Nityanand gopalika Patent 2


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Nityanand gopalika Patent 2

  1. 1. Patents by Nityanand GopalikaPub. No.: US 2010/0140485 A1Pub. Date: Jun. 10, 2010IMAGING SYSTEM AND METHOD WITH SCATTER CORRECTIONPub. No.: US 2009/0086911 A1Pub. Date: Apr. 2, 2009INSPECTION TOOL FOR RADIOGRAPHIC SYSTEMSPatent No.: US 7,480,363 B2Date of Patent: Jan.20,2009CONVERTING A DIGITAL RADIOGRAPH TO AN ABSOLUTE THICKNESS MAP Nityanand Gopalika
  2. 2. 111111 1111111111111111111111111111111111111111111111111111111111111 US007480363B2c12) United States Patent (10) Patent No.: US 7,480,363 B2 Lasiuk et al. (45) Date of Patent: Jan.20,2009(54) CONVERTING A DIGITAL RADIOGRAPH TO (56) References Cited AN ABSOLUTE THICKNESS MAP U.S. PATENT DOCUMENTS(75) Inventors: Brian W. Lasiuk, Spring, TX (US); 4,926,452 A * 5/1990 Baker et al .................... 378/22 Thomas J. Batzinger, Burnt Hills, NY 4,928,257 A * 5/1990 Yerkes eta!. ................. 702/40 5,243,664 A * 9/1993 Tuy ............................ 382/130 (US); Manoharan Venugopal, 5,335,260 A * 8/1994 Arnold ....................... 378/207 Bangalore (IN); Elizabeth L. Dixon, 5,377,250 A 12/1994 Hu Delanson, NY (US); Michael R. 5,565,678 A * 10/1996 Manian ................... 250/252.1 Hopple, Scotia, NY (US); Nityanand 5,698,854 A 12/1997 Gupta Gopalika, Bihar (IN); Sivaramanivas (Continued) Ramaswamy, Bangalore Kamataka (IN); Debasish Mishra, Bangalore (IN); FOREIGN PATENT DOCUMENTS Rajashekar Venkatachalam, Bangalore EP 1072861 1/2001 (IN); Vamishi Krishna Reddy Kommareddy, Bangalore (IN) (Continued) Primary Examiner-Allen C. Ho(73) Assignee: GE Betz, Inc., Trevose, PA (US) (74) Attorney, Agent, or Firm-Wegman, Hessler & Vanderburg( *) Notice: Subject to any disclaimer, the term of this patent is extended or adjusted under 35 (57) ABSTRACT U.S.C. 154(b) by 296 days. A digital radiography imaging system for acquiring digital(21) Appl. No.: 11/108,498 images of an object, and a method for transforming digital images into an absolute thickness map characterizing the(22) Filed: Apr. 18, 2005 object under inspection. The system includes a radiation source for directing radiation through a desired region of the(65) Prior Publication Data object, and a radiation detector having a plurality of sensing US 2006/0058974 Al Mar. 16, 2006 elements for detecting radiation passing through the object. Numerical data generated from each sensing element is cali- Related U.S. Application Data brated, for example by correcting for variations in radiation paths between the source and detector, by correcting for(60) Provisional application No. 60/609,934, filed on Sep. variations in the spatial frequency response (MTF) of the 15, 2004. detector, by correcting for variations in the geometric profile of the object under inspection, and by correcting for material(51) Int. Cl. contained in and/or around the object. The calibrated data is GOJB 15102 (2006.01) processed in order to generate and display an absolute thick-(52) U.S. Cl. ............................. 378/54; 378/56; 378/58; ness map of the object. The calibration procedures are 378/59 adapted for extracting a thickness map from both isotope(58) Field of Classification Search ................... 378/51, sources and X-ray tube sources. 378/54,56,57,58,59,207,55 See application file for complete search history. 23 Claims, 12 Drawing Sheets
  3. 3. US 7,480,363 B2 Page 2 U.S. PATENT DOCUMENTS 6,600,806 B1 * 7/2003 Istar ............................ 378/59 6,614,874 B2 9/2003 Avinash5,907,593 A 511999 Hsieh eta!. 6,618,464 B2 * 9/2003 Mizobuchi eta!. ............ 378/555,970,115 A * 10/1999 Colbeth eta!. ................ 378/62 6,628,744 B1 * 9/2003 Luhta eta!. ................... 378/156,137,860 A * 10/2000 Ellegood eta!. .............. 378/58 6,632,020 B2 * 10/2003 Kaufhold eta!. ............ 378/2076,148,057 A * 1112000 Urchuk eta!. ................ 378/18 6,872,949 B2 * 3/2005 Mizuoka eta!. .......... 250/358.16,175,613 B1 * 112001 Boutenko et a!. .......... 378/98.46,201,850 B1 3/2001 Heumann FOREIGN PATENT DOCUMENTS6,347,131 B1 * 212002 Gusterson .................... 378/54 JP 05099806 4/19936,377,654 B1 4/2002 Williems eta!. JP 62277542 2/19976,410,921 B1 * 6/2002 Nakazawa ............. 250/370.09 JP 2002162217 7/20026,459,754 B1 10/2002 Besson et a!. wo wo 02061455 8/20026,521,886 B2 2/2003 Aufrichtig eta!.6,570,955 B1 * 5/2003 Siffert eta!. .................. 378/54 * cited by examiner
  6. 6. U.S. Patent Jan.20,2009 Sheet 3 of 12 US 7,480,363 B2 PIPE DIAMETER 34 X-RAY STEP TUBE MATERIAL WEDGE DETECTOR FIG.3
  7. 7. U.S. Patent Jan.20,2009 Sheet 4 of 12 US 7,480,363 B2 S.D.DI ~---s.oo i 1 p 30 33 DETECTOR FIG.4A r - - - - - - S.D.D -----.! ---~~~ .................. ·· S.O.D ~------ DETECTOR 33 .................................................. 30 FIG.4B PHOTON SCATTER TRAJECTORY PHOTON INCIDENT TRAJECTORY WHERE: 0 =PHOTON SCATTER ANGLE FIG.4C
  8. 8. U.S. Patent Jan.20,2009 Sheet 5 of 12 US 7,480,363 B2 16477.40 Ci3 ~ 15960.60 I ~ ~ 15443.80 GS= a(tl 1-e -bM -J § 14927.00 >- 14410.20 ""~ ~ ~ r--.... (!) 13633.40 13376.60 ~ - - 1.0 1.1 1.2 1.3 1.4 1.5 1.6 MAGNIFICATION FIG.5
  9. 9. U.S. Patent Jan.20,2009 Sheet 6 of 12 US 7,480,363 B2 68 60 / FIG.6A
  10. 10. U.S. Patent Jan.20,2009 Sheet 7 of 12 US 7,480,363 B2 <Y 14000 0 ~ 12000 LU 10000 -J 8000 ~ C/) 6000 603 >- y=14773e- · 4000 ~ (!) 2000 R =0.9539 0 0 200 400 600 BOO FE THICKNESS (MILS) FIG.6B
  11. 11. U.S. Patent Jan.20,2009 Sheet 8 of 12 US 7,480,363 B2 RAW SPECTRUM 7026 E FIG.?A DIFFERENTIAL SPECTRUM 12657~~--------------------~ 541~~~~~~~~~~~~~ OS E FIG.?B
  12. 12. U.S. Patent Jan.20,2009 Sheet 9 of 12 US 7,480,363 B2 1 MTF 0 0 lplmm n FIG.8
  13. 13. U.S. Patent Jan.20,2009 Sheet 10 of 12 US 7,480,363 B2 91 ~92 93 90 FIG.9
  14. 14. U.S. Patent Jan. 20, 2009 Sheet 11 of 12 US 7,480,363 B2 11678 9135 8742 s E FIG.1 0 12216 9164 8404 s E FIG.11
  15. 15. U.S. Patent Jan.20,2009 Sheet 12 of 12 US 7,480,363 B2 FIG.12
