ASTM E3125-17

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: E3125 − 17
Standard Test Method for
Evaluating the Point-to-Point Distance Measurement
Performance of Spherical Coordinate 3D Imaging Systems
in the Medium Range
This standard is issued under the fixed designation E3125; 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.
1. Scope 1.5 SI units are used for all calculations and results in this
standard.
1.1 This test method covers the performance evaluation of
laser-based, scanning, time-of-flight, single-detector 3D imag- 1.6 This test method is not intended to replace more
ing systems in the medium-range and provides a basis for
in-depth methods used for instrument calibration or
comparisonsamongsuchsystems.Thisstandardbestappliesto compensation, and specific measurement applications may
spherical coordinate 3D imaging systems that are capable of
require other tests and analyses.
producing a point cloud representation of an object of interest.
1.7 This standard does not purport to address all of the
In particular, this standard establishes requirements and test
safety concerns, if any, associated with its use. It is the
procedures for evaluating the derived-point to derived-point
responsibility of the user of this standard to establish appro-
distance measurement performance throughout the work vol-
priate safety, health, and environmental practices and deter-
ume of these systems. Although the tests described in this
mine the applicability of regulatory limitations prior to use.
standardmaybeusedfornon-sphericalcoordinate3Dimaging
Some aspects of the safe use of 3D imaging systems are
systems,thetestmethodmaynotnecessarilybesensitivetothe
discussed in Practice E2641.
error sources within those instruments.
1.8 This international standard was developed in accor-
1.2 System performance is evaluated by comparing mea-
dance with internationally recognized principles on standard-
sured distance errors between pairs of derived-points to the
ization established in the Decision on Principles for the
manufacturer-specified, maximum permissible errors (MPEs).
Development of International Standards, Guides and Recom-
In this standard, a derived-point is a point computed using
mendations issued by the World Trade Organization Technical
multiple measured points on the target surface (such as the
Barriers to Trade (TBT) Committee.
center of a sphere). In the remainder of this standard, the term
point-to-point distance refers to the distance between two
2. Referenced Documents
derived-points.
2.1 ASTM Standards:
1.3 The term “medium-range” refers to systems that are
E284Terminology of Appearance
capableofoperatingwithinatleastaportionoftherangesfrom
E1164PracticeforObtainingSpectrometricDataforObject-
2 m to 150 m. The term “time-of-flight systems” includes
Color Evaluation
phase-based, pulsed, and chirped systems. The word “stan-
E1331Test Method for Reflectance Factor and Color by
dard” in this document refers to a documentary standard in
Spectrophotometry Using Hemispherical Geometry
accordance with Terminology E284.
E2544Terminology for Three-Dimensional (3D) Imaging
Systems
1.4 This test method may be used once to evaluate the
E2641PracticeforBestPracticesforSafeApplicationof3D
Instrument Under Test (IUT) for a given set of conditions or it
Imaging Technology
may be used multiple times to assess the performance of the
E2919Test Method for Evaluating the Performance of
IUT for various conditions (for example, surface reflectance
Systems that Measure Static, Six Degrees of Freedom
factors, environmental conditions).
(6DOF), Pose
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 For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Terrestrial Stationary Systems. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Current edition approved Oct. 1, 2017. Published December 2017. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E3125-17. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E3125 − 17
E2938Test Method for Evaluating the Relative-Range Mea- quantity values with measurement uncertainties provided by
surement Performance of 3D Imaging Systems in the measurement standards and corresponding indications with
Medium Range associated measurement uncertainties and, in a second step,
uses this information to establish a relation for obtaining a
2.2 ASME Standards:
measurement result from an indication. JCGM 200:2012
ASME B89.4.19-2006Performance Evaluation of Laser-
(VIM) – 2.39
Based Spherical Coordinate Measurement Systems
ASME B89.7.3.1-2001Guidelines for Decision Rules: Con-
3.1.4 combined standard uncertainty, n—standard uncer-
sidering Measurement Uncertainty in Determining Con-
tainty of the result of a measurement when that result is
formance to Specifications
obtainedfromthevaluesofanumberofotherquantities,equal
ASME Y14.5-2009Dimensioning and Tolerancing
to the positive square root of a sum of terms, the terms being
2.3 ISO Standards:
the variances or covariances of these other quantities weighted
ISO 1:2016Geometrical product specifications (GPS)—
according to how the measurement result varies with changes
Standard reference temperature for the specification of
in these quantities. JCGM 100:2008 (GUM) – 2.3.4
geometrical and dimensional properties
3.1.5 coverage factor, n—numerical factor used as a multi-
ISO 10360-10:2016 Geometrical product specifications
plierofthecombinedstandarduncertaintyinordertoobtainan
(GPS)—Acceptanceandreverificationtestsforcoordinate
expanded uncertainty. JCGM 100:2008 (GUM) – 2.3.6
measuring systems (CMS)—Part 10: Laser trackers for
measuring point-to-point distances
3.1.5.1 Discussion—Acoverage factor, k, is typically in the
2.4 JCGM Standards:
range 2 to 3.
