# ASTM E1695-95 (Reapproved 2013)

Designation: E1695 − 95 (Reapproved 2013)Standard Test Method forMeasurement of Computed Tomography (CT) SystemPerformance1This standard is issued under the fixed designation E1695; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the U.S. Department of Defense.1. Scope1.1 This test method provides instruction for determiningthe spatial resolution and contrast sensitivity in X-ray and γ-raycomputed tomography (CT) images. The determination isbased on examination of the CT image of a uniform disk ofmaterial. The spatial resolution measurement is derived froman image analysis of the sharpness at the edge of the disk. Thecontrast sensitivity measurement is derived from an imageanalysis of the statistical noise at the center of the disk.1.2 This test method is more quantitative and less suscep-tible to interpretation than alternative approaches because therequired disk is easy to fabricate and the analysis is immune tocupping artifacts. This test method may not yield meaningfulresults if the disk image occupies less than a significant fractionof the field of view.1.3 This test method may also be used to evaluate otherperformance parameters. Among those characteristics of a CTsystem that are detectable with this test method are: themid-frequency enhancement of the reconstruction kernel, thepresence (or absence) of detector crosstalk, the undersamplingof views, and the clipping of unphysical (that is, negative) CTnumbers (seeAir Force Technical Report WL-TR-94-40212). Itis highly likely that other characteristics as well can be detectedwith this test method.1.4 The values stated in SI units are to be regarded as thestandard. Inch-pound units are provided for information only.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3E1316 Terminology for Nondestructive ExaminationsE1441 Guide for Computed Tomography (CT) ImagingE1570 Practice for Computed Tomographic (CT) Examina-tion3. Terminology3.1 Definitions—The definitions of terms relating toGamma- and X-Radiology, which appear in TerminologyE1316 and Guide E1441, shall apply to the terms used in thistest method.3.2 Definitions of Terms Specific to This Standard:3.2.1 phantom—a part or item being used to quantify CTsystem performance.3.2.2 examination object—a part or specimen being sub-jected to CT examination.3.3 Acronyms:3.3.1 ERF—edge response function.3.3.2 PSF—point spread function.3.3.3 MTF—modulation transfer function.3.3.4 CDF—contrast discrimination function.4. Significance and Use4.1 Two factors affecting the quality of a CT image aregeometrical unsharpness and random noise. Geometrical un-sharpness limits the spatial resolution of a CT system, that is,its ability to image fine structural detail in an object. Randomnoise limits the contrast sensitivity of a CT system, that is, itsability to detect the presence or absence of features in anobject. Spatial resolution and contrast sensitivity may bemeasured in various ways. ASTM specifies spatial resolution1This test method is under the jurisdiction of ASTM Committee E07 onNondestructive Testing and is the direct responsibility of Subcommittee E07.01 onRadiology (X and Gamma) Method.Current edition approved June 1, 2013. Published June 2013. Originallyapproved in 1995. Last previous edition approved in 2006 as E1695 - 95(2006)ε1.DOI: 10.1520/E1695-95R13.2X-Ray Computed Tomography Standards (WL-TR-94-4021). Bossi, R. H. andNelson, J. M. Air Force Contract No. F33615-88-C-5404. Source documentavailable from Air Force Research Laboratory, AFRL/MLLP Building 655, 2230Tenth Street, Suite 1, Wright-Patterson AFB, OH 45433–7814.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1be quantified in terms of the modulation transfer function(MTF) and contrast sensitivity be quantified in terms of thecontrast discrimination function (CDF) (see Guide E1441 andPractice E1570). This test method allows the purchaser or theprovider of CT systems or services, or both, to measure andspecify spatial resolution and contrast sensitivity.5. Apparatus5.1 Disk Phantom—The disk phantom shall be a rightcylinder of uniform material conforming to the design andmaterial requirements in Table 1 and Fig. 1. Since spatialresolution and contrast sensitivity depend on the examinationtask (that is, the examination object and the specified CTparameters), the application requirements must be fixed beforethe phantom can be designed. In general, each examinationtask will require a separate phantom. The diameter of the diskrelative to the field of view shall be such that the reconstructedimage of the disk occupies a significant fraction of the imagematrix. Recommended sizes are given in Table 2. The diameterand opacity of the disk