ASTM E2544-11A(2019)e1
(Terminology)Standard Terminology for Three-Dimensional (3D) Imaging Systems
Standard Terminology for Three-Dimensional (3D) Imaging Systems
SCOPE
1.1 This terminology contains common terms, definitions of terms, descriptions of terms, nomenclature, and acronyms associated with three-dimensional (3D) imaging systems in an effort to standardize terminology used for 3D imaging systems.
1.2 The definitions of the terms presented in 3.1 are obtained from various standard documents developed by various standards development organizations. The intent is not to change these universally accepted definitions but to gather, in a single document, terms and their definitions that may be used in current or future standards for 3D imaging systems.
1.2.1 In some cases, definitions of the same term from two standards have been presented to provide additional reference. The text in parentheses to the right of each defined term is the name (and, in some cases, the specific section) of the source of the definition associated with that term.
1.3 The definitions in 3.2 are specific terms developed by this committee for 3D imaging systems. Some terms may have generally accepted definitions in a particular community or are defined in existing standards. If there are conflicting definitions, our preference is to adapt (modify) the ISO standard (if available) for this standard.
1.4 A definition in this terminology is a statement of the meaning of a word or word group expressed in a single sentence with additional information included in notes or discussions.
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
Note 1: The subcommittee responsible for this standard will review definitions on a five-year basis to determine if the definition is still appropriate as stated. Revisions will be made when determined necessary.
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
General Information
Relations
Buy Standard
Standards Content (Sample)
This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
´1
Designation: E2544 − 11a (Reapproved 2019)
Standard Terminology for
Three-Dimensional (3D) Imaging Systems
This standard is issued under the fixed designation E2544; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Sections 3.2 and 3.3 were updated editorially in March 2022 to include all current terms developed by Commit-
tee E57.
1. Scope 1.6 This international standard was developed in accor-
dance with internationally recognized principles on standard-
1.1 Thisterminologycontainscommonterms,definitionsof
ization established in the Decision on Principles for the
terms, descriptions of terms, nomenclature, and acronyms
Development of International Standards, Guides and Recom-
associated with three-dimensional (3D) imaging systems in an
mendations issued by the World Trade Organization Technical
efforttostandardizeterminologyusedfor3Dimagingsystems.
Barriers to Trade (TBT) Committee.
1.2 The definitions of the terms presented in 3.1 are ob-
tained from various standard documents developed by various
2. Referenced Documents
standards development organizations. The intent is not to
2.1 ASTM Standards:
change these universally accepted definitions but to gather, in
E456Terminology Relating to Quality and Statistics
asingledocument,termsandtheirdefinitionsthatmaybeused
E2919Test Method for Evaluating the Performance of
in current or future standards for 3D imaging systems.
Systems that Measure Static, Six Degrees of Freedom
1.2.1 In some cases, definitions of the same term from two
(6DOF), Pose
standards have been presented to provide additional reference.
E2938TestMethodforEvaluatingtheRelative-RangeMea-
The text in parentheses to the right of each defined term is the
surement Performance of 3D Imaging Systems in the
name(and,insomecases,thespecificsection)ofthesourceof
Medium Range
the definition associated with that term.
E3124Test Method for Measuring System Latency Perfor-
1.3 The definitions in 3.2 are specific terms developed by
mance of Optical Tracking Systems that Measure Six
thiscommitteefor3Dimagingsystems.Sometermsmayhave
Degrees of Freedom (6DOF) Pose
generallyaccepteddefinitionsinaparticularcommunityorare
E3125Test Method for Evaluating the Point-to-Point Dis-
defined in existing standards. If there are conflicting
tance Measurement Performance of Spherical Coordinate
definitions, our preference is to adapt (modify) the ISO
3D Imaging Systems in the Medium Range
standard (if available) for this standard.
E2807Specificationfor3DImagingDataExchange,Version
1.0
1.4 A definition in this terminology is a statement of the
meaning of a word or word group expressed in a single 2.2 ASME Standard:
sentence with additional information included in notes or
B89.4.19Performance Evaluation of Laser Based Spherical
discussions. Coordinate Measurement Systems
1.5 This standard does not purport to address all of the 2.3 ISO Standard:
VIMInternational vocabulary of metrology -- Basic and
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro- general concepts and associated terms
ISO 11146–1 Lasers and laser-related equipment — Test
priate safety, health, and environmental practices and deter-
mine the applicability of regulatory limitations prior to use. methods for laser beam widths, divergence angles and
NOTE 1—The subcommittee responsible for this standard will review
definitions on a five-year basis to determine if the definition is still
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
appropriateasstated.Revisionswillbemadewhendeterminednecessary.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
theASTM website.
