Abstract:
A quantitative radiographic method and apparatus of determining the depth of a selected feature inside a three-dimensional object from a stereoscopic pair of left and right radiographic images to be presented to the left eye and right eye, respectively, of an operator. The method includes the steps of (a) producing the pair of images on the same object at slightly different angles, (b) operating image display devices to present the two images, and (c) performing and measuring horizontal shifting motions of the two images and obtaining the coordinates (X GA ,Y GA ,Z GA ) of an internal feature A with respect to a marker G according to a specified procedure. The procedure begins with aligning the image points of the marker G with their respective reference lines. The two reference lines lie on or very close to the image plane. Preferably, the same procedure is followed again for a second marker. The next step involves aiming and aligning the image points of the internal feature with respect to their respective reference lines. These procedures are carried out to allow for more convenient and accurate measurements of various image parallax values, which are in turn used to precisely calculate the location of an internal feature image of interest, such as a structural defect.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates to improved stereo radiographic image analysis methods and apparatus and, more particularly, to methods and apparatus for stereoscopically displaying radiographic images and quantitatively evaluating the size and location of a feature or defect inside a three-dimensional object such as a structural component or a human body.  
         BACKGROUND OF THE INVENTION  
         [0002]    High-energy radiations such as X-rays, gamma rays and neutrons are commonly used for non-destructive evaluation (NDE) of the internal defects of an object or for examination of the anomalies inside a human body. Radiographic images for either industrial NDE or medical diagnostic applications can be obtained by radiography-on-film, fluoroscopy (including digital radiography or computed radiography), and computed tomography (CT) methods. Each method has its advantages and disadvantages for a specific application.  
           [0003]    Film radiography involves producing a sharp, natural size, permanent image of the internal features (e.g. flaws or anomalies) in an object. Such an image is usually not difficult to interpret. However, film radiography is often relatively slow and expensive.  
           [0004]    Fluoroscopy or radioscopy entails the conversion of X-ray intensities into light intensities by utilizing a fluorescent screen. By placing the screen in the X-ray beam behind the specimen, one can produce an image of the specimen on the screen. The high X-ray absorbing capability of selected materials could result in low brightness images and hence poor sensitivity. One method to improve the fluoroscopic performance is to use a closed-circuit television (CCTV) camera to transfer the image on the fluorescent conversion screen on to a display monitor, relying on the electronic circuitry to enhance the signal and produce a bright image. Another technique is to use an image intensifier tube to convert X-rays into photons, which are then picked up by an image sensor. Commonly used image sensors are tube type TV cameras such as isocon, vidicons, and solid state charge coupled device (CCD) cameras. Another type of image sensor is the linear diode array (LDA), which can digitize and store the image to be viewed on a TV monitor. The digitization of the television signal has allowed a computer to be built into the system, and this advancement has greatly improved the attainable image quality. This development has also made it possible to perform real-time radiography.  
           [0005]    Both the conventional film radiography and fluoroscopy only provide a two-dimensional (2-D) view of an object. In industrial applications, a 2-D image does not give a NDE technician an adequate perspective view on the spatial distribution of multiple flaws in a structural component, nor does it allow the technician to determine the depth of a particular flaw. For medical uses, a 2-D image may not provide a diagnostician adequate information as to the extent of a particular disorder, such as the exact depth of a foreign object in a human body.  
           [0006]    To overcome some of the drawbacks of 2-D radiography, the approach of tomography was developed. Computed tomography (CT) involves obtaining and stacking a sequence of images representing 2-D cross sections or “slices” of the object. The 2-D images are acquired by rotating a thin, fan shaped beam of X-ray about the long axis of the object. X-ray attenuation measurements are obtained from many different directions across each slice. The 2-D images are reconstructed from these data through a sophisticated mathematical convolution and back projection procedure. A major drawback of tomography is that a NDE technician or diagnostician must mentally “stack” an entire series of 2-D slices in order to infer the structure of a 3-D object. The interpretation of a series of stacked 2-D images by an observer requires a great deal of specialized knowledge and skill. Further, such an approach is extremely time consuming and is prone to inaccuracy. The market price of a CT system typically exceeds a million U.S. dollars and, therefore, only select large hospitals or highly specialized governmental or industrial facilities could afford to have a CT system. Clearly, a need exists to develop a more affordable stereography system for 3-D inspection of the internal structure of an object.  
           [0007]    Three-dimensional (3-D) or stereoscopic viewing provides a means for showing actual, more understandable spatial relationships among various features or flaws inside a body. Stereoscopic radiology was first introduced near the turn of the century. Extensive patent and open literature can be found that describes the methods or apparatus for producing stereoscopic radiographs.  
           [0008]    Most of the techniques that have been used to achieve the stereo effect is based on the theory of parallax. Specifically, an image recorded from the perspective of the right eye must be seen by the right eye while an image recorded from the perspective of the left eye must be seen by the left eye. A simple way to accomplish this is to provide distinct and separate optical paths to each eye from each recorded image. For instance, the right and left eye image pairs may be recorded as transparencies which, when inserted in a common hand-held 3-D viewer, are presented to each eye separately through magnifying lenses. A second example using the principle of distinct and separate optical paths is the mirror based viewer system. In this system, the image pairs are positioned under a viewer which, through two pairs of angled mirrors, directs each image to its corresponding observing eye. These conventional 3-D viewers, normally without proper markers or references, do provide the observer a 3-D perspective. However, they do not readily permit determination of the specific depths in which certain features (or flaws) are located relative to a predetermined reference.  