JCGM100:2008Evaluationofmeasurementdata—Guideto
3.1.6 diffuse reflectance factor, n—the ratio of the flux
the expression of uncertainty in measurement (GUM), 1st
reflected at all angles within the hemisphere bounded by the
edition
plane of measurement except in the direction of the specular
JCGM 200:2012International vocabulary of metrology—
reflectionangle,tothefluxreflectedfromtheperfectreflecting
Basic and general concepts and associated terms (VIM),
diffuser under the same geometric and spectral conditions of
3rd edition
measurement. E284-13b – 4.1
3. Terminology
3.1.6.1 Discussion—The size of the specular reflection
angle depends on the instrument and the measurement condi-
3.1 Definitions:
tionsused.Foritsprecisedefinitionthemakeandmodelofthe
3.1.1 3D imaging system, n—a non-contact measurement
instrument or the aperture angle or aperture solid angle of the
instrument used to produce a 3D representation (for example,
specularly reflected beam should be specified.
a point cloud) of an object or a site. E2544-11a – 3.2
3.1.7 documentary standard, n—document, arrived at by
3.1.1.1 Discussion—Some examples of a 3D imaging sys-
open consensus procedures, specifying necessary details of a
tem are laser scanners (also known as LADARs or LIDARs or
methodofmeasurement,definitionsofterms,orotherpractical
laser radars), optical range cameras (also known as flash
matters to be standardized. E284-13b – 4.1
LIDARs or 3D range cameras), triangulation-based systems
3.1.8 expanded measurement uncertainty (expanded
such as those using pattern projectors or lasers, and other
systems based on interferometry. uncertainty), n—product of a combined standard measurement
uncertainty and a factor larger than the number one. JCGM
3.1.1.2 Discussion—In general, the information gathered by
a 3D imaging system is a collection of n-tuples, where each 200:2012 (VIM) – 2.35
n-tuple can include but is not limited to spherical or Cartesian
3.1.9 limiting conditions, n—manufacturer’sspecifiedlimits
coordinates,returnsignalstrength,color,timestamp,identifier,
on the environmental, utility, and other conditions within
polarization, and multiple range returns.
which an instrument may be operated safely and without
3.1.1.3 Discussion—3D imaging systems are used to mea-
damage. ASME B89.4.19-2006 – 4
sure from relatively small scale objects (for example, coin,
statue, manufactured part, human body) to larger scale objects 3.1.9.1 Discussion—Manufacturer’s performance specifica-
orsites(forexample,terrainfeatures,buildings,bridges,dams, tions are not assured over the limiting conditions.
towns, archeological sites).
3.1.10 maximum permissible measurement error (maximum
3.1.2 beam width, n—the extent of the irradiance distribu-
permissible error), n—extreme value of measurement error,
tioninacrosssectionofalaserbeam(inadirectionorthogonal
with respect to a known reference quantity value, permitted by
to its propagation path). E2544-11a – 3.2
specifications or regulations for a given measurement, measur-
ing instrument, or measuring system. JCGM 200:2012 (VIM)
3.1.3 calibration, n—operation that, under specified
– 4.26
conditions, in a first step, establishes a relation between the
3.1.10.1 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.
3.1.10.2 Discussion—The term “tolerance” should not be
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
4th Floor, New York, NY 10036, http://www.ansi.org. used to designate ‘maximum permissible error’.
E3125 − 17
3.1.11 measurand, n—quantity intended to be measured. a specified multiple of it), or the half-width of an interval,
JCGM 200:2012 (VIM) – 2.3 having a stated coverage probability.
3.1.15.3 Discussion—Measurement uncertainty comprises,
3.1.11.1 Discussion—The specification of a measurand re-
ingeneral,manycomponents.Someofthesemaybeevaluated
quires knowledge of the kind of quantity, description of the
by Type A evaluation of measurement uncertainty from the
state of the phenomenon, body, or substance carrying the
statistical distribution of the quantity values from series of
quantity, including any relevant component, and the chemical
measurementsandcanbecharacterizedbystandarddeviations.
entities involved.
The other components, which may be evaluated by Type B
3.1.11.2 Discussion—In the second edition of the VIM and
evaluation of measurement uncertainty, can also be character-
in IEC 60050-300:2001, the measurand is defined as the
izedbystandarddeviations,evaluatedfromprobabilitydensity
‘particular quantity subject to measurement’.
functions based on experience or other information.
3.1.11.3 Discussion—The measurement, including the mea-
3.1.15.4 Discussion—In general, for a given set of
suringsystemandtheconditionsunderwhichthemeasurement
information, it is understood that the measurement uncertainty
is carried out, might change the phenomenon, body, or sub-
is associated with a stated quantity value attributed to the
stance such that the quantity being measured may differ from
measurand. A modification of this value results in a modifica-
the measurand as defined. In this case, adequate correction is
tion of the associated uncertainty.
necessary.
