Patent Publication Number: US-9423492-B2

Title: Method for finding a home reference distance using a spherically mounted retroreflector

Description:
FIELD OF INVENTION 
     The present invention relates in general to methods for measuring spherically mounted retroreflectors (SMRs) and in particular to methods for determining surface coordinates and three-dimensional distances based on measurements of SMRs. 
     BACKGROUND 
     There is a class of instruments that measures the coordinates of a point by sending a laser beam to a retroreflector target in contact with the point. The instrument 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 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. 
     The laser tracker is a particular type of coordinate-measuring device that tracks the retroreflector target with one or more laser beams it emits. There is another category of instruments known as total stations or tachymeters that may measure a retroreflector or a point on a diffusely scattering surface. Laser trackers, which typically have accuracies on the order of a thousand 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 throughout this application. 
     Ordinarily the laser tracker sends a laser beam to a retroreflector target. A common type of retroreflector target is the SMR. In most cases, the term SMR is applied to a cube-corner retroreflector embedded within a metal sphere. However, the term SMR may also be applied to a cateye retroreflector embedded with a metal exterior spherical portion. Such a cateye retroreflector may be constructed in a shape of a sphere or in the shape of two adjoining hemispheres. A cube-corner retroreflector includes three mutually perpendicular reflectors. The vertex, which is the common point of intersection of the three reflectors, is located near the center of the sphere. In its normal tracking mode, the laser tracker sends a beam of light from the tracker to a position near the vertex of the SMR. As long as the beam of light strikes the vertex, the beam of returning beam of light retraces the path of the outgoing beam of light back to the tracker. If the beam of light strikes the SMR slightly off the vertex, the beam of light will return parallel to, but not exactly coincident with, the outgoing beam of light. A servo system within the tracker adjusts the direction of the beam emitted by the tracker to bring it back to the center, thereby allowing the beam to follow a moving retroreflector. Because the vertex is nearly coincident with the sphere center of the SMR, the perpendicular distance from the vertex to any surface on which the SMR rests remains nearly constant, even as the SMR is rotated. Consequently, the laser tracker can measure the 3D coordinates of a surface to a relatively high accuracy 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 characterize the 3D coordinates of a surface. 
     An SMR may also be used to measure the distance between two nests. A particularly useful kind of nest is a kinematic nest, which has the property that an SMR can be repeatably positioned in the nest. One type of nest makes contact with the SMR surface at three points. Some types of nests are magnetic nests that hold the SMR securely in place against the nest contact points. 
     Some laser trackers have the ability to measure six degrees of freedom (DOF), which may include three translations, such as x, y, and z, and three rotations, such as pitch, roll, and yaw. An exemplary six-DOF laser tracker system is described in U.S. Pat. No. 7,800,758 (&#39;758) to Bridges, et al., incorporated by reference herein. The &#39;758 patent discloses a probe that holds a cube corner retroreflector, onto which marks have been placed. The cube corner retroreflector is illuminated by a laser beam from the laser tracker, and the marks on the cube corner retroreflector are captured by an orientation camera within the laser tracker. The three orientational degrees of freedom, for example, the pitch, roll, and yaw angles, are calculated based on the image obtained by the orientation camera. The laser tracker measures a distance and two angles to the vertex of the cube-corner retroreflector. When the distance and two angles, which give three translational degrees of freedom of the vertex, are combined with the three orientational degrees of freedom obtained from the orientation camera image, the position of a probe tip, arranged at a prescribed position relative to the vertex of the cube corner retroreflector, can be found. Such a probe tip may be used, for example, to measure the coordinates of a “hidden” feature that is out of the line of sight of the laser beam from the laser tracker. 
     As explained hereinabove, the vertex of a cube corner retroreflector within an SMR is ideally placed at the exact center of the sphere into which the cube corner is embedded. In practice, the position of the vertex is off the center of the sphere by up to a few thousandths of an inch. In some cases, the difference in the positions of the vertex and the sphere center are known to high accuracy, but this data is not used to correct the tracker readings. In the accurate measurements made with laser trackers, this error in the centering of the cube corner retroreflector in the sphere is sometimes larger than the errors from the distance and angle meters within the laser tracker. Consequently, there is a need for a method to correct this centering error. 
     Most of the SMRs in use today contain open-air cube corner retroreflectors. There are some SMRs that use glass cube corner retroreflectors, but in most cases these have limited accuracy. Because of the bending of the light entering such glass cube corners, the light appears to travel in a direction that is not the true direction within the cube corner. Consequently, SMRs made with glass cube corners tend to be made very small, as this reduces error, and they tend to be used in applications where the highest accuracy is not required. A method for minimizing this error using a six-DOF laser tracker is given in U.S. Pat. No. 8,467,072, the contents of which are incorporated by reference. 
     In a 3D coordinate measurement device such as a laser tracker, a procedure is carried out using SMRs to determine a home reference distance to which a distance meter within the device is set. Errors in the procedure arise because of the SMR depth error. A method is needed to correct this error. 
     SUMMARY 
     According to one aspect of the invention, a method is provided for determining a home reference distance, the method comprising: providing a spherically mounted retroreflector (SMR), the SMR including a body and a retroreflector, the SMR including a reference point, the body having a spherical exterior portion that has a sphere center and a sphere radius, the body containing a cavity, the cavity sized to hold the retroreflector, the cavity open to a region outside the body, the retroreflector at least partially disposed in the cavity, the retroreflector being an open-air cube-corner retroreflector, the retroreflector having a set of three mutually perpendicular planar reflectors that intersect in a set of three lines and in a common vertex point, the cavity including an air-filled region interior to reflecting surfaces of the set of three planar reflectors, the retroreflector having an axis of symmetry relative to the set of three lines, the SMR having an SMR runout plane perpendicular to the axis of symmetry and passing through the sphere center, the SMR having an SMR intersection point, the SMR intersection point being a point of intersection of the axis of symmetry with the SMR runout plane, the SMR having an error vector extending from the vertex point to the sphere center, the SMR error vector having an SMR depth error vector component and an SMR runout error vector component, the SMR depth error vector component being a vector that extends from the vertex point to the SMR intersection point, the SMR runout error vector component being a vector that extends from the SMR intersection point to the sphere center, the SMR depth error vector component having a magnitude equal to an SMR depth error; providing a three-dimensional (3D) coordinate measurement device including a base, a first motor, a second motor, a first angle measuring device, a second angle measuring device, a distance meter, a home position nest, and a processor, the 3D coordinate measurement device having a device frame of reference, the 3D coordinate measurement device configured to send an emitted beam of light to the SMR, the retroreflector returning a portion of the emitted beam as a reflected beam, the first motor and the second motor together directing the emitted beam in an emitted direction, the emitted direction determined by a first angle of rotation about a first axis and a second angle of rotation about a second axis, the first angle of rotation produced by the first motor and the second angle of rotation produced by the second motor, the rotation of the first axis and the second axis made with respect to the base, the second axis having a rotation point lying on a line coinciding with the emitted beam, the first angle measuring device measuring the first angle of rotation and the second angle measuring device measuring the second angle of rotation, the distance meter measuring a target distance from the 3D coordinate measurement device to the retroreflector based at least in part on the reflected beam received by the 3D coordinate measurement device, the home position nest being affixed to the base and being configured to receive the spherical exterior portion; providing a second nest and a third nest, the second nest and the third nest configured to repeatably receive the spherical exterior portion, the second nest having a second nest point corresponding to the sphere center when the SMR is in the second nest, the third nest having a third nest point corresponding to the sphere center when the SMR is in the third nest, a distance between the second nest point and the third nest point being a nest-to-nest distance, the second nest and the third nest having a nest center line, the nest center line being a line passing through the second nest point and the third nest point, the nest center line having an interior portion and an exterior portion, the interior portion being that portion of the nest center line between the second nest point and the third nest point, the exterior portion being the nest center line excluding the interior portion; providing a processor and a memory; providing computer readable media having computer readable instructions which when executed by the processor determines the home reference distance; determining the SMR depth error; recording the SMR depth error as a recorded data set; reading by the processor the recorded data set; placing the SMR in the home position nest; sending from the 3D coordinate measurement device to the SMR in the home position nest a first emitted beam; measuring with the 3D coordinate measurement device a first target distance to the SMR in the home position nest; placing the rotation point of the 3D coordinate measurement device on the interior portion; placing the SMR in the second nest; sending from the 3D coordinate measurement device to the SMR in the second nest a second emitted beam; measuring with the 3D coordinate measurement device a second target distance to the SMR in the second nest; placing the SMR in the third nest; sending from the 3D coordinate measurement device to the SMR in the third nest a third emitted beam; measuring with the 3D coordinate measurement device a third target distance to the SMR in the third nest; executing by the processor the computer readable instructions, the computer readable instructions performing calculations to determine the home reference distance, the home reference distance being a distance from the rotation point to the sphere center of the SMR in the home position nest, the home reference distance based at least in part on the nest-to-nest distance, the first target distance, the second target distance, the third target distance, and the SMR depth error; and storing the home reference distance. 