           [0009]    Disclosed in U.S. Pat. No. 3,984,684 (1976) is a technique that allows both production of the stereo effect and measurements of the depth and size of one or more internal parts of an object. The technique entails successively directing the X-ray beams from an X-ray tube through the object, then through a parallax grating, and finally onto the film. The grating is mounted on the film support system. The object and the film support system together are translated in parallel paths laterally with respect to the beam path at different speeds. These speeds are such that the film and the object are maintained in congruent alignment with the X-ray tube. The grating moves slightly out of congruency causing the beam passing through the grating to slightly scan the film during the transverse. Also, the angle at which the object is exposed to radiation from the X-ray tube gradually changes. The film image contains a series of side-by-side variable aspect views or images of the object, corresponding in number to the number of slits in the grating. These images when viewed with a lenticular screen produce a 3-D perception. This technique requires the utilization of a complicated radiograph-taking system and a lenticular screen as described above. The stringent congruent alignment requirement has made this technique not readily adaptable to existing X-ray radiography apparatus.  
           [0010]    Liu and co-workers (International Journal of Pressure Vessels &amp; Piping, Vol.44, 1990, pp.353-364 and Vol.48, 1991, pp.331-341) have proposed a quantitative stereoscopic method which not only provides a 3-D perspective view of the internal features but permits convenient calculations of the coordinates (X,Y,Z) of one or more flaws inside an object. The method begins with taking a pair of radiograph films with the X-ray tube shifted laterally in a plane parallel to the film between the two exposures (while the object remains stationary). Alternatively, the same result can be achieved by shifting the object laterally while the X-ray source remains fixed. These radiograph films are then examined in a stereoscopic viewer. With a suitable marker placed on the specimen surface when the radiographic films are being exposed, the position of a defect image inside the specimen can be determined. Two reference wires were placed above the pair of radiographic films to help on the calculation of the parallax distance. The method proposed by Liu, et al. provides a sound basis upon which more effective stereoscopes for quantitative radiography can be designed. This method, however, has been limited to film radiography. The procedures were lengthy and complicated. What is clearly needed is an improved method, which is based on Liu&#39;s principle and the various positive attributes of fluoroscopy, for conducting quantitative stereo radiology. The present inventor and his co-worker have developed several methods and related apparatus for quantitative stereoscopic radiography (U.S. Pat. No. 6,118,843, issued Sep. 12, 2000 and U.S. Pat. No. 6,115,449, Sep. 5, 2000, both to Huang and Jang). Further studies have led to the present invention which includes improved, more user-friendly, and faster methods for analyzing a pair of stereo radiographic images. The improved method and apparatus differ from the earlier versions (the above-cited two patents) in several aspects:  
           [0011]    (1). The present method involves preferably placing the two reference lines very close to the image plane (e.g., positioning the reference wires almost in physical contact with the underlying films) or exactly on the image plane (e.g., reference lines internally generated on a monitor and the two images are on the same plane). Such an arrangement makes it easier to aim the reference lines on the respective images and makes the measurement of the parallax distances more accurate.  
           [0012]    (2). The present inventor has found that by allowing the left reference line to coincide with the left image point of a selected feature or marker and the right reference line to coincide with the corresponding right image point, regardless if the left image, the right image, or both being shifted, the relative shift distance between the two images could be used to calculate the parallax distance. This has made it possible to eliminate several steps that were required in the earlier methods.  
           [0013]    (3). In such an arrangement, it becomes unnecessary to use a stereoscope to ensure that the two images are accurately positioned and orientated to provide a 3-D view of the images. With the conditions as set forth in the above (1) and (2) being met, the pair of images are automatically in perfect registry to provide a 3-D perspective. A stereoscope can still be used, however, to observe the spatial dispersion of various features or defects inside the 3-D object and to help identify desired features or defects whose coordinates can be measured with the present method.  
           [0014]    (4) By using a pattern recognition program, once an image point of a feature or marker in one of the two images (say, left image) is identified and positioned to coincide with a reference line (the left reference line), the corresponding image point of this feature or marker on the other image (right image) can be automatically identified and positioned to coincide with the other reference line (the right reference line).  
           [0015]    (5) The apparatus includes two secondary platforms, instead of one secondary platform supported by one primary platform. The two secondary platforms are capable of sliding on an independent and separate basis along a horizontal X-axis direction. Displacement-metering sensors are provided to directly measure the relative displacement between one secondary platform and the other. It is this relative displacement value that is needed to calculate the parallax value of a particular image point.  
         OBJECTS OF THE INVENTION  
         [0016]    The principal objects of the present invention are:  
           [0017]    (1) to provide an improved method of stereoscopically displaying radiography images and to allow for more convenient and faster determination of the location of an internal feature such as a broken bone in a human body.  
           [0018]    (2) to provide an improved method and apparatus for not only stereoscopic viewing of the internal defect dispersion of an object through radiographic films but also quantitative determination of the location of a defect inside an object.  