shall be such that the phantomapproximates the attenuation range of the examination object.If possible, the phantom should be of the same material as theexamination object, but the other requirements take precedenceand may dictate the selection of another material. The design ofthe disk phantom is a matter of agreement between thepurchaser and the supplier.6. Procedure6.1 The phantom shall be mounted on the CT system withthe orientation of the axis of revolution of the disk normal tothe scan plane. The alignment shall not compromise themeasurement of geometrical unsharpness. Unless otherwiseagreed upon between purchaser and supplier, the phantom shallbe placed at the center of the field of view used for theexamination object.6.2 Unless otherwise agreed upon between purchaser andsupplier, the data acquisition parameters shall be identical tothose used for examination object scans. The slice plane shallintercept the phantom approximately midway between the flatfaces of the disk.6.3 Unless otherwise agreed upon between purchaser andsupplier, the reconstruction parameters shall be identical tothose used for examination object reconstructions.6.4 Unless otherwise agreed upon between purchaser andsupplier, the display parameters shall be identical to those usedTABLE 1 Disk Phantom Design RequirementsMaterial The material, in conjunction with the diameter of the disk,shall be such that the phantom approximates theattenuation range of the examination object. The materialshould preferably be the same as that of the examinationobject.Diameter The diameter shall be such that the reconstruction of the diskoccupies a significant fraction of the resulting image. Inconjunction with the material, the diameter shall be suchthat the phantom approximates the attenuation range of theexamination object.Thickness The thickness of the disk shall be greater than the slicethickness used to inspect the examination object.Shape The perpendicularity of the axis of revolution with respect tothe surface used to mount the phantom on the CT systemshall not compromise the measurement of geometricalunsharpness.Finish The surface texture roughness of the curved surface shall notcompromise the measurement of geometrical unsharpness.FIG. 1 Disk PhantomTABLE 2 Suggested Measurement ParametersImage MatrixSize(Pixels)Disk ImageDiameter(Pixels)Maximum TileSize(Pixels)ERF BinSize(Pixels)Numberof FitPoints256 235 12 0.100 11512 470 24 0.050 211024 940 48 0.025 41E1695 − 95 (2013)2for examination object display. It shall be verified by exami-nation that the disk image occupies an image at least two-thirdsof the image matrix. Recommended guidelines are given inTable 2.7. Interpretation of Results7.1 Spatial Resolution—From the CT image data, generatethe composite profile of the edge of the disk to obtain the edgeresponse function (ERF). Calculate the derivative of the ERFto obtain the point spread function (PSF). Calculate theamplitude of the Fourier Transform4of the PSF and normalizethe results to unity at zero frequency to obtain the modulationtransfer function (MTF).7.1.1 Unless otherwise agreed upon between the purchaserand supplier, the ERF shall be generated as follows:7.1.1.1 Calculate the center of mass of the disk.7.1.1.2 Select the inner and outer radii with respect to thecenter of mass that comfortably bracket the edge.7.1.1.3 Compute the distance to the center of mass for allpixels between the inner and outer radii.7.1.1.4 Generate a table of pixel values in order of theirpixel distance from the center of mass.7.1.1.5 Segregate the values into equal bins sized to a smallfraction of one pixel. The bin size should be as small aspractical without causing some bins to be empty. Recom-mended sizes are given in Table 2.7.1.1.6 Average the members of each bin to obtain a table ofvalues at constant increments from the inner to outer radius.7.1.1.7 Starting at one end of the table and iterating until theentire table has been processed, smooth the pixel values byperforming a piece-wise, least-squares cubic fit to an oddnumber of table values and replacing the center value with thatpredicted by the fit. The number of values to include in the fitshould be large compared to the order of the polynomial andsmall compared to the fine ERF structure. Recommendedguidelines for the number of values to use in the fit are givenin Table 2.7.1.1.8 Determine how much of the table to include in theanalysis and delete the unwanted portions of the leading andtrailing tails to obtain the ERF.7.1.2 Unless otherwise agreed upon between the purchaserand supplier, the PSF shall be generated as follows:7.1.2.1 Starting at one end of the table and iterating until theentire table has been