ASTM E2938-15(2023)

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.
Designation: E2938 − 15 (Reapproved 2023)
Standard Test Method for
Evaluating the Relative-Range Measurement Performance of
3D Imaging Systems in the Medium Range
This standard is issued under the fixed designation E2938; 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.
1. Scope conditions (for example, additional ranges, various
reflectances, environmental conditions).
1.1 This standard describes a quantitative test method for
evaluating the range measurement performance of laser-based,
1.2 The values stated in SI units are to be regarded as
scanning, time-of-flight, 3D imaging systems in the medium
standard. No other units of measurement are included in this
range. The term “medium range” refers to systems that are
standard. SI units are used for all calculations and results in this
capable of operating within at least a portion of ranges from 2
standard.
to 150 m. The term “time-of-flight systems” includes phase-
1.3 The method described in this standard is not intended to
based, pulsed, and chirped systems. The word “standard” in
replace more in-depth methods used for instrument calibration
this document refers to a documentary standard as per Termi-
or compensation, and specific measurement applications may
nology E284. This test method only applies to 3D imaging
require other tests and analyses.
systems that are capable of producing a point cloud represen-
tation of a measured target. 1.4 This standard does not purport to address all of the
1.1.1 As defined in Terminology E2544, a range is the safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
distance measured from the origin of a 3D imaging system to
a point in space. This range is often referred to as an absolute priate safety, health, and environmental practices and deter-
mine the applicability of regulatory limitations prior to use.
range. However, since the origin of many 3D imaging systems
is either unknown or not readily measurable, a test method for Some aspects of the safe use of 3D Imaging Systems are
discussed in Practice ASTM E2641.
absolute range performance is not feasible for these systems.
Therefore, in this test method, the range is taken to be the
1.5 This international standard was developed in accor-
distance between two points in space on a line that passes
dance with internationally recognized principles on standard-
through the origin of the 3D imaging system. Although the
ization established in the Decision on Principles for the
error in the calculated distance between these two points is a
Development of International Standards, Guides and Recom-
relative-range error, in this test method when the term range
mendations issued by the World Trade Organization Technical
error is used it refers to the relative-range error. This test
Barriers to Trade (TBT) Committee.
method cannot be used to quantify the constant offset error
component of the range error.
2. Referenced Documents
1.1.2 This test method recommends that the first point be at
2.1 ASTM Standards:
the manufacturer-specified target 1 range and requires that the
E284 Terminology of Appearance
second target be on the same side of the instrument under test
E1164 Practice for Obtaining Spectrometric Data for Object-
(IUT) as the first target. Specification of target 1 range by the
Color Evaluation
manufacturer minimizes the contribution to the relative range
E1331 Test Method for Reflectance Factor and Color by
measurement error from the target 1 range measurement.
Spectrophotometry Using Hemispherical Geometry
1.1.3 This test method may be used once to evaluate the IUT
E2544 Terminology for Three-Dimensional (3D) Imaging
for a given set of conditions or it may be used multiple times
Systems
to better assess the performance of the IUT for various
E2641 Practice for Best Practices for Safe Application of 3D
Imaging Technology
This test method is under the jurisdiction of ASTM Committee E57 on 3D
Imaging Systems and is the direct responsibility of Subcommittee E57.20 on
Terrestrial Stationary Systems. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Dec. 1, 2023. Published December 2023. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 2015. Last previous edition approved in 2015 as E2938 – 15. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E2938-15R23. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2938 − 15 (2023)
2.2 ASME Standards: 3.1.3 combined standard uncertainty, n—standard uncer-
ASME B89.1.9-2002 Gage Blocks tainty of the result of a measurement when that result is
ASME B89.4.19-2006 Performance Evaluation of Laser- obtained from the values of a number of other quantities, equal
Based Spherical Coordinate Measurement Systems to the positive square root of a sum of terms, the terms being
ASME B89.7.2-1999 Dimensional Measurement Planning the variances or covariances of these other quantities weighted
according to how the measurement result varies with changes
2.3 ISO Standards:
in these quantities. JCGM 100:2008 (GUM) – 2.3.4
ISO 14253-1:1998 Geometrical Product Specifications
(GPS)—Inspection by measurement of workpieces and
3.1.4 compensation, n—the process of determining system-
measuring equipment—Part 1: Decision rules for proving
atic errors in an instrument and then applying these values in an
conformance or non-conformance with specifications
error model that seeks to eliminate or minimize measurement
ISO 14253-2:1999 Geometrical Product Specifications
errors. ASME B89.4.19
(GPS)—Inspection by measurement of workpieces and
3.1.5 covariance—the covariance of two random variables
measuring equipment—Part 2: Guide to the estimation of
is a measure of their mutual dependence. JCGM 100:2008
uncertainty in GPS measurement, in calibration of mea-
(GUM) – C.3.4
suring equipment and in product verification
3.1.6 coverage factor, n—numerical factor used as a multi-
2.4 JCGM Standards:
plier of the combined standard uncertainty in order to obtain an
JCGM 200:2012 International vocabulary of metrology—
expanded uncertainty.