           [0019]    (3) to provide an improved method and apparatus for stereoscopic viewing of radiographic images displayed on a TV screen or a computer monitor and for determining the location of an internal feature.  
         SUMMARY OF THE INVENTION  
         [0020]    The present invention provides methods for conducting quantitative stereoscopic radiography, including film, video, digital, and computed radiography. These methods include the improved version of the above-mentioned Liu&#39;s method of film-based stereo radiography and further improvements over our earlier methods. Particularly included are methods that involve integrating reference line-based approaches with the great electronic imaging capabilities commonly associated with video radiography, digital radiography, or computer radiography.  
           [0021]    Specifically, in one preferred embodiment, a method is disclosed which involves displaying a pair of radiographic images on the corresponding right and left video display devices of a stereoscopic viewing system. The pair of images can be obtained by transferring (e.g., scanning or digitizing) the corresponding radiography transparencies (films or negatives) or opaque prints onto one cathode ray tube (CRT), or two separate CRT monitors by using a common image scanner or TV camera. Alternatively, the images can be obtained by directly using common fluoroscopy devices to display the images without going through the intermediate film-taking procedure. This can be accomplished by directing the beam of an X-ray source (or other types of high energy radiation) through an object and by using an image intensifier to convert the radiation into visible light, allowing the image to be shown on a fluorescent screen. Alternatively, the light photons emitted from the image intensifier may be recorded by an image sensor or reader which delivers the images either directly to video display devices (including computer monitors) or to an image storage device. In the latter case, the images will be later played back to the video display devices for examination.  
           [0022]    As an example, referring to FIG. 1(A), both the right and left video display devices are each provided with a vertical reference line, which can be simply a thin opaque wire attached vertically (herein referred to as transversely, or in the Y-coordinate direction) to the display screen. The reference lines may be written onto the screen surface by using a marking pen or internally generated on a computer monitor. Proper movement means are provided to allow the two images to be shifted laterally (horizontally, in the X-coordinate direction) either simultaneously in congruency or with respect to each other. The X-axis also lies substantially parallel to the line segment connecting the two eyes of an operator. Displacement-metering devices are given to measure and record these shift distances. Shifting of the two images can be accomplished by positioning the two display devices on a slidable platform, hereinafter referred to as the primary platform, and then horizontally translating this platform. Either the left or the right display device is also supported on a secondary platform which is capable of moving horizontally, independent from the movement of the primary platform. Alternatively, both display devices can be supported on two separate secondary platforms. The secondary platform(s) is (are) slidably attached to the top surface of the primary platform. The movements of both secondary and primary platforms can be recorded by any movement-measuring means such as a micrometer, sliding caliper, optical encoder, linear slide, laser beam-based displacement sensor, linear variable differential transformer (LVDT), or any other type of displacement sensor. These measuring means are used to measure out the shift distances of both marker and defect images on one of the image pair relative to those on the other image.  
           [0023]    It may be noted that, by referring to FIG. 1(A) again, the X-coordinate direction is the X-ray source shifting direction (when the radiography image is taken), which is also parallel to the platform movement direction. The transverse direction on the image plane is the Y-coordinate direction, which is the vertical direction in FIG. 1(A). The Z-coordinate direction is perpendicular to both the X-direction and Y-direction; i.e. being normal to the image plane and substantially in the sample depth direction.  
           [0024]    In another embodiment, the pair of radiography images may be shown side by side on the same display unit, such as a TV monitor or a computer monitor. The monitor screen is artificially divided into two zones: a left zone showing the image to be presented to the left eye and a right zone showing the image to be presented to the right eye of an observer. Vertically across each zone is one of the afore-mentioned reference lines or wires. There exist commercially available image processing software-hardware packages that are capable of providing and measuring the concurrent and separate movements of the two images on a TV screen or computer monitor. In yet another embodiment, the monitor is mounted on a horizontally slidable primary platform, which provides simultaneous shifting of the two images. Shifting of one image with respect to the other can be executed on the monitor by a simple computer command.  
           [0025]    The two images may be viewed by an optical observing unit (a stereoscope) which is composed of two optical paths, one for observing the left image by the left eye and the other for observing the right image by the right eye of an observer. Each optical path begins with an objective lens that is capable of seeing a broad image area and directing the image to a pair of angled mirrors or prisms. The mirrors or prisms in turn send the image through an eyepiece into one eye of the observer. The separation between the two eyepieces is adjustable to suit different observers. The separation between the two objective lenses is designed to be in accord with the dimensions of, and the separation between the two images to ensure a broad viewing field. This pair of optical paths preferably are provided with a vertical movement means which is in turn supported by a sturdy stand. This vertical movement provision permits the observer to cover a wider viewing area in cases the display screen is wider than the range covered by the pair of objective lenses when in one specific height. It may be noted that the present method does not require the utilization of a stereoscope, but it can be used advantageously to provide a stereo perspective of how one internal feature is spatially related to other features, particularly in the depth direction.  