3.1.16 point cloud, n—a collection of data points in 3D
Example 1: The length of a steel rod in equilibrium with
space(frequentlyinthehundredsofthousands),forexampleas
the ambient Celsius temperature of 23 °C will be different
obtained using a 3D imaging system. E2544-11a – 3.2
from the length at the specified temperature of 20 °C, which
is the measurand. In this case, a correction is necessary.
3.1.16.1 Discussion—The distance between points is gener-
3.1.12 measurement error, n—measured quantity value mi-
ally non-uniform and hence all three coordinates (Cartesian or
nusareferencequantityvalue. JCGM 200:2012 (VIM) – 2.16
spherical) for each point must be specifically encoded.
3.1.17 rated conditions, n—manufacturer-specified limits
3.1.12.1 Discussion—The concept of ‘measurement error’
on the environmental, utility, and other conditions within
can be used both a) when there is a single reference quantity
which the manufacturer’s performance specifications are guar-
value to refer to, which occurs if a calibration is made by
anteed at the time of installation of the instrument. ASME
means of a measurement standard with a measured quantity
B89.4.19-2006 - 4
value having a negligible measurement uncertainty or if a
conventional quantity value is given, in which case the
3.1.18 reference length, n—calibrated value of the distance
measurementerrorisknown,andb)ifameasurandissupposed
between two points in space at the time and conditions when a
toberepresentedbyauniquetruequantityvalueorasetoftrue
test is performed. ASME B89.4.19-2006 – 4
quantityvaluesofnegligiblerange,inwhichcasethemeasure-
3.1.19 reflectance, n—ratio of the reflected radiant or lumi-
ment error is not known.
nousfluxtotheincidentfluxinthegivenconditions. E284-13b
3.1.12.2 Discussion—Measurementerrorshouldnotbecon-
– 4.1
fused with production error or mistake.
3.1.13 measurement precision, n—closeness of agreement 3.1.19.1 Discussion—Thetermreflectanceisoftenusedina
between indications or measured quantity values obtained by general sense or as an abbreviation for reflectance factor. Such
replicate measurements on the same or similar objects under usage may be assumed unless the above definition is specifi-
specified conditions. JCGM 200:2012 (VIM) – 2.15 cally required by context.
3.1.20 reflectance factor, n—ratio of the flux reflected from
3.1.14 measurement repeatability, n—measurement preci-
the specimen to the flux reflected from the perfect reflecting
sion under a set of repeatability conditions of measurement.
diffuser under the same geometric and spectral conditions of
JCGM 200:2012 (VIM) – 2.21
measurement. E284-13b – 4.1
3.1.14.1 Discussion—See also 3.1.13, measurement
3.1.21 repeatabilityconditionofmeasurement,n—condition
precision, and 3.1.21, repeatability condition of measurement.
of measurement, out of a set of conditions that includes the
3.1.15 measurement uncertainty, n—non-negative param-
samemeasurementprocedure,sameoperators,samemeasuring
eter characterizing the dispersion of the quantity values being
system, same operating conditions and same location, and
attributed to a measurand, based on the information used.
replicate measurements on the same or similar objects over a
JCGM 200:2012 (VIM) – 2.26
short period of time. JCGM 200:2012 (VIM) – 2.20
3.1.15.1 Discussion—Measurement uncertainty includes
3.1.22 retroreflector, n—passive device that reflects light
components arising from systematic effects, such as compo-
back parallel to the incident direction over a range of incident
nents associated with corrections and the assigned quantity
angles. ASME B89.4.19-2006 – 4
values of measurement standards, as well as the definitional
3.1.22.1 Discussion—Typical retroreflectors are the cat’s-
uncertainty. Sometimes estimated systematic effects are not
corrected for but, instead, associated measurement uncertainty eye and the cube corner.
components are incorporated. 3.1.23 spherically mounted retroreflector (SMR),
3.1.15.2 Discussion—Theparametermaybe,forexample,a n—retroreflectorthatismountedinasphericalhousing. ASME
standarddeviationcalledstandardmeasurementuncertainty(or B89.4.19-2006 – 4
E3125 − 17
3.1.23.1 Discussion—Inthecaseofanopen-aircubecorner, 3.2.5 elevation angle, n—the angle between the laser beam
thevertexistypicallyadjustedtobecoincidentwiththesphere and the orthogonal projection of the laser beam on a plane
center. perpendicular to the vertical (standing) axis of the instrument,
3.1.24 standard uncertainty, n—uncertainty of the result of measured from that plane.
a measurement expressed as a standard deviation. JCGM 3.2.5.1 Discussion—Some systems report the zenith angle
100:2008 (GUM) – 2.3.1 instead of the elevation angle. The sum of the elevation and
zenith angle is equal to 90°, therefore elevation angle can be
3.1.25 systematic measurement error (systematic error),
determined if the zenith angle is known.
n—component of measurement error that in replicate measure-
ments remains constant or varies in a predictable manner. 3.2.6 frontsight, n—measurement mode, where the target is
JCGM 200:2012 (VIM) – 2.17 measured with the laser beam emerging from the front-face of
the instrument.
