscopic plasma, which is less than 50 microns in diameter and is as small as 12 microns in diameter or smaller. In contrast, the visible 500 microns focal-spot of a conventional medical x-ray source, which is produced by an electron beam, is 100-times larger in area than a laser-produced x-ray source. As described in the methods of the present invention, a collimated, high-flux x-ray line-beam (i.e., a slice-beam or a fan-beam) that is appropriate for phase-contrast imaging can be created from a highly-elongated and microscopically narrow laser-produced focal-line.  
         [0081]    As described in the methods of the present invention, the use of a coherent x-ray beam generated from a microscopic laser-plasma x-ray source, is intended either for high-resolution medical imaging purposes or for the non-destructive testing of industrial materials.  
         [0082]    The optical geometry of the quantitative phase-contrast imaging technique (described in the methods of the present invention), entails the use of an in-line geometry, with the object placed between the laser-plasma x-ray source and the detector.  
         [0083]    In the present invention (using a coherent beam of x-rays generated from a microscopic laser-plasma x-ray source), a low noise phase-contrast (refraction) image may be reconstructed digitally. In prior art, digital processing may be accomplished by employing mathematical algorithms which use detector intensity measurements as variables.  
         [0084]    Particularly, it has not previously been known that a microscopic laser-produced (collisional plasma) x-ray source can be used for quantitative phase contrast imaging techniques which use image reconstruction algorithms based upon the Fresnel-Kirchhoff integral. As described in the methods of the present invention, when using a microscopic laser-produced (collisional plasma) x-ray source, image reconstruction may be performed using calculations based upon the Fresnel-Kirchhoff integral (to derive a phase image of the gradients of refractive indices within the object and importantly, the dimensions of the objects internal structures).  
         [0085]    Crystal monochromators are often used for the production of an appropriately monochromatic, spectrally pure x-ray beam, such as from a synchrotron. As described in the methods of the present invention, the crystal monochromators placed before the object may be embodied in either Bragg or Laue geometries using asymmetrically-cut perfect crystals, such as silicon. In the methods of the present invention, asymmetrically-cut crystal monochromators may be bent and tilted in order to project (away from the polychromatic primary beam), a quasimonochromatic x-ray beam of high flux and high collimation towards the object and detector.  
         [0086]    X-ray beams produced by an initially incoherent, but microscopic, laser-plasma source, will (after traversing the monochromator crystals) be more highly coherent and of greater intensity, compared to a beam produced using no crystal optic. As described in the present invention, additional collimating optics, such as microcapillary (Kumakhov) lenses and curved microchannel plates, might be used as primary capture devices for laser produced x-ray photons. The optics may be designed for a focal-point x-ray source or a focal-line x-ray source. As described in the methods of the present invention, after the primary optic, a secondary optic such as a monochromator may be used to produce a more highly-collimated and high-flux x-ray line-wave (that is parallel to the optical axis). In this manner, a microscopically narrow slice-beam or fan-beam can be produced.  
         [0087]    Using a quasimonochromatized and highly coherent x-ray beam, one may eliminate both the source size and the large distance-to-detector variables from the computed value of the Fresnel-Kichhoff integral used for image reconstruction (as described in prior art by Snigirev et al using a synchrotron x-ray source). Thus, the methods of the present invention use a simplified (i.e., approximate) Fresnel-Kirchhoff integral, for quantitative phase-contrast image reconstruction techniques, which are specified for use with a highly coherent laser-produced x-ray beam (that is quasimonochromatic or monochromatic).  
         [0088]    In the methods of the present invention, when using a quasimonochromatic and highly-coherent laser-produced x-ray beam (i.e., when the paraxial condition is valid), the simplified approximation of the Fresnel-Kirchhoff integral (eqs. 8 and 9) can be used to calculate a phase-contrast image from measurements of detector intensities.  
         [0089]    Central to the methods of quantitative phase contrast imaging, as known in the prior art, is the special case for a highly coherent point source, when r0&gt;&gt;r1, so that the size of the source (x1−x0) and the distance (r0) of the source to the object are not so important mathematically (and can be eliminated). As described in the methods of the present invention, for the case of a laser-produced coherent plane-wave incident upon the object—when r0 approaches infinity and with a point-like source (when both x0 and y0 approach zero)—one can use the simplified approximation of the Fresnel-Kirchhoff integral to obtain the maximum value of the phase-shift, j0. The phase-shift, j0, is the maximum value of j(x) at the detector (in the near-field Fresnel region), which is derived from the value of c(x1)b, in eq. 8.  
         [0090]    As it is known in prior art, using a coherent beam of x-rays: 
         j0=2 pdh/l,   (eq. 10) 
         [0091]    where “d” is the decrement of refraction (within a volume of a low absorbing material) and “h” is the maximum thickness of the object in the direction of the x-ray beam. Thus, from intensity variances on the plane of the detector, one can derive the maximum phase-shift (where j(x)=j0) of the object-modulated plane-wave and from that value, the location in space of the object with the dimension of value, h (in the x-direction). The object radius is h/2.  
         [0092]    Thus, in the present invention, quantitative phase-contrast x-ray imaging methods (utilizing a laser-produced x-ray source) may be used to detect cancerous tumors, metastasis and tumor-associated connective tissues, microcalcifications and abnormal vasculature at a microscopic level of detail.  