Basic and general concepts and associated terms (VIM),
3.1.6.1 Discussion—A coverage factor, k, is typically in the
3rd edition
range 2 to 3. JCGM 100:2008 (GUM) 2.3.6
JCGM 100:2008 Evaluation of measurement data—Guide to
3.1.7 diffuse reflectance factor, R , n—the ratio of the flux
the expression of uncertainty in measurement (GUM), 1st
d
reflected at all angles within the hemisphere bounded by the
edition
plane of measurement except in the direction of the specular
3. Terminology reflection angle, to the flux reflected from the perfect reflecting
diffuser under the same geometric and spectral conditions of
3.1 Definitions:
measurement. E284 Section 3.1
3.1.1 3D imaging system, n—a non-contact measurement
3.1.7.1 Discussion—The size of the specular reflection
instrument used to produce a 3D representation (for example,
angle depends on the instrument and the measurement condi-
a point cloud) of an object or a site. E2544
tions used. For its precise definition the make and model of the
3.1.1.1 Discussion—Some examples of a 3D imaging sys-
instrument or the aperture angle or aperture solid angle of the
tem are laser scanners (also known as LADARs or LIDARs or
specularly reflected beam should be specified.
laser radars), optical range cameras (also known as flash
3.1.8 documentary standard, n—document, arrived at by
LIDARs or 3D range cameras), triangulation-based systems
such as those using pattern projectors or lasers, and other open consensus procedures, specifying necessary details of a
systems based on interferometry. method of measurement, definitions of terms, or other practical
3.1.1.2 Discussion—In general, the information gathered by matters to be standardized. E284
a 3D imaging system is a collection of n-tuples, where each
3.1.9 expanded test uncertainty, n—product of a combined
n-tuple can include but is not limited to spherical or Cartesian
standard measurement uncertainty and a factor larger than the
coordinates, return signal strength, color, time stamp, identifier,
number one. JCGM 200:2012 (VIM) – 2.35
polarization, and multiple range returns.
3.1.10 flatness, n—the minimum distance between two par-
3.1.1.3 Discussion—3D imaging systems are used to mea-
allel planes between which all points of the measuring face lie.
sure from relatively small scale objects (for example, coin,
ASME B89.1.9 – 3.5
statue, manufactured part, human body) to larger scale objects
3.1.11 limiting conditions, n—the manufacturer’s specified
or sites (for example, terrain features, buildings, bridges, dams,
limits on the environmental, utility, and other conditions within
towns, archeological sites).
which an instrument may be operated safely and without
3.1.2 calibration, n—operation that, under specified
damage. ASME B89.4.19
conditions, in a first step, establishes a relation between the
3.1.11.1 Discussion—The manufacturer’s performance
quantity values with measurement uncertainties provided by
specifications are not assured over the limiting conditions.
measurement standards and corresponding indications with
3.1.12 maximum permissible error (MPE), n—extreme
associated measurement uncertainties and, in a second step,
value of measurement error, with respect to a known reference
uses this information to establish a relation for obtaining a
quantity value, permitted by specifications or regulations for a
measurement result from an indication. JCGM 200:2012
given measurement, measuring instrument, or measuring
(VIM) – 2.39
system. JCGM 200:2012 (VIM) – 4.26
3.1.12.1 Discussion—Usually, the term “maximum permis-
Available from American Society of Mechanical Engineers (ASME), ASME
sible errors” or “limits of error” is used where there are two
International Headquarters, Two Park Ave., New York, NY 10016-5990, http://
extreme values.
www.asme.org.
3.1.12.2 Discussion—The term “tolerance” should not be
Available from American National Standards Institute (ANSI), 25 W. 43rd St.,
4th Floor, New York, NY 10036, http://www.ansi.org. used to designate ‘maximum permissible error’.
E2938 − 15 (2023)
3.1.13 measurand, n—quantity intended to be measured. 3.1.16 measurement uncertainty, n—non-negative param-
JCGM 200:2012 (VIM) – 2.3 eter characterizing the dispersion of the quantity values being
attributed to a measurand, based on the information used.
3.1.13.1 Discussion—The specification of a measurand re-
JCGM 200:2012 (VIM) – 2.26
quires knowledge of the kind of quantity, description of the
3.1.16.1 Discussion—Measurement uncertainty includes
state of the phenomenon, body, or substance carrying the
components arising from systematic effects, such as compo-
quantity, including any relevant component, and the chemical
nents associated with corrections and the assigned quantity
entities involved.
values of measurement standards, as well as the definitional
3.1.13.2 Discussion—In the second edition of the VIM and
uncertainty. Sometimes estimated systematic effects are not
in IEC 60050-300:2001, the measurand is defined as the
corrected for but, instead, associated measurement uncertainty
‘quantity subject to measurement’.
components are incorporated.