1 3
This terminology is under the jurisdiction of Committee E57 on 3D Imaging Available from American Society of Mechanical Engineers (ASME), ASME
Systems and is the direct responsibility of Subcommittee E57.10 on Terminology. International Headquarters, Three Park Ave., New York, NY 10016-5990, http://
Current edition approved March 1, 2019. Published March 2019. Originally www.asme.org.
approved in 2007. Last previous edition approved in 2011 as E2544 – 11a. DOI: Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
10.1520/E2544-11AR19E01. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
E2544 − 11a (2019)
beam propagation ratios — Part 1: Stigmatic and simple a conventional true value and (2) the CODATA(1986) recom-
astigmatic beams mended value for the Avogadro constant, N : 6 022 136 7 ×
A
23 -1
10 mol .
2.4 NIST/SEMATECH Standard:
(2)Conventional true value is sometimes called assigned
NIST/SEMATECHe-Handbook of Statistical Methods
value, best estimate of the value, conventional value, or
3. Terminology reference value.
(3)Frequently, a number of results of measurements of a
3.1 Definitions:
quantity is used to establish a conventional true value.
accuracy of measurement, n—closeness of the agreement
between the result of a measurement and a true value of the
error (of measurement), n—result of a measurement minus a
measurand. (VIM 3.5)
true value of the measurand. (VIM 3.10)
DISCUSSION—
DISCUSSION—
(1)Accuracy is a qualitative concept.
(1)Since a true value cannot be determined, in practice, a
(2)Theterm“precision”shouldnotbeusedfor“accuracy.”
conventional true value is used (see true value and conven-
tional true value).
bias (of a measuring instrument), n—systematic error of the
(2)When it is necessary to distinguish “error” from “
indication of a measuring instrument. (VIM 3.25)
relative error,” the former is sometimes called “absolute error
DISCUSSION—
of measurement.” This should not be confused with the “
(1)The bias of a measuring instrument is normally esti-
absolute value of error,” which is the modulus of error.
mated by averaging the error of indication over an appropriate
number of repeated measurements.
indicating (measuring) instrument, n—measuringinstrument
that displays an indication. (VIM 4.6)
bias, n—differencebetweentheaverageorexpectedvalueofa
DISCUSSION—
distribution and the true value.
(1)Examples include analog indicating voltmeter, digital
(NIST/SEMATECH e-Handbook)
frequency meter, and micrometer.
DISCUSSION—
(2)The display may be analog (continuous or discontinu-
(1)In metrology, the difference between precision and
ous) or digital.
accuracy is that measures of precision are not affected by bias,
(3)Values of more than one quantity may be displayed
whereas accuracy measures degrade as bias increases.
simultaneously.
calibration, n—setofoperationsthatestablish,underspecified
(4)Adisplaying measuring instrument may also provide a
conditions, the relationship between values of quantities
record.
indicatedbyameasuringinstrumentormeasuringsystem,or
limiting conditions, n—the manufacturer’s specified limits on
values represented by a material measure or a reference
theenvironmental,utility,andotherconditionswithinwhich
material,andthecorrespondingvaluesrealizedbystandards.
an instrument may be operated safely and without damage.
(VIM 6.11)
(ASME B89.4.19)
DISCUSSION—
DISCUSSION—
(1)Theresultofacalibrationpermitseithertheassignment
(1)The manufacturer’s performance specifications are not
ofvaluesofmeasurandstotheindicationsorthedetermination
assured over the limiting conditions.
of corrections with respect to indications.
(2)A calibration may also determine other metrological
maximum permissible error (MPE), n—extremevaluesofan
properties such as the effect of influence quantities.
errorpermittedbyspecification,regulations,andsoforthfor
(3)The result of a calibration may be recorded in a
a given measuring instrument. (VIM 5.21)
document, sometimes called a calibration certificate or a
calibration report. measurand, n—particular quantity subject to measurement.
(VIM 2.6)
compensation, n—the process of determining systematic er-
DISCUSSION—
rors in an instrument and then applying these values in an
(1)Example includes vapor pressure of a given sample of
error model that seeks to eliminate or minimize measure-
water at 20°C.
ment errors. (ASME B89.4.19)
(2)The specification of a measurand may require state-
mentsaboutquantitiessuchastime,temperature,andpressure.
conventional true value (of a quantity), n—value attributed
to a particular quantity and accepted, sometimes by
precision, n—closeness of agreement between independent
convention, as having an uncertainty appropriate for a given
test results obtained under stipulated conditions.
purpose. (VIM 1.20)
(ASTM E456)
DISCUSSION—
DISCUSSION—
(1)Examples: (1) at a given location, the value assigned to
(1)Precisiondependsonrandomerrorsanddoesnotrelate
the quantity realized by a reference standard may be taken as
to the true value or the specified value.