         [0093]    In the present invention, laser-produced x-rays are ideally suited for the quantitative phase-contrast imaging of any connective-tissues of animals (such as collagenous tendons, ligaments basal lamina or hyaline cartilage) and fatty adipose tissues.  
         [0094]    In the present invention, the simplified Fresnel-Kirchhoff integral may be used for image reconstruction, to analyze x-ray diffraction phenomena from the surface of microscopic crystalline calcifications associated with either tumors or connective-tissue lesions.  
         [0095]    Thus, in the methods of the present invention, laser-produced x-rays are ideally suited for mammography—with microscopic resolution—utilizing quantitative phase-contrast imaging methods.  
         [0096]    As described in the methods of the present invention, a high enough flux of quasiparallel x-rays can accommodate the purposeful elimination of unwanted portions of the x-ray spectrum—so that in being either nearly or partially monochromatic—phase-contrast is maximized, while both beam hardening and dosage are reduced. Because a much higher energy range of x-rays can be used to produce a high quality phase-contrast x-ray image of soft-tissues, the absorbed dosage is significantly reduced compared to the absorptive radiography of soft-tissues (such as mammography, which is based on the use of lower energy photons required for photoelectric absorption).  
         [0097]    Notably, it has also not previously been known that a microscopic laser-produced x-ray source can be used for non-quantitative phase contrast imaging techniques. The collimation requirements are similarly stringent for non-quantitative phase-contrast x-ray imaging techniques, whether performing phase-contrast x-ray imaging using an analyzer crystal (after the object) or interferometric holography. As described in the methods of the present invention, the use of a quasimonochromatized and coherent laser-produced x-ray beam may be applied to non-quantitative phase-contrast imaging techniques (which utilize either an analyzer crystal after the object or holographic interferometry).  
         [0098]    The non-quantitative phase-contrast x-ray image improvement that occurs when using a quasimonochromatized and coherent laser-produced x-ray beam may still be explained by an analysis of the x-ray wavelength and beam coherence requirements explicit in the simplified Fresnel-Kirchhoff integral. Thus, in the methods of the present invention, the use of a quasimonochromatic, highly collimated laser-produced x-ray beam is desirable for non-quantitative phase-contrast medical imaging techniques and the approximated Fresnel-Kirchhoff integral is also relevent towards understanding these analog cases.  
         [0099]    As described in the methods of the present invention, a quasimonochromatic and coherent laser-produced beam of x-rays may also be utilized for object illumination in non-quantitative phase-contrast imaging for medical purposes (such as to detect cancerous tumors, connective tissues, microcalcifications and abnormal vasculature at microscopic detail).  
         [0100]    As described in the methods of the present invention, a quasimonochromatic and coherent laser-produced x-ray source is also ideal for a compact device (for object illumination purposes) for both quantitative and non-quantitative phase-contrast microscopy, for microtomography and for the non-destructive testing of industrial materials. In the present invention, for purposes of phase-contrast x-ray microscopy, a Bragg Fresnel zone-plate (placed before the object) may be used in conjuntion with a laser-plasma x-ray source. [Dec. 12, 1991] 
         [0101]    Specifically, in the methods of the present invention, a monochromatized and coherent laser-produced x-ray beam will serve to maximize the acquisition of refractive phase information that is extracted by the analyzer crystal (at the optimal location of the rocking curve for such purposes). Thus, the methods of the present include diffraction enhanced imaging (DEI). In the methods of the present invention, a quasimonochromatized and coherent laser-produced x-ray beam will also serve to maximize the acquisition of phase information from interferometric holography.  
         [0102]    The x-ray beam coherence problem related to the large size x-ray focal-spot (that is generated from an electron beam in a conventional x-ray tube) prevents the high-resolution phase-contrast imaging of microscopic detail and is compounded by the short source-to-object distance requirement for a compact clinical radiographic device. For phase-contrast imaging, the microscopic x-ray source produced by a laser-plasma allows for a reduced source-to-object distance, because of an increased coherence length. Because the methods of the present invention use a quasimonochromatized and collimated laser-produced x-ray beam (generated from a microscopic plasma), the construction of compact (laser-based) phase-contrast clinical imaging device is made possible.  
         [0103]    In the methods of the present invention, notably for medical imaging, phase-contrast computed tomography employing laser-produced x-rays (from a plasma source) can be performed with multiple images taken from different angles around the cental axis. Filtered back-projection algorithms can be used (in a similar manner as in absorptive computed tomography) to reconstruct a three-dimensional refractive representation of the internal stucture of the object (such as, a human torso or the head and neck). Different tomographic systems (as described in the methods of the present invention) can employ either in-line geometry, an analyzer crystal after the object or interferometric holography.  
         [0104]    One embodiment of the present invention is the use of a microscopically-thin line-scan beam (i.e., a very narrow-field slice-beam or fan-beam) to reduce the registration of Compton scatter that would otherwise impinge upon the detector and degrade the phase image, as may occur when using an areal beam. An ultrafine line-scan beam has improved coherence properies, notably, in the vertical direction. Additionally, the narrowness of the scaning ultrathin slice-beam, if combined with very small size detector pixels, contributes to the elimination of motion blur. Moreover, various anti-scatter modalities after the object—such as a Bucky grid or an air-gap may be employed in different embodiments of the present invention, whether in conjunction with a line-scan or an areal beam.  
         [0105]    In one embodiment of the present invention, a scintillation screen may be placed after the object, but near the detector, to amplify the signal reaching the detector.  
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