Patent Publication Number: US-9885560-B2

Title: Length artifact and method of measurement

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of and claims the benefit of U.S. Non-Provisional patent application Ser. No. 14/662,450, filed Mar. 19, 2015, and U.S. Provisional Patent Application No. 62/010,043, filed Jun. 10, 2014, the contents of both of which are incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     The present disclosure relates to a length artifact to determine the measurement errors associated with a three-dimensional (3D) measurement instrument and with methods of measurement using the length artifact. 
     Portable metrology instruments, such as portable laser trackers and articulated arm coordinate measuring machines (AACMMs), find widespread use in the manufacturing or production of parts where there is a need to rapidly and accurately verify the dimensions of the parts during various stages of the manufacturing or production (e.g., machining). Portable metrology instruments represent an improvement over known stationary or fixed, cost-intensive and relatively difficult to use measurement installations, particularly in the amount of time it takes to perform dimensional measurements of relatively complex parts. 
     A laser tracker is in a class of instruments that measure coordinates of a point by sending a beam of light to the point. The beam of light may impinge on a retroreflector target in contact with the point. The laser tracker determines the coordinates of the point by measuring the distance and the two angles to the target. The distance is measured with a distance-measuring device such as an absolute distance meter (ADM) or an interferometer. The angles are measured with an angle-measuring device such as an angular encoder. A gimbaled beam-steering mechanism within the instrument directs the laser beam to the point of interest. A related instrument is a total station (tachymeter) that measures to either a retroreflector or a point on a diffusely scattering surface. Laser trackers, which typically have accuracies on the order of a thousandth of an inch and as good as one or two micrometers under certain circumstances, are usually much more accurate than total stations. The broad definition of laser tracker, which includes total stations, is used through this application. 
     Ordinarily the laser tracker sends a laser beam to a retroreflector target. A common type of retroreflector target is the spherically mounted retroreflector (SMR), which comprises a cube-corner retroreflector embedded within a metal sphere. The cube-corner retroreflector comprises three mutually perpendicular mirrors. The vertex, which is the common point of intersection of the three mirrors, is located at the center of the sphere. Because of this placement of the cube corner within the sphere, the perpendicular distance from the vertex to any surface on which the SMR rests remains constant, even as the SMR is rotated. Consequently, the laser tracker can measure the 3D coordinates of a surface by following the position of an SMR as it is moved over the surface. Stating this another way, the laser tracker needs to measure only three degrees of freedom (one radial distance and two angles) to fully characterize the 3D coordinates of a surface. 
     Periodically it is desirable to evaluate the performance of a 3D measuring instrument. One way to do this is to measure a length artifact, also known as a length standard or a reference length, and to compare a length of the artifact as obtained from a calibration to the length as obtained from a measurement with the 3D measuring instrument. The difference between the measured and calibrated length values is the error, which is an indicator of performance of the 3D measuring instrument. Today, there is a need for a length artifact that is stable, easily calibrated, and easily measured with a 3D measuring instrument such as a laser tracker, articulated arm CMM, or similar device. 
     Accordingly, while existing length artifacts are suitable for their intended purposes, the need for improvement remains, particularly in providing an improved length artifact and method of measuring with a 3D measuring device. 
     BRIEF DESCRIPTION OF THE INVENTION 
     In accordance with an embodiment, a length artifact is provided, the length artifact having an artifact frame of reference, the length artifact including a first side wall and a second side wall, the first side wall and the second side wall separated by an air gap, the air gap being at least four millimeters wide, the first side wall having a first bottom surface, a first left surface, and a first right surface, the second side wall having a second bottom surface, a second left surface, and a second right surface; and a base portion in contact with the first bottom surface and the second bottom surface, the base portion having a first platform region and a second platform region, the first platform region extending beyond the first left surface and the second left surface, the second platform region extending beyond the first right surface and the second right surface, the first platform region including a first nest, the first nest configured to accept a spherical surface of a retroreflector target, the spherical surface having a sphere center, the second platform region including a second nest, the second nest configured to accept the spherical surface of the retroreflector target, the length artifact further including a first nest center and a second nest center, the first nest center being first three-dimensional (3D) coordinates in the artifact frame of reference of the sphere center when the retroreflector target is placed in the first nest, the second nest center being second 3D coordinates in the artifact frame of reference of the sphere center when the retroreflector target is placed in the second nest, the length artifact further having a neutral surface in the artifact frame of reference, the neutral surface being a surface above which the length artifact is in tension and below which the length artifact is in compression in accordance with an embodiment. 