(2)The measure of precision is usually expressed in terms
ofimprecisionandcomputedasastandarddeviationofthetest
Available from National Institute of Standards and Technology (NIST), 100
results. Less precision is reflected by a larger standard devia-
Bureau Dr., Stop 1070, Gaithersburg, MD 20899-1070, http://www.nist.gov.
e-Handbook available at http://www.itl.nist.gov/div898/handbook/. tion.
´1
E2544 − 11a (2019)
(3)“Independent test results” means results obtained in a (3)Reproducibility may be expressed quantitatively in
manner not influenced by any previous result on the same or terms of the dispersion characteristics of the results.
similar test object. Quantitative measures of precision depend (4)Results are usually understood to be corrected results.
critically on the stipulated conditions. Repeatability and repro-
systematic error, n—mean that would result from an infinite
ducibility conditions are particular sets of extreme stipulated
number of measurements of the same measurand carried out
conditions.
under repeatability conditions minus a true value of the
precision, n—in metrology, the variability of a measurement
measurand. (VIM 3.14)
process around its average value.
DISCUSSION—
(NIST/SEMATECH e-Handbook)
(1)Systematic error is equal to error minus random error.
DISCUSSION—
(2)Like true value, systematic error and its causes cannot
(1)Precision is usually distinguished from accuracy, the
be completely known.
variability of a measurement process around the true value.
(3)For a measuring instrument, see “bias.”
Precision, in turn, can be decomposed further into short-term
true value (of a quantity), n—value consistent with the
variation or repeatability and long-term variation or reproduc-
definition of a given particular quantity. (VIM 1.19)
ibility.
DISCUSSION—
random error, n—result of a measurement minus the mean
(1)This is a value that would be obtained by a perfect
that would result from an infinite number of measurements
measurement.
of the same measurand carried out under repeatability
(2)True values are by nature indeterminate.
conditions. (VIM 3.13)
(3)Theindefinitearticle“a,”ratherthanthedefinitearticle
DISCUSSION—
“the,” is used in conjunction with “true value” because there
(1)Random error is equal to error minus systematic error.
may be many values consistent with the definition of a given
(2)Because only a finite number of measurements can be
particular quantity.
made, it is possible to determine only an estimate of random
error. uncertainty of measurement, n—parameter, associated with
theresultofameasurement,thatcharacterizesthedispersion
rated conditions, n—manufacturer-specified limits on
of the values that could reasonably be attributed to the
environmental,utility,andotherconditionswithinwhichthe
measurand. (VIM 3.9)
manufacturer’s performance specifications are guaranteed at
DISCUSSION—
the time of installation of the instrument.
(1)The parameter may be, for example, a standard devia-
(ASME B89.4.19)
tion (or a given multiple of it) or the half width of an interval
relative error, n—error of measurement divided by a true
having a stated level of confidence.
value of the measurand. (VIM 3.12)
(2)Uncertainty of measurement comprises, in general,
DISCUSSION—
many components. Some of these components may be evalu-
(1)Since a true value cannot be determined, in practice a
ated from the statistical distribution of the results of series of
conventional true value is used.
measurements and can be characterized by experimental stan-
dard deviations. The other components, which can also be
repeatability (of results of measurements), n—closeness of
characterized by standard deviations, are evaluated from as-
the agreement between the results of successive measure-
sumed probability distributions based on experience or other
ments of the same measurand carried out under the same
information.
conditions of measurement. (VIM 3.6)
(3)Itisunderstoodthattheresultofthemeasurementisthe
DISCUSSION—
best estimate of the value of the measurand, and that all
(1)These conditions are called repeatability conditions.
(2)Repeatability conditions include: the same measure- components of uncertainty, including those arising from sys-
tematiceffects,suchascomponentsassociatedwithcorrections
ment procedure; the same observer; the same measuring
instrument used under the same conditions; the same location; and reference standards, contribute to the dispersion.
and repetition over a short period of time.
3.2 Definitions of Terms Specific to This Standard:
(3)Repeatability may be expressed quantitatively in terms
3D imaging system, n—a non-contact measurement instru-
of the dispersion characteristics of the results.
ment used to produce a 3D representation (for example, a
point cloud) of an object or a site.
reproducibility (of results of measurements), n—closeness
DISCUSSION—
oftheagreementbetweentheresultsofmeasurementsofthe
(1)Some examples of a 3D imaging system are laser
same measurand carried out under changed conditions of
scanners (also known as LADARs or LIDARs or laser radars),
measurement. (VIM 3.7)
optical range cameras (also known as flash LIDARs or 3D
DISCUSSION—
(1)Avalue statement of reproducibility requires specifica- range cameras), triangulation-based systems such as those
tion of the conditions changed. using pattern projectors or lasers, and other systems based on
(2)T
...