     According to one aspect of the invention, a method is provided for determining a home reference distance, the method comprising: providing a first spherically mounted retroreflector (SMR), the first SMR including a first body and a first retroreflector, the first SMR including a first reference point, the first body having a first spherical exterior portion that has a first sphere center and a first sphere radius, the first body containing a first cavity, the first cavity sized to hold the first retroreflector, the first cavity open to a first region outside the body, the first retroreflector at least partially disposed in the first cavity, the first retroreflector being an open-air cube-corner retroreflector, the first retroreflector having a first set of three mutually perpendicular planar reflectors that intersect in a first set of three lines and in a common first vertex point, the first cavity including a first air-filled region interior to reflecting surfaces of the first set of three planar reflectors, the first retroreflector having a first axis of symmetry relative to the first set of three lines, the first SMR having a first SMR runout plane perpendicular to the first axis of symmetry and passing through the first sphere center, the first SMR having a first SMR intersection point, the first SMR intersection point being a first point of intersection of the first axis of symmetry with the first SMR runout plane, the first SMR having a first error vector extending from the first vertex point to the first sphere center, the first SMR error vector having a first SMR depth error vector component and a first SMR runout error vector component, the first SMR depth error vector component being a vector that extends from the first vertex point to the first SMR intersection point, the first SMR runout error vector component being a vector that extends from the first SMR intersection point to the first sphere center, the first SMR depth error vector component having a magnitude equal to a first SMR depth error; providing a second SMR, the second SMR including a second body and a second retroreflector, the second SMR including a second reference point, the second body having a second spherical exterior portion that has a second sphere center and a second sphere radius, the second body containing a second cavity, the second cavity sized to hold the second retroreflector, the second cavity open to a second region outside the second body, the second retroreflector at least partially disposed in the second cavity, the second retroreflector being an open-air cube-corner retroreflector, the second retroreflector having a second set of three mutually perpendicular planar reflectors that intersect in a second set of three lines and in a common second vertex point, the second cavity including a second air-filled region interior to reflecting surfaces of the second set of three planar reflectors, the second retroreflector having a second axis of symmetry relative to the second set of three lines, the second SMR having a second SMR runout plane perpendicular to the second axis of symmetry and passing through the second sphere center, the second SMR having a second SMR intersection point, the second SMR intersection point being a second point of intersection of the second axis of symmetry with the second SMR runout plane, the second SMR having a second error vector extending from the second vertex point to the second sphere center, the second SMR error vector having a second SMR depth error vector component and a second SMR runout error vector component, the second SMR depth error vector component being a vector that extends from the second vertex point to the second SMR intersection point, the second SMR runout error vector component being a vector that extends from the second SMR intersection point to the second sphere center, the second SMR depth error vector component having a magnitude equal to a second SMR depth error; providing a third SMR, the third SMR including a third body and a third retroreflector, the third SMR including a third reference point, the third body having a third spherical exterior portion that has a third sphere center and a third sphere radius, the third body containing a third cavity, the third cavity sized to hold the third retroreflector, the third cavity open to a third region outside the third body, the third retroreflector at least partially disposed in the third cavity, the third retroreflector being an open-air cube-corner retroreflector, the third retroreflector having a third set of three mutually perpendicular planar reflectors that intersect in a third set of three lines and in a common third vertex point, the third cavity including a third air-filled region interior to reflecting surfaces of the third set of three planar reflectors, the third retroreflector having a third axis of symmetry relative to the third set of three lines, the third SMR having a third SMR runout plane perpendicular to the third axis of symmetry and passing through the third sphere center, the third SMR having a third SMR intersection point, the third SMR intersection point being a third point of intersection of the third axis of symmetry with the third SMR runout plane, the third SMR having a third error vector extending from the third vertex point to the third sphere center, the third SMR error vector having a third SMR depth error vector component and a third SMR runout error vector component, the third SMR depth error vector component being a vector that extends from the third vertex point to the third SMR intersection point, the third SMR runout error vector component being a vector that extends from the third SMR intersection point to the third sphere center, the third SMR depth error vector component having a magnitude equal to a third SMR depth error; providing a three-dimensional (3D) coordinate measurement device including a base, a first motor, a second motor, a first angle measuring device, a second angle measuring device, a distance meter, a home position nest, and a processor, the 3D coordinate measurement device having a device frame of reference, the 3D coordinate measurement device configured to send an emitted beam of light to a target SMR, the target SMR including a target body and a target retroreflector the target retroreflector returning a portion of the emitted beam as a reflected beam, the first motor and the second motor together directing the emitted beam in an emitted direction, the emitted direction determined by a first angle of rotation about a first axis and a second angle of rotation about a second axis, the first angle of rotation produced by the first motor and the second angle of rotation produced by the second motor, the rotation of the first axis and the second axis made with respect to the base, the second axis having a rotation point lying on a line coinciding with the emitted beam, the first angle measuring device measuring the first angle of rotation and the second angle measuring device measuring the second angle of rotation, the distance meter measuring a target distance from the 3D coordinate measurement device to the target retroreflector based at least in part on the reflected beam received by the 3D coordinate measurement device, the home position nest being affixed to the base and being configured to hold the target SMR; providing a second nest and a third nest, the second nest configured to repeatably receive the second spherical exterior portion, the second nest having a second nest point corresponding to the second sphere center of the second SMR when the second SMR is placed in the second nest, the third nest configured to repeatably receive the third spherical exterior portion, the third nest having a third nest point corresponding to the third sphere center of the third SMR when the third SMR is placed in the third nest, a distance between the second nest point and the third nest point being a nest-to-nest distance, the second nest and the third nest having a nest center line, the nest center line being a line passing through the second nest point and the third nest point, the nest center line having an interior portion and an exterior portion, the interior portion being that portion of the nest center line between the second nest point and the third nest point, the exterior portion being the nest center line excluding the interior portion; providing a processor and a memory; providing computer readable media having computer readable instructions which when executed by the processor determines the home reference distance; determining the first SMR depth error; determining the second SMR depth error; determining the third SMR depth error; recording, in a recorded data set, the first SMR depth error, the second SMR depth error, and the third SMR depth error; reading by the processor the recorded data set; placing the first SMR in the home position nest; sending from the 3D coordinate measurement device to the first SMR a first emitted beam; measuring with the 3D coordinate measurement device a first target distance to the first SMR; placing the rotation point of the 3D coordinate measurement device on the interior portion; placing the second SMR in the second nest; sending from the 3D coordinate measurement device to the second SMR a second emitted beam; measuring with the 3D coordinate measurement device a second target distance to the second SMR; placing the third SMR in the third nest; sending from the 3D coordinate measurement device to the third SMR a third emitted beam; measuring with the 3D coordinate measurement device a third target distance to the third SMR; executing by the processor the computer readable instructions, the computer readable instructions performing calculations to determine the home reference distance, the home reference distance being a distance from the rotation point to the first sphere center of the first SMR in the home position nest, the home reference distance based at least in part on the nest-to-nest distance, the first target distance, the second target distance, the third target distance, the first SMR depth error, the second SMR depth error, and the third SMR depth error; and storing the home reference distance. 