  16. 16. US 7,480,363 B2 1 2 CONVERTING A DIGITAL RADIOGRAPH TO and predict if and when a failure will occur. The more com- AN ABSOLUTE THICKNESS MAP plete the inspection information is, the more certain the con- clusions will be since less reliance must be made on extrapo- CROSS REFERENCE TO RELATED lation and estimation. However, a fully condition-based APPLICATION maintenance program is difficult to deploy owing to the lack of availability of a complete quantitative survey of asset con- This application claims the priority benefit of U.S. Provi-sional Patent Application Ser. No. 60/609,934 filed Sep. 15, ditions. Furthermore many of the different inspection and2004. monitoring modalities utilized in evaluating the fitness for 10 service of a plant are unable to give a quantitative assessment FIELD OF THE INVENTION of condition over large areas. Digital imaging systems are becoming increasingly wide- The present invention relates generally to radiographic spread for producing digital data that can be reconstructedimaging systems, and more particularly to methods and algo- into useful radiographic images. An exemplary system isrithms for characterizing the condition of containment ves- 15 described in our prior U.S. application Ser. No. 10/646,279,sels and fluid transport piping installations in a quantitative filed Aug. 22, 2003, now U.S. Pat. No. 6,925,145, the disclo-(and qualitative) fashion over large areas. Specifically, the sure of which is hereby incorporated by reference herein. Inalgorithms and methods of the present invention are used to addition, ultrasound (UT) technology gives very accurateconvert a digital measure of a transmitted X -ray spectrum to measurements of material (i.e., wall) thickness. However, UTan absolute measure of material thickness with high accuracy 20 technology is in general limited to measurements over areasand precision. The imaging system developed in accordance of point like dimensions. While this is sufficient for uniformwith the present invention is adapted to deliver an X-raysource and detector to a pipe or vessel installation in a well general corrosion, localized corrosion and damage mecha-defined geometrical relation, without using the pipework nisms that can produce such features as deep narrow pits anditself as a support structure. 25 steep gradients of material erosion, are difficult to detect and measure accurately without the use of an imaging based BACKGROUND OF THE INVENTION modality. This is becoming less of an issue with the introduc- tion of phased array ultrasound which allows UT data to be Most industrial complexes utilize piping and containment acquired over a more extended area. However, this fundamen-vessels to transport and deliver fuel, water, and other neces- 30 tal technique is still a contact modality and is thus restricted tosary solid and fluidic chemical materials. In installations, materials, and conditions, that support transmission of acous-such as oil and gas fields, power stations, petrochemical tic energy. UT measurements are sometimes difficult toplants, etc., the fluids and the environments in which they deploy since a good acoustic coupling must be made betweenreside can be quite hostile. High temperatures and pressures the transducer and the material under inspection. As such, anyexist in the presence of volatile, toxic, and corrosive chemical 35 thermal insulation that is present on piping or vessels must bemixtures. As these substances are transported throughout a removed, or an inspection port need be installed so that directplant, they can cause both mechanical as well as chemical access to the surface is available. Furthermore, piping that isdegradation of the piping and vessel infrastructure. The dam- insulated is quite often at an elevated temperature, and UTage is seen in terms of physical material loss due to corrosion sensors may not be able to function efficiently under suchand erosion or a weakening of the infrastructure due to 40 conditions. Another problem with acoustic inspection meth-increased stress. Processes which cause material loss, ods is that multiple measurements must be made of the iden-degrade the structural and mechanical integrity of plants. In tical region over an extended period of time in order to trackorder to ensure safe and reliable operating conditions, suchplants and facilities must be continuously inspected and the evolution of these defects. These measurements havemonitored. significant compromises in the ultimate precision that can be 45 The key to maintaining reliability of an operating industrial attained, and such measurements carmot be made in real-timecomplex is to develop and implement a regularly scheduled in order to correlate with plant operating conditions. In manymaintenance program. Minimal requirements that define cases a non-contact modality, like radiography, is used tobasic safe operating procedures for maintenance and inspec- screen for regions where more detailed wall thickness infor-tion are legislated in most areas of the world. However, these 50 mation is required.standards are not aimed at maintaining peak operating effi- Other long term monitoring techniques, for example cou-ciency of the plant, nor are they specified to ensure maximal pon evaluation, are known to provide information over aup-time for plant operations. Plant efficiency and up-time are larger portion of a plant. However it is almost impossible toimportant considerations in establishing a maintenance plan correlate coupons with specific plant operating conditions inas there is a direct link to commercial profitability. Optimi- 55 real-time or to identify small regions of enhanced or acceler-zation of a maintenance plan requires the acquisition and ated corrosive activity. This technique is sensitive to condi-detailed analysis of a multitude of both qualitative and quan- tions which are generally integrated over long time scales,titative data. The analysis is done to facilitate an assessment and large areas. Specific information about small areas are notof the condition of the plant infrastructure and determine the monitored well with this technique. Furthermore, unlike thefitness for service of specific components, vessels, pipes, etc. 60 other non-destructive testing (NDT) methods, installationOnce an evaluation is made, necessary adjustments can bemade to the operating conditions of the plant and/or corrosion and extraction of a coupon is an intrusive measurement.prevention program. Film based radiography systems suffer from a different The cost and quality of the decisions is primarily driven by problem. Although the raw data captured in a radiographthe precision, accuracy, and completeness of the measure- 65 gives information over an extended area, it has been veryments in the inspection. The better the precision and accuracy difficult to extract quantitative information from the grayof the measurement, the better one can assess the condition, scale shading or rendering from a piece of film. Furthermore,