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
´1
Designation: E2544 − 11a (Reapproved 2019)
Standard Terminology for
Three-Dimensional (3D) Imaging Systems
This standard is issued under the fixed designation E2544; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Sections 3.2 and 3.3 were updated editorially in March 2022 to include all current terms developed by Commit-
tee E57.
1. Scope 1.6 This international standard was developed in accor-
dance with internationally recognized principles on standard-
1.1 This terminology contains common terms, definitions of
ization established in the Decision on Principles for the
terms, descriptions of terms, nomenclature, and acronyms
Development of International Standards, Guides and Recom-
associated with three-dimensional (3D) imaging systems in an
mendations issued by the World Trade Organization Technical
effort to standardize terminology used for 3D imaging systems.
Barriers to Trade (TBT) Committee.
1.2 The definitions of the terms presented in 3.1 are ob-
tained from various standard documents developed by various
2. Referenced Documents
standards development organizations. The intent is not to
2.1 ASTM Standards:
change these universally accepted definitions but to gather, in
E456 Terminology Relating to Quality and Statistics
a single document, terms and their definitions that may be used
E2919 Test Method for Evaluating the Performance of
in current or future standards for 3D imaging systems.
Systems that Measure Static, Six Degrees of Freedom
1.2.1 In some cases, definitions of the same term from two
(6DOF), Pose
standards have been presented to provide additional reference.
E2938 Test Method for Evaluating the Relative-Range Mea-
The text in parentheses to the right of each defined term is the
surement Performance of 3D Imaging Systems in the
name (and, in some cases, the specific section) of the source of
Medium Range
the definition associated with that term.
E3124 Test Method for Measuring System Latency Perfor-
1.3 The definitions in 3.2 are specific terms developed by
mance of Optical Tracking Systems that Measure Six
this committee for 3D imaging systems. Some terms may have
Degrees of Freedom (6DOF) Pose
generally accepted definitions in a particular community or are
E3125 Test Method for Evaluating the Point-to-Point Dis-
defined in existing standards. If there are conflicting
tance Measurement Performance of Spherical Coordinate
definitions, our preference is to adapt (modify) the ISO
3D Imaging Systems in the Medium Range
standard (if available) for this standard.
E2807 Specification for 3D Imaging Data Exchange, Version
1.0
1.4 A definition in this terminology is a statement of the
meaning of a word or word group expressed in a single
2.2 ASME Standard:
sentence with additional information included in notes or B89.4.19 Performance Evaluation of Laser Based Spherical
discussions.
Coordinate Measurement Systems
2.3 ISO Standard:
1.5 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the VIM International vocabulary of metrology -- Basic and
general concepts and associated terms
responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter- ISO 11146–1 Lasers and laser-related equipment — Test
methods for laser beam widths, divergence angles and
mine the applicability of regulatory limitations prior to use.
NOTE 1—The subcommittee responsible for this standard will review
definitions on a five-year basis to determine if the definition is still
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
appropriate as stated. Revisions will be made when determined necessary.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
1 3
This terminology is under the jurisdiction of Committee E57 on 3D Imaging Available from American Society of Mechanical Engineers (ASME), ASME
Systems and is the direct responsibility of Subcommittee E57.10 on Terminology. International Headquarters, Three Park Ave., New York, NY 10016-5990, http://
Current edition approved March 1, 2019. Published March 2019. Originally www.asme.org.
approved in 2007. Last previous edition approved in 2011 as E2544 – 11a. DOI: Available from American National Standards Institute (ANSI), 25 W. 43rd St.,
10.1520/E2544-11AR19E01. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
E2544 − 11a (2019)
beam propagation ratios — Part 1: Stigmatic and simple a conventional true value and (2) the CODATA (1986) recom-
astigmatic beams mended value for the Avogadro constant, N : 6 022 136 7 ×
A
23 -1
10 mol .
2.4 NIST/SEMATECH Standard:
(2) Conventional true value is sometimes called assigned
NIST/SEMATECH e-Handbook of Statistical Methods
value, best estimate of the value, conventional value, or
reference value.
3. Terminology
(3) Frequently, a number of results of measurements of a
3.1 Definitions:
quantity is used to establish a conventional true value.
accuracy of measurement, n—closeness of the agreement
between the result of a measurement and a true value of the
error (of measurement), n—result of a measurement minus a
measurand. (VIM 3.5)
true value of the measurand. (VIM 3.10)
DISCUSSION—
DISCUSSION—
(1) Accuracy is a qualitative concept.