3.1.13.3 Discussion—The measurement, including the mea-
3.1.16.2 Discussion—The parameter may be, for example, a
suring system and the conditions under which the measurement
standard deviation called standard measurement uncertainty (or
is carried out, might change the phenomenon, body, or sub-
a specified multiple of it), or the half-width of an interval,
stance such that the quantity being measured may differ from
having a stated coverage probability.
the measurand as defined. In this case, adequate correction is
3.1.16.3 Discussion—Measurement uncertainty comprises,
necessary.
in general, many components. Some of these may be evaluated
Example 1—The potential difference between the termi-
by Type A evaluation of measurement uncertainty from the
nals of a battery may decrease when using a voltmeter with
statistical distribution of the quantity values from series of
a significant internal conductance to perform the measure-
measurements and can be characterized by standard deviations.
ment. The open-circuit potential difference can be calculated
The other components, which may be evaluated by Type B
from the internal resistances of the battery and the voltmeter.
evaluation of measurement uncertainty, can also be character-
Example 2—The length of a steel rod in equilibrium with
ized by standard deviations, evaluated from probability density
the ambient Celsius temperature of 23°C will be different
functions based on experience or other information.
from the length at the specified temperature of 20°C, which
3.1.16.4 Discussion—In general, for a given set of
is the measurand. In this case, a correction is necessary.
information, it is understood that the measurement uncertainty
3.1.13.4 Discussion—In chemistry, “analyte”, or the name
is associated with a stated quantity value attributed to the
of a substance or compound, are terms sometimes used for
measurand. A modification of this value results in a modifica-
‘measurand’. This usage is erroneous because these terms do
tion of the associated uncertainty.
not refer to quantities.
3.1.17 point cloud, n—a collection of data points in 3D
3.1.14 measurement accuracy, n—closeness of agreement
space (frequently in the hundreds of thousands), for example as
between a measured quantity value and a true quantity value of
obtained using a 3D imaging system. E2544
a measurand. JCGM 200:2012 (VIM) – 2.13
3.1.17.1 Discussion—The distance between points is gener-
3.1.14.1 Discussion—The concept ‘measurement accuracy’
ally non-uniform and hence all three coordinates (Cartesian or
is not a quantity and is not given a numerical quantity value. A
spherical) for each point must be specifically encoded.
measurement is said to be more accurate when it offers a
3.1.18 range, n—the distance, in units of length, between a
smaller measurement error.
point in space and an origin fixed to the 3D imaging system
3.1.14.2 Discussion—The term “measurement accuracy”
that is measuring that point. E2544
should not be used for measurement trueness and the term
3.1.18.1 Discussion—In general, the origin corresponds to
measurement precision should not be used for ‘measurement
the instrument origin.
accuracy’, which, however, is related to both these concepts.
3.1.19 rated conditions, n—manufacturer-specified limits
3.1.14.3 Discussion—‘Measurement accuracy’ is sometimes
on environmental, utility, and other conditions within which
understood as closeness of agreement between measured
the manufacturer’s performance specifications are guaranteed
quantity values that are being attributed to the measurand.
at the time of installation of the instrument. ASME B89.4.19
3.1.15 measurement error, n—measured quantity value mi-
3.1.20 repeatability (of results of measurements),
nus a reference quantity value. JCGM 200:2012 (VIM) – 2.16
n—closeness of the agreement between the results of succes-
3.1.15.1 Discussion—The concept of ‘measurement error’
sive measurements of the same measurand carried out under
can be used both: (1) when there is a single reference quantity
the same conditions of measurement. JCGM 200:2012 (VIM)
value to refer to, which occurs if a calibration is made by
– 3.6
means of a measurement standard with a measured quantity
3.1.20.1 Discussion—These conditions are called repeat-
value having a negligible measurement uncertainty or if a
ability conditions.
conventional quantity value is given, in which case the
3.1.20.2 Discussion—Repeatability conditions include: the
measurement error is known; and (2) if a measurand is
same measurement procedure; the same observer; the same
supposed to be represented by a unique true quantity value or
measuring instrument used under the same conditions; the
a set of true quantity values of negligible range, in which case
same location; and repetition over a short period of time.
the measurement error is not known.
3.1.20.3 Discussion—Repeatability may be expressed quan-
3.1.15.2 Discussion—Measurement error should not be con- titatively in terms of the dispersion characteristics of the
fused with production error or mistake. results.
E2938 − 15 (2023)
3.1.21 reflectance, n—ratio of the reflected radiant or lumi- 3.2.4.2 Discussion—The target 1 range is not necessarily
nous flux to the incident flux in the given conditions. E284 the same as the minimum range specified by the manufacturer,
Section 3.1 but may be close to it.
