Designation: E2938 − 15Standard Test Method forEvaluating the Relative-Range Measurement Performance of3D Imaging Systems in the Medium Range1This standard is issued under the fixed designation E2938; 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.1. Scope1.1 This standard describes a quantitative test method forevaluating the range measurement performance of laser-based,scanning, time-of-flight, 3D imaging systems in the mediumrange. The term “medium range” refers to systems that arecapable of operating within at least a portion of ranges from 2to 150 m. The term “time-of-flight systems” includes phase-based, pulsed, and chirped systems. The word “standard” inthis document refers to a documentary standard as per Termi-nology E284. This test method only applies to 3D imagingsystems that are capable of producing a point cloud represen-tation of a measured target.1.1.1 As defined in Terminology E2544,arange is thedistance measured from the origin of a 3D imaging system toa point in space. This range is often referred to as an absoluterange. However, since the origin of many 3D imaging systemsis either unknown or not readily measurable, a test method forabsolute range performance is not feasible for these systems.Therefore, in this test method, the range is taken to be thedistance between two points in space on a line that passesthrough the origin of the 3D imaging system. Although theerror in the calculated distance between these two points is arelative-range error, in this test method when the term rangeerror is used it refers to the relative-range error. This testmethod cannot be used to quantify the constant offset errorcomponent of the range error.1.1.2 This test method recommends that the first point be atthe manufacturer-specified target 1 range and requires that thesecond target be on the same side of the instrument under test(IUT) as the first target. Specification of target 1 range by themanufacturer minimizes the contribution to the relative rangemeasurement error from the target 1 range measurement.1.1.3 This test method may be used once to evaluate the IUTfor a given set of conditions or it may be used multiple timesto better assess the performance of the IUT for variousconditions (for example, additional ranges, variousreflectances, environmental conditions).1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard. SI units are used for all calculations and results in thisstandard.1.3 The method described in this standard is not intended toreplace more in-depth methods used for instrument calibrationor compensation, and specific measurement applications mayrequire other tests and analyses.1.4 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. Some aspects of thesafe use of 3D Imaging Systems are discussed in PracticeASTM E2641.2. Referenced Documents2.1 ASTM Standards:2E284 Terminology of AppearanceE1164 Practice for Obtaining Spectrometric Data for Object-Color EvaluationE1331 Test Method for Reflectance Factor and Color bySpectrophotometry Using Hemispherical GeometryE2544 Terminology for Three-Dimensional (3D) ImagingSystemsE2641 Practice for Best Practices for Safe Application of 3DImaging Technology2.2 ASME Standards:3ASME B89.1.9-2002 Gage BlocksASME B89.4.19-2006 Performance Evaluation of Laser-Based Spherical Coordinate Measurement SystemsASME B89.7.2-1999 Dimensional Measurement Planning1This test method is under the jurisdiction of ASTM Committee E57 on 3DImaging Systems and is the direct responsibility of Subcommittee E57.02 on TestMethods.Current edition approved April 1, 2015. Published June 2015. DOI: 10.1520/E2938–15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3Available from American Society of Mechanical Engineers (ASME), ASMEInternational Headquarters, Two Park Ave., New York, NY 10016-5990, http://www.asme.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States12.3 ISO Standards:4ISO 14253-1:1998 Geometrical Product Specifications(GPS)—Inspection by measurement of workpieces andmeasuring equipment—Part 1: Decision rules for provingconformance or non-conformance with specificationsISO 14253-2:1999 Geometrical Product Specifications(GPS)—Inspection by measurement of workpieces andmeasuring equipment—Part 2: Guide to the estimation ofuncertainty in GPS measurement, in calibration of mea-suring equipment and in product verification2.4 JCGM Standards:JCGM 200:2012 International vocabulary of metrology—Basic and general concepts and associated terms (VIM),3rd editionJCGM 100:2008 Evaluation of measurement data—Guide tothe expression of uncertainty in measurement (GUM), 1stedition3. Terminology3.1 Definitions:3.1.1 3D imaging system, n—a non-contact measurementinstrument used to produce