(1) Since a true value cannot be determined, in practice, a
(2) The term “precision” should not be used for “accuracy.”
conventional true value is used (see true value and conven-
tional true value).
bias (of a measuring instrument), n—systematic error of the
(2) When it is necessary to distinguish “error” from “
indication of a measuring instrument. (VIM 3.25)
relative error,” the former is sometimes called “absolute error
DISCUSSION—
of measurement.” This should not be confused with the “
(1) The bias of a measuring instrument is normally esti-
absolute value of error,” which is the modulus of error.
mated by averaging the error of indication over an appropriate
number of repeated measurements.
indicating (measuring) instrument, n—measuring instrument
that displays an indication. (VIM 4.6)
bias, n—difference between the average or expected value of a
DISCUSSION—
distribution and the true value.
(1) Examples include analog indicating voltmeter, digital
(NIST/SEMATECH e-Handbook)
frequency meter, and micrometer.
DISCUSSION—
(2) The display may be analog (continuous or discontinu-
(1) In metrology, the difference between precision and
ous) or digital.
accuracy is that measures of precision are not affected by bias,
(3) Values of more than one quantity may be displayed
whereas accuracy measures degrade as bias increases.
simultaneously.
calibration, n—set of operations that establish, under specified
(4) A displaying measuring instrument may also provide a
conditions, the relationship between values of quantities
record.
indicated by a measuring instrument or measuring system, or
limiting conditions, n—the manufacturer’s specified limits on
values represented by a material measure or a reference
the environmental, utility, and other conditions within which
material, and the corresponding values realized by standards.
an instrument may be operated safely and without damage.
(VIM 6.11)
DISCUSSION— (ASME B89.4.19)
(1) The result of a calibration permits either the assignment DISCUSSION—
(1) The manufacturer’s performance specifications are not
of values of measurands to the indications or the determination
assured over the limiting conditions.
of corrections with respect to indications.
(2) A calibration may also determine other metrological
maximum permissible error (MPE), n—extreme values of an
properties such as the effect of influence quantities.
error permitted by specification, regulations, and so forth for
(3) The result of a calibration may be recorded in a
a given measuring instrument. (VIM 5.21)
document, sometimes called a calibration certificate or a
calibration report.
measurand, n—particular quantity subject to measurement.
(VIM 2.6)
compensation, n—the process of determining systematic er-
DISCUSSION—
rors in an instrument and then applying these values in an
(1) Example includes vapor pressure of a given sample of
error model that seeks to eliminate or minimize measure-
water at 20°C.
ment errors. (ASME B89.4.19)
(2) The specification of a measurand may require state-
ments about quantities such as time, temperature, and pressure.
conventional true value (of a quantity), n—value attributed
to a particular quantity and accepted, sometimes by
precision, n—closeness of agreement between independent
convention, as having an uncertainty appropriate for a given
test results obtained under stipulated conditions.
purpose. (VIM 1.20)
(ASTM E456)
DISCUSSION—
DISCUSSION—
(1) Examples: (1) at a given location, the value assigned to
(1) Precision depends on random errors and does not relate
the quantity realized by a reference standard may be taken as
to the true value or the specified value.
(2) The measure of precision is usually expressed in terms
of imprecision and computed as a standard deviation of the test
Available from National Institute of Standards and Technology (NIST), 100
results. Less precision is reflected by a larger standard devia-
Bureau Dr., Stop 1070, Gaithersburg, MD 20899-1070, http://www.nist.gov.
e-Handbook available at http://www.itl.nist.gov/div898/handbook/. tion.
´1
E2544 − 11a (2019)
(3) “Independent test results” means results obtained in a (3) Reproducibility may be expressed quantitatively in
manner not influenced by any previous result on the same or terms of the dispersion characteristics of the results.
similar test object. Quantitative measures of precision depend (4) Results are usually understood to be corrected results.
critically on the stipulated conditions. Repeatability and repro-
systematic error, n—mean that would result from an infinite
ducibility conditions are particular sets of extreme stipulated
number of measurements of the same measurand carried out
conditions.
under repeatability conditions minus a true value of the
precision, n—in metrology, the variability of a measurement
measurand. (VIM 3.14)
process around its average value.
DISCUSSION—
(NIST/SEMATECH e-Handbook)
(1) Systematic error is equal to error minus random error.
DISCUSSION—
(2) Like true value, systematic error and its causes cannot
(1) Precision is usually distinguished from accuracy, the
be completely known.
variability of a measurement process around the true value.
(3) For a measuring instrument, see “bias.”
Precision, in turn, can be decomposed further into short-term
true value (of a quantity), n—value consistent with the
variation or repeatability and long-term variation or reproduc-
definition of a given particular quantity. (VIM 1.19)
ibility.