3.1.21.1 Discussion—The term reflectance is often used in a 3.2.4.3 Discussion—Since the origin of a 3D imaging sys-
general sense or as an abbreviation for reflectance factor. Such tem is either unknown or not readily measurable in many cases,
usage may be assumed unless the above definition is specifi- a user may not be able to place Target 1 at the target 1 range
cally required by context. with a known error. Thus, the target 1 range is a nominal value
that represents the approximate distance from the origin of the
3.1.22 reflectance factor, n—ratio of the flux reflected from
IUT at which Target 1 should be placed.
the specimen to the flux reflected from the perfect reflecting
diffuser under the same geometric and spectral conditions of
3.2.5 target 2 range, n—the range, as chosen by the person
measurement. E284 Section 3.1
conducting this test, from the IUT to the second target used in
this standard.
3.1.23 target, n—an object to be measured. ASME B89.7.2-
3.2.5.1 Discussion—The target 2 range must be between (or
at) the minimum and maximum ranges of the IUT, as specified
3.1.24 uncertainty budget, n—statement summarizing the
by the manufacturer.
estimation of the uncertainty components that contributes to
3.2.5.2 Discussion—Since the origin of a 3D imaging sys-
the uncertainty of a result of a measurement. ISO 14253-
tem is either unknown or not readily measurable in many cases,
2:1999
a user may not be able to place Target 2 at the target 2 range
3.1.25 variance—the variance of a random variable is the
with a known error. Thus, the target 2 range is a nominal value
expectation of its quadratic deviation about its expectation.
that represents the approximate distance from the origin of the
JCGM 100:2008 (GUM) – C.3.2
IUT at which Target 2 should be placed.
3.2 Definitions of Terms Specific to This Standard:
4. Significance and Use
3.2.1 IUT, n—instrument under test.
3.2.2 maximum permissible relative-range error, R , 4.1 This standard provides a test method for obtaining the
MPE
n—extreme value of the relative-range error, expressed in units range error for medium-range 3D imaging systems. The results
of length, permitted by specifications or regulations for a 3D from this test method may be used to evaluate or to verify the
imaging system. range measurement performance of medium-range 3D imaging
3.2.2.1 Discussion—The maximum permissible value of the systems. The results from this test method may also be used to
relative-range error, R , can be expressed as: compare performance among different instruments.
MPE
R = minimum of (A + B*L) and C, or
MPE
4.2 The range performance of the IUT obtained by the
R = (A + B*L), or
MPE
application of this test method may be different from the range
R = C
MPE
performance of the IUT under some real-world conditions. For
where:
example, object geometry, texture, temperature and reflectance
A and C are positive constants, expressed in millimeters
as well as vibrations, particulate matter, thermal gradients,
and supplied by the manufacturer;
ambient lighting, and wind in the environment will affect the
B is a dimensionless positive constant supplied by the
range performance.
manufacturer; and
4.3 The test may be carried out for instrument acceptance,
L is equal to the target 2 range, in millimeters (distance
warranty or contractual purposes by mutual agreement between
from the origin of the 3D imaging system to Target 2).
the manufacturer and the user. The IUT is tested in accordance
Different values for A, B, and C may be provided by the
with manufacturer-supplied specifications, rated conditions,
manufacturer for different range intervals for the IUT.
and technical documentation. This test may be repeated for any
3.2.3 relative-range error, n—the difference in the distance
target 2 range within the manufacturer’s specifications and for
between two points measured by an instrument and the
any rated conditions.
reference distance between the same points, where the points
4.4 For the purposes of understanding the behavior of the
are on the same side of the instrument and lie on a line that
IUT and without warranty implications, this test may be
passes through the origin of the instrument.
modified as necessary to characterize the range measurement
3.2.3.1 Discussion—The relative-range error does not in-
performance of the IUT outside the manufacturer’s rated
clude the error caused by any constant offset between the
conditions, but within the manufacturer’s limiting conditions.
optical and mechanical origins of the instrument. Any constant
offsets in the two range measurements will cancel each other
4.5 The manufacturer may provide different values for the
when the relative range is calculated. This offset is sometimes
specifications for different sets of rated conditions, for
referred to as the R0 error.
example, better range measurement performance might be
3.2.4 target 1 range, n—the range, as specified by the 3D specified under a set of more restrictively rated environmental
imaging instrument manufacturer, from the IUT to the first conditions. The user is advised that the IUT’s performance may
target used in this standard. differ significantly in other modes of operation or outside the
3.2.4.1 Discussion—The target 1 range will usually be the rated conditions and should inquire with the manufacturer for
range from the IUT at which the error in the range measure- specifications of the mode that best represents the planned
ment is minimized. usage. If a target other than that described in Section 7, or if
E2938 − 15 (2023)
procedures other than those described in Section 8 are used, must be clearly described so that they can be reproduced by
additional analysis not covered in this test method may be any qualified user (see Note 3).
required.