     According to one aspect of the invention, a method is provided for adjusting a distance meter by an offset distance, the method comprising: providing a spherically mounted retroreflector (SMR), the SMR including a body and a retroreflector, the body having a spherical exterior portion that has a sphere center, the body containing a cavity, the cavity sized to hold the retroreflector, the cavity open to a region outside the body, the retroreflector at least partially disposed in the cavity, the retroreflector being an open-air cube-corner retroreflector, the retroreflector having a set of three mutually perpendicular planar reflectors that intersect in a set of three lines and in a common vertex point, the cavity including an air-filled region interior to reflecting surfaces of the set of three planar reflectors, the retroreflector having an axis of symmetry relative to the set of three lines, the SMR having an SMR runout plane perpendicular to the axis of symmetry and passing through the sphere center, the SMR having an SMR intersection point, the SMR intersection point being a point of intersection of the axis of symmetry with the SMR runout plane, the SMR having an error vector extending from the vertex point to the sphere center, the SMR error vector having an SMR depth error vector component, the SMR depth error vector component being a vector that extends from the vertex point to the SMR intersection point, the SMR depth error vector component having a magnitude equal to an SMR depth error; providing a three-dimensional (3D) coordinate measurement device including a base, a first motor, a second motor, a first angle measuring device, a second angle measuring device, the distance meter, and a processor, the 3D coordinate measurement device configured to send an emitted beam of light to the SMR, the retroreflector returning a portion of the emitted beam as a reflected beam, the first motor and the second motor together directing the emitted beam of light to an emitted direction, the emitted direction determined by a first angle of rotation about a first axis and a second angle of rotation about a second axis, the first angle of rotation produced by the first motor and the second angle of rotation produced by the second motor, the rotation of the first axis and the second axis made with respect to the base, the second axis having a rotation point lying on a line coinciding with the emitted beam, the first angle measuring device measuring the first angle of rotation and the second angle measuring device measuring the second angle of rotation, the distance meter measuring a target distance from the 3D coordinate measurement device to the retroreflector based at least in part on the reflected beam received by the 3D coordinate measurement device; providing a first nest and a second nest, the first nest and the second nest configured to repeatably receive the spherical exterior portion, the first nest having a first nest point corresponding to the sphere center of the SMR when the SMR is placed in the first nest, the second nest having a second nest point corresponding to the sphere center of the SMR when the SMR is placed in the second nest, the distance between the first nest point and the second nest point being a nest-to-nest distance, the first nest and the second nest having a nest center line, the nest center line being a line passing through the first nest point and the second nest point, the nest center line having an interior portion and an exterior portion, the interior portion being that portion of the nest center line between the first nest point and the second nest point, the exterior portion being the nest center line excluding the interior portion; providing a processor and a memory; providing computer readable media having computer readable instructions which when executed by the processor determines the offset distance; determining the SMR depth error; recording the SMR depth error as a recorded data set; reading by the processor the recorded data set; placing the rotation point of the 3D coordinate measurement device on the interior portion; placing the SMR in the first nest; sending from the 3D coordinate measurement device to the SMR in the first nest a first emitted beam; measuring with the 3D coordinate measurement device a first target distance to the SMR in the first nest; placing the SMR in the second nest; sending from the 3D coordinate measurement device to the SMR in the second nest a second emitted beam; measuring with the 3D coordinate measurement device a second target distance to the SMR in the second nest; executing by the processor the computer readable instructions, the computer readable instructions performing calculations to determine the offset distance, the offset distance based at least in part on the nest-to-nest distance, the first target distance, the second target distance, and the SMR depth error; and measuring the target distance with the distance meter further based on the offset distance. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments will now be described, by way of example only, with reference to the accompanying drawings which are meant to be exemplary, not limiting, and wherein like elements are numbered alike in several figures, in which: 
         FIG. 1  is a perspective view of a laser tracker and an SMR according to an embodiment; 
         FIG. 2  is an illustration of a laser tracker, an auxiliary unit, and an external computer according to an embodiment; 
         FIG. 3  is a block diagram showing elements in the payload of a laser tracker according to an embodiment; 
         FIG. 4  is a perspective view of elements used in replicating a cube corner retroreflector; 
         FIGS. 5A-C  are perspective, cross-sectional, and front views, respectively, of an SMR that includes an open-air cube-corner slug embedded within a sphere according to embodiments; 
         FIGS. 6A-C  are perspective views of the SMRs to which have been added a reflective region, a barcode pattern or serial number, and an RF identification tag, respectively, according to embodiments; 
         FIGS. 7A-B  are front and side sectional views, respectively, of an SMR having a cube corner retroreflector not perfectly centered within a sphere; 
         FIG. 8A  is a perspective view of a portion of a cube corner retroreflector with its axis of symmetry, and  FIG. 8B  is magnified view of the SMR vertex point and sphere center with error vector and error vector components according to an embodiment; 
         FIG. 9A  is a perspective view of a portion of a cube corner retroreflector including a reference mark and an SMR runout reference plane, and  FIG. 9B  is a magnified view of the SMR vertex point and sphere center showing the SMR runout reference ray and the SMR runout reference angle according to an embodiment; 
         FIG. 9C  is a perspective view of a portion of a cube corner retroreflector including a reference mark and a beam runout reference plane, and  FIG. 9D  is a magnified view of the SMR vertex point and sphere center showing the beam runout reference ray and the beam runout reference angle according to an embodiment; 
         FIGS. 10A, 10C  are perspective and front views, respectively, of an SMR that provides a connector socket, and  FIG. 10B  is a cross-sectional view of an SMR showing a temperature sensor configured for electrical connection to connector cable, also shown, according to an embodiment; 
         FIG. 10D  shows the elements of  FIG. 10C  with the addition of self-contained temperature measurement and communication unit,  FIG. 10E  is a schematic view of electrical components within the temperature measurement and communication unit, and  FIG. 10F  is a pictorial representation of a hand holding an SMR, wherein a temperature measurement and communication unit is attached to the hand; 
         FIG. 11  is an SMR to which is attached an interface unit that includes a battery and antenna for use with a temperature sensor; 
         FIGS. 12A-E  are schematic illustrations of the errors resulting from the misalignment of the axis of symmetry of an SMR with the beam of light from a 3D measurement device; 
         FIGS. 13A-13F  are perspective and schematic representations of alternative methods for aligning an axis of symmetry of an SMR with a beam of light from a 3D measurement device according to an embodiment; 
         FIG. 14A  shows a kinematic nest and support axis, and  FIG. 14B  shows a kinematic nest receiving an SMR; 
         FIG. 15  shows a mathematical model of the kinematic nest of  14 A; 
         FIGS. 16A, 16B  show front and side views of SMRs held by kinematic nests, respectively, and  FIG. 16C  shows that errors in the SMR radius do not significantly affect a measured length; 
         FIG. 17A  shows side views of SMRs held by kinematic nests with one of the nests perpendicular to a desired measurement direction, and  FIG. 17B  shows that errors may be significant for this case; 
         FIG. 18  illustrates a method of obtaining accurate 3D measurements of an SMR sphere center for a device located at two stations while performing an SMR alignment at a single station; 
         FIGS. 19A, 19B  illustrate that the direction of the maximum runout error vector component, which may in an embodiment be aligned to a reference point on the SMR, may have a significant effect on measurement error; 
         FIGS. 19C, 19D  illustrate a general approach to aligning a runout error vector component to minimize measurement error; 
         FIGS. 20A, 20B  show a distance measurement made to an SMR in frontsight and backsight modes, respectively, and  FIG. 20C  shows a distance measurement made to a home position; 
         FIG. 21A  shows a method for measuring a distance between two spherically mounted retroreflectors,  FIG. 21B  shows a method for determining finding an offset error in measured distance, and  FIG. 21C  shows a method for finding the axis offset value for a coordinate measurement device; 
         FIG. 22  shows a method for setting a distance to the vertex of an SMR in a home position; and 
         FIG. 23  shows electronics and processors within a laser tracker according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     An exemplary laser tracker  10  is illustrated in  FIG. 1 . An exemplary gimbaled beam-steering mechanism  12  of laser tracker  10  includes zenith carriage  14  mounted on azimuth base  16  and rotated about azimuth axis  20 . Payload  15  is mounted on zenith carriage  14  and rotated about zenith axis  18 . Zenith mechanical rotation axis (not shown) and azimuth mechanical rotation axis (not shown) intersect orthogonally, internally to tracker  10 , at gimbal point  22 , which is typically the origin for distance measurements. Laser beam  46  virtually passes through gimbal point  22  and is pointed orthogonal to zenith axis  18 . In other words, laser beam  46  is in a plane normal to zenith axis  18 . Laser beam  46  is pointed in the desired direction by motors within the tracker (not shown) that rotate payload  15  about zenith axis  18  and azimuth axis  20 . Zenith and azimuth angular encoders, internal to the tracker (not shown), are attached to zenith mechanical axis (not shown) and azimuth mechanical axis (not shown) and indicate, to relatively high accuracy, the angles of rotation. Laser beam  46  travels to external retroreflector  26  such as the SMR described above. By measuring the radial distance between gimbal point  22  and retroreflector  26  and the rotation angles about the zenith and azimuth axes  18 ,  20 , the position of retroreflector  26  is found within the spherical coordinate system of the tracker. 