     In accordance with another embodiment, a method of calibrating a length artifact is provided, the method including providing a retroreflector target configured to retroreflect a beam of light, the retroreflector target having a spherical portion, the spherical portion having a sphere center; providing the length artifact, the length artifact having a first side wall, a second side wall, and a base portion, the first side wall and the second side wall separated by an air gap, a bottom portion of the first side wall and a bottom portion of the second side wall in contact with the base portion, the base portion including a first nest and a second nest, the first nest configured to accept the spherical portion when the sphere center is at a first nest center, the second nest configured to accept the spherical portion when the sphere center is at a second nest center; providing a laser tracker, the laser tracker configured to project a beam of light to the retroreflector target, to track the retroreflector target, and to determine three-dimensional (3D) coordinates of the retroreflector target, the 3D coordinates based at least in part on a distance from the laser tracker to the retroreflector target, the distance determined by a distance meter within the laser tracker, the distance based at least in part on a speed of light in air; aligning the beam of light with the first nest center and the second nest center; placing the retroreflector target in the first nest; sending the beam of light to the retroreflector target; measuring with the laser tracker a first distance to the first nest center; placing the retroreflector target in the second nest; sending the beam of light through the air gap between the first side wall and the second side wall to the retroreflector target; measuring with the laser tracker a second distance to the second nest center; and determining a first artifact length based at least in part on the first distance and the second distance 
     These and other advantages and features will become more apparent from the following description taken in conjunction with the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
       The subject matter, which is regarded as the invention, is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other features, and advantages of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which: 
         FIG. 1A  is a perspective view of a laser tracker in accordance with an embodiment of the invention; 
         FIG. 1B  is a block diagram showing elements of tracker electronics in accordance with an embodiment of the invention; 
         FIG. 2  is a perspective view of a portable articulated arm coordinate measuring machine (AACMM) in accordance with an embodiment of the invention; 
         FIG. 3  is a perspective view of a prior art method for establishing a reference length; 
         FIGS. 4A-G  are views of a length artifact: perspective, top, front, left side, right side, section, and nest-SMR detail, respectively, in accordance with an embodiment of the invention; 
         FIGS. 5A-C  are views of a mount according to embodiments; 
         FIGS. 6A-C  are schematic illustrations of the effect of retroreflector target placement on a length artifact; 
         FIGS. 7A and 7B  are perspective and side views, respectively, of an artifact that includes a temperature sensor; and 
         FIG. 8  is a flowchart of a method of determining a length of a length artifact according to an embodiment. 
     
    
    
     The detailed description explains embodiments of the invention, together with advantages and features, by way of example with reference to the drawings. 
     DETAILED DESCRIPTION OF THE INVENTION 
     An embodiment of the present invention provides a length artifact having features that provide convenience, stability, and accuracy in the evaluation of the performance of 3D measuring devices such as laser trackers and articulated arm CMMs. 