processed, perform a piece-wise, least-squares cubic fit to the ERF using for the fit the same numberof values as were used to smooth the data (see 7.1.1).7.1.2.2 For each fit, calculate the analytical derivative of theresultant polynomial and determine its numerical value at thecenter of the piece-wise window.7.1.2.3 Generate a table of derivative values as a function ofdistance from the center of the disk.7.1.2.4 Normalize the peak value of the resulting curve tounity to obtain the PSF.7.1.3 Unless otherwise agreed upon between the purchaserand supplier, the MTF shall be generated as follows:7.1.3.1 Calculate the Fourier Transform4of the PSF. Themaximum frequency of the resultant transform should be atleast four times the cut-off frequency of the matrix, which bydefinition is 0.5 line-pairs per pixel. The sampling frequency inthe Fourier domain should be small enough that the transformis smooth within the frequency range of interest. A samplingfrequency of 0.01, or smaller, is recommended.7.1.3.2 Calculate the magnitude of the transform by takingthe square root of the product of the transform and itsconjugate.7.1.3.3 Normalize the magnitude at zero frequency to unityto obtain the MTF.7.1.4 Unless otherwise agreed upon between the purchaserand supplier, the MTF shall be visually displayed or plotted, orboth, and the frequency at 10 % modulation quantitativelyindicated. Although not mandatory, the ERF and the PSFshould also be graphically presented, with the full width at halfmaximum of the latter quantitatively indicated.7.2 Contrast Sensitivity—From the CT image data, generatea sequence of tile patterns which fit within the central region ofthe disk. For each pattern, calculate the mean CT value withineach tile and store the result in a table specific to that pattern.For each table of results, calculate the standard deviation toobtain the standard error in the mean and store the result in aseparate table in order of ascending tile size. Express eachstandard error in the mean as a percent of its respectiveensemble average and multiply by a factor of 3 to obtain thecontrast discrimination function (CDF).7.2.1 Unless otherwise agreed upon between the purchaserand supplier, the sequence of tile patterns shall be generated asfollows:7.2.1.1 Select a circular region of interest at the center of thedisk. The diameter of the region should be large enough toencompass a statistically significant number of tiles but not solarge that the single-pixel noise or cupping, or both, (if present)changes appreciably over the selected region. (The two influ-ences act in opposite directions: statistical noise decreases withincreasing radius and will lower the standard error in the meanif too large a radius is chosen; whereas, cupping increases withincreasing radius and will increase the standard error in themean if too large a radius is chosen.) As a rule of thumb, theseconditions will be satisfied when the diameter of the centralregion is about one-third that of the disk. For each newapplication, it is recommended that the validity of theserequirements be verified empirically by monitoring the behav-ior of the CDF as the size of the region of interest is increased(see 7.2.3).7.2.1.2 For tiles ranging in size from a single pixel to n2pixels, generate a sequence of patterns that tessellate theselected central region of the disk with a checkerboard ofnon-overlapping squares (see Fig. 2). (For the special case ofsingle-pixel tiles, the requirement for non-overlapping tiles issatisfied trivially.) Terminate the sequence of patterns when thesize of the tiles becomes too large to obtain a statisticallysignificant number of tiles. It is recommended that the mini-mum number of tiles be on the order of 25. See Table 2 forsuggested maximum tile sizes.4The Fourier Transform and Its Applications, Ronald M. Bracewell, McGraw-Hill, NY, ISBN 0-07-007013-X.E1695 − 95 (2013)37.2.2 Unless otherwise agreed upon between the purchaserand supplier, the CDF shall be generated as follows:7.2.2.1 Starting with the finest pattern of tiles and iteratinguntil the entire sequence of patterns has been exhausted,calculate the mean value of the CT numbers within each tileand store the results in a table unique to each pattern. (For thespecial case of the single-pixel tiles, the calculation of means istrivial.)7.2.2.2 For each table of results, calculate the standarddeviation of the ensemble of measurements to obtain thestandard error in the mean. (For the special case of thesingle-pixel tiles, the standard error in the mean is equal to thestandard deviation.)7.2.2.3 Generate a table of the standard error in the mean asa function of increasing tile size, where the size of a tile isdefined a