     The device frame of reference  30  of the laser tracker  10  is fixed with respect to the azimuth base  16 , which is typically stationary with respect to the tracker&#39;s surroundings. The device frame of reference  30  may be represented in a variety of coordinate systems. It may be represented in a Cartesian coordinate system having three perpendicular axes x′, y′, and z′. It may be represented in a spherical coordinate system, a point  74  being represented by a radial distance  73  ( r ), a first (zenith) angle  72  (θ), and a second (azimuth) angle  71  (φ). The angle θ is obtained by using the projection of the point  74  onto the z axis. The angle φ is obtained by using the projection of the point  74  onto the x′-y′ plane. The laser tracker  10  inherently measures in a spherical coordinate system using one distance meter to measure r and two angular encoders to measure θ and φ. However, a point measured in spherical coordinates may be easily converted to Cartesian coordinates. In an embodiment, the gimbal point  22  is selected as the origin. Other coordinate systems are possible and may be used. 
     The laser tracker  10  also includes rotating frames of reference. One of the rotating frames of reference is the payload frame of reference  35  that aims the beam of light  46  toward the SMR  26 . The payload frame of reference rotates about the axis  20  and the axis  18 . It should be understood that the term payload frame of reference may refer to the final beam delivery portion of any type of beam delivery system, not just the payload  15  of  FIG. 1 . For example, the payload  15  may be replaced by a mirror that reflects the beam of light  46  toward the SMR  26 . The payload frame of reference  35  may be represented in a Cartesian coordinate system having three perpendicular axes x″, y″, and z″ as shown in  FIG. 1 . In an exemplary payload frame of reference, the x″ axis points in the direction of the outgoing laser beam  46 , the y″ axis points in the direction of the zenith axis  18 , and the z″ axis points in a direction perpendicular to the x″ and y″ axes. The y″-z″ plane is perpendicular to the direction x″ of the laser beam. In an embodiment, the gimbal point  22  is the origin of the payload frame of reference  35 . 
     The SMR  26  has an SMR frame of reference  40 . The SMR frame of reference may be represented, for example, in a Cartesian coordinate system having three perpendicular axes x, y, and z. The x, y, and z axes of the SMR frame of reference  40  move with the SMR  26  and are not in general parallel to the corresponding axes x″, y″, and z″ of the payload frame of reference  35 . In an embodiment, a vertex of a cube corner retroreflector within the SMR is the origin of the SMR frame of reference. The SMR  26  may be placed in contact with the workpiece surface  61  at a point  63 . To find the three-dimensional (3D) coordinates of the point  63 , the tracker first determines the 3D coordinates of the vertex of the SMR  26  using the distance and two angles it has measured. It then shifts the 3D coordinates of the SMR vertex toward the surface by an amount equal to the sphere radius of the SMR. The SMR  26  may also be used to measure 3D coordinates when placed on a kinematic nest, as further explained hereinbelow. 
     Laser beam  46  may include one or more laser wavelengths, or the beam  46  may be a beam of light other than laser light. For the sake of clarity and simplicity, a steering mechanism of the sort shown in  FIG. 1  is assumed in the following discussion. However, other types of steering mechanisms are possible. For example, it would be possible to reflect a laser beam off a mirror rotated about the azimuth and zenith axes. The techniques described here are applicable, regardless of the type of steering mechanism. 
     In exemplary laser tracker  10 , locator cameras  52 ,  56  and light sources  54  are located on payload  15 . Light sources  54  illuminate one or more retroreflector targets  26 . In an embodiment, light sources  54  are LEDs electrically driven to repetitively emit pulsed light. Each locator camera  52  and  56  includes a photosensitive array and a lens placed in front of the photosensitive array. The photosensitive array may be a CMOS or CCD array, for example. In an embodiment, the lens of locator camera  52  has a relatively wide field of view, for example, 30 or 40 degrees. In contrast, the lens of locator camera  56  may have a relatively narrow field of view, for example, to enable clear reading of a bar code or a serial number of an SMR  26  held in a home nest  17 , as discussed further hereinbelow. The purpose of the lens in a camera  52 ,  56  is to form an image on the photosensitive array of objects within the field of view of the lens. The image on the photosensitive array is sent to electronics, which may be internal or external to the photosensitive array, to provide an electrical signal to a processor. The electrical signal is evaluated by the processor to extract relevant information such as images, text, array locations, and so forth. Usually at least one light source  54  is placed near a locator camera  52  so that light from light source  54  is reflected off each retroreflector target  26  onto the locator camera  52 . In this way, retroreflector images are readily distinguished from the background on the photosensitive array as their image spots are brighter than background objects and are pulsed. In an embodiment, there are two locator cameras  52  and two light sources  54  placed about the line of laser beam  46 . By using two locator cameras  52  in this way, the principle of triangulation can be used to find the three dimensional coordinates of any SMR within the field of view of the locator camera. In addition, the three dimensional coordinates of an SMR can be monitored as the SMR is moved from point to point. 
     For a locator camera  56  designed to read bar codes, a light source is not placed close to the camera as the bright flash of retroreflected light would prevent the camera from reading the much dimmer lines of a bar code. Instead, the lights  54 , which are too far away from the locator camera  56  to retro-reflect the light from the retroreflector target  26  into the locator camera  56 , may be used to illuminate the bar codes, if needed. 
     As shown in  FIG. 2 , auxiliary unit  70  may be a part of laser tracker  10 . The purpose of auxiliary unit  70  is to supply electrical power to the laser tracker body and in some cases to also supply computing and clocking capability to the system. It is possible to eliminate auxiliary unit  70  altogether by moving the functionality of auxiliary unit  70  into the tracker body. In most cases, auxiliary unit  70  is attached to general purpose computer  80 . Application software loaded onto general purpose computer  80  may provide application capabilities such as reverse engineering. It is also possible to eliminate general purpose computer  80  by building its computing capability directly into laser tracker  10 . In this case, a user interface, possibly providing keyboard and mouse functionality may be built into laser tracker  10 . The connection between auxiliary unit  70  and computer  80  may be wireless or through a cable of electrical wires. Computer  80  may be connected to a network, and auxiliary unit  70  may also be connected to a network. Plural instruments, for example, multiple measurement instruments or actuators, may be connected together, either through computer  80  or auxiliary unit  70 . In an embodiment, auxiliary unit  70  is omitted and connections are made directly between laser tracker  10  and computer  80 . 
     The laser tracker  10  measures a distance r using either an interferometer or an ADM. It measures an azimuth angle φ and a zenith angle θ using angular encoders. Hence the laser tracker measures in a spherical coordinate system, although the coordinate values for any measured point may be converted into coordinates in any other desired coordinate system, for example, the Cartesian coordinate system  30  of  FIG. 1 . 
     It should be similarly understood that three degrees of translational freedom means three independent degrees of translational freedom. Another way of saying this is that the three directions corresponding to the three degrees of translational freedom form a basis set in three-dimensional space. In other words, each of the three directions corresponding to a degree of translational freedom has a component orthogonal to each of the other two directions. 
       FIG. 3  shows an embodiment for electro-optical assembly  400  of the laser tracker  10 . Source elements  405  and  410  represent light sources and possibly additional electrical and optical components. For example, source element  410  may represent a red helium-neon laser in combination with an interferometer. Source element  405  may represent an infrared laser in combination with an ADM. Alternatively, the system may have only an interferometer or only an ADM. One of the source elements  405  or  410  may have only a source of light without a distance meter. There may be additional light sources (not shown) besides those contained within source elements  405  and  410 . The source elements  405  and  410  may be located in payload  15  or they may be located in one of the other parts of the tracker such as the zenith carriage  14  or azimuth base  16 . The light source may be located in one section, for example, the azimuth base, and the distance meter located in another section such as the payload  15 . The light may be routed from one location to another by optical fibers, as explained in the &#39;758 patent. Alternatively, the light from the source may be reflected off a mirror that is steered about the zenith axis, and the distance meters kept in the azimuth base  16 . The light sources may include lasers, superluminescent diodes, light emitting diodes, or others. 