     An exemplary laser tracker system  5  illustrated in  FIG. 1A  includes a laser tracker  10 , a retroreflector target  26 , an optional auxiliary unit processor  50 , and an optional auxiliary computer  60 . An exemplary gimbaled beam-steering mechanism  12  of laser tracker  10  comprises a zenith carriage  14  mounted on an azimuth base  16  and rotated about an azimuth axis  20 . A payload  15  is mounted on the zenith carriage  14  and rotated about a zenith axis  18 . Zenith axis  18  and azimuth axis  20  intersect orthogonally, internally to tracker  10 , at gimbal point  22 , which is typically the origin for distance measurements. A laser beam  46  virtually passes through the gimbal point  22  and is pointed orthogonal to zenith axis  18 . In other words, laser beam  46  lies in a surface (plane) approximately perpendicular to the zenith axis  18  and that passes through the azimuth axis  20 . Outgoing laser beam  46  is pointed in the desired direction by rotation of payload  15  about zenith axis  18  and by rotation of zenith carriage  14  about azimuth axis  20 . A zenith angular encoder, internal to the tracker, is attached to a zenith mechanical axis aligned to the zenith axis  18 . An azimuth angular encoder, internal to the tracker, is attached to an azimuth mechanical axis aligned to the azimuth axis  20 . The zenith and azimuth angular encoders measure the zenith and azimuth angles of rotation to relatively high accuracy. Outgoing laser beam  46  travels to the retroreflector target  26 , which might be, for example, a spherically mounted retroreflector (SMR) as described above. By measuring the radial distance between gimbal point  22  and retroreflector  26 , the rotation angle about the zenith axis  18 , and the rotation angle about the azimuth axis  20 , the position of retroreflector  26  is found within the spherical coordinate system of the tracker. 
       FIG. 1B  is a block diagram depicting a dimensional measurement electronics processing system  1500  that includes a laser tracker electronics processing system  1510 , processing system of a temperature sensor peripheral  1582 , computer  1590 , and other networked components  1600 , represented here as a cloud. Exemplary laser tracker electronics processing system  1510  includes a master processor  1520 , payload functions electronics  1530 , azimuth encoder electronics  1540 , zenith encoder electronics  1550 , display and user interface (UI) electronics  1560 , removable storage hardware  1565 , radio frequency identification (RFID) electronics  1570 , and an antenna  1572 . The payload functions electronics  1530  includes a number of subfunctions including the six-DOF electronics  1531 , the camera electronics  1532 , the ADM electronics  1533 , the position detector (PSD) electronics  1534 , and the level electronics  1535 . 
       FIG. 2  shows an exemplary AACMM  200  that may comprise a six or seven axis articulated measurement device having a probe end  201  that includes a measurement probe housing  202  coupled to an arm portion  204  of the AACMM  200  at one end. The arm portion  204  comprises a first arm segment  206  coupled to a second arm segment  208  by a rotational connection having a first grouping of bearing cartridges  210  (e.g., two bearing cartridges). A second grouping of bearing cartridges  212  (e.g., two bearing cartridges) couples the second arm segment  208  to the measurement probe housing  202 . A third grouping of bearing cartridges  214  (e.g., three bearing cartridges) couples the first arm segment  206  to a base  216  located at the other end of the arm portion  204  of the AACMM  200 . Each grouping of bearing cartridges  210 ,  212 ,  214  provides for multiple axes of articulated movement. Also, the probe end  201  may include a measurement probe housing  202  that comprises the shaft of the seventh axis portion of the AACMM  200  (e.g., a cartridge containing an encoder system that determines movement of the measurement device, for example a contact probe tip  218 , in the seventh axis of the AACMM  100 ). In this embodiment, the probe end  201  may rotate about an axis extending through the center of measurement probe housing  202 . In use the base  216  is typically affixed to a work surface. 
     Each bearing cartridge within each bearing cartridge grouping  210 ,  212 ,  214  typically contains an encoder system (e.g., an optical angular encoder system). The encoder system (i.e., transducer) provides an indication of the position of the respective arm segments  206 ,  208  and corresponding bearing cartridge groupings  210 ,  212 ,  214  that all together provide an indication of the position of the probe  218  with respect to the base  216  (and, thus, the position of the object being measured by the AACMM  100  in a certain frame of reference—for example a local or global frame of reference). 
     The probe tip  218  is detachably mounted to the measurement probe housing  202 , which is connected to bearing cartridge grouping  212 . In exemplary embodiments, the probe housing  202  houses a removable probe tip  218 . In other embodiments, the measurement is performed, for example, by a non-contacting device such as a laser line probe (LLP). In an embodiment, the handle  226  is replaced with the LLP using the quick-connect interface. Other types of accessory devices may replace the removable handle  226  to provide additional functionality. 