           [0026]    In summary, the present invention discloses improved methods for stereoscopically displaying radiographic images of the internal structure of an object and for determining the spatial coordinates of selected feature images inside the object. The method is composed of several steps:  
           [0027]    (a) producing a pair of images on the same object taken from slightly different angles with image reference markers being placed near or on selected positions (preferably on or near the top or bottom surface) of the object when irradiated; (b) operating image display devices to present this pair of images with the two images being set up in a definitive orientation so that when the images are being viewed with both eyes by an observer, the two lines of sight connecting the eye balls and the corresponding image points of the image pair intersect; the two images being respectively provided with two stationary, transversely aligned reference lines across the image plane in the Y-direction; (c) performing and measuring horizontal shifting motions of the two images according to a sequence of procedures to be specified at a later section. These procedures basically involve aiming and aligning the image points of an internal feature with their respective reference lines. The same procedures are then repeated to align the image points of a marker with their respective reference lines. Preferably, the same procedures are followed again for a second marker. These procedures are carried out to allow for more convenient and accurate measurements of various image parallax values, which are in turn used to precisely calculate the location of an internal feature image of interest. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0028]    [0028]FIG. 1(A) Schematic showing the major components of a preferred apparatus for a stereoscopic radiograph observing and measuring apparatus; the apparatus including a slidable secondary platform  28  supported by a slidable primary platform  30  with both platforms being supported by a stationary base  42  or frame. (B) An apparatus similar to (A), but with two separate secondary platforms  28 , 29 , which are capable of undergoing displacements with respect to each other and are supported by a base  42 .  
         [0029]    [0029]FIG. 2 Schematic showing the two optical paths in the observing compartment (a stereoscope).  
         [0030]    [0030]FIG. 3(A) Geometrical relationships between a lead marker G, an internal defect A, and their images g 1 , g 2  and a 1 , a 2  on a radiographic film or image intensifier screen (referred to as image plane, p). An image is recorded (e.g., a radiograph p 1  is taken) when the X-ray source is located at S 1 . A second image is recorded (e.g., a second radiograph p 2  is taken) when the source is at S 2 . (B) The corresponding situation where the two images are taken sequentially; the second image is taken after the object is shifted laterally while keeping the X-ray source stationary.  
         [0031]    [0031]FIG. 4 Geometrical relationships between two lead markers G, K, an internal defect A, and their respective images g 1 , g 2 , k 1 , k 2  and a 1 , a 2  on a radiographic film or an image intensifier screen (eventually on a computer monitor or video display screen). This diagram helps illustrate the derivation of the formulae used in depth calculations of internal defects.  
         [0032]    [0032]FIG. 5 Geometrical relationships between the lead marker G, an internal defect A, and their respective images g 1 , g 2 , and a 1 , a 2  on a radiographic film or an image intensifier screen (eventually on a computer monitor or video display screen). This diagram helps illustrate the derivation of the formulae used in the calculations of horizontal image shifts or the X-coordinate value of an internal defect position.  
         [0033]    [0033]FIG. 6 Geometrical relationships between the lead marker G, an internal defect A, and their images g 1 , g 2 , and a 1 , a 2  on a radiographic film or an image intensifier screen (eventually on a computer monitor or video display screen). This diagram helps illustrate the derivation of the formulae used in the calculations of transverse image shifts or the Y-coordinate value of an internal defect position.  
         [0034]    [0034]FIG. 7 Schematic showing the procedure to follow for measuring and calculating the depth of a defect.  
         [0035]    [0035]FIG. 8 A block diagram illustrating the major components and steps involved in the production and display of image pairs on video display devices. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0036]    A detailed description of preferred embodiments of the present invention are disclosed herein. The described embodiments are to be understood as merely exemplary of the invention, which may be embodied in various forms. Therefore, specific structural and functional details disclosed herein are not to be construed as limiting, but merely as a basis for the claims and as a representative basis for teaching those who are skilled in the art to variously employ the present invention for a wide range of appropriately detailed structures.  
         [0037]    [0037]FIG. 1(A) schematically shows the major components of a preferred design for a stereoscopic radiograph observing and measuring apparatus that can be used to carry out the procedures specified in the presently invented method. Two video display devices  12 ,  14  are used to display a pair of radiographic images. Two reference lines  16 ,  18  are provided across the respective screens of the two display devices. These two reference lines may be two thin opaque wires located in front of, but very close, to the screen plane. These wires may be physically held in place by fastening means (not shown) on the apparatus base  42 . These wires are not allowed to move along with the display devices  12 , 14  and will provide the necessary position references for measuring the image shifts and defect locations (to be explained later).  
         [0038]    Both display devices are supported by a slidable platform  30 , referred to as the primary platform, through their respective stands,  20  and  22 . One of the two video display devices (shown to be the left one  12  in FIG. 1(A), but could have been the right one  14 ), through its stand  20 , is positioned on a slidable platform  28 , referred to as the secondary platform. The stand  20  is preferably fastened to or integrated with platform  28 . Also, the stand  22  is preferably fastened to or integrated with platform  30 . Platform  28  is allowed to slide horizontally between two guiding posts  24 ,  26  forming a trough to slidably accommodate platform  28 . The sliding movement of platform  28  may be driven by any drive means. Shown in FIG. 1(A) is a simple driving mechanism that is constituted by a threaded shaft  32 , supported by a shaft housing  33 , a micrometer  34 , and a turning handle  36 . By turning the handle  36 , one can advance or retreat the shaft screw  32  to drive the secondary platform  28  horizontally. The motion of the shaft may be either manually driven (e.g., by spinning the handle to a desired number of turns) or driven by any power tool (e.g., an electrical motor, hydraulic piston, pneumatic, solenoid, or other types of actuators). What is schematically shown in the left portion of FIG. 1(A) represents one of the many common sliding mechanisms that can be utilized to generate reversible sliding motions for a part. Those who are skilled in mechanical art may select from a wide array of sliding mechanisms that are commonly used and are mostly commercially available. For example, those worm shaft-worm gear combinations commonly used in moving the platforms of a milling machine or a lathe may be used for moving the secondary platform and measuring its travel distance. Similarly, a drive means, represented by  38 , 40  is also provided for the primary platform  30 , to move the two images simultaneously. A displacement measuring means, such as a micrometer, is provided for this primary platform. The secondary platform  28  is used to horizontally shift one image with respect to the other. The two drive mechanisms need not be of same type or dimensions. The complete assembly is supported by a sturdy base  42 .  