  17. 17. US 7,480,363 B2 3 4the small dynamic range of film means that wide variations in the image can be displayed in a manner similar to its filmmaterial thickness cannot be imaged effectively in single based renderings. As with film-based radiography, details ofexposures. The technique utilized in extracting a material the structure of the object as well as dimensions of featuresthickness is to compare it with a calibrated shim or wedge of can be determined, in similar manners; that is, by comparisonmaterial ofwell-defined thickness. The general use of radi- to standard objects with known dimension. However, givenography has been to utilize its property of being a non-con- access to the discrete numerical data of a digital image, pro-tract image based measurement to identifY locations where cedures and algorithms can be automated to improve thefeatures or defects exist. Since radiography is sensitive to the speed, accuracy, and convenience of the path integral of the material between the source of radia- These algorithms utilize well-known automated thresholdtion and the detector plate, the different contrasts and shading 10 detection and filtering algorithms to detect the spatial extentare used to extract qualitative information regarding such of features by quantifying the regions of contrast changefeatures and defects in the radiograph; that is, a lack of fusion within the weld, or cracks show up as a variation in the gray shading. Others have utilized digital radiography (DR) technologyQuantification of this effect is very difficult. If a feature or to compare a numerical gray scale value over a line or profiledefect is identified, the location is usually measured with an 15 to a gray scale produced by a calibrated shim or wedge ofalternate modality, such as ultra -sound, to extract a true quan- known thickness. Such methods allow one to estimate thetitative measurement. value of a material thickness. However the precision and While the quantitative behavior of the gray-scale is typi- accuracy of such a procedure is compromised in all but thecally difficult to interpret, the dimensioning capability of most simple cases where the impulse (or thin material)measuring the spatial extent of a feature is quite easy because 20 approximation is valid. Many have taken the path of devel-radiography is image based. As such, the size and dimension oping and patenting digital analogs of older methods, such asof a feature in the plane of the image can be easily deduced by edge detection to facilitate automated dimensioning and tan-comparing the feature to a reference object of known dimen- gental radiography, for example as disclosed in U.S. Pat. No.sion. The precision of such a measurement is determined by 6,377,654. However, limitations still exist in the applicationthe spatial resolution of the detector (i.e., film, imaging plate, 25 of radiography to extract precision absolute measurements ondetector, etc.), and the knowledge of the geometry of the thicknesses over large areas.source, object and film orientation. This is the fundamental Thus, there exists a strong need to develop a method forprinciple behind the extraction of wall measurement thick- quantitatively transforming a complete radiographic imagenesses with the technique of profile or tangental radiography into an image representing the absolute thickness measure-(radioscopy). In this technique, the wall thickness is surmised 30 ment, i.e., thickness map, of the taking a radiographic exposure tangental to the pipe, orvessel. A profile of the wall thickness is imaged and delimited SUMMARY OF THE INVENTIONby a contrast difference in the radiograph, which can be usedto dimension the wall thickness. A simple correction is made A digital radiography imaging system for acquiring digitalfor the shot magnification as defined by the relative distances 35 images of a physical structure, and a method for transformingbetween the X-ray source and detector, and the X-ray source digital images into an absolute thickness map characterizingand object under inspection. Correction by this factor allows the object under inspection. The imaging system includes anthe dimensioning of an object in absolute units to a high X -ray source for directing X -rays through a desired region ofprecision. Unfortunately this technique is restricted to the structure and an X-ray detector having a plurality ofextracting the wall thickness at the position perpendicular to 40 sensing elements for detecting X-rays passing through thethe tangent of the pipe, and a complete series of shots need be structure. Numerical data generated from each sensing ele-taken to cover the complete area of the pipe, for example as ment is calibrated, for example by correcting for variations indescribed in U.S. Pat. No. 6,377,654. X-ray paths between the source and detector, by correcting The advent of digital technology has significantly for variations in the spatial frequency response i.e. modula-increased the capabilities of radiography, although the fun- 45 tion transfer function (MTF) of the detector, by correcting fordamental technique of transmission radiography has not variations in the geometric profile of the object under inspec-changed-that is, an X-ray radiation source illuminates an tion, and by correcting for material contained in and/orobject under inspection. Typically, a radiation detector is around the object. The calibrated data is processed so as toplaced behind the object so that it measures the X-ray spec- generate and display an absolute thickness map of the object.trum transmitted through the object. The intensity of the 50 The calibration procedure is adapted for extracting a thick-transmitted spectrum is modulated by the material structure ness map from both isotope sources and X-ray tube sources.and density. The degree of intensity variation on the detector,or contrast variations, can be used to extract information BRIEF DESCRIPTION OF THE DRAWINGSabout the material structure and integrity. With film radiog-raphy, the interpretation is generally qualitative. However, 55 FIG. lA is a flow diagram describing a procedure fordigital detectors provide a discrete numerical value that gives generating a thickness image from a gray scale image ina measure of the transmitted X-ray flux on each individual accordance with an embodiment of the invention.sensing element, or pixel. This numerical value is propor- FIG. lB is a flow diagram describing a procedure for gen-tional to the number of photons transmitted through the mate- erating a reference thickness map, and comparing same torial under inspection and incident on the detector. The size 60 acquired thickness image of FIG. lA.and shape of the detector pixels, or sensing elements are a FIGS. 2A and 2B illustrate how the heel effect creates asignificant geometrical parameter, which along with the variation in measured intensity across the beam cone whenresponse of the detector components (i.e., material, electron- comparing different energies (El and E2, where El <E2) ofics, etc.) determine the spatial resolution and sensitivity of the air images, where the amount of filtering of the X -ray beamdetector. This determines the minimum size of a feature that 65 fan through the anode depends on the energy of thee-beam.can be resolved. The discrete numerical value of the trans- FIG. 3 illustrates a set up configuration to model the scat-mitted X-ray flux can then be mapped to a gray scale so that tering profile from a double-walled object.