3.1.25.1 Discussion—A reference quantity value for a sys-
3.2.6.1 Discussion—The front-face may be arbitrarily cho-
tematic measurement error is a true quantity value, or a
sen or may be defined in terms of the zenith angle of the
measured quantity value of a measurement standard of negli-
spinningprismmirrorthatdirectsthelaserbeam.Forexample,
gible measurement uncertainty, or a conventional quantity
the face of the instrument from which the laser beam emerges
value.
thatcorrespondstoazenithanglebetween0°and180°maybe
3.1.25.2 Discussion—Systematicmeasurementerror,andits
defined as the front-face.
causes,canbeknownorunknown.Acorrectioncanbeapplied
3.2.6.2 Discussion—See also backsight (3.2.2).
to compensate for a known systematic measurement error.
3.2.7 instrument settings, n—parameters that a user is al-
3.1.25.3 Discussion—Systematic measurement error equals
lowed to select prior to performing a measurement, such as
measurement error minus random measurement error.
point spacing, filtering options, valid intensity range.
3.1.26 uncertainty budget, n—statement of a measurement
uncertainty, of the components of that measurement 3.2.8 IUT, n—instrument under test.
uncertainty, and of their calculation and combination. JCGM
3.2.9 measurement axis, n—a radial line, passing through
200:2012 (VIM) – 2.33
the origin of the IUT, along which a relative-range test is
performed.
3.1.26.1 Discussion—An uncertainty budget should include
3.2.9.1 Discussion—The derived-points of the target at the
the measurement model, estimates, and measurement uncer-
reference position and the test position also lie on this axis.
tainties associated with the quantities in the measurement
model, covariances, type of applied probability density
3.2.10 operating mode, n—a collection of instrument set-
functions, degrees of freedom, type of evaluation of measure- tings pre-selected by the manufacturer for a particular type of
ment uncertainty, and any coverage factor.
measurement.
3.1.27 work volume, n—physical space, or region within a
3.2.10.1 Discussion—Forexample,operatingmodeAmight
physical space, that defines the bounds within which a pose
include a pre-defined scanning acquisition rate and spatial
measurement system is acquiring data. E2919-14 – 3.2.8 averaging.Auser might select this operating mode in conjunc-
tion with other instrument settings for a particular measure-
3.2 Definitions of Terms Specific to This Standard:
ment task.
3.2.1 azimuth angle, n—the angle between the orthogonal
3.2.10.2 Discussion—Because some systems can measure a
projection of the laser beam on a plane perpendicular to the
target in frontsight and in backsight, these are also considered
vertical (standing) axis of the instrument and a fixed (refer-
to be operating modes.
ence) axis in that plane.
3.2.11 origin of the IUT, n—the point in space that corre-
3.2.2 backsight, n—measurement mode, where the target is
sponds to a range value of zero.
measured with the laser beam emerging from the back-face of
3.2.11.1 Discussion—Ideally, the intersection of the hori-
the instrument.
zontal and vertical axes of the IUT lies on the face of the
3.2.2.1 Discussion—The back-face may be arbitrarily cho-
spinning mirror and is also the point of zero range.
sen or may be defined in terms of the zenith angle of the
spinningprismmirrorthatdirectsthelaserbeam.Forexample, 3.2.12 RI, n—reference instrument.
the face of the instrument from which the laser beam emerges
3.2.13 SMR-integrated sphere target, n—a special artifact
that corresponds to a zenith angle between 180° and 360° may
consisting of a hollow partial sphere with a kinematic nest
be defined as the back-face.
located inside so that an SMR mounted on this nest is
3.2.2.2 Discussion—See also frontsight (3.2.6).
concentric with the outer spherical surface of the hollow
3.2.3 derived-point, n—a point (such as the center of a sphere.
sphere) that is not measured directly but computed using
3.2.14 two-face test, n—a test to characterize certain geo-
multiple measured points on a target surface.
metric errors of the instrument by measuring a target in the
3.2.4 derived-point to derived-point distance, n—the dis- frontsight mode followed immediately by a measurement of
tance between two derived-points. the same target in the backsight mode.
3.2.4.1 Discussion—The derived-point to derived-point dis- 3.2.14.1 Discussion—The apparent distance, perpendicular
tance is also referred to as point-to-point distance in this to the laser beam, between the measurement results from each
standard. of the measurement modes yields the test result.
E3125 − 17
3.2.15 zenith angle, n—the angle between the laser beam 4.3 The test may be carried out for instrument acceptance,
and the vertical axis of the instrument, measured from the pole warrantyorcontractualpurposesbymutualagreementbetween
(point directly above the instrument when the instrument is the manufacturer and the user.The IUTis tested in accordance
mounted right-side up). with manufacturer-supplied specifications, rated conditions,
and technical documentation.