a 3D representation (for example,a point cloud) of an object or a site. E25443.1.1.1 Discussion—Some examples of a 3D imaging sys-tem are laser scanners (also known as LADARs or LIDARs orlaser radars), optical range cameras (also known as flashLIDARs or 3D range cameras), triangulation-based systemssuch as those using pattern projectors or lasers, and othersystems based on interferometry.3.1.1.2 Discussion—In general, the information gathered bya 3D imaging system is a collection of n-tuples, where eachn-tuple can include but is not limited to spherical or Cartesiancoordinates, return signal strength, color, time stamp, identifier,polarization, and multiple range returns.3.1.1.3 Discussion—3D imaging systems are used to mea-sure from relatively small scale objects (for example, coin,statue, manufactured part, human body) to larger scale objectsor sites (for example, terrain features, buildings, bridges, dams,towns, archeological sites).3.1.2 calibration, n—operation that, under specifiedconditions, in a first step, establishes a relation between thequantity values with measurement uncertainties provided bymeasurement standards and corresponding indications withassociated measurement uncertainties and, in a second step,uses this information to establish a relation for obtaining ameasurement result from an indication. JCGM 200:2012(VIM) – 2.393.1.3 combined standard uncertainty, n—standard uncer-tainty of the result of a measurement when that result isobtained from the values of a number of other quantities, equalto the positive square root of a sum of terms, the terms beingthe variances or covariances of these other quantities weightedaccording to how the measurement result varies with changesin these quantities. JCGM 100:2008 (GUM) – 2.3.43.1.4 compensation, n—the process of determining system-atic errors in an instrument and then applying these values in anerror model that seeks to eliminate or minimize measurementerrors. ASME B89.4.193.1.5 covariance—the covariance of two random variablesis a measure of their mutual dependence. JCGM 100:2008(GUM) – C.3.43.1.6 coverage factor, n—numerical factor used as a multi-plier of the combined standard uncertainty in order to obtain anexpanded uncertainty.3.1.6.1 Discussion—A coverage factor, k, is typically in therange 2 to 3. JCGM 100:2008 (GUM) 2.3.63.1.7 diffuse reflectance factor, Rd,n—the ratio of the fluxreflected at all angles within the hemisphere bounded by theplane of measurement except in the direction of the specularreflection angle, to the flux reflected from the perfect reflectingdiffuser under the same geometric and spectral conditions ofmeasurement. E284 Section 3.13.1.7.1 Discussion—The size of the specular reflectionangle depends on the instrument and the measurement condi-tions used. For its precise definition the make and model of theinstrument or the aperture angle or aperture solid angle of thespecularly reflected beam should be specified.3.1.8 documentary standard, n—document, arrived at byopen consensus procedures, specifying necessary details of amethod of measurement, definitions of terms, or other practicalmatters to be standardized. E2843.1.9 expanded test uncertainty, n—product of a combinedstandard measurement uncertainty and a factor larger than thenumber one. JCGM 200:2012 (VIM) – 2.353.1.10 flatness, n—the minimum distance between two par-allel planes between which all points of the measuring face lie.ASME B89.1.9 – 3.53.1.11 limiting conditions, n—the manufacturer’s specifiedlimits on the environmental, utility, and other conditions withinwhich an instrument may be operated safely and withoutdamage. ASME B89.4.193.1.11.1 Discussion—The manufacturer’s performancespecifications are not assured over the limiting conditions.3.1.12 maximum permissible error (MPE), n—extremevalue of measurement error, with respect to a known referencequantity value, permitted by specifications or regulations for agiven measurement, measuring instrument, or measuringsystem. JCGM 200:2012 (VIM) – 4.263.1.12.1 Discussion—Usually, the term “maximum permis-sible errors” or “limits of error” is used where there are twoextreme values.3.1.12.2 Discussion—The term “tolerance” should not beused to designate ‘maximum permissible error’.3.1.13 measurand, n—quantity intended to be measured.JCGM 200:2012 (VIM) – 2.33.1.13.1 Discussion—The specification of a measurand re-quires knowledge of the kind of quantity, description of thestate of the phenomenon, body, or substance carrying thequantity, including any relevant component, and the chemicalentities involved.4Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http://www.ansi.org.E2938 − 1523.1.13.2 Discussion—In the second edition of the