     Light from source element  410  passes through beam splitter  420 . Light from source element  405  reflects off mirror  415  and beam splitter  420 . If source elements  405 ,  410  contain light of different wavelengths, beam splitter  420  may advantageously be a dichroic beam splitter that transmits the wavelength of light emitted by source element  410  and reflects the wavelength of light emitted by source element  405 . 
     Most of the light from beam splitter  420  passes through beam splitter  425 . A small amount of light is reflected off beam splitter  425  and is lost. The light passes through beam expander  435 , which expands the size of the beam on the way out of the tracker. Expanding the beam of light is helpful because it enables the light to propagate a longer distance with less change in beam size. The laser light  440  leaving the tracker  10  travels to a retroreflector target  26 . A portion of this laser light reflects off the retroreflector  26  and returns to the tracker. The beam expander  435  reduces the size of the beam on the way back into the tracker. 
     Part of the returning light travels to beam splitter  425 . Most of the light passes on to elements  405 ,  410  but a small amount is split off and strikes position detector  450 . In some cases, the light may pass through a lens after reflecting off beam splitter  425  but before striking position detector  450 . The position detector  450  may be of several types—for example, a position sensitive detector or photosensitive array. A position sensitive detector might be a lateral effect detector or a quadrant detector, for example. A photosensitive array might be a CMOS or CCD array, for example. Position detectors are responsive to the position of the returning light beam. The motors attached to the azimuth mechanical axes and the zenith mechanical axes are adjusted by a control system within the tracker  10  to keep the returning light beam centered, as nearly as possible, on the position detector  450 . 
     The SMR  26  includes a body having a spherical exterior portion and a retroreflector. The spherical exterior portion contains a cavity sized to hold a cube corner retroreflector, which is at least partially disposed in the cavity. The spherical exterior portion has a spherical center. A cube corner retroreflector may be an open-air cube corner or a glass cube corner. An open-air cube corner retroreflector has an interior portion of air, while a glass cube corner retroreflector has an interior portion of glass. 
     A cube corner retroreflector includes three planar reflectors that are mutually perpendicular. The three planar reflectors intersect at a common vertex, which in the ideal case is a point. Each of the planar reflectors has two intersection junctions, each intersection junction of which is shared with an adjacent planar reflector for a total of three intersection junctions within the cube corner retroreflector. The cube corner retroreflector has an interior portion that is a region of space surrounded on three sides by the planar reflectors. In the case of an open-air cube corner retroreflector, which is the subject of the present application, the cavity includes an air-filled portion interior to the three planar reflectors, the three intersection junctions, and the vertex. The cavity is open to an exterior of the body, which provides a means for light to be sent into and reflected from the retroreflector. 
     There are at least three common methods for making open-air cube corner retroreflectors: a replication process, a mirror insertion process, and an ECM process.  FIG. 4  illustrates the replication process. A master element  510  is carefully machined to produce the characteristics desired in the final replicated retroreflector. For example, the master element  510  may be machined to make each of the three planar reflector faces  512  almost exactly perpendicular to its two neighbors  512 . The three planar reflector faces  512  of the master element  510  may be perpendicular to each of the neighboring reflectors to within one or two arc seconds. The master element  510  is coated with a reflective material such as gold. A cube corner slug  520  includes a machined blank  522  coated with a thin adhesive layer of material such as epoxy. The cube corner slug  520  is brought in contact with the master element  510 . In doing so, the epoxy layer is brought into conformance with the shape of the master element  510 . After the epoxy cures and the slug  520  is lifted off the master element  510 , the gold layer sticks to the epoxy, thereby providing the cube corner slug  520  with a reflective coating. 
     The second common method of making open-air cube corner retroreflectors is the mirror insertion process in which mirror panels joined into a cube-corner assembly are inserted into a cavity in the spherical exterior portion. Three mirror panels are joined together to be mutually perpendicular. 
     The third common method of making open-air cube corner retroreflectors is the electrochemical machining (ECM) process. In some cases, the retroreflector and the spherical exterior portion are integrated into a single unit. Such an SMR may be created, for example, by removing the cavity using a combination of traditional machining and ECM. Such an ECM process may be used to create three mutually perpendicular surfaces that are flat and smooth. Such surfaces may be covered with a reflective coating such as gold or silver to provide the three reflective surfaces. 
     An SMR having an open-air cube corner retroreflector is illustrated in  FIGS. 5A-C .  FIG. 5A  shows an SMR  700 , which includes a spherical exterior portion  720 , an open-air cube corner retroreflector  710 , a collar  905 , and a reference mark, or feature,  930 . In an embodiment, a cavity in the spherical exterior portion  720  is sized to accept the cube corner retroreflector  710 . The cube corner retroreflector  710  is at least partially disposed in spherical exterior portion  720 , possibly with adhesive. The collar  905  provides protection for the cube corner retroreflector  710  and provides a convenient grip. The reference mark, or feature,  930  may be used to establish an orientation of the SMR in space, as discussed in more detail hereinbelow. The reference feature  930  may also be a textural feature such as a dimple or bump. It might be a serial number, a reflective region (as in  610  of  FIG. 6A ), a barcode (as in  630  of  FIG. 6B ), a radio frequency identification (RFID) tag, or other feature. In this case, the reference mark may be selected by convention to be for example a center, a left side, or a right side of a given feature. The reference feature may be any feature that enables the user or a reading device to distinguish an orientation of the retroreflector  710 .  FIG. 5B  shows a cross sectional view taken through the center of the SMR  700 . The cross section reveals the open-air cube corner  710  to be of the replicated type, but a cube corner retroreflector formed of three mirror panels or directly formed using ECM could equally well be used.  FIG. 5C  shows a front view of the SMR  700 . 
       FIGS. 6A-C  depict three embodiments of SMRs. In  FIG. 6A , the SMR  700  includes a spherical exterior portion  720 , a cube corner retroreflector  710 , and a collar  905 . A region of reflecting material  610  is placed on the front surface of collar  905  in  FIG. 6A . This region of reflecting material  610  is illuminated by light from the laser tracker and its position determined by a locator camera disposed on the tracker. For example, the light might be provided by the light sources  54  and the image of the illuminated SMR captured by one or more locator cameras  52  as shown in  FIG. 1 . The position of the region  610  may be used to find an orientation of the SMR  700  as explained further hereinbelow. In  FIG. 6B , the SMR  700  includes the same elements as in  FIG. 6A  except that the region of reflecting material  610  is replaced by a barcode pattern  630 . The barcode pattern  630  may be a one-dimensional barcode pattern or a two-dimensional barcode pattern. Two dimensional barcode patterns are sometimes referred to as matrix barcodes, 2D barcodes, 2D codes or by names such as QR that indicate the specific form of the code. The barcode may serve to provide an identification of the SMR or to store one or more parameters of the SMR as is described in more detail hereinbelow. The barcode  630  may also act as a reference mark (serving the function of  930  in  FIG. 5A ) or as a region of reflecting material to provide an orientation of the SMR  700 . If desired, the barcode pattern may extend around the entire circumference of the collar lip rather than only a portion of the lip as shown in  FIG. 6B . If desired, the type of barcode pattern known as a radial pattern may be used. In  FIG. 6C , the SMR  700  includes the same elements as in  FIG. 6A  except that the region of reflecting material  610  is replaced by an RF identification chip  650 . This chip may be interrogated by an RF transmitter/receiver, which might be, for example, a handheld unit or a unit located on a laser tracker  10 , to obtain information about the SMR  700 . This information may be a serial number or one or more parameters of the SMR  700 . 
       FIGS. 7A, 7B  show front view and side-sectional views of an SMR  700 . The SMR includes a spherical exterior portion  720  and a retroreflector  710 . The retroreflector  710  is a cube corner retroreflector having three planar reflectors  825 AB,  825 BC, and  825 AC that are mutually perpendicular and intersect in three intersection junctions  810 A,  810 B, and  810 C and a vertex  820 . In an ideal SMR the three intersection junctions are intersection lines and the vertex is a point. In this application, the term line is often used to refer to an intersection junction even if the junction is not a perfectly straight and sharp line. Similarly the term vertex is often used to represent the intersection of region point of the three planes even if the actual region of intersection is not a perfect point. The spherical exterior portion  720  has a sphere center  860 , which in general is at a different point in space than the vertex  820 . 