     In accordance with an embodiment, the base  216  of the portable AACMM  200  contains or houses an electronic data processing system that includes a base processing system that processes the data from the various encoder systems within the AACMM  200  as well as data representing other arm parameters to support 3D positional calculations. An electronic data processing system in the base  216  may communicate with the encoder systems, sensors, and other peripheral hardware located away from the base  216  (e.g., a LLP that can be mounted to or within the removable handle  226  on the AACMM  200 ). The electronics that support these peripheral hardware devices or features may be located in each of the bearing cartridge groupings  210 ,  212 ,  214  located within the portable AACMM  200 . 
       FIG. 3  shows a prior art method for establishing a reference length L between a retroreflector target in a first position  320 A and a second position  320 B. The laser tracker  310  includes a calibrated distance meter such as an interferometer or ADM. For this measurement of a length L between two points, an appropriately calibrated laser tracker may have metrological traceability whereby the result of the measured length can be related to stated references, usually national or international standards, through an unbroken chain of comparisons all having stated uncertainties. The error in the measured length L of the reference artifact is minimized by aligning the beam of light  315 A from the laser tracker  310  to the positions  320 A,  320 B of the retroreflector target. The reason for the reduced error is that the length L is determined based only on the readings of the distance meter and not only the angle readings of the tracker  310 , which are less accurate. 
     The retroreflector target may be an SMR similar to element  26  of  FIG. 1A . An SMR, which has a spherically shaped outer portion surface, may be repeatably placed in a suitable nest. An example of a nest that may provide repeatable positioning for the spherically shaped outer portion of an SMR is a nest that includes three small spheres spaced apart by 120 degrees. The larger spherical surface of the SMR makes contact at the same points on the three spheres regardless of how the sphere is rotated. The vertex of an open-air cube corner retroreflector is adjusted to coincide with the center of the sphere so that the vertex also remains at a fixed location as the SMR is rotated in the nest. By this means, the center of the SMR may be repeatably measured at positions  320 A,  320 B, thereby enabling repeatable determination of the length L. The nests at positions  320 A,  320 B are placed on instrument stands  335 ,  340 , respectively. The positions  320 A,  320 B correspond to the centers of the retroreflector when placed on the nests of the stands  335 ,  340 , respectively. The beam of light  315 A is sent from the tracker  310  on the instrument stand  330  to the retroreflector at position  320 A. The beam of light returns to the tracker  310  along the same beam path. The retroreflector is moved to the second position  320 B and the beam of light  315 B is sent to and returns from the retroreflector in the new position. 
     After a reference length L has been determined in calibration laboratory according to the arrangement of  FIG. 3 , other measuring instruments may be tested using the test setup  300  to evaluate their performance (determine their measurement errors). 3D instruments under test may be placed in a variety of positions relative to the positions  320 A,  320 B. For example, a laser tracker may be placed to the side of the instrument stands so as to use its angular measuring capability in addition to its distance measuring capability. In this way, the performance of the tracker may be determined for a variety of measurement conditions. 
     The method of establishing a reference length L shown in  FIG. 3  is suited to a relatively permanent installation. It is less well suited to a quick check of the performance of a 3D instrument, especially if there is a need to test instrument performance in a variety of locations. For this purpose, it is preferable to provide a physical artifact having a reference length rather than the arrangement of  FIG. 3 . It is desirable that such a physical artifact have metrological traceability as described above. 
     A common (prior art) physical artifact having a reference length is a ballbar. A ballbar includes a sphere attached to and centered on each end of cylindrical shaft. The distance between the centers of the two spheres is measured in a calibration laboratory to provide a traceable reference length. The performance of a 3D instrument is established by measuring the length between the two spheres. The reference length is subtracted from the length measured by the 3D instrument to obtain an error. This error is compared to a maximum permissible error (MPE) given in a data sheet provided by the manufacturer of the 3D instrument. By comparing the observed error to the specified MPE value, the instrument is found to be within the manufacturer&#39;s specifications or outside the manufacturer&#39;s specifications. 
     The 3D instrument under test determines the distance between the ballbar sphere centers by measuring the 3D coordinates of the sphere surface at a number of positions on the surface. This data is used in a mathematical optimization procedure to obtain a best-fit sphere having a sphere center. The 3D coordinates of the centers of the two best-fit spheres at the positions  320 A,  320 B are used to find the ballbar length. 