VIM andin IEC 60050-300:2001, the measurand is defined as the‘quantity subject to measurement’.3.1.13.3 Discussion—The measurement, including the mea-suring system and the conditions under which the measurementis carried out, might change the phenomenon, body, or sub-stance such that the quantity being measured may differ fromthe measurand as defined. In this case, adequate correction isnecessary.Example 1—The potential difference between the termi-nals of a battery may decrease when using a voltmeter witha significant internal conductance to perform the measure-ment. The open-circuit potential difference can be calculatedfrom the internal resistances of the battery and the voltmeter.Example 2—The length of a steel rod in equilibrium withthe ambient Celsius temperature of 23°C will be differentfrom the length at the specified temperature of 20°C, whichis the measurand. In this case, a correction is necessary.3.1.13.4 Discussion—In chemistry, “analyte”, or the nameof a substance or compound, are terms sometimes used for‘measurand’. This usage is erroneous because these terms donot refer to quantities.3.1.14 measurement accuracy, n—closeness of agreementbetween a measured quantity value and a true quantity value ofa measurand. JCGM 200:2012 (VIM) – 2.133.1.14.1 Discussion—The concept ‘measurement accuracy’is not a quantity and is not given a numerical quantity value. Ameasurement is said to be more accurate when it offers asmaller measurement error.3.1.14.2 Discussion—The term “measurement accuracy”should not be used for measurement trueness and the termmeasurement precision should not be used for ‘measurementaccuracy’, which, however, is related to both these concepts.3.1.14.3 Discussion—‘Measurement accuracy’ is sometimesunderstood as closeness of agreement between measuredquantity values that are being attributed to the measurand.3.1.15 measurement error, n—measured quantity value mi-nus a reference quantity value. JCGM 200:2012 (VIM) – 2.163.1.15.1 Discussion—The concept of ‘measurement error’can be used both: (1) when there is a single reference quantityvalue to refer to, which occurs if a calibration is made bymeans of a measurement standard with a measured quantityvalue having a negligible measurement uncertainty or if aconventional quantity value is given, in which case themeasurement error is known; and (2) if a measurand issupposed to be represented by a unique true quantity value ora set of true quantity values of negligible range, in which casethe measurement error is not known.3.1.15.2 Discussion—Measurement error should not be con-fused with production error or mistake.3.1.16 measurement uncertainty, n—non-negative param-eter characterizing the dispersion of the quantity values beingattributed to a measurand, based on the information used.JCGM 200:2012 (VIM) – 2.263.1.16.1 Discussion—Measurement uncertainty includescomponents arising from systematic effects, such as compo-nents associated with corrections and the assigned quantityvalues of measurement standards, as well as the definitionaluncertainty. Sometimes estimated systematic effects are notcorrected for but, instead, associated measurement uncertaintycomponents are incorporated.3.1.16.2 Discussion—The parameter may be, for example, astandard deviation called standard measurement uncertainty (ora specified multiple of it), or the half-width of an interval,having a stated coverage probability.3.1.16.3 Discussion—Measurement uncertainty comprises,in general, many components. Some of these may be evaluatedby Type A evaluation of measurement uncertainty from thestatistical distribution of the quantity values from series ofmeasurements and can be characterized by standard deviations.The other components, which may be evaluated by Type Bevaluation of measurement uncertainty, can also be character-ized by standard deviations, evaluated from probability densityfunctions based on experience or other information.3.1.16.4 Discussion—In general, for a given set ofinformation, it is understood that the measurement uncertaintyis associated with a stated quantity value attributed to themeasurand. A modification of this value results in a modifica-tion of the associated uncertainty.3.1.17 point cloud, n—a collection of data points in 3Dspace (frequently in the hundreds of thousands), for example asobtained using a 3D imaging system. E25443.1.17.1 Discussion—The distance between points is gener-ally non-uniform and hence all three coordinates (Cartesian orspherical) for each point must be specifically encoded.3.1.18 range, n—the distance, in units of length, between apoint in space and an origin fixed to the 3D imaging systemthat is measuring that point. E25443.1.18.1 Discussion—I