3.3 Symbols:
3.3.1 The following symbols are used in this standard. 4.4 For the purposes of understanding the behavior of the
IUT and without warranty implications, this test may be
modified as necessary to evaluate the point-to-point distance
TABLE 1 Symbols
measurement performance of the IUT outside the manufactur-
Symbol Meaning
er’s rated conditions, but within the manufacturer’s limiting
(r, θ, ϕ) Range, azimuth angle, and elevation angle, respectively, of a
single point measured by the IUT or of the derived-point
conditions.
obtained from the IUT point set
(x, y, z) Cartesian coordinates of a single point measured by the IUT or 4.5 The manufacturer may provide different performance
of the derived-point obtained from the IUT point set
specification values for different sets of rated conditions, for
(X, Y, Z) Cartesian coordinates of a single point measured by the RI or
example, better point-to-point distance measurement perfor-
of the derived-point obtained from the RI point set
E Two-face error mance might be specified under a set of more restrictive
two-face
E Derived-point to derived-point distance error
distance
environmental conditions. The user is advised that the IUT’s
E MPE specification for two-face error
two-face,MPE
performance may differ significantly in other modes of
E MPE specification for derived-point to derived-point distance
distance, MPE
error
operation, with other instrument settings, or outside the rated
R Calibrated radius of a sphere target
conditions, and should consult the manufacturer for perfor-
D Distance between two derived-points as obtained by the IUT
meas
mance specifications of the operating mode and instrument
D Distance between two derived-points as obtained by the RI
ref
U Expanded test uncertainty (k=2)
settings that best represent the planned usage.
α The angle as shown in Figs. 2 and 3. In general, α is the
angular sweep between two targets measured by the IUT in 4.6 Thisstandardisintendedtoexpandandcomplementthe
the plane containing the origin of the IUT and the derived-
ranging tests described in Test Method E2938. While Test
points of the two targets, except in Fig. 3(e) and (f).
Method E2938 specifically describes the evaluation of the
e MPE specification for range measurement error of the IUT
r,MPE
e MPE specification for transverse measurement error of the IUT ranging capability of any medium-range 3D imaging system,
t,MPE
d Distance of the target from the IUT in the horizontal plane
this standard provides test procedures to evaluate the point-to-
S Sphere point set
point distance error due to the combined effect from angular
P Plane point set
s Standard deviation of residuals andrangingerrorsofaparticulartypeofthesesystems,thatis,
spherical coordinate 3D imaging systems.
4. Significance and Use
5. Introduction
4.1 This standard provides a test method for obtaining the
5.1 Overview:
point-to-point distance measurement errors for medium-range
5.1.1 This standard consists of two types of test procedures
3D imaging systems.The results from this test method may be
to evaluate the point-to-point distance performance of 3D
used to evaluate or to verify the point-to-point distance
imaging systems – two-face tests and point-to-point distance
measurement performance of medium-range 3D imaging sys-
tests.
tems. The results from this test method may also be used to
5.1.2 Two-face tests can be regarded as a special case of a
compare performance among different instruments.
point-to-point distance test, with zero reference length. These
tests are quick and easy to perform, and are sensitive to many
4.2 The purpose of this document is to provide test proce-
sources of mechanical and optical misalignments within the
dures that are sensitive to instrument error sources. The
IUT. Similar two-face tests are used to evaluate the perfor-
point-to-point distance measurement performance of the IUT
mance of laser trackers which are also spherical coordinate
obtainedbytheapplicationofthistestmethodmaybedifferent
measurement systems (see ASME B89.4.19-2006 or ISO
from the point-to-point distance measurement performance of
10360-10:2016).
theIUTundersomereal-worldconditions.Forexample,object
geometry, texture, surface reflectance factor, and temperature, 5.1.3 The point-to-point distance tests involve measuring a
reference length in many positions and orientations within the
as well as particulate matter, thermal gradients, atmospheric
pressure, humidity, ambient lighting in the environment, me- IUT work volume. These tests are not only sensitive to all
known mechanical and optical misalignments in the IUT, but
chanicalvibrations,andwindinducedtestsetupinstabilitywill
affect the point-to-point distance measurement performance also provide the connection to the SI unit of length, the meter.
Point-to-pointdistancetestsarefurthercategorizedassymmet-
(see Appendix X10 for a discussion on thermal effects). A
derived-point such as the center of a suitable sphere or plate ric tests, asymmetric tests, inside test, relative-range tests, and
user-selected tests.