     A practical difficulty in using a ballbar to determine the performance of a laser tracker is that it is difficult to obtain an acceptable sample of 3D coordinates for the sphere farthest from the tracker. In other words, suppose the spheres of a ball bar were located in the positions  320 A and  320 B of  FIG. 3  (with the ballbar cylindrical shaft connecting the two spheres). If the laser tracker were aligned to the ballbar spheres as in  FIG. 3 , it would be difficult or impossible for the tracker  310  to measure 3D coordinates of the near and far sides of the farthest ballbar sphere (at the position  320 B). The portion of the farthest sphere nearest the tracker is obscured by the cylindrical shaft of the ballbar. The portion of the farthest sphere that is farthest from the tracker cannot be contacted with the tracker SMR without pointing the retroreflector away from the beam  315 B, thereby breaking the beam. Therefore, for the farthest sphere in the ballbar, points can only be collected for the sphere central region, decreasing the ability to accurately fit the collected data to a sphere. This has the undesirable consequence of increasing the uncertainty in the tracker measurement. 
     Another practical difficulty in using a ballbar to measure devices such as laser trackers or AACMMs is that the ballbar needs to be mounted at two positions, ordinarily underneath the two spheres. As in the case of the arrangement shown in  FIG. 3 , ballbars are more suited to permanent, rather than flexible or impromptu, measurements of instrument performance. Another disadvantage of using a ballbar is that multiple points must be measured and a best-fit procedure carried out. 
     Another prior art method for establishing a reference length to verify the performance of a laser tracker or AACMM is described in U.S. Pat. No. 8,051,575 (&#39;575) to Bridges, et al., the contents of which are herein incorporated by reference. This patent describes a method in which a mount applied at two different positions along a length artifact may place the neutral surface of the mounted artifact to coincide with the SMR centers, thereby minimizing measurement error. An example of such a mounted artifact is shown in  FIG. 3  of the &#39;575 patent. This type of artifact and mounting arrangement is well suited to relatively large artifacts but is unnecessarily complex for measurements in which the length artifact can be mounted on a single structure or stand. 
     The mounted length artifact  490  described by  FIGS. 4A-G  overcome the limitations of the prior art methods described hereinabove. The mounted length artifact  490  includes a length artifact  400 , which is optionally attached to a mount  450 . The length artifact  400  includes a base portion  405  that extends the length of the artifact. Attached to the base portion  405  are a first sidewall  425  and a second sidewall  430 . Between the first sidewall and the second sidewall is an air gap  435 , the air gap being wide enough to permit passage of a beam of light from a laser tracker from one end of the artifact to the other end. In practice, this means that the air gap needs to be at least four millimeters wide. Each of the first sidewall and the second sidewall has a left surface as seen in  FIG. 4D , a right surface as seen in  FIG. 4E , and a bottom surface, which is in contact with the base portion  405 . In the embodiment illustrated in  FIG. 4 , the base portion, first sidewall, and second sidewall are formed or machined from a single piece of material, but these three components could be fabricated separately. 
     The base portion has a first platform region and a second platform region, the first platform region extending beyond the left surfaces of the sidewalls and the second platform extending beyond the right surfaces of the sidewalls. The first platform includes a first nest  410 A and the second platform includes a second nest  410 B. In  FIG. 4 , an SMR  470  is shown placed on the second nest  410 B. Each nest  410 A,  410 B includes contact points  412  that make contact with an outer spherical portion  472  of the SMR  470  to permit repeatable positioning of the SMR, usually to within one or two micrometers. A magnet  414  may be included in each of the nests  410 A,  410 B to securely hold the SMR in place. A cavity  474  in the SMR is sized to hold a cube-corner retroreflector (not shown), the cube corner having three perpendicular reflectors that form a cube-corner vertex. The SMR vertex coincides with the sphere center  478  of the spherical portion  472 . The SMR  470  may include a collar  476  to simplify handling of the SMR by an operator. Recesses  415  may be placed to either side of the nests  410 A,  410 B to accommodate the collar  476 . 