     An axis of symmetry  840  is symmetrical with respect to the three intersection lines  810 A,  810 B, and  810 C. The angle between the axis of symmetry and any of the three intersection lines is cos −1 (1/√{square root over (3)})=54.7°. A runout plane  865  that passes through the sphere center  860  is drawn perpendicular to the axis of symmetry  840 . The axis of symmetry  840  intersects the runout plane  865  in an intersection point  870 . An SMR error vector  885 , which extends from the vertex  820  to the sphere center  860 , decomposes into two vector components: an SMR depth error vector component  880  that extends from vertex  820  to the intersection point  870  and an SMR runout error vector component  890  that extends from the intersection point  870  to the sphere center  860 . The SMR depth error vector component  880  has a length equal to an SMR depth error, and the SMR runout error vector component  890  has a length equal to an SMR runout error. The SMR depth error vector component  880  and the SMR runout error vector component  890  are shown in  FIG. 7B , which is a side view of a cross section drawn through line A-A in the front view of  FIG. 7A . The SMR has an SMR frame of reference  730  that is fixed relative to the SMR. An example of a possible SMR frame of reference is shown in  FIGS. 7A, 7B . All of the elements of the SMR, including the SMR error vector, the SMR depth error vector, and the SMR runout error vector, are fixed relative to the SMR frame of reference. The SMR frame of reference may conveniently be placed at either the vertex point  820  or the sphere center  860 . 
     The elements of  FIGS. 7A, 7B  are shown in  FIGS. 8A, 8B  in perspective view.  FIG. 8A  shows a portion of the SMR  700  that includes the three planar reflectors  825 AB,  825 BC,  825 AC, the three intersection junctions  810 A,  810 B,  810 C, the vertex  820 , and the axis of symmetry  840 .  FIG. 8B  shows a magnified view of the region near the center of the SMR, with the vertex  820  shown in line with the axis of symmetry  840 . The runout plane  865  is perpendicular to the axis of symmetry  840  and passes through the sphere center  860 . The axis of symmetry intersects the runout plane at an SMR intersection point  870 . The SMR error vector  885  extends from the vertex  820  to the sphere center  860 . The SMR depth error vector  880  extends from the vertex  820  to the SMR intersection point  870 . The SMR runout error vector  890  extends from the SMR intersection point  870  to the sphere center  860 . 
       FIG. 9A  shows a portion  900  of an SMR that includes a collar  905  onto which is affixed a reference feature  910 , which might be a serial number or barcode, for example. In this example, the reference mark  930  is selected by convention as being in the center of the reference feature  910 . In another embodiment, the reference mark is a line  930  inscribed on the collar as in  FIG. 5A . In another embodiment, the reference mark is affixed directly to the spherical exterior portion  720 . Associated with the reference mark  930  is a reference point  932 . An SMR reference plane  920  encompasses the reference point  932  and the axis of symmetry  840 . 
     A magnified perspective view near the center of the SMR is shown in  FIG. 9B . The vertex point  820  is shown in both  FIGS. 9A, 9B . An SMR reference ray  940  is a ray coincident with the line of intersection between the SMR reference plane  920  and the SMR runout plane  865 , wherein the SMR reference ray  940  begins at the SMR intersection point  870  and is directed along the half of the SMR reference plane  920  that includes the reference point  932 . The angle between the SMR reference ray  940  and the SMR runout error vector  890  is the SMR runout reference angle  950 . The numerical value of the SMR runout reference angle of a particular SMR is a property of that SMR. In an embodiment, the SMR depth error, the SMR runout error, and the SMR runout reference angle are determined for each SMR by carrying out measurements as discussed hereinbelow. 
       FIG. 9C  shows the same portion  900  of an SMR as in  FIG. 9A . A beam of light  46  from a device  10  intersects the vertex point  820 . A beam depth error vector  962  has a magnitude equal to the SMR depth error  880  and extends along the direction of the beam  46  from the vertex point  820  to a beam intersection point  970 , as shown in  FIG. 9D  in a magnified perspective view near the center of the SMR. A beam runout plane  965  includes the beam intersection point  970  and is perpendicular to the beam depth error vector  962 . A beam reference plane  975  encompasses the reference point  932  and the beam depth error vector  962 . 
     A beam reference ray  972  is a ray coincident with the line of intersection between the beam reference plane  975  and the beam runout plane  965 , wherein the beam reference ray  972  begins at the beam intersection point  970  and is directed along the half of the beam reference plane  975  that includes the reference point  932 . The angle between the beam reference ray  972  and the beam runout error vector  976  is the beam runout reference angle  982 . To the extent that the beam of light  46  is not aligned with the axis of symmetry  840 , there will be a difference between the calculated 3D coordinates of the sphere center  978  and the actual 3D coordinates 860 of the sphere center. This difference is discussed further with reference to  FIGS. 12A-E . 
     Measurements are performed on each SMR to determine the position of the sphere center relative to the vertex. The results of such measurements may be described in several different ways. One such description of the sphere center relative to the vertex point includes the SMR depth error  880 , the SMR runout error  890 , and the SMR runout reference angle  950 . A different but equivalent description includes component lengths of the SMR error vector using Cartesian coordinates. For example, such component lengths may be given along Cartesian axes x, y, z within a frame of reference of the SMR such as the frame of reference  730  of  FIGS. 7A, 7B . Some alternative descriptions are now given. Other coordinate systems are also possible, as will be clear to one of ordinary skill in the art. 
       FIG. 9B  shows the frame of reference  40 , which is fixed to the SMR as shown in  FIG. 1 . If the vertex  820  is taken as the origin in the frame of reference  40 , the 3D coordinates of the sphere center (C) are given in the frame of reference  40  as (x C , y C , z C ), where x C  is the SMR depth error and y C , z C  are coordinates in the SMR runout plane of an SMR runout error vector. In this case, the z axis is taken along the direction of the SMR reference ray  940 . An alternative approach is to use a frame of reference  988 , for which the z C ′″ axis is aligned to the position of maximum runout, which is to say that the z C ′″ axis is aligned to the SMR runout error vector  890 . In this case, the 3D coordinates of the sphere center (C) are given as (x C ′″, y C ′″, z C ′″)=(x C ′″, 0, z C ′″) since z C ′″ is zero for this case. The frame of reference  988  may be realized by aligning the reference mark  930  to the position of maximum runout of the retroreflector. 
     A Cartesian frame of reference may also be applied to the beam runout plane  965 .  FIG. 9D  shows the frame of reference  996 . If the vertex  820  is taken as the origin in the frame of reference  996 , the 3D coordinates of the calculated sphere center  978  based on the direction of the beam (B) of light are given as (X B , Y B , Z B ), where X B  is the SMR depth error along the direction of the beam of light (the X B  axis) and Y B ,Z B  are coordinates in the beam runout plane of the beam runout error vector. The magnitudes of the components Y B ,Z B  are the same as the magnitudes of the components Y C ,Z C , only shifted from the plane  865  to the plane  965 . An alternative approach is to use a frame of reference  998 , for which the Z B ′ axis is aligned to the beam runout error vector  976 . In this case, the 3D coordinates of the calculated sphere center (B) are given as (X B ′, Y B ′,Z B ′)=(X B ′, 0,Z B ′) since Y B ′ is zero for this case. 
     There are many ways to find the position of the sphere center  860  relative to the vertex  820 . One method is to measure the SMR with a Cartesian coordinate measuring machine (CMM). With this method, the position of the vertex relative to the sphere center can be found to a fraction of a micrometer. For example, with a very good Cartesian CMM, an expanded uncertainty of the position of the center relative to the vertex may be better than 0.4 micrometer along each of three Cartesian axes x, y, z. This error is much less than the centering error of an SMR, which, in a typical SMR is 0.0005 inch=12.7 micrometers along the axes x, y, z. In a very good SMR, the specified centering error components may be as small as 0.0001 inch=2.54 micrometers. 
     Another way to measure the depth of the sphere center  860  relative to the vertex  820  makes use of an absolute interferometer or other type of ADM having a high accuracy. In an embodiment, a kinematic nest configured to repeatably center a spherically shaped object is arranged to push upwards on an SMR. A reference SMR is measured with an accurate Cartesian CMM to find the SMR error vector  885 . The reference SMR is placed in the nest and the absolute interferometer is used to measure the distance along a horizontal line from the absolute interferometer to the vertex of the SMR. An SMR under test is next placed in the nest and the measurement repeated. Let the SMR depth error of the reference SMR, E DepthRefSMR , be taken as generally positive in the direction from a distance measuring device to the SMR. Then, following the above procedure, the SMR depth error of a test SMR is
 
 E   DepthTestSMR   =d   TestSMR   −d   RefSMR   +E   DepthRefSMR ,  (1)
 
where d TestSMR , d RefSMR  are the measured distances to the SMR under test and the reference SMR, respectively.