target that meets the requirements described in Section 7
providesareliablepointinspacethatisminimallyimpactedby 5.1.4 The two-face tests, symmetric tests, asymmetric tests,
target-related properties such as geometry, surface texture, and the inside test are performed using sphere targets. In some
color, and reflectivity. Additional tests not described in this cases, especially when the sphere target is far away from the
standard may be required to assess the contribution of these IUT, the sphere center appears closer to or farther away from
influence factors on point-to-point distance measurements. the IUT due to sphere target geometry induced error. This is
E3125 − 17
described in Appendix X9. Since the relative-range tests may 6.1.1 The rated conditions are manufacturer-specified limits
involve longer distances, these tests are performed using plate on environmental, utility, and other conditions within which
targetstoeliminatethistarget-inducederror.Iftheuserchooses the manufacturer-specified MPEs are guaranteed. Rated con-
to perform additional relative-range tests as the user-selected ditions may include minimum and maximum measurement
tests,theyareperformedusingplatetargets;otherwise,theuser ranges, target characteristics (Section 7), minimum and maxi-
selected tests are performed using sphere targets. mum temperatures of operation, maximum thermal gradient
5.1.5 See Appendix X3 for a discussion on the rationale for (°C/mand°C/h).Iflimitsarenotspecifiedforacondition,then
the selection of test positions and orientations required in this it is assumed that the manufacturer’s specifications will be
standard. valid for any range of that condition.
6.1.2 The rated conditions also include manufacturer-
5.2 Two-face Tests:
specified limits on instrument settings such as point density or
5.2.1 The objective of the two-face tests is to quantify the
point-to-point spacing, and scanning acquisition rate. The
errors in measured coordinates generated by the IUT due to
manufacturer must state the limits for the instrument settings
mechanical and optical misalignments within the IUT. This is
under which the specified MPEs are valid.
achieved by first measuring the derived-point of a stationary
6.1.3 Some instruments do not allow the user to select
sphere target in the IUT’s frontsight mode and immediately
individual settings and only allow certain pre-set operating
repeating the measurement in the IUT’s backsight mode. The
modes. The rated conditions therefore also include
difference in distance between the two derived-points, perpen-
manufacturer-specified operating modes. The manufacturer
diculartothelaserbeam,fromeachofthemeasurementmodes
must state the operating modes for which the specified MPEs
yields the test result. This test result depends on the range, the
are valid.
azimuth, and the elevation of the sphere target with respect to
6.1.4 Operating modes and instrument settings must be
theIUT.Therefore,thetwo-facetestsareperformedatdifferent
clearly described and reproducible by any qualified user (see
positions in the work volume of the instrument.
Note 1). If no limits are specified for a specific instrument
5.2.2 Some 3D imaging systems may not be designed to
setting (for example, point density), then it is assumed that the
measure any part of the work volume in the backsight mode.
MPE will be valid for any value of that setting. If no operating
The two-face tests cannot be performed on those systems. For
modes are specified, it is assumed that the MPE is valid for all
allother3Dimagingsystemswhereatleastsomeportionofthe
operating modes available to the user (see Note 2).
work volume can be measured in both faces, two-face tests are
mandatory.
NOTE1—Aqualifieduserisapersonwhohasbeentrainedintheproper
5.2.3 Two-face tests can be performed quicker than the
operation of the IUT.
point-to-point distance tests described in this standard and will
NOTE 2—As an example, the manufacturer may specify the MPE to be
valid for the following rated conditions: target range between2mand
immediately reveal problems with the IUT. It is therefore
100m; point density from 30 points/degree to 90 points/degree along
recommendedthatthesetestsbeperformedfirsttoverifyifthe
azimuthandelevationangledirections;operatingmodeA(whichincludes
IUT meets the two-face MPE specifications before proceeding
a certain pre-set scanning acquisition rate and spatial averaging), and
with the point-to-point distance tests.
indoor measurements only with temperature in the range 20 °C 6 5 °C.
Because the manufacturer does not specify other factors such as target
5.3 Point-to-point Distance Tests:
reflectivity, temperature gradient limits, bounds on atmospheric pressure,
5.3.1 The objective of the point-to-point distance tests is to
etc., the MPE is assumed to be valid for any value of those settings/
evaluate the point-to-point distance measurement performance
conditions.
of the IUT by comparing the point-to-point distance between
6.1.5 When the test is carried out for verifying manufactur-
two targets as measured by the IUT against the calibrated
er’s specifications, the conditions of the test environment,
distance obtained by a reference instrument (RI).
instrument settings and operating modes shall remain within
5.3.2 Such comparison against a calibrated reference length
the bounds of the manufacturer’s rated conditions throughout
is performed for all point-to-point distance tests, that is,
the test.
symmetric tests, asymmetric tests, inside test, relative-range
6.1.6 The IUT shall be operated in accordance with the
tests, and user-selected tests.
procedures given in the manufacturer’s User Manual. All
5.3.3 Mechanical and optical misalignments within the IUT
applicable procedures described in the manufacturer’s User
introduce systematic errors in the measured point coordinates
5 Manual for the proper use of the instrument, such as machine
(range, azimuth angle, and elevation angle), see Ref (1). In
start-up/warm-up time, compensation procedures and manu-
ordertoadequatelycaptureknownsourcesofsystematicerrors
facturer maintenance requirements, shall be adhered to.
within the IUT, reference lengths (realized as the distance
between two sphere targets or two plate targets) are positioned 6.2 Test Uncertainty:
at different distances and orientations within the work volume.