6.2.2 The IUT shall be operated in accordance with the
procedures given in the manufacturer’s User Manual. All
5. Introduction
applicable procedures described in the manufacturer’s User
5.1 This standard involves measuring the distance between Manual for the proper use of the instrument, such as machine
the centers of two flat target plates that are nominally parallel
startup/warm-up, compensation procedures and manufacturer
to each other by scanning them with the IUT (see Note 1). Line
maintenance requirements, shall be adhered to.
A, as shown in Fig. 1, is a virtual line that passes through the
NOTE 3—A qualified user is a person who has been trained in the proper
geometrical centers of the front sides of the two target plates.
use of the IUT.
The two target plates are oriented so that their front surfaces
6.3 Target Location Requirements:
are perpendicular to Line A. Line A should ideally go through
the origin of the IUT in order to minimize the contribution of 6.3.1 For the purposes of comparing the range measurement
any angular errors to the range error. If Line A does not go performance of the IUT with the manufacturer’s specifications,
Target 1 shall be placed at the target 1 range specified by the
through the origin of the IUT, any offset distance of the origin
of the IUT from Line A should be minimized (see Appendix manufacturer. If the target 1 range is not specified by the
manufacturer, the user may select any range between and
X2). The distance between the two target plates as measured by
the IUT is then compared to the corresponding distance (a including the minimum range and the maximum range of the
IUT. In the case where the manufacturer specifies a target 1
reference distance) measured using a reference instrument and
the difference between them is defined as the range error (see range, and the user does not choose to use it, then the IUT’s
range measurement performance may differ from the manufac-
Note 2). This range error is the metric used to quantify the
relative-range measurement performance of the IUT. turer’s specifications.
NOTE 1—The user may use either the same physical flat target plate to
6.3.2 For the purposes of understanding the behavior of the
represent both Target 1 and Target 2 or may use two different physical flat
IUT and without warranty implications, the user may select
target plates.
any range between and including the minimum range and the
NOTE 2—Because the range is calculated as the distance between two
maximum range of the IUT for Target 1.
points, the R0 error cancels out and cannot be determined using this test
method. Appendix X2, Section X2.2.11 describes the R0 error.
6.3.3 Target 1 and Target 2 shall be located on the same side
of the IUT so that the normals of the front face of both targets
6. Test Conditions and Requirements
are pointing in the same direction and toward the IUT (as
6.1 Rated Conditions:
shown in Fig. 1).
6.1.1 The rated conditions should be provided by the
6.3.4 Target 2 shall be located between (or at) the minimum
manufacturer. Recommended rated conditions include target 1
and maximum ranges of the IUT, as specified by the
range, minimum and maximum ranges, target characteristics
manufacturer, and may be located closer to the IUT than Target
(7.1), minimum and maximum temperatures, and thermal
1.
gradient (°C/m and °C/h). If any rated condition is not
6.4 Test Uncertainty:
specified, then it is assumed that the test will be valid for any
6.4.1 An estimate of the errors associated with the limita-
range of that condition.
tions in the present test method to properly evaluate the
6.1.2 The conditions of the test environment must remain
within the bounds of the manufacturer’s rated conditions relative-range measurement performance of the IUT is called
the test uncertainty. This is the uncertainty of the calculated
throughout the test.
range error (E in Section 10.1) of the IUT.
range
6.2 Operating Modes:
6.4.2 In this test method, the expanded test uncertainty, U, is
6.2.1 Operating modes for an instrument typically define the
equal to two times the combined standard uncertainty (that is,
instrument settings such as point spacing, scanning acquisition
a coverage factor, k = 2).
rate, and integration time. The manufacturer must state the
operating modes under which the specified performance values
NOTE 4—According to ISO 14253-1, Section 4, by default the coverage
are valid. Operating modes must be available to the user and factor is k = 2.
FIG. 1 Top View Showing the IUT and the Position and Orientation of the Target Plates Relative to the IUT
E2938 − 15 (2023)
6.4.3 U must be less than or equal to ⁄4 (simple 4:1 decision
rule) of the maximum permissible range error, R , which
MPE
shall be specified by the manufacturer of the IUT. See
Appendix X2 for an example of how to calculate U.
NOTE 5—Industry practice is to use a simple 4:1 decision rule ratio of
MPE to expanded uncertainty. For example, Section 6.2 of ASME
FIG. 2 The Target Edge Radius
B89.4.19-2006 standard specifies that the expanded uncertainty of the
reference length should not exceed one quarter of the MPE of the IUT to
components, while the diffuse reflectance factor excludes the specular
MPE
obtain a measurement capability index, C 5 , of 4.
m component.