  18. 18. US 7,480,363 B2 5 6 FIG. 4A illustrates the higher flux of photons accepted by other measurable parameters of such physical objects couldthe detector under lower geometric magnification, where also be mapped without departing from the broader scope ofMagnification=SDD/SOD. Photons in the full forward hemi- the present invention.sphere are accepted. Referring to FIG. 1A, in step 101, a digital radiograph FIG. 4B illustrates the lower flux of photons accepted by image of the pipe or other object under inspection is obtainedthe detector under higher geometric magnification, where after the detector response has been calibrated with a flat fieldMagnification=SDD/SOD. Photons in a subset of the forward image. The flat field image produces the individual channelhemisphere are accepted. (i.e. pixel) gain values. In step 102, calibration data, which FIG. 4C illustrates the scatter angle of a photon from its measures the digital detector response to a series of wellincident trajectory. The region -90° to +90° defines the full 10 known thicknesses is acquired. The calibration data is thenforward hemisphere. applied to the raw ADC map utilizing a non-linear interpola- FIG. 5 is a graph illustrating a gray scale translation as a tion and extrapolation algorithm. In step 103, corrections arefunction of magnification. applied to the raw calibration which includes scattering FIG. 6A illustrates a center-line-path overlaid on the gray effects, undercut, geometry, finite spatial frequency response,scale image of a step wedge. 15 etc. to generate a thickness calculation. In step 104, the thick- FIG. 6B is a graph illustrating the correlation of gray scale ness of the pipe or object under inspection is calculated andboundaries ofFIG. 6A to material thickness parameterized as put in a format that allows rendering on a display.a single exponential. FIG.1B shows a procedure where the thickness map can be FIG. 7A is a graph illustrating the gray scale of the step compared to a nominal reference object. The reference imagewedge as a function of the position down the center line 68 of 20 can be calculated analytically, or acquired from a sampleFIG. 6A. pipe. The initial step 111 generates a thickness profile from a FIG. 7B is a graph illustrating the differential spectrum of reference pipe (i.e. object) given specific geometry, magnifi-FIG. 7A where the boundaries of the steps as seen in FIG. 6A cation parameters. In step 112, the reference object is alignedare identified as peaks. with the actual inspection object as rendered in step 104. In FIG. 8 is a graph illustrating a typical modulation transfer 25 step 113, a comparison of the thickness on a pixel-by-pixelfunction (MTF) curve as a function of spatial frequency, here basis can then be made. This is done in step 105. In the finalin line pairs per millimeter (lp/mm). step 106, an image (color coded or otherwise) can be gener- FIG. 9 is a front view of a sample fluid vessel with a series ated with such that a view of the defects can be enhanced.of holes used to demonstrate an imaging capability of an In order to extract an absolute thickness measurement fromembodiment of the invention. 30 a radiograph, a flat field image must first be acquired. A flat FIG. 10 is a graph illustrating a gray value distribution field image is an image where the response of each individualacross the series ofholes of FIG. 9 without MTF correction. pixel (i.e., the number of counts registered by the electronics FIG. 11 is a graph illustrating a gray value distribution of the channel) when exposed to a radiation source, is uniformacross the series of holes of FIG. 9 with MTF correction. throughout the area of the detector panel. In an exemplary FIG. 12 is a sketch illustrating ray interactions with a 35 detector panel, for example our GE DXR 250RT detectortubular pipe geometry. panel, the exceptionally low noise electronics yields a varia- tion from a mean value of less than 0.5%. Although it is DETAILED DESCRIPTION OF EXEMPLARY obviously desirable to attain as low a variation in the signal as EMBODIMENTS possible, this technique is not limited to such low noise detec- 40 tors. The exemplary embodiments of the present invention will In order to measure a flat field image, an offset (i.e., null)be described below with reference to the accompanying image must be acquired. The offset image is used to establishdrawings. In the following description, well known functions the detector response to a null or zero intensity X-ray spec-or constructions are not described in detail to avoid obscuring trum. Thus, any signal that is registered in the detector is duethe invention in unnecessary detail. 45 to extraneous sources, most notably due to dark or leakage The motivation for the invention is to utilize radiography currents in a digital detector. This is the intrinsic response tofor quantitative inspection purposes, rather than its primary the detector merely being powered. This offset value must beuse as a qualitative screening tool. Instead of using radiogra- subtracted from any image taken when the detector is exposedphy as a screening tool that serves to identifY features or to radiation so that a true measure of any radiation can bedefects, our aim is to use radiography as a primary inspection 50 separated from the intrinsic properties of the detector.modality that is capable of estimating wall thicknesses at a Once this offset image is established, the detector can belevel competitive with state of the art ultra-sound technology. exposed to a radiation dose, with no object attenuating theIf the level of absolute precision in the radiographic measure- beam between the source and detector. It is known that thement is 2-10%, radiography has the potential of yielding more source should be fixed with respect to the detector in such acomplete information during an inspection because it is an 55 way that the line defining the minimum distance between theimage-based modality which can cover a large area. However, source and detector falls at the centroid of the detector. Inde-in order to realize the prescribed precision, a detailed proce- pendent of whether the radiation source is an X-ray tube, ordure involving calibration and corrections procedures must radioisotope emitting X-ray or gamma radiation, the responsebe implemented. The following paragraphs detail the meth- of the detector should produce a maximum signal (i.e., maxi-odology and claims put forward in the disclosure. 60 mum number of counts) at the point intersection the shortest Referring now to FIGS. 1A and 1B, there is shown a pair of line from the source to detector. The response or count levelflow charts summarizing improved methods for generating a should fall off in a radial pattern in the detector consistentthickness map in accordance with the present invention. It is with an inverse square law reflecting the source to detectorimportant to note that although the invention will be distance. As such, the pixel value counts will fall off as onedescribed with reference to acquiring a thickness map of 65 moves out from the center of the detector panel. Using thehollow pipeline objects, it is understood that the invention is ratio of the pixel values with respect to the maximal pixelalso applicable to many other types of objects, and that many value at the center of the detector, one can calculate a relative
  19. 19. US 7,480,363 B2 7 8gain value for each pixel. The inverse of this gain value can be Accordingly, the gain factors required to produce a flatused to multiplicatively scale the response of each pixel in field image must be determined for each particular tube andorder to equalize the response of each pixel to incident radia- for each particular end-point energy used. The change intion. counts across the detector as a function of end-point energy While this is a self-contained procedure for radiation from can not only be parameterized as a simple linear function, but can be determined analytically given the anode angle, a prop-an isotope, there are complicated factors which occur for erty oftheX-raytube, and the cone angle oftheemittedX-rayradiation generated from an X-ray tube. With reference to spectrum. This eliminates the need to acquire a "flat fieldFIG. 