6.2.1 A test value is an estimate of the IUT error under a
certain set of conditions and at a certain instant in time. Test
6. Test Conditions and Requirements
value uncertainty (or test uncertainty) is the uncertainty of the
test value and is a quantitative measure of the dispersion of
6.1 Rated Conditions:
values that could reasonably be attributed to the (true) error.
Examples of test values in this document are (1) the IUT error
in a particular instance of determining a point-to-point
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this standard. distance, and (2) the IUT error in a particular instance of
E3125 − 17
measuring the same derived-point using frontsight and back- component be reported if possible (see Note 3). If the reflec-
sight measurements of a sphere target (the error being repre- tance factor is not specified by the manufacturer, the user is
sented by the distance between the two derived-points perpen- free to use target material with any reflectance factor for the
dicular to the laser beam). tests.
6.2.2 In the case of a point-to-point distance test described
NOTE 3—The reflectance factor consists of both diffuse and specular
in this standard, the test value uncertainty is determined by the
components, while the diffuse reflectance factor excludes the specular
uncertainty in the reference length.
component.
6.2.3 In the case of the two-face tests, the test value
7.3 Target Mechanical Requirements:
uncertainty is determined by the possible displacement of the
7.3.1 The minimum plate target size should be specified by
target between frontsight and backsight measurements. For a
themanufacturer,andshallbesufficienttoyieldaminimumof
rigidly-mounted target and a short period of time (a few
100pointsafterpointselectionasdescribedinSection10.The
minutes) between measurements that minimizes thermal drift,
front-side of the plate target shall consist of a single planar
the test value uncertainty should be a negligibly small quantity
surface made of a single material.The edges of the target shall
and can be considered zero.
havearadiusoflessthanorequaltoonequarterofthesmallest
6.2.4 In this standard, the expanded test value uncertainty,
beam width of the IUT (see Fig. 2 in Test Method E2938).
U, is equal to two times the combined standard uncertainty
7.3.2 In the case of point-to-point distance tests that require
(that is, a coverage factor of k = 2). This standard follows the
the use of plate targets (for example, relative-range tests), the
4:1 simple acceptance/simple rejection decision rule described
flatnessoftheplatetargetshallnotexceed20%ofthesmallest
in ASME B89.7.3.1-2001 to make conformance decisions
relative-range MPE (that is, the smallest MPE from tests PP16
(pass/fail). For this purpose, the expanded test value uncer-
through PP18 in Table 6). The flatness should be measured in
tainty U shall be less than or equal to ⁄4 of the MPE
accordance with the procedures in Section 5.4.2 of ASME
(E for point-to-point distance tests and E
distance,MPE two-face,MPE
Y14.5-2009.
for two-face tests). The MPE values shall be specified by the
7.3.3 The minimum sphere target size should be specified
manufacturer of the IUT.
bythemanufacturer,andshallbesufficienttoyieldaminimum
of 300 points after point selection as described in Section 9.
7. Apparatus
The sphere target may be hollow or solid and the front
(measurement)surfaceshallconsistofasinglesurfacemadeof
7.1 Target Geometry:
7.1.1 Two target geometries are specified in this standard: a a single material.
spheretargetandaplatetarget.Theplatetargetmaybesquare, 7.3.4 The radius of the sphere target along with its uncer-
rectangular, circular or any other planar shape for which a tainty shall be determined through a calibration procedure.
Typically, such calibration is performed using a contact probe
boundary is easily defined; however, for illustration purposes,
a square- or rectangular-shaped target is assumed throughout coordinatemeasuringmachine(CMM),butothermethodsmay
thisdocument.Thespheretargetshallbeatleastahemisphere, be used.The uncertainty in radius shall be accounted for in the
oriented in such a way that the hemispherical surface is fully determinationofthetestvalueuncertainty(seeX5.2.7,X6.2.8,
visible to the IUT. and X7.2.5 for examples).
7.3.5 In the case of point-to-point distance tests that require
7.2 Target Material and Optical Requirements:
the use of sphere targets, the circularity of the sphere target
7.2.1 Different materials have different optical characteris-
shall not exceed 20 % of the smallest point-to-point distance
tics such as surface reflectance factor at the IUT’s operating
MPE excluding the relative-range tests and the user-selected
wavelength, optical penetration depth (volumetric scattering),
tests(thatis,thesmallest MPEfromtestsPP1throughPP15in
and surface scattering characteristics, which means that the
Tables 3-5). The circularity should be measured in accordance
values of the errors may differ for different materials.
with the procedures in Section 5.4.3 of ASME Y14.5-2009.