DISCUSSION—
random error, n—result of a measurement minus the mean
(1) This is a value that would be obtained by a perfect
that would result from an infinite number of measurements
measurement.
of the same measurand carried out under repeatability
(2) True values are by nature indeterminate.
conditions. (VIM 3.13)
(3) The indefinite article “a,” rather than the definite article
DISCUSSION—
“the,” is used in conjunction with “true value” because there
(1) Random error is equal to error minus systematic error.
may be many values consistent with the definition of a given
(2) Because only a finite number of measurements can be
particular quantity.
made, it is possible to determine only an estimate of random
error. uncertainty of measurement, n—parameter, associated with
the result of a measurement, that characterizes the dispersion
rated conditions, n—manufacturer-specified limits on
of the values that could reasonably be attributed to the
environmental, utility, and other conditions within which the
measurand. (VIM 3.9)
manufacturer’s performance specifications are guaranteed at
DISCUSSION—
the time of installation of the instrument.
(1) The parameter may be, for example, a standard devia-
(ASME B89.4.19)
tion (or a given multiple of it) or the half width of an interval
relative error, n—error of measurement divided by a true
having a stated level of confidence.
value of the measurand. (VIM 3.12)
(2) Uncertainty of measurement comprises, in general,
DISCUSSION—
many components. Some of these components may be evalu-
(1) Since a true value cannot be determined, in practice a
ated from the statistical distribution of the results of series of
conventional true value is used.
measurements and can be characterized by experimental stan-
dard deviations. The other components, which can also be
repeatability (of results of measurements), n—closeness of
characterized by standard deviations, are evaluated from as-
the agreement between the results of successive measure-
sumed probability distributions based on experience or other
ments of the same measurand carried out under the same
information.
conditions of measurement. (VIM 3.6)
(3) It is understood that the result of the measurement is the
DISCUSSION—
(1) These conditions are called repeatability conditions. best estimate of the value of the measurand, and that all
components of uncertainty, including those arising from sys-
(2) Repeatability conditions include: the same measure-
ment procedure; the same observer; the same measuring tematic effects, such as components associated with corrections
and reference standards, contribute to the dispersion.
instrument used under the same conditions; the same location;
and repetition over a short period of time.
3.2 Definitions of Terms Specific to This Standard:
(3) Repeatability may be expressed quantitatively in terms
3D imaging system, n—a non-contact measurement instru-
of the dispersion characteristics of the results.
ment used to produce a 3D representation (for example, a
reproducibility (of results of measurements), n—closeness point cloud) of an object or a site.
DISCUSSION—
of the agreement between the results of measurements of the
(1) Some examples of a 3D imaging system are laser
same measurand carried out under changed conditions of
scanners (also known as LADARs or LIDARs or laser radars),
measurement. (VIM 3.7)
DISCUSSION— optical range cameras (also known as flash LIDARs or 3D
(1) A value statement of reproducibility requires
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
´1
Designation: E2544 − 11a (Reapproved 2019) E2544 − 11a (Reapproved 2019)
Standard Terminology for
Three-Dimensional (3D) Imaging Systems
This standard is issued under the fixed designation E2544; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Sections 3.2 and 3.3 were updated editorially in March 2022 to include all current terms developed by Commit-
tee E57.
1. Scope
1.1 This terminology contains common terms, definitions of terms, descriptions of terms, nomenclature, and acronyms associated
with three-dimensional (3D) imaging systems in an effort to standardize terminology used for 3D imaging systems.
1.2 The definitions of the terms presented in 3.1 are obtained from various standard documents developed by various standards
development organizations. The intent is not to change these universally accepted definitions but to gather, in a single document,
terms and their definitions that may be used in current or future standards for 3D imaging systems.
1.2.1 In some cases, definitions of the same term from two standards have been presented to provide additional reference. The text
in parentheses to the right of each defined term is the name (and, in some cases, the specific section) of the source of the definition
associated with that term.
1.3 The definitions in 3.2 are specific terms developed by this committee for 3D imaging systems. Some terms may have generally
accepted definitions in a particular community or are defined in existing standards. If there are conflicting definitions, our
preference is to adapt (modify) the ISO standard (if available) for this standard.
1.4 A definition in this terminology is a statement of the meaning of a word or word group expressed in a single sentence with
additional information included in notes or discussions.
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
NOTE 1—The subcommittee responsible for this standard will review definitions on a five-year basis to determine if the definition is still appropriate as
stated. Revisions will be made when determined necessary.
1.6 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
This terminology is under the jurisdiction of Committee E57 on 3D Imaging Systems and is the direct responsibility of Subcommittee E57.01 on Terminology.