2, an X-ray tube produces radiation by accelerating an calibration spectrum" for every single end-point energy thatelectron beam produced at a cathode to a specific energy and 10 is used. It is noteworthy that without correction of this effect,depositing the beam into an anode, which is cut at an angle. a non uniform response to a specific thickness will be seenThe specific energy defines the "end-point" energy of the across the area of the detector. Once a nominal flat field imageemitted EM spectrum. In FIG. 2A, the energy is El. In FIG. is acquired, a calibration from a known thickness of material2B, the energy is E2. For this illustration, El is less than E2. can be acquired, as described below.Usually this anode is made of tungsten as it is a highly effi- 15 As shown in FIG. 3, a step wedge 33, or series of shims withcient stopping material and its high melting point allows large known material thickness are placed at a nominal positionelectron beam currents to be used. Electromagnetic (EM) between the source 30 and detector 34, although in an exem-radiation is produced in bremmstrahlung ("braking") pro- plary embodiment the geometry chosen will mimic similarcesses, where electrons are decelerated and stopped in mate- geometry of the pipe or vessel placement. The step wedgerial. A continuous spectrum of radiation is produced contain- 20 models a variation in thickness for the back wall, while theing all the energies from zero, all the way up to the energy of material31 nearest the X -ray tube is placed there to model thethe electron beam, the end-point energy. front wall. The detector response is measured as a function of Due to the fact that radiation is absorbed in different frac- the magnification of the object, which is calculated at thetions as a function of energy, further corrections must be made system iso-center 32. If the geometry is identical between thefor tube-based radiation to account for the spectral composi- 25 calibration set-up and the actual imaging geometry, no cor-tion. Since the anode is cut at an angle, the resultant EM is rection for the effect of the beam scatter will be necessary, asemitted in a cone beam perpendicular to the direction of the it is accurately parameterized into the thickness map. Theelectron beam. Because of the construction of the anode, correction for scattered radiation will be discussed later. If thethere is a spectral difference in the EM radiation profile as a shims do not project a shadow on the detector that covers thefunction of position in the cone. The part of the cone that is 30 complete detector area, it is necessary to shield or mask theemitted on the open side of the anode does not have to pass areas of the detector that will be exposed to the un-attenuatedthrough as much anode material and is therefore attenuated beam. This is necessary because at sharp material boundaries,less than the part of the spectrum that must pass through a scattering effects of the EM radiation scatter as well as inter-significant thickness of material at the anode. Such differen- element scatter and under-cutting will reduce the effect of thetial filtration due to the varying path length of the material 35 transition due to strong scatter from the object and back-through which the EM radiation passes is responsible for the scatter from the detector volume. As such, the material thick-position dependence of the spectral contribution in the emit- ness near the edge of the objects will appear to transmit moreted EM cone. If a detector has even a slight proportional radiation than regions away from the edge. If this effect is notresponse to the energy of the radiation, this energy depen- dealt with, an inappropriate correlation between the transmit-dence in the beam will show up as an increasing number of 40 ted radiation, registered by the detector pixels will be madecounts across the detector. The rate at which this change in with the material thickness. While this correlation can becounts occurs across the detector is strictly a function of the made experimentally, this effect can also be analytically cal-X-ray tube (i.e., anode angle) and the end-point energy of the culated knowing the type of material being investigated, theX-ray spectrum. distances between the source, detector, and object, and the Referring again to FIGS. 2A and 2B, the amount of pen- 45 geometry of the object. As with the flat field image acquisi-etration of thee-beam into the X-ray tube anode depends on tion, the procedure is slightly more complicated when utiliz-the energy of the beam. As shown in FIG. 2B, the e-beam ing an X -ray tube rather than an isotope because of the neces-penetrates into the anode. The higher the energy, the more sity to convolute the numerous spectral energies and the factpenetration. As the penetration increases, the amount of fil- that the absorption and scattering cross section (i.e., probabil-tering across the beam fan changes. That is, the side of the 50 ity) depend on the EM energy.beam fan that is closest to the open side of the anode has lessfiltering (i.e., it does not have to traverse the material in the Scatter and Magnificationanode), and therefore more flux. As such, the profile of a flat As mentioned above, a method for the correction of scat-field image changes depending on the energy of the beam. tered radiation will now be described. It is to be noted thatWhile the same noise level is seen in the detector at a different 55 although this method was used at a specific magnification, itX-ray tube energy, a systematic rise is seen across the detec- can be generalized to be applicable at any arbitrary magnifi-tor. This is due to the difference in X-ray spectral shape due to cation. As the magnification is changed, the total integratedthe shape of the X-ray anode. This change in spectral shape is amount of scattered X -ray radiation that is within the detectorknown as the heel effect. In order to maintain control of the acceptance will change with respect to the total amount oferror on the extracted thickness, the variation in gray scale 60 primary (i.e., unscattered) radiation.must be removed. This can be done in two fashions: 1) acquire In order to generalize this procedure for use at arbitrarythe flat field image at the same energy that the radiograph of magnification, the ratio of primary to scattered radiation mustthe object to be inspected will be acquired, or 2) remove the be determined as a function of magnification. This will allowsystematic variation of the detector gray scale count with a a single calibration radiograph to be scaled for the appropriatecalibration curve. This can be directly measured or param- 65 geometrical shooting conditions. Otherwise, a calibrationeterized to correct for the effect, and produce a true flat field image at the appropriate magnification must be taken for eachimage. specific magnification used.
  20. 20. US 7,480,363 B2 9 10 The amount of scattered radiation that is within the accep- object, specifically a pipe, and extract a meaningful correla-tance of the detector will greatly alter the value of the gray tion with a calibrated step wedge. The step wedge models ascale that the detector reports. Scattered radiation results variation in thickness for the back wall, while the materialwhen X -rays are not fully absorbed in the material, and scatter nearest the X-ray tube is placed there to model the front wall.with atomic electrons. At energies relevant to us, this is The detector response is measured as a function of the mag-known as Compton scattering. This scattering process nification of the object, which is calculated at the systemchanges the trajectory of the photons. Those skilled in the art iso-center.appreciate that this is an important consideration in imaging The Step wedge models a variation in thickness for thesystems as it has the effect of increasing the size of the source,which decreases the sharpness of any edges and boundaries. 10 back wall, while the material nearest the X -ray tube is placedIt is known that the differential scattering cross-section (i.e., there to model the front wall. The detector response is mea-scattering probability) for photon scattering through an angle sured as a function of the magnification of the object, which8 (FIG. 4C) due to Compton-like processes is given by a is calculated as the system iso-center. A parameterization offormula known as the Klein-Nishima formula: the gray scale (GS) is done for each step thickness (t) as a 15 function of magnification (M). In this specific case, a func- tional form, sometimes referred to as the "logistic" model is 2 2 2 used, as seen in equation 2, where a(t) is the gray scale as a dia- 2( 1 ) ( 1 + cos 8)( cl(1- cos8) ) dlfl = Zro 1 + a:(1- cos8) - - 2 - 1 + ""(1:-+-co-s" 2 8:::-)o:-[1_+_a:--:(-:-1---c-os--;e"")] function of thickness at a fixed magnification, and b is a constant dependent on the material and SDD. 20where Z is the atomic number of the scattering center, r0 , is theclassical electron radius, and a is Ejmec 2 , where Eo is the a(t) (eqn 2) GS = 1-e-bMenergy of the incident photon, and me is the mass of theelectron, and c is the speed oflight. The Klein-Nishima for-mula enables us to calculate the fraction of photons that are 25 FIG. 5 is a graph illustrating the gray scale value of fixedscattered into a solid angle (dQ=r sin 8 d8 d<jl) given the thickness as a function of magnification for the geometry ofphoton energy. Given