     The base portion  405 , first sidewall  425 , and second sidewall  430  may be formed from a single piece of material. In an embodiment, the material is a metal having a low coefficient of thermal expansion (CTE) to minimize changes in artifact length over temperature. Examples of low CTE material are Invar (CTE from 0.5 to 2 μm/m/T) and Super Invar (CTE from 0.3 to 1 μm/m/° C.). In another embodiment, the material is a non-metal having a low CTE. An example of such a material is a carbon-fiber composite, which may have a CTE less than 1 μm/m/° C. Other low CTE materials include certain ceramics and glasses. In other embodiments, the artifact  400  is made of material that does not have a low CTE. Examples of such materials include steel (CTE approximately 11.5 μm/m/° C.) and aluminum (CTE approximately 23 μm/m/° C.). 
     In an embodiment, the height and thickness of the first sidewall  425  and second sidewall  430  are selected relative to the height and width of the base portion  405  so as to make the neutral plane (surface)  440  of the artifact  400  coincide with the center  478  of the SMR  475  when placed in the nests  410 A,  410 B. This coincidence is shown in  FIGS. 4C-E . A length artifact  400  has an artifact frame of reference  495  that is tied to the artifact. Suppose that the gravity vector in  FIG. 6  is along the y direction as shown in  FIG. 6 . Then the neutral surface is found by taking the first moment of y over the mass of the structure. The length artifact  400  of  FIG. 6  is made of homogeneous material and has most of the weight concentrated in the central portion that includes the first and second sidewalls  425 ,  430 . In this case, the neutral axis to a good approximation passes through the centroid of a cross section of the length artifact  400  in a part of the artifact that includes the side walls. The neutral plane  440  passes through the neutral axis and lies in the x-z plane. 
     In  FIG. 4 , the mount  450  attaches to the center of the artifact  400 . In one embodiment, the mount  450  screws onto an instrument stand. In an embodiment shown in  FIGS. 5A, 5B , the mount  450  attaches to the length artifact  400  with four screws  455 . In another embodiment, a mount  450  attaches to the length artifact  400  with two screws  465  as shown in  FIG. 5C . Because the screws in either  FIG. 5B  or  FIG. 5C  are relatively close together, the support provided by the mount  450  can be modeled as a single point  605  as shown in  FIG. 6 . 
     The distributed forces of gravity  620  of  FIG. 6B  cause the length artifact  400  to bend along a slight arc. Hence the neutral plane is actually a neutral surface. The portion of the length artifact above the neutral surface is in tension and the portion of the length artifact below the neutral surface is in compression. The reference length L of the length artifact  400  is determined along the x direction shown in  FIG. 6 . The gravity-induced angles of bending of the test artifact are small relative to the x direction and hence, for the case of the SMR  470  placed on the neutral surface in the nests  410 A,  410 B, the error in the measured length is just proportional to a cosine of the angle, which is a negligible error. In other words, in  FIG. 6 , the measured distance for the SMR  470  placed on the nests  410 A,  410 B is L 1 , which is very nearly equal to the true length L. On the other hand, if the SMR  470  were placed on the upper surface of a length artifact as for the SMR  670  in  FIG. 6C , the angle of tilt of the SMR  670  would cause the distance between the SMR center at the two nests to be increased to a distance L 2 . Even though the angle of tilt is not large, the center of the SMR along the x direction shifts by a distance equal to the sine of the angle times the distance of the SMR above the neutral plane, which can be a relatively large error. In other words, for a small angle of tilt θ, cos(θ)˜1−θ 2 /2, which is nearly equal to 1, while for the same small angle, sin(θ)˜θ, which in the situation described hereinabove is likely to be significantly larger than zero. By adjusting the neutral surface to coincide with the SMR centers, the error in the measured length is made negligible. By placing the SMR center off the neutral axis, the measured length may be significantly affected by gravity-induced bending. 