         [0039]    Alternatively, each display device may be provided with a separate secondary platform. As shown in FIG. 1(B), two separate secondary platforms  28 , 29  are both supported on a stationary base  42 . The two secondary platforms are capable of sliding horizontally along the X-axis direction of an X-Y-Z coordinate system indicated in FIG. 1(B). The relative separation of these two secondary platforms can be measured by any displacement-metering means. For instance, a set of optical encoder represented by  37 , 39  are attached to  29  and  28 , respectively. When one platform is shifted relative to the other, the encoder picks up the displacement signals, which may be acquired and displayed by a digital display unit and/or computer. Advantageously, additional two micrometers or sliding calipers may be respectively attached to the two secondary platforms. The difference in readings shown on these two micrometers would indicate the relative displacement between the two display units or between the two images thereon.  
         [0040]    In FIG. 1(A) and  1 (B), the micrometers are connected in-line to measure the sliding distances of the two platforms (two secondary platforms or one primary plus one secondary platform). Again, there are many simple ways of measuring the travel distance of a part. One may choose to use an optical encoder, a laser beam, a linear slide (commonly used in a CNC mill), or just a simple sliding caliper, etc. In FIG. 1(A), two sets of optical encoder,  37 , 39  and  45 , 47 , are used to acquire the displacement signals, which are displayed by a digital display unit  43  and/or computer  45 . To use any other type of drive means or travel measuring means in the present context would merely represent a simple variation of the present invention. In a further preferred embodiment, the micrometer may be replaced by or supplemented with a displacement sensor that is capable of converting the mechanical displacement data into electrical signals in analog or digital form. These sensors are very commonly used in the field of physical measurements. Examples include the linear variable differential transformer (LVDT) or an extensometer-type sensor commonly used in the mechanical testing of materials. Preferably, the analog signals are further converted into digital signals through an analog-to-digital (AD) converter means. These digital signals then are directly displayed in a digital display means such as a liquid crystal display. These signals may also be further used by a computer to calculate the acquired image shift distances and the spacial coordinates (X,Y,Z) of an internal feature of an object.  
         [0041]    The two images shown on the screens of display devices  12 , 14  are to be viewed by the observing unit, shown on the right lower portion of FIG. 1(A) or that of FIG. 1(B). Housed in casings  44 , 46 , 48  are mirrors and lenses that are required to direct the light from the two images to an adjustable binocular  50  including two eyepieces  52 , 54 . This optical assembly,  44  through  54 , provides two distinct and separate optical paths to meet the parallax requirement of generating a stereo perception; i.e. an image recorded from the perspective of the right eye now can be seen by the right eye while an image recorded from the perspective of the left eye seen by the left eye. The arrangement of the two optical paths is schematically shown in FIG. 2, in which the two images  70 , 72  are respectively reflected and re-directed through mirrors or prisms  74 , 78  and  76 , 80 , and then through the lenses  82 , 84  in eyepieces  52 , 54  into the left and right eye of an observer. Such an optical path assembly device is essentially a mirror stereoscope commonly used in viewing geological survey maps.  
         [0042]    The optical path assembly device is supported by a stand  56 , which preferably has a height-adjusting means (not shown) to move the assembly up and down as desired. Any releasable fastening means with sliding provisions, any proper ball bearing-screw combination or chain-wheel combination possibly driven by a motor means, can be set up to drive the optical assembly up and down. The stand  56  is connected to or integrated with a sturdy base  62 , which can be connected to or integrated with the base  42  of the two platforms. Such an optical path assembly device may also be directly attached to one or two sides of a computer monitor or video display device (not shown).  
         [0043]    The operating principles for the presently invented quantitative stereoscopic radiography apparatus may be best illustrated by referring to FIGS.  3 - 7 . Prior to taking radiographs or generating X-ray images on an image intensifier (or image sensor and reader), the image orientation must be defined and reference markers established. Reference markers are set up to meet specific measurement needs. For example, in order to measure the vertical depth from the top surface of an object to an internal flaw, a small-sized lead marker may be placed on the top surface of the object. This reference marker may be selected to be any surface or internal feature of the object with a known position. The basic procedures for carrying out radiography are shown in FIG. 3(A). An imaging plate P (either a radiographic film or an image intensifying device) is placed behind the object. An image is produced on plate P 1  at a focal length F with the radiation source located at S 1 . On this image plate P 1  are shown the image point g 1  of a reference marker G and the image point a 1  of a flaw A. The radiation source is then shifted laterally by a distance B to a new position S 2  while the object remains stationary. A second image is then produced on plate P 2  with a focal length F. This plate P 2  now contains the image point g 2  of G and the image point a 2  of A. Alternatively, one may choose to maintain the radiation source stationary while shifting the object laterally by a distance B (FIG. 3(B)). With all other parameters maintained constant, both modes of image acquisition will yield the same results.  