U
7.1.2 Mechanical Requirements:
7. Apparatus
7.1.2.1 The minimum target plate size should be specified
7.1 Target—The target is a flat plate with optical and
by the manufacturer, and must be sufficient to yield a minimum
mechanical requirements determined by the expected perfor-
of 100 points after point selection (see 9.2). The front side of
mance of the IUT as discussed below. The target may be
the target plate shall consist of a single surface made of a single
square, rectangular, circular or any other shape for which a
material. The edges of the target shall have a radius (R in Fig.
boundary is easily defined. However, for illustration purposes,
2) of less than or equal to one quarter ( ⁄4) of the smallest beam
a square- or rectangular-shaped target is assumed throughout
width of the IUT.
this document.
7.1.2.2 The flatness of the target plate shall not exceed 20 %
7.1.1 Optical Requirements:
of the MPE of the range error of the IUT at the relevant target
7.1.1.1 Different materials have different optical character-
range. The flatness should be measured in accordance with the
istics such as reflectance, optical penetration depth (volumetric
procedures in Section 5.4.2 of ASME Y14.5.1M-1994-R2009.
scattering), color, and surface scattering characteristics, which
7.1.3 Mounting:
means that the values of the measured range errors may differ
7.1.3.1 The target plate shall be rigidly mounted on stable
for different materials. Materials that may be used for the target
supports and the front surface of the target plate shall be
include, but are not limited to, ceramic, steel and aluminum.
unobstructed. In addition, any part of the target plate support
One candidate target is constructed of aluminum with a
that is visible to the IUT should be sufficiently separated from
vapor-blasted surface finish.
the target plate so that any measured points on the support may
7.1.1.2 The types of target materials, and their optical
be easily removed in the data segmentation in 9.1. Fig. 3 shows
characteristics (for example, target reflectance), used in the test
examples of acceptable and unacceptable configurations of the
should be specified by the manufacturer. If a material other
target plate support.
than that specified by the manufacturer is used, the perfor-
7.1.4 Alignment:
mance of the IUT using this material may not meet the
7.1.4.1 The required quality of the target plate and IUT
manufacturer’s specifications. If the target material is not
alignment (position and orientation with respect to Line A) is
specified by the manufacturer, the user is free to use any
primarily determined by the specifications of the IUT. Accept-
material for the test. It is recommended that the manufacturer
able alignment criteria need to be determined by conducting an
use target materials for the testing that may be obtained at a
uncertainty analysis for the specific test setup and IUT utilized.
reasonable cost to the user.
An example of how to determine the uncertainty budget for the
7.1.1.3 The reflectance factor of the target surface as mea-
specific test setup given in “Appendix X1 – Example Proce-
sured in accordance with Practice E1164 and Test Method
dure” is provided in “Appendix X2 – Assessing Test Uncer-
E1331 must be within the manufacturer’s specifications. It is
tainty.”
strongly recommended that the reflectance factor with and
7.2 Reference Instrument—The reference instrument shall
without the specular component be reported, if possible. If the
measure the reference distance with an expanded uncertainty
reflectance factor is not specified by the manufacturer, the user
(k = 2) less than that of the manufacturer-specified maximum
is free to use any reflectance factor for the test.
permissible range error, R , of the IUT. The choice of
MPE
NOTE 6—The reflectance factor consists of both diffuse and specular reference instrument should be such that its MPE would result
FIG. 3 The Target Plate Supports shown in (a) and (b) will Meet the Requirement in this Section whereas the Target Plate Supports
Shown in (c), (d) and (e) Will Not Meet the Requirement
E2938 − 15 (2023)
Target 2 with the IUT. Alternatively, the same physical target may be
in an expanded test uncertainty, U (as described in Appendix
scanned at target 1 range and at target 2 range sequentially if appropriate.
X2 – Assessing Test Uncertainty), that is in conformance with
NOTE 8—Ensure that the points on the target can be clearly distin-
6.4. The reference instrument shall be maintained and used in
guished from the background. This may require that nearby objects be 1 m
accordance with the manufacturer’s instructions.
or more from the target and that highly reflective surfaces in the field of
view of the IUT be removed or covered.
8. Test Procedure
9. Determination of Target Plate Centers
8.1 The test procedure for acquiring data consists of the
NOTE 9—This section describes the steps required to determine the
steps outlined below; however, the sequence of the steps may
geometric centers of Target 1 and Target 2 using the measured points
differ from one test to another depending on the specific test
obtained from the IUT. Details of the procedure can be found in the
requirements. A schematic of an example experimental setup is
subsequent sections and a summary of the steps is as follows: (1)
shown in Fig. 1. Appendix X1 describes one way in which the
Eliminate from the IUT data set all those measured points that are part of
the background, surroundings, and target plate supports (9.1). (2) Select
test procedure may be implemented.
measured points that will be used for the plane fit by omitting the
8.1.1 Set up Target 1 at target 1 range and Target 2 at target
measured points that are in the edge exclusion regions (9.2). (3) Fit planes
2 range and ensure that there are no objects (other than the
and calculate the standard deviations of the residuals (9.3). (4) Eliminate
target supports) within 1 m of either Target 1 or Target 2. Target
measured points on the target plates for which the magnitude of the
1 and Target 2 may or may not be set up at the same time.
residuals are greater than twice the standard deviation of the residuals of
the plane fit (9.4). (5) Determine the geometric centers of the target plates
8.1.2 Align the front surfaces of the target plates so that they
(9.5).
are as perpendicular as possible to the line that connects their
9.1 First Data Segmentation:
geometrical centers (Line A) according to 7.1.4.