     The error caused by bending is particularly important when a relatively long artifact is supported by a single structure or stand. In this case, bending may be significant so that any changes in the test conditions can cause a relatively large change in the measured length. For example, an AACMM may be tested with a length artifact  400 . For example, the nests may be configured to accept spherical surfaces having a diameter of ⅞ inch. The AACMM may be fitted with a ball probe having a diameter of ⅞ inch. By placing the AACMM ball probe in each nest and measuring the corresponding 3D coordinates in each case, the distance between the nest centers may be calculated. However, different operators may apply different amounts of force to the ball probe when putting it into the nest. An operator applying a greater amount of force will cause a greater amount of bending than would an operator applying a smaller amount of force. Hence, to obtain repeatable measurements using a length artifact  400 , it is important that the neutral surface coincide as well as possible to the nest (ball probe) centers. Similarly, different SMRs, even of a given diameter, may have different weights depending on construction. These weight differences can changes in the amount of bending, resulting in different measured lengths if the SMR is measured with the SMR center off the neutral surface. 
     In some cases, it is desirable to use the same artifact on different types of mounts. For example, in one instance, it may be desirable to measure the artifact having a mount shown in  FIG. 5C . In another instance, it may be desirable to remove the mount  450  and clamp the length artifact  400  to a granite table. For SMRs (or ball probes) placed in nests so as to align the sphere centers with the neutral surface, the same measured length L should be obtained in each case. 
     In an embodiment, a temperature sensor  780  is attached to a length artifact  700 . The temperature sensor, which might be a thermistor, for example, obtains an electrical signal that it sends to electronics  782  that uses the received signal to determine a temperature. The electrical signals may be sent to the electronics by over wires or wirelessly. In an initial step, the reference length of the artifact is determined using a laser tracker having a calibrated distance meter. The reference temperature T REF  of the artifact is recorded at the time of this measurement. Later the length of the artifact is measured with a 3D instrument to evaluate the accuracy of the instrument with the artifact having a test temperature T TEST . The length of the artifact is corrected by an amount L*(T EST −T REF )*CTE to account for the difference in temperatures. 
     In a method  800  described in  FIG. 8 , a laser tracker is used to determine a length of an artifact. A step  805  is providing a spherical retroreflector target, which might be an SMR, for example. The retroreflector includes a spherical portion that has a sphere center. A step  810  is providing a length artifact. The length artifact has a first side wall, a second side wall, and a base portion. The base portion includes a first nest and a second nest configured to accept the spherical retroreflector, with the retroreflector center at the first nest and the second being the first nest center and the second nest center, respectively. A step  815  is providing a laser tracker configured to project light to the retroreflector target, track the retroreflector target, and measure 3D coordinates of the center of the retroreflector target. 
     A step  820  is aligning the laser tracker to the length artifact so that the beam of light from the tracker travels in a straight line along a path connecting the first nest center and the second nest center. A step  825  is placing the retroreflector target in the first nest, which is taken here to be the nest closer to the tracker. It should be understood that the steps in the method  800  do not have to be carried out in the order given, which means that order of measuring the near and far nests may be reversed. A step  830  is measuring with the laser tracker a first distance to the first nest center. A step  835  is placing the retroreflector target in the second nest. A step  840  is sending the beam of light through the air gap between the first side wall and the second side wall to the retroreflector target. An example of a way of placing the retroreflector target in the second nest is now given. While tracking the retroreflector with the beam of light, the retroreflector is moved from the first nest over the top of the length artifact and then placed into the second nest. The beam of light passes through the air gap to the retroreflector. A step  840  is measuring with the laser tracker a second distance to the second nest center. A step  845  is determining a first artifact length based at least in part on the first distance and the second distance. 
     Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions. 
     These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the Figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions. 
     While the invention has been described in detail in connection with only a limited number of embodiments, it should be readily understood that the invention is not limited to such disclosed embodiments. Rather, the invention can be modified to incorporate any number of variations, alterations, substitutions or equivalent arrangements not heretofore described, but which are commensurate with the spirit and scope of the invention. Additionally, while various embodiments of the invention have been described, it is to be understood that aspects of the invention may include only some of the described embodiments. Accordingly, the invention is not to be seen as limited by the foregoing description, but is only limited by the scope of the appended claims. Moreover, the use of the terms first, second, etc. do not denote any order or importance, but rather the terms first, second, etc. are used to distinguish one element from another. Furthermore, the use of the terms a, an, etc. do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced item.