 
     Another way to measure the SMR runout error and SMR runout reference angle (or, equivalently, the Cartesian errors in the SMR runout plane) is to rotate an SMR under a microscope according to a method well known in the art. A description of this method is given in Section B-2.1 of Appendix B of ASME Standard B89.4.19-2006 , Performance Evaluation of Laser - Based Spherical Coordinate Measurement Systems , which is incorporated by reference herein. With this method, an SMR under test is placed on a kinematic nest that rests on a microscope stand. A light source illuminates the frame of the microscope. The focus is adjusted to view a speck of dust (or other small object) on the microscope frame. An operator rotates the SMR about the sphere center within the kinematic nest and observes on the microscope the radius of the runout circle. The observed radius is divided by four to get the SMR runout error, which is the magnitude of the SMR runout error vector  890 . The procedure discussed in this paragraph is used as a method of determining whether an SMR meets it runout (centering) specifications. For example, a manufacturer may provide a specification for an SMR stating that the SMR has a centering error of less than 0.0005 inch. This would be interpreted to mean that the SMR has an SMR depth error of less than 0.0005 inch and SMR runout error of less than 0.0005 inch. Although the depth error and the runout error have been measured in the past for SMRs, provision has not heretofore been made to use these values by a processor to correct readings of device  10  based on SMR compensation parameters, the compensation parameters which might include SMR depth error and SRM runout error vector component information. 
     The observed position of the SMR runout error relative to a reference mark on the SMR may be used to determine the SMR runout reference angle  950 . In an embodiment, discussed further with respect to  FIGS. 19A, 19B , the reference mark  930  is aligned to the observed position of maximum runout during the test procedure. The effect of this is to make the SMR runout reference angle equal to zero. In an embodiment, a calibration laboratory technician places the reference mark  930  at the position of maximum runout. In other words, the laboratory technician places the reference point  932  within the reference plane  920 . 
     Besides errors in SMR centering (SMR depth error and SMR runout error vector component), there are also errors in SMR radius. In other words, the SMR radius is not exactly that indicated in a manufacturer&#39;s specifications. As an example, some high quality SMRs are manufactured from grade 25 steel balls having a diameter tolerance of ±0.0001 inch=±2.54 micrometers, which is equivalent to a radius tolerance of ±1.27 micrometers. In other words, for an SMR manufactured with this type of steel ball, the actual SMR radius is expected to lie within ±1.27 micrometers of the nominal (specified) radius, at least at portions of the spherical surface not too close to the cavity that holds the retroreflector. 
     There are several ways to measure the radius of an SMR. A Cartesian CMM can be used to accurately measure the radius of an SMR under test. The radius error is found by taking the difference between the measured radius and a reference or nominal radius. 
     An absolute interferometer may also be used to measure the radius error of an SMR under test. With this method, a reference sphere (ball) is measured with a coordinate measuring instrument such as a Cartesian CMM or Talyrond® roundness measuring device to find the radius of the reference sphere. In an embodiment, a kinematic nest configured to repeatably center a spherically shaped object is arranged to push upwards on a spherical surface. The reference sphere is placed in the nest and the absolute interferometer focused onto the sphere surface along a line normal to the surface. The absolute interferometer measures a distance from the interferometer to the surface. An SMR under test is next placed in the nest. The SMR is rotated to enable the beam from the absolute interferometer to be collinear with a normal vector to the spherical exterior portion  720 , and the absolute interferometer is used to measure the distance. The difference between the measured distance to the SMR under test and the measured distance to the test sphere is the radius error. 
     Changes in temperature of the SMR may cause the vertex  820  to shift its position relative to the sphere center  860 . Such changes in SMR temperature may result from (1) changes in the ambient temperature of the air surrounding the SMR, (2) heating of the SMR by the operator&#39;s hand, and (3) contact of the SMR with a relatively warm object such as a home position nest  17  of a laser tracker  10  of  FIG. 1 . 
     With some types of SMRs, the effect of temperature may be relatively small. For example, as discussed hereinabove, one type of SMR is made of a single piece of steel into which the three mutually perpendicular surfaces are etched using ECM. With this type of SMR, the change in the SMR depth error with temperature will equal the coefficient of thermal expansion (CTE) times the change in SMR temperature times the initial SMR depth error. If the initial SMR depth error is 0.001 inch=25.4 micrometers and the SMR is made of steel having a coefficient of thermal expansion of 11.5 micrometers/meter/° C., the change in the SMR depth error over a 30 degree Celsius change in SMR temperature is (25.4×10 −6 )(11.5)(30) micrometer=0.009 micrometer, which is a negligible amount. 
     With some other types of SMRs, the thermal effects are larger. For example, consider the type of SMR that includes an aluminum slug put into a 1.5 inch (38.1 mm) diameter spherical exterior portion of steel. Suppose that the aluminum slug extends 10 mm below the vertex and is glued to the steel portion at that position. Neglecting the thermal expansion of the glue bond and considering a point of contact at which the axis of symmetry intersects the spherical exterior portion, the relative change in the vertex position with temperature is the difference in the CTE values for aluminum and steel times the 10 mm extension times the change in temperature. Suppose that the CTE of steel is 11.5 micrometers/meter/° C., the CTE of aluminum is 23 micrometers/meter/° C., the depth extension is 10 mm, and the change in temperature is 30° C. The change in the vertex relative to the sphere center is then (0.01)(23−11.5)(30) micrometers=4.45 micrometers. 
     To correct for the movement of the SMR vertex as a result of thermal expansion, a temperature sensor such as a thermistor or RTD may be embedded in the SMR. In an embodiment shown in  FIGS. 10A, 10B, 10C , a small connector socket  1030  is disposed on or in the SMR  1000 . The connector socket is attached through a collection of wires  1032  (typically two or three wires) to the temperature sensor  1034 . The temperature sensor  1034  might be a thermistor, RTD, thermocouple, or other device. A sensor cable  1040  includes a second collection of wires  1044  attached to a first connector  1042  on one end of the cable  1040  and to a second connector  1046  on the opposite end of the cable. The first connector  1042  attaches to the connector socket  1030  and the second connector  1046  attaches to a temperature measurement system disposed on a laser tracker  10 , computer  80 , accessory box  70 , temperature meter, or other device. Many types of temperature measurement systems may be used. A simple temperature measurement system (not shown) may include electronics based on a Wheatstone bridge having three internal resistors. A first internal resistor may be attached to a voltage source, a second internal resistor attached to a ground, and the external temperature sensor  1034  and wires in cable  1044  providing a fourth external resistive leg of the bridge. Such temperature measurement systems are well known in the art. The temperature measurement system converts observed voltages into a temperature of the SMR. Coefficients stored in memory may then be used to correct the position of the vertex relative to the sphere center. The memory may be included in a laser tracker  10 , computer  80 , accessory box  70 , or other device. Measurements are carried out ahead of time for a particular type of SMR to obtain information that describes SMR thermal expansion characteristics. In a simple case, a single CTE value or CTE value times SMR depth error may be sufficient to describe the vertex movement relative to the sphere center. For example, in the example given above in which the vertex moves by 4.45 micrometers over 30 degrees Celsius, the single parameter might be used to give a value of 0.1483 for CTE times depth error, the value having units of micrometers per degree Celsius. In another embodiment, a table of values or coefficients is provided. 
     Use of an embedded temperature sensor  1034  with a sensor cable  1040  has the advantage of avoiding the need for a battery, temperature circuit, or wireless communications system within the SMR. With this system an SMR might be checked, for example, when the SMR is returned to a tracker home position. 
     As shown in  FIG. 10D , one possibility is to attach the cable  1040  through socket  1052  to temperature electronics module  1050 . In an embodiment illustrated in  FIG. 10E , a battery  1054  provides electrical power over wires  1062  to the embedded temperature sensor  1034 , temperature processing electronics  1056 , and wireless communications electronics  1058 . In an embodiment, the temperature processing electronics  1056  includes a Wheatstone bridge, resistors, and a microprocessor to provide a digital signal through wire  1064  to wireless communications electronics  1058 . The digital signal represents a temperature measured by the temperature sensor  1034 . In an embodiment, the wireless communications electronics  1058  launches a digital representation of the measured temperature over antenna  1059 . In an embodiment, the wireless communications electronics is configured to send the digital representation over antenna  1059  at regular intervals, for example, every five minutes. The interval time may be selected to provide adequate temperature information while saving battery power. The wireless signal from the antenna  1059  may be received by electronics within a device  10  shown in  FIG. 1  and the received temperature values used to improve compensation of the 3D coordinates of the SMR sphere center. In an embodiment, the temperature electronics module  1050  may be placed in a pocket of the operator—for example, a shirt pocket or trousers pocket. 