7.2.2 The types of target materials, and their optical char-
7.3.6 In the case of two-face tests, the circularity of the
acteristics (for example, surface diffuse reflectance factor),
sphere target shall not exceed 20 % of the smallest two-face
used in the tests should be specified by the manufacturer. If a
MPE (that is, the smallest MPE from tests TF1 through TF12
material other than that specified by the manufacturer is used
in Table 2). The circularity should be measured in accordance
for the tests, the performance of the IUT using this material
with the procedures in Section 5.4.3 of ASME Y14.5-2009.
may not meet the manufacturer’s specifications. If the target
material or material characteristics are not specified by the 7.4 Practical Realization of the Target:
manufacturer, the user is free to use any material for the tests. 7.4.1 The relative-range portion of the point-to-point dis-
It is recommended that the manufacturer specify target mate- tance tests shall be performed with a plate target as described
rials for the tests that may be obtained at a reasonable cost to in 7.2 and 7.3. If there are no fiducials attached to the plate to
the user. Suggested materials that may be used for the target facilitate identification of the derived-point, the plate shall be
include, but are not limited to, steel and aluminum.
carefully aligned with the measurement axis. That is, the plate
7.2.3 The reflectance factor of the target surface, as mea- shall be perpendicular to the measurement axis (see 7.5.1 for
sured in accordance with Practice E1164 and Test Method alignment tolerance requirements) and the derived-point shall
E1331, must be within the manufacturer’s specifications. It is lie on that axis. It is also permissible to add fiducials to the
strongly recommended that the reflectance factor (measured at platetofacilitateidentificationofthederived-point.Iffiducials
the IUT’s operating wavelength) with and without the specular areused,theyshallbemountedonthesidesorbackoftheplate
E3125 − 17
FIG. 1 Two-Face Test (a) on sphere target A that is at an elevation angle ϕ of 45° 6 10° (b) on sphere target B that is at IUT height (el-
evation angle ϕ of 0° 6 10°), (c) on sphere target C that is at an elevation angle ϕ of -45° 6 10°, (d) using three sphere targets mounted
on a column, (e) using a single sphere target and two mirrors
in such a manner that they do not occlude or generate the front (measurement) surface of the targets. In addition, any
multi-path measurement signals from the central region of the part of the target support that is visible to the IUT should be
plate that is used to determine the derived-point for the IUT. sufficiently separated from the target so that any measured
Examples of plate target designs are described in Appendix points on the support can be easily removed in the data
X8. segmentation described in Sections 9 and 10.
7.4.2 All point-to-point distance tests except the relative-
7.7 Reference Instrument:
range tests shall be realized using sphere targets that meet the
7.7.1 The RI shall measure the point-to-point distance with
requirements described in 7.2 and 7.3. If a laser tracker is used
anexpandeduncertaintyUthatisinconformancewith6.2.The
to obtain reference measurements, the derived-point of the
RI shall be calibrated, maintained, and operated in accordance
sphere may be obtained by manually probing a spherically
with the manufacturer’s instructions.
mounted retro-reflector (SMR) on the surface of the sphere
target (Ref (2)). It is also permissible to use SMR-integrated
8. Test Procedure
sphere targets that contain a kinematic nest to mount an SMR
inside the sphere, accessible from the back, and for which the
8.1 Overview:
center of the SMR coincides with the center of the outer
8.1.1 The test procedure described in this section may take
surface of the sphere target. In this case, the reference
several hours to execute depending on the procedure to realize
measurements are obtained using a laser tracker and the SMR
the reference lengths. It is recommended that the user assess
locatedinsidethespheretarget.Ifthistypeoftargetisused,the
the stability of the IUT and the targets by performing simple
concentricitybetweentheoutersurfaceofthespheretargetand
repeatability tests, such as those suggested in Appendix X1,
the SMR center shall be accounted for in the determination of
prior to commencing the test procedures described in this
the test value uncertainty. Various methods to realize point-to-
section.
point distance tests using sphere targets are described in
8.1.2 The rationale for selection of the test positions and
Appendix X4.
orientations is given in Appendix X3.
7.5 Alignment of the Plate Target:
8.1.3 The instrument settings and operating modes for the
7.5.1 The required alignment of the plate target (position
testprocedureshallbechosen,withinratedconditions,toyield
and orientation with respect to the measurement axis) is
a minimum of 300 measured points on the sphere target after
primarily determined by the specifications of the IUT.Accept-
point selection as described in Section 9, or 100 measured
able alignment criteria shall be determined by conducting an
points on the plate target after point selection as described in
uncertaintyanalysisforthespecifictestsetupandIUTutilized.
Section 10.
An example of the procedure to determine the uncertainty
8.1.4 IUT data is acquired in the instrument coordinate
budgetforaspecifictestsetupisgiveninAppendixX2ofTest
frame, that is, the origin and orientation of the coordinate
Method E2938.
systemofthedatashallalsobetheoriginandorientationofthe
IUT coordinate frame.
7.6 Mounting:
7.6.1 The targets (both sphere and plate) shall be rigidly 8.1.5 ItispermissibletounmounttheIUTfromitsstandand
mounted on stable supports and the supports shall not obstruct remount it on a different stand between tests.
E3125 − 17
TABLE 2 Two-Face Test Positions (see Fig. 1)
Distance of target from E
...