Current edition approved March 1, 2019. Published March 2019. Originally approved in 2007. Last previous edition approved in 2011 as E2544 – 11a. DOI:
10.1520/E2544-11AR19.10.1520/E2544-11AR19E01.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
E2544 − 11a (2019)
2. Referenced Documents
2.1 ASTM Standards:
E456 Terminology Relating to Quality and Statistics
E2919 Test Method for Evaluating the Performance of Systems that Measure Static, Six Degrees of Freedom (6DOF), Pose
E2938 Test Method for Evaluating the Relative-Range Measurement Performance of 3D Imaging Systems in the Medium Range
E3124 Test Method for Measuring System Latency Performance of Optical Tracking Systems that Measure Six Degrees of
Freedom (6DOF) Pose
E3125 Test Method for Evaluating the Point-to-Point Distance Measurement Performance of Spherical Coordinate 3D Imaging
Systems in the Medium Range
E2807 Specification for 3D Imaging Data Exchange, Version 1.0
2.2 ASME Standard:
B89.4.19 Performance Evaluation of Laser Based Spherical Coordinate Measurement Systems
2.3 ISO Standard:
VIM International vocabulary of metrology -- Basic and general concepts and associated terms
ISO 11146–1 Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles and beam
propagation ratios — Part 1: Stigmatic and simple astigmatic beams
2.4 NIST/SEMATECH Standard:
NIST/SEMATECH e-Handbook of Statistical Methods
3. Terminology
3.1 Definitions:
accuracy of measurement, n—closeness of the agreement between the result of a measurement and a true value of the
measurand. (VIM 3.5)
DISCUSSION—
(1) Accuracy is a qualitative concept.
(2) The term “precision” should not be used for “accuracy.”
bias (of a measuring instrument), n—systematic error of the indication of a measuring instrument. (VIM 3.25)
DISCUSSION—
(1) The bias of a measuring instrument is normally estimated by averaging the error of indication over an appropriate number
of repeated measurements.
bias, n—difference between the average or expected value of a distribution and the true value.
(NIST/SEMATECH e-Handbook)
DISCUSSION—
(1) In metrology, the difference between precision and accuracy is that measures of precision are not affected by bias, whereas
accuracy measures degrade as bias increases.
calibration, n—set of operations that establish, under specified conditions, the relationship between values of quantities
indicated by a measuring instrument or measuring system, or values represented by a material measure or a reference material,
and the corresponding values realized by standards. (VIM 6.11)
DISCUSSION—
(1) The result of a calibration permits either the assignment of values of measurands to the indications or the determination
of corrections with respect to indications.
(2) A calibration may also determine other metrological properties such as the effect of influence quantities.
(3) The result of a calibration may be recorded in a document, sometimes called a calibration certificate or a calibration report.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from American Society of Mechanical Engineers (ASME), ASME International Headquarters, Three Park Ave., New York, NY 10016-5990, http://
www.asme.org.
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
Available from National Institute of Standards and Technology (NIST), 100 Bureau Dr., Stop 1070, Gaithersburg, MD 20899-1070, http://www.nist.gov. e-Handbook
available at http://www.itl.nist.gov/div898/handbook/.
´1
E2544 − 11a (2019)
compensation, n—the process of determining systematic errors in an instrument and then applying these values in an error
model that seeks to eliminate or minimize measurement errors. (ASME B89.4.19)
conventional true value (of a quantity), n—value attributed to a particular quantity and accepted, sometimes by convention,
as having an uncertainty appropriate for a given purpose. (VIM 1.20)
DISCUSSION—
(1) Examples: (1) at a given location, the value assigned to the quantity realized by a reference standard may be taken as a
23 -1
conventional true value and (2) the CODATA (1986) recommended value for the Avogadro constant, N : 6 022 136 7 × 10 mol .
A
(2) Conventional true value is sometimes called assigned value, best estimate of the value, conventional value, or reference
value.
(3) Frequently, a number of results of measurements of a quantity is used to establish a conventional true value.
error (of measurement), n—result of a measurement minus a true value of the measurand. (VIM 3.10)
DISCUSSION—
(1) Since a true value cannot be determined, in practice, a conventional true value is used (see true value and conventional true
value).
(2) When it is necessary to distinguish “error” from “ relative error,” the former is sometimes called “absolute error of
measurement.” This should not be confused with the “ absolute value of error,” which is the modulus of error.
indicating (measuring) instrument, n—measuring instrument that displays an indication. (VIM 4.6)
DISCUSSION—
(1) Examples include analog indicating voltmeter, digital frequency meter, and micrometer.
(2) The display may be analog (continuous or discontinuous) or digital.
(3) Values of more than one quantity may be displayed simultaneously.