         [0044]    Referring to FIG. 3(A), the depth from the reference marker G to flaw point A may be derived as follows: Let Z GA  be the vertical distance from point G to point A, h the distance from the top surface of the object to the imaging plate, then H=F−h. (Related mathematical symbols are herein defined: ˜ means “being similar between two triangles”; ∵ means “because”; ∴ means “therefore”; Δ, when followed by three letters, denotes a triangle; a 1 a 2  means the distance between a 1  and a 2 )  
             ∵     Δ                   S   1        A                     S   2     ~   Δ                     a   1        A                   a   2                                 ∴         a   1          a   2       B       =       h   -     Z     G                 A           H   +     Z     G                 A                                     T                 h                 e                 n                   Z     G                 A         =         B   ·   h     -       a   1            a   2     ·   h           B   +       a   1          a   2                   (   a   )               ∵     Δ                   S   1        G                     S   2     ~   Δ                     g   1        G                   g   2                                 ∴         g   1          g   2       B       =     h   H                               T                 h                 e                 n                 h     =         g   1            g   2     ·   H       B             (   b   )                               
 
         [0045]    Substitution of (b) into (a) gives  
               Z     G                 A       =           (         g   1          g   2       -       a   1          a   2         )        H       B   +       a   1          a   2           =       H   B            (         g   1          g   2       -       a   1          a   2         )     ·       (     1   +         a   1          a   2       B       )       -   1                     (   c   )                               
 
         [0046]    In a normal radiographic image taking situation, Z GA &lt;&lt;H, hence a 1 a 2 &lt;&lt;B; therefore, Eq.(c) may be simplified as:  
               Z     G                 A       =       H   B          (         g   1          g   2       -       a   1          a   2         )               (   d   )                               
 
         [0047]    In Eq.(d), H and B can be determined during the image taking step, (g 1 g 2 −a 1 a 2 ) can be measured by examining the images on plates P 1  and P 2 . Therefore, Z GA  can be readily calculated provided that the apparatus permits determination of (g 1 g 2 −a 1 a 2 ). The detailed procedure for determining (g 1 g 2 −a 1 a 2 ) is given as follows (see FIG. 7):  
         [0048]    Step 1: Place the images of plates P 1  and P 2  in a correct orientation according to the directional marks of the plate. The two images must be parallel to each other side by side.  
         [0049]    Step 2: Gently shift the primary platform  30  and the secondary platform  28  (referring to FIG. 1(A)) or shift the two secondary platforms (referring to FIG. 1(B)), sequentially or concurrently, to insure that the left reference line coincides with the left image point g 1  and the right reference line coincides with the right image point g 2 . At this moment of time the relative shift distance between the two films (or the two digital images or video images), specified by P G,  may be read off from one micrometer (FIG. 1(A)) or two micrometers if there are two secondary platforms FIG. 2(B)). A displacement sensor, such as a LVDT mounted between the two display devices, may be used to directly measure out the relative displacement. The P G  values may be automatically computed by a computer if the displacement signals are digitally transferred into the computer. If the shifting of the images is conducted directly on a computer monitor by using a mouse, the relative shift distance between the two images can also be automatically calculated by, for instance, counting the number of pixels traversed by such a shifting.  
         [0050]    Step 3: Follow a similar procedure to move the platforms to bring image a 2  to fall on the right reference line  18  and to bring image a 1  to fall on left reference line  16 . Then, record the relative travel distance P A  of the two platforms. Here, P G −P A =ΔP GA =(g 1 g 2 −a 1 a 2 ).  
         [0051]    In actual radiography practice, the focal length F may not be accurately measurable, resulting in some inaccuracy in defining H=F−h. Consequently, there may be a large error with Z GA =H/BΔP GA  In order to overcome this potential problem, one may set up another lead marker K preferably at the bottom surface of the object. Based on FIG. 4, another depth equation for Z GA  may be derived as follows: A simple manipulation of Eq.(b) leads to H=Bh/g 1 g 2  which, upon substitution into Eq.(d), gives  
           Z     G                 A       =         h       g   1          g   2              (         g   1          g   2       -       a   1          a   2         )       =         h        (     1   -         a   1          a   2           g   1          g   2           )            
     ∵       a   1          a   2         =       K                   a   1       -     K                   a   2               ;               g   1          g   2       =       K                   g   1       -     K                   g   2           ;          
     ∴     Z     G                 A         =     h        (     1   -         K                   a   1       -     K                   a   2             K                   g   1       -     K                   g   2             )                       L                 e                 t        :        K                   a   1       -     K                   a   2         =     Δ                   P     K                 A           ;         K                   g   1       -     K                   g   2         =     Δ                   P     K                 G                     T                 h                 e                 n        :          Z     G                 A         =     h        (     1   -       Δ                   P     K                 A           Δ                   P     K                 G             )                             
 
         [0052]    Here, h is a parameter (the separation between the top surface of the object and the imaging plate) that can be measured accurately. Further, ΔP KA  and ΔP KG  are parameters that can be measured by the presently proposed apparatus. Their measurement procedures are similar to those for ΔP GA  (Step 4).  