8.1.3 Align the IUT (as shown in Fig. 1) in order to 9.1.1 For the purposes of analysis, measured points from the
minimize the offset distance of the origin (center of rotation) of target plate may be manually segmented from measured points
the IUT from Line A according to 7.1.4. from other sources such as from the background and the target
8.1.4 Measure the distance, L , between the geometrical plate support using data manipulation software. This manual
ref
centers of the target plates with the reference instrument. The segmentation may be achieved using the best available method
method used for calculating L will vary depending on the such as visual identification of the boundaries of the target
ref
reference instrument and targets used, and is left to the user. plate from the intensity image.
8.1.5 Scan each target plate with the IUT using the same
9.1.2 Measured points collected from the target plate shall
operating mode settings for all scans, ensuring that the IUT not be removed or filtered out. The resulting set of points for
scans beyond the edges of the target plate. The operating mode
each target plate shall be called Point Set A1 for Target 1 and
settings shall be chosen to yield, after point selection per 9.2, Point Set A2 for Target 2.
a minimum of 100 measured points within the point selection
9.2 Selection of Points on the Target Plate for Fitting a
region. An image (or screen capture), from the point of view of
Plane:
the IUT, showing the distribution of the data on each target
9.2.1 Measured points from a region within the target plate
plate shall be provided as part of the report.
and away from the edges of the target plate shall be selected
8.1.6 Repeat the above steps three times under the same
from Point Sets A1 and A2 for fitting a plane in 9.3. This point
repeatability conditions for a total of three repetitions and
selection region shall not include measured points within the
report the results for all repetitions. Scanning the same target
exclusion regions near the edges of the target plate. The widths
three times consecutively is not considered three repetitions.
of the exclusion regions shall be provided by the manufacturer
NOTE 7—Target 1 may need to be removed in order to be able to scan and may differ along the two scan axes. The widths, a and b,
FIG. 4 A Schematic of a Target Plate having Dimensions W × L Showing the Selection Regions and the Widths a and b of the Exclusion
Region
E2938 − 15 (2023)
of the exclusion regions shall be measured parallel to the edges centers may be 2D or 3D methods. These methods include, but
of the target plate (see Fig. 4). In the absence of information are not limited to, using 2D bounding rectangles, 3D bounding
from the manufacturer about the widths of the exclusion
boxes, 2D or 3D convex hulls, centroids, or intersections of
regions, the widths shall be set equal to (or greater than) the diagonals. The method used to estimate the geometric centers
laser beam width at the target plate location.
will generate centers that are offset from the true geometric
centers of the targets (the offsets are e and e in Appendix X2).
1 2
NOTE 10—Measured points close to the edges of the targets may
The user shall estimate e and e and include them in the
introduce an additional error into the plane fit due to phenomena such as
1 2
multiple returns; therefore, those measured points shall not be used in the calculation of the test uncertainty.
plane fit.
9.5.1.2 If the method used to estimate the geometric centers
NOTE 11—The selection of measured points for the plane fit may be
in Step 1 is a 2D method, then the resulting geometric centers
done visually or computationally.
are the geometric centers of the targets. If the method used to
9.2.2 The point selection region shall:
estimate the geometric centers in Step 1 is a 3D method, then
9.2.2.1 Cover 50 % of the target plate area, at a minimum,
the resulting geometric centers must be projected onto the
but should not exceed the maximum selection region, as shown
respective planes obtained in 9.3. The resulting projected
in Fig. 4.
coordinates are the geometric centers of the targets.
9.2.2.2 Have a height and width no smaller than 10 times
9.5.2 The geometric centers of Target 1 and Target 2 will
the IUT laser beam width at the target plate location.
have coordinates (x , y , z ) and (x , y , z ), respectively.
9.2.2.3 Be nominally centered on the target plate. 1 1 1 2 2 2
9.2.2.4 Contain at least 100 points.
10. Calculation and Interpretation of the Results
9.2.3 The resulting set of points for each target plate shall be
called Point Set B1 for Target 1 and Point Set B2 for Target 2.