(4) A displaying measuring instrument may also provide a record.
limiting conditions, n—the manufacturer’s specified limits on the environmental, utility, and other conditions within which an
instrument may be operated safely and without damage. (ASME B89.4.19)
DISCUSSION—
(1) The manufacturer’s performance specifications are not assured over the limiting conditions.
maximum permissible error (MPE), n—extreme values of an error permitted by specification, regulations, and so forth for a
given measuring instrument. (VIM 5.21)
measurand, n—particular quantity subject to measurement. (VIM 2.6)
DISCUSSION—
(1) Example includes vapor pressure of a given sample of water at 20°C.
(2) The specification of a measurand may require statements about quantities such as time, temperature, and pressure.
precision, n—closeness of agreement between independent test results obtained under stipulated conditions.
(ASTM E456)
DISCUSSION—
(1) Precision depends on random errors and does not relate to the true value or the specified value.
(2) The measure of precision is usually expressed in terms of imprecision and computed as a standard deviation of the test
results. Less precision is reflected by a larger standard deviation.
(3) “Independent test results” means results obtained in a manner not influenced by any previous result on the same or similar
test object. Quantitative measures of precision depend critically on the stipulated conditions. Repeatability and reproducibility
conditions are particular sets of extreme stipulated conditions.
precision, n—in metrology, the variability of a measurement process around its average value.
(NIST/SEMATECH e-Handbook)
DISCUSSION—
(1) Precision is usually distinguished from accuracy, the variability of a measurement process around the true value. Precision,
in turn, can be decomposed further into short-term variation or repeatability and long-term variation or reproducibility.
´1
E2544 − 11a (2019)
random error, n—result of a measurement minus the mean that would result from an infinite number of measurements of the
same measurand carried out under repeatability conditions. (VIM 3.13)
DISCUSSION—
(1) Random error is equal to error minus systematic error.
(2) Because only a finite number of measurements can be made, it is possible to determine only an estimate of random error.
rated conditions, n—manufacturer-specified limits on environmental, utility, and other conditions within which the
manufacturer’s performance specifications are guaranteed at the time of installation of the instrument.
(ASME B89.4.19)
relative error, n—error of measurement divided by a true value of the measurand. (VIM 3.12)
DISCUSSION—
(1) Since a true value cannot be determined, in practice a conventional true value is used.
repeatability (of results of measurements), n—closeness of the agreement between the results of successive measurements of
the same measurand carried out under the same conditions of measurement. (VIM 3.6)
DISCUSSION—
(1) These conditions are called repeatability conditions.
(2) Repeatability conditions include: the same measurement procedure; the same observer; the same measuring instrument used
under the same conditions; the same location; and repetition over a short period of time.
(3) Repeatability may be expressed quantitatively in terms of the dispersion characteristics of the results.
reproducibility (of results of measurements), n—closeness of the agreement between the results of measurements of the same
measurand carried out under changed conditions of measurement. (VIM 3.7)
DISCUSSION—
(1) A value statement of reproducibility requires specification of the conditions changed.
(2) The changed conditions may include: principle of measurement; method of measurement; observer; measuring instrument;
reference standard; location; conditions of use; and time.
(3) Reproducibility may be expressed quantitatively in terms of the dispersion characteristics of the results.
(4) Results are usually understood to be corrected results.
systematic error, n—mean that would result from an infinite number of measurements of the same measurand carried out under
repeatability conditions minus a true value of the measurand. (VIM 3.14)
DISCUSSION—
(1) Systematic error is equal to error minus random error.
(2) Like true value, systematic error and its causes cannot be completely known.
(3) For a measuring instrument, see “bias.”
true value (of a quantity), n—value consistent with the definition of a given particular quantity. (VIM 1.19)
DISCUSSION—
(1) This is a value that would be obtained by a perfect measurement.
(2) True values are by nature indeterminate.
(3) The indefinite article “a,” rather than the definite article “the,” is used in conjunction with “true value” because there may
be many values consistent with the definition of a given particular quantity.
uncertainty of measurement, n—parameter, associated with the result of a measurement, that characterizes the dispersion of
the values that could reasonably be attributed to the measurand. (VIM 3.9)
DISCUSSION—
(1) The parameter may be, for example, a standard deviation (or a given multiple of it) or the half width of an interval having
a stated level of confidence.
(2) Uncertainty of measurement comprises, in general, many components. Some of these components may be evaluated from
the statistical distribution of the results of series of measurements and can be characterized by experimental standard deviations.
The other components, which can also be characterized by standard deviations, are evaluated from assumed probability
distributions based on experience or other information.
´1
E2544 − 11a (2019)
(3) It is understood that the result of the measurement i
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.