         [0053]    Step 4: Referring to FIG. 7 again and follow a procedure similar to Step 2 or 3. Move the platforms to bring image k 2  to fall on the right reference line  18  and to bring image k 1  to fall on left reference line  16 . Then, record the relative travel distance P K  of the two platforms. Here, P G −P K =ΔP GK =(g 1 g 2 −k 1 k 2 ) and P K −P A =ΔP k  =(k 1 k 2 −a 1 a 2 ). Utilization of the above equations can significantly improve the accuracy for Z GA .  
         [0054]    Based on FIG. 5, the horizontal coordinate from flaw point A to reference marker point G can be derived as follows: Draw a vertical line from the radiation source S 1 ,S 2  to the plate P. Let X GA =the horizontal distance from point G to point A; X A =the distance from point A to the vertical line; X G =the distance from point G to the vertical line; X a =the distance from point a 1  to the vertical line; X g =the distance from point g 1  to the vertical line. Then,  
           ∵     tan                 ϑ       =         X   G     H     =           X   g     F          
     ∴     X   G       =         X   g     ·   H     F           ;       X   g     =             X   G     ·   F     H          
     ∵     tan                 φ       =         X   A       H   +     Z     G                 A           =           X   a     F          
     ∴     X   A       =             X   a          (     H   +     Z     G                 A         )       F     :     X   a       =       F   ·     X   A         H   +     Z     G                 A                                           
 
         [0055]    Also, let ΔXag be the horizontal distance from the image point g 1  to image point a 1 , then ΔXag=Xg−Xa. Substitution of the expressions for Xa and Xg into this equation leads to:  
         Δ                   X     g                 a         =             F   ·     X   G       H     -       F   ·     X   A         H   +     Z     G                 A                  
     ∴     X   A       =         (     H   +     Z     G                 A         )          (       F   ·     X   G       -       H   ·   Δ                     X     g                 a           )         F   ·   H                               
 
         [0056]    Since X GA =X G −X A  and if the condition of X G =B/2 can be met during the radiography imaging step, then X GA  can be expressed as:  
         X     G                 A       =       B   2     -         (     H   +     Z     G                 A         )          (         F   ·   B     2     -       H   ·   Δ                     X     g                 a           )         F   ·   H                               
 
         [0057]    where ΔXga is an unknown variable; however, it may be determined by examination of the image from P 1  with a transversely aligned ruler on the apparatus (or by simply moving a cursor on a computer monitor in the case of digital images). Then, by plugging ΔXga into the equation for X GA , one obtains the value of X GA .  
         [0058]    By following similar procedures, the longitudinal distance Y GA  from the reference point G to flaw point A may be derived as follows:  
         Y   A     =         F   ·       Y   G          (     H   +     Z     G                 A         )         -         H        (     H   +     Z     G                 A         )       ·   Δ                     Y     g                 a             H   ·   F                             
 
         [0059]    Deducting from both sides of the equation by the same amount Y G , one obtains  
         Y     G                 A       =         Δ                     Y     g                 a            (     H   +     Z     G                 A         )         F     -         Y   G     ·     Z     G                 A         H                             
 
         [0060]    In real practice, Z GA &lt;&lt;H, therefore,  
         Y     G                 A       =         Δ                     Y     g                 a            (     H   +     Z     G                 A         )         F     .                           
 
         [0061]    With the present radiography apparatus, one can use a transversely aligned ruler to measure ΔYga directly on the film P 1  or P 2  and, therefore, readily obtain the value of Y GA . In the case of digital image analysis, the value of ΔYga may be readily obtained by moving a cursor.  
         [0062]    In the equations for X GA  and Y GA , F and H can not be accurately measured. In order to avoid the potential error, one may obtain the values of F and H through further calculations. Referring to FIG. 4 again:  
             ∵     Δ                   S   1        G                     S   2     ~   Δ                     g   1        G                   g   2              
     ∴     H   B       =         h       g   1          g   2              
     ∵       g   1          g   2         =         k                   g   1       -     K                   g   2         =         Δ                   P     G                 K              
     ∴   H     =       h     Δ                   P     G                 K           ·   B             ;     F   =       H   +   h     =     h        (     1   +     B     Δ                   P     G                 K             )                                 
 
         [0063]    In the above equations, ΔP GK  can be accurately measured by the proposed apparatus, the measurement method being the same as that for ΔP GA  described earlier.  
         [0064]    When viewing an object with both eyes, one sees different sides of the object from two different directions. Therefore, if a proper pair of perspective drawings, photos or other type of images corresponding to these two sides of the object are separately provided in front of their respective eyes, then the images on the retinas will provide a perception identical to what would have been visioned with both eyes. A 3-D optical model in space is thus sensed or perceived. This stereoscopic vision, obtained from viewing the preserved images, may be termed reproduction of the stereoscopic effect. The drawings, photos or images of other form producing such an effect may be termed a “photo-couple”. This kind of observation with a stereoscopic effect is herein referred to as stereoscopic observation.  