an initial and final energy, the scattering FIG. 3. In the limit, as the magnification tends to infinity, theangle 8 and probability of scattering can be determined. gray-scale of a given thickness (t) approaches the asymptotic The highest probability scattering is for the photons to only limit a(t). This corresponds to the smallest amount of scat-slightly change direction, i.e., small angle scatter (8). The 30 tered radiation measured by the detector (i.e., smallest accep-probability decreases as the size of the angular scatter tance cone). A family of such curves for different thicknessesmcreases. can be generated to give a two-dimensional surface, which Magnification of the object is defined as the ratio of source- provides a gray scale translation to material thickness as adetector distance (SDD) divided by the source-object dis- function of magnification. This method allows an estimate oftance (SOD). In other words, Magnification=SDD/SOD. For 35 the effect of scatter for different geometries.a shooting geometry with a magnification of unity (i.e., An alternate method which does not rely on effective cali-SDD=SOD), the object is in an orientation directly in front of bration methods has also been used. In this method, the frac-the detector. As such, any photon that scatters within theforward cone (±90° from the incident normal) will register in tion of scattered radiation in the forward cone is calculatedthe detector (see FIGS. 4A, 4 B and 4C). As best shown in FIG. 40 according to the Klein-Nishima formula. In order to do this4B, as the geometric magnification increases, i.e., as the calculation, the geometric set-up is required, for example,source-object distance (SOD) decreases with respect to the source-detector distance (SDD) and source-object distancesource-detector distance (SDD), the fraction of scattered (SOD), as well as the dimensions of the detector. Using thisradiation that intersects the detector is reduced. FIG. 4A information, the geometry of the acceptance cone of theillustrates lower magnification, and FIG. 4B illustrates higher 45 detector can be determined from a completely analytical per-magnification. That is, the geometric acceptance of the scat- spective.tered radiation decreases as magnification increases as shown Using this cone, the fraction of scattered radiation that fallsin FIG. 4B. within this region can be analytically calculated from the The physical effect of this is that the amount of radiation Klein-Nishima formula to determine the fraction of radiationthat the detector measures, which is proportional to the gray 50 that falls within the acceptance cone. For a mono-energeticscale, will decrease as the geometric magnification increases. X-ray energy this is a single calculation. For an X-ray spec-The detector response, or measured gray scale, decreases as trum, all relevant X-ray energies must be taken into account,the geometric magnification of shooting parameters weighting each energy by the photon fluence.increases. As described above, this can be explained by the For a completely mono-energetic source, which is the casefact that the detector subtends a smaller solid angle of the 55 for some radio-isotopes, such as Cs-137, a straight-forwardX-ray field emanating from the object, as seen in FIG. 4B. correlation can be made between the material thickness andReferring again to FIG. 4B, as the magnification increases, a the number of counts registered by a detector pixel. This willsmaller fraction of the geometric acceptance is covered, be very close to the functional form given by the Lambert-which reduces the measured gray scale value. Beer law which states that in the thin material approximation, This was parameterized in two different distinct methods. 60 the number of transmitted photons decreases in number from The first was an effective calibration where we would the original un-attenuated flux, scaled by the exponential of ameasure the detector response with a step wedge shielded by quantity defined by the product of negative one, times thean appropriate amount of material, in order to mimic the attenuation coefficient, times the material path length. Com-object under inspection. In our application this is specifically plications to this elementary formula for mono-energeticdone to model a pipe geometry with a double-walled object. 65 sources occur for thicknesses beyond the order of several! 00 Referring again to FIG. 3, there is illustrated a set-up to mils, where the thin materials approximation does not holdmodel the X-ray scattering profile from a double walled because of the high probability of multiple interactions.
  21. 21. US 7,480,363 B2 11 12Moreover, the EM radiation cannot only be absorbed, but it tor at the edge or boundary of an object which can negativelycan scatter as well. While the scaling of the Lambert-Beer law impact the integrity of the correlation between measured grayby the well known build-up factor can parameterize some of scale and material thickness.these interactions, the effect of scatter can either be modeled FIG. 7A is a graph illustrating the raw spectrum of the grayby Monte Carlo simulation or measured experimentally. scale image, showing the steps in the gray scale pattern. The In order to describe the behavior with the spectrum pro- raw image is processed by a low pass filter in order to reduceduced from an X-ray tube, the spectral energy dependencies the noise. In FIG. 7B, the data is differentiated in order tomust be folded into these calculations. This is necessary detect the step boundaries which can be identified by thebecause the attenuation coefficient is a function of the photon strong peaks in the differential spectrum of FIG. 7B. Theenergy, and the spectrum is not nniformly attenuated by a 10 distance between successive peaks can be used to dimensionspecific material thickness. This effect is called beam hard- the steps and define the orientation of the step wedge.ening since the low energy spectral contributions are Referring now to FIG. 6B, it is apparent that the correlationabsorbed to a higher degree than the high-energy compo- of gray scale to thickness shows an approximate exponentialnents. This produces a higher mean spectral energy, or harder behavior. However, higher order effects, multiple interactionsspectrum. This beam hardening can be dealt with by allowing 15 and scatter effects show that a single component exponentialfor a multi-component exponential parameterization of the is a poor approximation over a large range of thicknesses asthickness to detector response correlation. By measuring the exemplified by the mismatch (605) at point 604. This isdegree of X -ray absorption for a wide range of material thick- because the correlation of gray scale to thickness displays annesses, a multi-component exponential fit can be used to fit increasing uncertainty with thickness. This is due to a higherthe data and parameterize the beam hardening. It is also 20 fraction of scatter with respect to primary radiation, due topossible to use a spline or semi-log interpolation to approxi- multiple interactions. To increase precision, a spline fit is usedmate the effect of a multi -component exponential behavior. to interpolate the data. It is also used to generate a model for This concludes the procedure to generate the calibration extrapolation beyond the data A procedure for automating the correlation of the gray With the large dynamic range of the GE digital detectors, itscale of the radiography with the thickness of the material will 25 has been fonnd that we are easily able to acquire a usablenow be described. signal over a range of ±1h" on a 1-3 inch sample of steel. This allows us to utilize several different thicknesses. In an exem- Referring to FIG. 6A, an image 60 of an object with several plary case, 8 different thickness samples, which differ indiscrete thickness regions 61-67 (i.e., steps of a step wedge) is thickness by lfs" were used. In order to deal with a case whenacquired. The object can be placed in any orientation, as long 30 less dynamic range is available, a Pb or other highly attenu-as the object is contained in the field of view of the detector. ating marker 602, which may be a Pb letter or any standardThis method has been defined using a geometric magnifica- IQI with embossed digit, is used as a marker at the edge of ation of nnity, but it does not preclude any other magnification specified step or shim (usually the center step). An edge-line-from being used. In order to maximize image quality (IQ), a path 69 is then calculated proximate an edge of the object, andlead (or any other highly X-ray attenuating material) mask 35 the pixel values are extracted to produce a function of pixel(not shown) may be used to cover the edges of the shims or value versus pixel number, as explained above. The functionwedge. This will effectively reduce the amonnt of under- is differentiated and compared with the differentiated fnnc-cutting around the edges of the object. A simple edge detec- tion down the mid-line of the step wedge. If no change istion algorithm is utilized to find the boundaries and orienta- found, the edge-line-path is recalculated so it is moved closertion of the object. Edges will be generated at the bonndaries of 40 to the centerline of the step wedge. This algorithm is appliedthe various thickness steps, intermediate step separations and iteratively until a difference, attributable to the presence ofother sources. A Hough transform is then used to map these the Pb marker 602 is detected. Once the presence of theedges to straight lines. Since the Hough transform generates marker is detected, a positive identification of the step numberduplicate lines, suitable distance criteria are used to identify can be made.those, which correspond to the bounds of the step wedge. 