10.1 Range Error:
9.2.4 Once the selection region is defined, all measured
10.1.1 The range error, E , is:
range
points that fall within that point selection region must be
E 5 L 2 L (1)
included in Point Set B1 for Target 1 and Point Set B2 for
range meas ref
Target 2, respectively, and no points shall be manually or
where L is the distance between the centers of the two
ref
computationally removed or filtered from that selection region.
target plates as obtained by the reference instrument, and L
meas
9.3 Fit of a Plane to the Target Plate Data:
is the distance between the centers of the two target plates as
9.3.1 For each Point Set B1 and Point Set B2 as defined in
determined in 9.5, and is calculated as follows:
9.2, a plane is fit to estimate the front surface of the corre-
2 2 2
L 5 = x 2 x 1 y 2 y 1 z 2 z (2)
sponding target plate. The plane fitting method shall use all ~ ! ~ ! ~ !
meas 1 2 1 2 1 2
points in the point set and shall not, to the best knowledge of
10.1.2 If |E | ≤ R as specified by the manufacturer,
range MPE
the user, eliminate any of the points during the fitting process.
then the IUT is in conformance with the manufacturer speci-
Where possible the plane fitting method should minimize the
5 fications.
residual error in a total least-squares sense. If the user cannot
10.1.3 If |E | > R as specified by the manufacturer,
determine which plane fitting method is being used or if they
range MPE
then the IUT is not in conformance with the manufacturer
choose to use a different plane fitting method, this must be
specifications.
reported. Record the standard deviations, s and s , of the
1 2
residuals of the plane fits for Target 1 and Target 2, respec-
10.1.4 The range error calculation (10.1.1) shall be per-
tively.
formed for each of the three repetitions per Section 8.
9.4 Second Data Segmentation:
10.2 RMS Dispersion:
9.4.1 For each of Point Set A1 and Point Set A2 (see 9.1),
10.2.1 The user shall report the dispersion of the residuals
eliminate points for which the magnitudes of the residuals are
based on a least-squares fit to a plane for both Point Set C1 and
greater than 2s and 2s (from 9.3), respectively. The residuals
1 2
Point Set C2. The dispersion shall be reported as the RMS
are the orthogonal distances of all measured points in each
dispersion, RMS and RMS , for Target 1 and Target 2,
1 2
point set to its respective plane determined in 9.3.
respectively. The RMS dispersions, RMS and RMS , are found
1 2
9.4.2 The resulting set of points for each target plate shall be
by calculating the square root of the average squared residual
called Point Set C1 for Target 1 and Point Set C2 for Target 2.
for Point Set C1 and Point Set C2, respectively. In general, the
Point Set C1 and Point Set C2 represent approximately 95 % of
RMS is calculated as:
all measured points on Target 1 and Target 2, respectively.
N
9.5 Determination of the Geometric Target Plate Center:
d
( i
9.5.1 The target plate centers of Target 1 and Target 2 are i51
RMS 5 (3)
!
N
determined by performing the following steps using Point Set
C1 and Point Set C2, respectively (as defined in 9.4):
where:
9.5.1.1 Find the best estimate of the geometric centers of
d = residual distance of measured point i to the plane
i
Target 1 and Target 2. Methods for estimating the geometric
determined in 9.3, and
N = total number of measured points in Point Set C1 for
Golub, Gene H., and Van Loan, Charles F., “An Analysis of the Total Least
RMS or Point Set C2 for RMS .
1 2
Squares Problem,” SIAM Journal on Numerical Analysis, 17.6, 1980, pp. 883-893.
E2938 − 15 (2023)
10.2.2 The RMS dispersion may be used as an indication of 11.1.1.12 Temperature at the IUT at the beginning and the
the expected measurement dispersion of the IUT when mea- end of the test, in °C;
suring the target material used in this test under the same test 11.1.1.13 Temperature at both targets at the beginning and
conditions. the end of the test, in °C;
11.1.1.14 Whether the test was conducted indoors or out-
10.3 Acceptance Criteria:
doors;
10.3.1 If the range errors are in conformance for all three
11.1.1.15 Manufacturer-specified R ; and
MPE
repetitions, then the IUT is considered to be in conformance
11.1.1.16 Report author signature and date signed.
with the manufacturer specifications. If any of the range errors
11.1.2 The following test results shall be reported:
for any of the three repetitions is not in conformance, then the
11.1.2.1 Measured distance between targets, in m for all
IUT is considered to not be in conformance with the manufac-
three repetitions;
turer specifications.
11.1.2.2 Reference distance between targets, in m for all
11. Report
three repetitions;
NOTE 12—An example of a reporting form is given in Appendix X3.
11.1.2.3 Range error, e , in mm for all three repetitions;
range
11.1 Mandatory Reporting: 11.1.2.4 Dispersion of the residuals of the plane fits, RMS
11.1.1 The following information about the test conditions and RMS (10.2), in mm for all three repetitions;
shall be reported:
11.1.2.5 For each
...