         [0065]    The above-described principle of stereoscopic observation suggests that the following conditions must be fulfilled in order to obtain reproduction of the stereoscopic effect with a photo-couple: (1) A pair of images must be taken on the same object at slightly different angles; (2) The observer must be able to use his eyes separately in viewing the images at the same time, i.e. to make each eye see only the corresponding image separately and simultaneously; (3) The photo-couple must be set up in a definitive orientation, i.e. when viewing with both eyes, the two lines of sight from the corresponding points of the photo-couple must intersect. The presently discussed apparatus are designed to fulfill these conditions.  
         [0066]    A further scrutiny on the general formulas derived above for the coordinates of feature points in space suggests that one has to measure the parallax differences of the corresponding point images. Hence, the following conditions must be further fulfilled in the design and construction of a quantitative stereoscopic radiography instrument: (4) There must be a device or a pair of devices to display a pair of images; (5) Two distinct sets of optical systems (preferably with some magnifying capability) may be advantageously used (also not a requirement) to facilitate the viewing by each eye of the respective image independently and simultaneously; (6) Adjustments must be allowed for the X- and Y-directional displacements for the image display devices and the eyepieces so that point images in various parts of the image can be seen. (7) The two images must be allowed to shift horizontally with respect to each other and there must be some devices for displacement measurements; (8) Reference lines and markers must be supplied for stereoscopic surveying. The presently discussed apparatus have fully met the above-cited requirements.  
         [0067]    The nature of the image display devices is further discussed herein. In its simplest form, the image plate may be just a radiographic film (negative film or transparency) or a positive print (opaque photographic paper). In the case of radiographic transparencies, a pair of film boxes with back illuminating light constitute the two required display devices. When positive prints are employed, the two display devices are simply some devices that are capable of holding a pair of prints on their flat front surfaces. When deemed necessary, the front surfaces may be illuminated with proper lighting to facilitate observation. Alternatively, referring to FIG. 8, the images in radiographs ( 90 , negative or positive) may be stored in an image data memory  94  through a commonly used scanner or digitizer  92  for further uses later.  
         [0068]    In fluoroscopy radiography, the images picked up by an image intensifier  96  (or any type of radiation sensor plate) may be recorded by a camera means  98 , or other type of image sensor/reader, and stored in the image data memory  94 . Image sensor means may include a fluorescence screen, a phosphor screen, an amorphous selenium plate, an amorphous silicon plate, a laser beam scanner, and combinations thereof. Memory  94  could be either an independent memory unit or a part of the mass storage  106  of a computer  99 . The system computer  99  includes a central processing unit (CPU)  100 , system memory  104 , system mass storage devices  106 , a keyboard  108 , and a screen location selection device (e.g., a mouse  102 ). The mass storage devices  106  may include floppy disk drives and hard disk drives for storing an operating system. These storage devices  106  also store application programs for the system computer  99  and routines for manipulating the images shown on the image display devices  12 , 14  and for communicating with imaging devices such as a scanner or digitizer  92 , image intensifier  96 , or image data memory  94 .  
         [0069]    In one embodiment of the present invention, image manipulating routines are used to drive devices such as an image manipulator  114 , image shift calculator  118 , video synchronization and control  116 , and video display processors  120 , 122 . Many commercially available image processing packages contain the above image manipulating and calculating capabilities. This mix of devices  114 , 116 , 118 , 120 , 122  provide capabilities of shifting the pair of images (photo-couple) horizontally together and with respect to each other, and computing the various image shift distances required in the calculation of the coordinates of an internal flaw. In another embodiment, the two images can be shown on the screen of an image display device; only one image display device is required. These two images can be shifted together as well as shifted with respect to each other as desired. In this case, the two reference wires  16 , 18  will be preferentially placed near the middle of the left portion and the middle of the right portion of the screen, respectively. The two references  16 , 18  can be just two internally generated or externally drawn straight lines that will remain stationary when the images are being shifted. In a further preferred embodiment, the image analysis software has an image or pattern recognition program. This program could allow the second reference line to be automatically relocated to coincide with the second image point of a feature on a second image (e.g., the right image) once the first line is positioned to coincide with the first image point of the same feature on a first image (e.g., the left image). During such an image recognition and shifting procedure, the relative shift distance may be automatically computed and recorded.  
         [0070]    In yet another embodiment in which a minimal image manipulating capability is needed, the sole purpose of this capability is to deliver the images to their respective image display devices  12 , 14 . Additional image enhancing functions to improve the image quality (resolution, contrast, etc.) are nice features to have, but are not strictly required. The movements of these images are to be executed by the primary platform  30  and secondary platform  28 . In still another embodiment, at least one of the two image display devices has the capability of shifting the image horizontally with reference to the other image so that the secondary platform  28  (in FIG. 1(A)) can be eliminated. In this situation, the two image display devices  12 , 14  are both held in place by the primary platform  30 , which provides simultaneous horizontal movements of the two display devices. The two display devices are maintained at a constant separation at all times.  
         [0071]    It is to be understood that while certain forms of the present invention have been illustrated and described herein, the invention is not to be limited to the specific forms or arrangement of the parts described and shown.