45 Now, given that the number of steps (i.e., discrete material As shown in FIG. 6A, a center-line-path 68 down the thickness) and step dimensions are known, an area to samplemiddle of the step wedge can be overlaid and the gray scale as the gray scale of each discrete thickness step can be defined.a function of position on the center-line 68 determined. The Several geometries have been used, however the best resultsbonndaries of the step wedge, as defined by the previous have been obtained when the inner central 25% of the stepoperations allow us to automatically extract this relationship. 50 area is utilized as shown in FIG. 6A. The mean pixel value ofIn order to reduce any edge effects, the gray scale (GS) value all the pixels in this area is determined as well as the standardof the pixels at the middle 1/4 of the step can be averaged. The deviation. The mean pixel value is then associated with thevariance of the detector pixel values over this region can be thickness of the step. This process is repeated for each stepused to assign an uncertainty to each value. Note the chosen that is identified and an effective fnnction 603 of gray scalegeometry of the central region of each step corresponds to 55 versus step thickness is produced. Naively, one would expectabout 25% of the inner area as illustrated by the squares 601 this to follow a Beers law exponential dependence, but asoverlaid on the gray scale pattern. This keeps edge effects to exemplified by the mismatch 605 at point 604, this is not thea minimum and maintains a good estimate of the gray scale on case owing to several reasons, including the presence of mul-each step. tiple interactions, scattering, finite spatial resolution, etc. Once the longer boundaries of the step wedge are identi- 60 However, as mentioned above, to increase precision, thefied, the center-line-path 68 is calculated down the length of pixel value correlation with the material thickness along withthe image at the mid-point of the width dimension and over- the associated error can be used effectively to extract thelaid on the image. The pixel values along the line 68 are then thickness of an arbitrary thickness of the same material byextracted and put into a functional representation giving the utilizing a spline fit to interpolate (or extrapolate) the tabularpixel value versus pixel number. Using a line path down the 65 data. It should be noted that we have also parameterized thecenter of the wedge allows us to exclude major effects of data into a multi -component exponential curve in order to getunder-cutting and inter-element back-scatter from the detec- a true fnnctional representation with equal success. By utiliz-
  22. 22. US 7,480,363 B2 13 14ing the error on the data points to weight the data point in a counts registered in a pixel) will depend not only on thefitting algorithm, such as least squares, or chi-square regres- thickness of material, but also on the spatial extent of thesion, a useful precision can be placed on the derived quantity, object. An object of a given thickness will have a differentwhether interpolated or extrapolated. response in the detector if it covers a large detector area as Note that utilizing this method, generalizations can be compared to an object with identical thickness but coversmade to other shooting conditions, including exposure, only a fraction of a pixel. The effect of this phenomenon isenergy, magnification, material thickness, etc. For instance, that the contrast of the response is modulated due to thethe radiation field falls off as 1/r2 , so the gray scale/thickness spatial response of the detector. Mathematically, the spatialcan be calculated at any arbitrary distance by the following frequency response of a detector can be quantified by theparameterization: 10 modulation transfer function (MTF). The MTF quantifies how well an imaging system responds to objects of varying spatial extent. Methods for determining the MTF have been described in the literature and are well known. In the case of a perfect detector, the MTF would have a 15 constant value independent of the spatial frequency. By con- vention, the MTF is normalized to a maximum value of 1 at 0where GS 0 is the gray scale of a specific thickness of material spatial frequency. However, real detectors have a finite spatialat a reference distance ro where ro measures the distance resolution and therefore the MTF will decrease with increas-between the source and detector (i.e., source-detector dis- ing spatial frequency. There are well known methods fortance or SDD). GS 1 is the gray scale expected for the same 20 determining the MTF of a detector, for example, as disclosedthickness under the same shooting parameters but at a source in U.S. Pat. No. 6,521,886, the disclosure of which is incor-detector spacing of r 1 . Likewise the gray scale (or thickness) porated by reference herein. Broadly speaking, the MTF canof an object can be scaled for the effective exposure of the be determined by imaging a sharp edge of highly opaqueradiograph. The gray scale can be scaled by a linear factor material. From such an image, the average pixel response ascalculated from the ratio of the exposures. The exposure of a 25 a function of position, in a direction perpendicular to the edgeradiograph is given as a product of the tube current (I) and the can be extracted. This function is called the edge spreadexposure time (t), or, for an isotope, the source activity and the function (ESF). In the ideal case this would be a step functionexposure time. For example, the gray scale is scaled as: with an infinite slope at the transition point. Differentiating the ESF will give a function, which is called the line spread 30 function (LSF). Again, in the ideal case, the LSF would be a delta function with zero width. In the case of a real physical detector, the LSF will have a finite width. The narrower the width of this function, the larger the MTF will be. Taking the Fourier transform of the LSF results in a frequency decom-where the gray scale at exposure 1 can be derived given the 35 position of the LSF. In the case of a delta function, all spatialgray scale and exposure of a reference radiograph. frequencies are equally populated or weighted. If a finite A scaling can be deduced as a function of tube endpoint width is measured in the LSF, as will be the case for any realenergy (kVP), where the tube output varies in a fairly well detector, this is an indication that the high frequency spatialdefined functional value as (kVPt where n is a power components are attenuated. As such the MTF function willbetween 2-3. However, experiments with several tubes found 40 begin to decrease as the spatial frequency is increased.this scaling factor to be dependant on the specific tube, and for The shape of a typical MTF curve is shown in FIG. 8. Thethe desired precision, it is usually more accurate to measure MTF curve 80 is normalized to unity at zero spatial frequencythe detector response at the specific voltage settings. and gradually decreases as frequency is increased, until at The automated method described above is advantageous in some point the modulation becomes zero and remains so forthat it is applicable to a wide range of geometries of inspected 45 all higher frequencies. A MTF value of unity indicates that theobjects, and is applicable to a wide variation of shooting average contrast for a given spatial frequency is perfectlyparameters. The method is applicable for a wide range of maintained, while zero MTF shows that the object was com-thicknesses in the step wedge or shims that may be used. pletely lost, or not "seen" in the imaging process. Generally,Importantly, the procedure does not depend on precise align- the higher the MTF, the better the preservation of detail by thement of the step wedges or shims on the detector. Accord- 50 imaging system. The MTF partially describes the spatial reso-ingly, the above method is robust and reduces operator vari- lution capabilities of a detector, but not the sensitivity, norability. Moreover, the above method reduces the amount of probability of detection properties.time required to generate a thickness map reference look-up Although the MTF is dominantly defined by the detectortable as compared to manual methods. properties themselves, there is also a dependence on the size Given this preliminary calibration procedure, an object 55 and shape of the source, as well as the relative geometricalwith similar X-ray attenuation properties to the calibration layout of the source, detector, and object being imaged. In theobject can be imaged and the material thickness extracted, above mentioned case, the spatial frequency response mani-assuming that the features are large compared to the spatial fests itself in producing a different contrast level betweenfrequency where the modulation transfer function (MTF) features that have different sizes or spatial frequencies. This isdrops to a modulation of approximately 20%. Specifically, 60 a very important aspect in detection of small features such asthis means features that have a slowly varying spatial extent or pits and micro-deposits, which are critical to dimension accu-long wavelength variations in their spatial frequency. In order rately when assessing fitness for service of an asset. Withoutto image short wavelength objects, a correction to the spatial taking the varying MTF into account, an underestimate willresponse of the detector must be made, as described below. be made in dimensioning and depth profiling small features. Those skilled in the art understand that all physical detec- 65 The spatial frequencies present in an image can be deter-tors have a finite frequency response. For X -ray detectors, this mined by calculating the 2-d Fourier transform (FT) of themeans that the amplitude of the response (i.e., the number of image. The relative amplitude of each spatial frequency com-
  23. 23. US 7,480,363 B2 15 16ponent is a measure of the content in the image. Each ampli- calculated using the known geometry and relative positions oftude of the image FT can be scaled by the inverse value of the the source, detector and object being imaged.MTF to appropriately weight the image component. This has As shown in FIG. 12, a geometric representation of exem-the effect of "magnifYing" the features in the image with a plary source trajectory rays R1 and R2 can be used to illus-value proportional to the measured detector response (i.e. trate a method for estimating the wall thickness of a tubularMTF). This will have the effect of increasing the amplitude of pipeline structure 90. It is relatively simple to compute a pathsmall spatial frequencies (i.e., small features) while leaving length of material defined by Rays 1 or 2 using known geom-slowly varying features (i.e., large features) largely unaf- etry. The ray angle a for each pixel within the X-ray conefected. Once the scaling is made, the inverse FT is applied to beam will be calculated and the corresponding ray interac- 10 tions with the pipe geometry can be evaluated. For a ray thatthe image, with results being a radiographic image corrected intersects both the cylinders as shown in R2, the thickness canfor the spatial frequency response of the detector. In order to be calculated as: Thickness=(t3-tl)+(t2-t4). If the ray inter-limit the amplification of unimportant noise and artifacts, sects only one cylinder (OD), the thickness can be calculatedwhich are associated with high frequency spatial compo- as: Thickness=(t2-tl). The path length calculated is a func-nents, the MTF scaling is not applied to portions of the image 15 tion of the incident angel a of the X-ray. The path length iswhich fall beyond the Nyquist frequency of the detector. In minimum for a=O, and increases non-linearly, reaching aorder to further suppress the amplification of noise, an maximum, and then falling to zero as the angle a goes fromelementary low-pass filtering algorithm can be applied to zero to the maximum angle a 0 .damp high frequency oscillations and prevent a large scale At the extreme, the material path integral can be calculatedamplification of the noise. An important aspect of this proce- 20 for every individual detector element or pixel. In order todure is that knowledge about the size or character of the increase the calculational speed, a group of pixels may beimaged feature/defect is not required before this procedure is approximated as a single pixel. The size of the group will becarried out. determined by the degree of precision that is required in the Referring now to FIG. 9, there is illustrated an exemplary measurement. It is important that the beam path calculationpipeline structure 90 having a series of holes 91-96 for dem- 25 be calculated with the appropriate aligument parameters.onstrating an imaging capability of the present invention. Once the beam path is determined, it can be compared with the measurement to estimate the degree of wall loss.Results of the imaging procedure are shown in FIG. 10, Fluid-filled pipes provide perhaps the most rigorous chal-wherein a graphical response representing the gray value lenge for extracting absolute wall thickness estimates. Todistribution across the holes 91-96 without MTF correction is 30 illustrate the most elementary case, it is assumed that thedisplayed. By comparison, FIG. 11 illustrates the same gray composition of the fluid is known. Given this information, thevalue distribution, but the results are corrected with the MTF. mean thickness of a single wall can be extracted from a singleThe effect ofMTF correction produces a more accurate quan- radiograph measurement if the radiographic thickness of thetification of the feature depth by as much as a factor of 10. The fluid is known in terms of the pipe or vessel material. In fact,peak response across the holes 91-96 is higher after MTF 35 this method can be generalized to multiple layers if the radio-correction. Actual depth measurements before and after MTF graphic equivalence thickness of each material is known. Thiscorrection are summarized in Table 1 below. As can be seen, determination can be done in several ways. For example, athe error in the feature size decreases dramatically after the Monte Carlo simulation can determine radiographic equiva-application of the MTF correction. lent thicknesses of materials by calculating the material thick- 40 ness which equalizes dose rates of transmitted X-ray spectra TABLE 1 with the pipe/vessel material and the fluid. This is a straight- Holes actual depths are compared with the depth measured before and forward procedure for a mono-energetic radiation source. after MTF correction. Care must be taken in using a spectral source, such as X-ray tubes where the beam hardening effects are not trivial. Again Without 45 one must do the calculations to have the appropriate weight- MTF WithMTF correction correction ing for the energy dependant absorption terms. The calcula- Diameter Actual Depth % Depth % tions must equalize the radiation doses in the same geometry DXR500 in mils Depth in mils Error in mils Error that they occur in the system to be inspected, otherwise, the Hole 1 20 80 ±8 43 46.25 60 25 differential absorption asymmetries will become a significant Hole 2 40 80 ±8 63 21.25 82 -2.5 50 source of error. This can also be done experimentally by Hole 3 80 80 ±8 80 0 89 -11.25 separately measuring thicknesses of material that represent Hole4 20 40 ±4 14 65 20 50 the pipe wall, pipe contents, as well as pipe insulation if Hole 5 40 40 ±4 33 17.5 46 -15 Hole 6 80 40 ±4 32 20 42 -5 necessary. The following equations are written to describe expres- 55 sions for extracting absolute wall thickness estimates from A further complication in producing an accurate thickness insulated fluid-filled pipes:map is to correct for the tubular geometry of a pipe or vessel.Since a radiograph projects the total integral path of materialonto the detector, one must account for the geometrical shape Equation Xtotaz= Xfe +Xwater+Xinsulation (2)of the pipe or vessel when extracting the total wall thickness. 60In other words, a cross sectional slice across the diameter of Equation J.lFe *X=Jlinsulation,FW*Xinsulation,the pipe will not result in a constant path length of material FW+J.lFe,Fw*Xwater+J.lFe,Bw*Xinsulation,BW (3)defined by the various chords drawn from the source to thedetector. The minimum amount of pipe material will exist in Where:the center of the detector. As the chord is shortened, the total 65 X=Fe equivalent thicknessamount of material will increase. In order to quantify this Xfe =Fe thicknesseffect, a nominal profile of the nominal path integral can be Xfe.water=Fe equivalent thickness of water