     In an embodiment shown in  FIG. 10F , the temperature processing electronics  1050  may be affixed to the wrist of an operator. In an embodiment, the operator wears a glove  1070  into which the temperature processing electronics  1050  and the cable  1040  are integrated. In an embodiment, the glove is an insulating glove to minimize the transfer of heat from the operator&#39;s hand to the SMR  1000 . In another embodiment, the glove is not an insulating glove but has finger openings to permit direct handling of the SMR by the operator. In another embodiment, the operator does not wear a glove. Instead temperature processing electronics  1050  is attached directly to the operator&#39;s wrist, for example, by means of a strap or elastic band. 
       FIG. 11  shows an interface component  1120  attached to an SMR  1100 . Interface component  1120  may contain a number of optional elements. The interface component  1120  may be connected to a temperature sensor mounted within the SMR  1100 . Antenna  1130  may be used to send and/or to receive wireless data in the form of radio frequency signals. Such an antenna may be attached to a small circuit board powered by a small battery  1128  that fits inside interface component  1120 . The small circuit board may be made of rigid-flex material which permits a very compact circuit to be enclosed within the interface component. By providing a temperature sensor and wireless communication system powered by a battery, the temperature of the SMR may be known at all times so that the measurements of the 3D coordinates of the SMR  1100  are as accurate as possible. 
     Numerical values used to compensate for imperfections in SMRs as a way of enabling more accurate 3D measurements are referred to as SMR compensation parameters. SMR compensation parameters are typically stored in memory of a measurement device or a computing device. For example, SMR compensation parameters may be stored in a memory of the laser tracker  10  of  FIG. 1 . A processor within the laser tracker  10  may be used to correct the 3D coordinates of the sphere center of SMR  26 . Alternatively, a processor within an external computer  80 , an accessory device, or a networked computing device may be used to access compensation values stored in memory and use these values to correct the 3D coordinates of the sphere center. Such compensations may account for differences in the position of the vertex relative to the sphere center. Such compensations may also account for the effect of errors in the sphere radius using methods described hereinbelow with respect to  FIGS. 14-17 . 
     In some cases, compensation calculations are made within a processor of a measurement device such as a laser tracker. For example, the tracker processor may identify the SMR being used for a particular measurement and automatically perform compensation calculations for that SMR to transform the measured vertex 3D coordinates to sphere center 3D coordinates. In other cases, compensations are made by application software. For example, application software may consider the position and orientation of the SMR in making a plurality of measurements and apply compensation calculations for the SMR radius to eliminate errors. In general, the term processor may be understood to mean a processor in a device such as a tracker, a processor in an external computer, or a processor in both. 
     There are several ways by which SMR compensation parameters can be entered into memory. In an embodiment, SMRs shipped with the device  10  from the factory come with compensation parameters pre-loaded into memory. In another embodiment, the user is provided with a list of numerical compensation values for each SMR. Application software embedded within the device  10  provides a means by which the user may enter the numerical values. Such values need only be entered once, as they are stored in memory within the device  10 . In another embodiment, the SMR compensation parameters are provided on a flash drive, CD ROM, or other medium read by device  10 , computer  80 , or other component for automatic storage in memory. In another embodiment, numerical values for compensation parameters are downloaded into the tracker over a network. In another embodiment, SMR compensation parameters are encoded into a one-dimensional or two-dimensional barcode  630 . A barcode reader may read the SMR compensation values on the barcode and automatically download these into memory in the device  10 . 
     In an embodiment, a close-range camera  56  shown in  FIG. 1  is pointed directly at an SMR when the device  10  locks onto (begins tracking) an SMR in one of the home nests  17 . In the device  10  of  FIG. 1 , the camera  56  is placed above the aperture through which the light beam  46  is emitted. To ensure that the camera can clearly read an SMR barcode, the camera assembly may be pointed toward the center of an SMR placed in a home position  17 . In other words, for the case shown in  FIG. 1 , the optical axis of the camera may be pointed slightly downward rather parallel to the beam of light  46 . In addition, in an embodiment, the camera  46  is configured to focus clearly on an SMR in a home nest  17 . This is generally different than for the cameras  52 , which are ordinarily designed to focus on retroreflectors relatively far from the tracker. In an embodiment, the camera  56  has a small enough field of view to provide adequate resolution for a bar code or serial number. For example, the field of view for such a camera might be about 20 degrees. The small field of view and clear focus at the home position may be obtained by correctly selecting the focal length and adjusting the position of the lens in the camera  56 . The combination of optimum pointing direction (toward the home positions  17 ), in-focus condition at the home position  17 , and relatively small field of view ensure that a relatively inexpensive camera  56  can clearly resolve the marks on a barcode  610 , which might be a one-dimensional or two-dimensional barcode, for example. Furthermore any lights near the SMR are turned off during the operation of the camera  56  to ensure that the camera photosensitive array is not blinded by a bright retroreflected light. Ordinarily any lights need to be located at least one retroreflector diameter away from the edge of the retroreflector to prevent this blinding effect. In other words, if the retroreflector is an open air cube corner retroreflector having a circular cross section and a diameter of one inch, any lights should be located at least one inch from an outer edge of the retroreflector. Because the laser beam  46  leaving the tracker is collimated and strikes the retroreflector in the center, in most cases, little light will scatter back into the camera  56 . However, it the laser beam  46  is too bright, it can be turned off during the reading of the barcode on the SMR. In an embodiment, the camera  56  is used in combination with optical character recognition (OCR) software to read a serial number. 
     Inasmuch as the resetting of SMR distance at the home position is routine, a measurement of the barcode on the SMR can be made in conjunction with the home position measurement without requiring extra steps on the part of the operator. In an exemplary method, the SMR is placed in the home position. The tracker first turns on the camera to view the barcode and extract the SMR parameters. It then turns on the beam of light, sends it to the vertex, measures the distance, and resets the distance to a home reference value. To reset the distance meter to the home reference value in the most accurate possible way, in an embodiment, software within the tracker sets the distance value to be applied at the SMR sphere center rather than the vertex point. This is important because it ensures that the home reference value is correctly applied for all SMRs, regardless of the SMR depth error. To determine the sphere center as accurately as possible, the SMR should be placed in a preferred orientation within the home position nest  17  or the camera  56  should be used to automatically determine the orientation of the SMR in the home position nest. These methods of establishing the position of the SMR in the home position nest are discussed in more detail hereinbelow. In  FIG. 17 , there are three different home position nests sized to accommodate three differently sized SMRs. In an embodiment, the SMRs are sized to accept SMRs having diameters of 1.5, 0.875, and 0.5 inch. A different home reference value is provided for each of these home position nests. 
     In an embodiment, SMR compensation parameters are encoded into an RFID tag  650 . The encoded information is retrieved using an RFID reader, which may be attached to the payload  12 , perhaps in place of the close-range camera  56 . The retrieved serial number may be used to access the SMR data from a networked system (the Cloud) or from a database of information saved within a device such as a tracker or computer. 
     In the general case, a 3D coordinate measurement device such as laser tracker  10  obtains measured 3D coordinates of the SMR vertex, for example, by measuring a distance and two angles to the SMR. The SMR compensation factors are applied to the measured 3D coordinates of the vertex to obtain the 3D coordinates of the sphere center using methods now described. In making a measurement, the operator holds the reference point  932  so as to place the SMR reference plane  920  in a preferred orientation. A preferred orientation may be selected in several different ways, depending on the measurement objectives. 
     In general, the operator will endeavor to align the axis of symmetry to the direction of the beam of light from the device. This was discussed hereinabove in reference to  FIGS. 12, 13 . The term preferred orientation as used herein refers to a positioning of the reference point as an additional step in the alignment procedure. A way to achieve the preferred orientation while leaving the axis of symmetry aligned with the beam of light is to rotate the SMR about the axis of symmetry following the aligning of the axis of symmetry to the beam of light. Since the SMR reference ray is perpendicular to the beam of light and is in the reference plane that includes the reference point, we may say that by turning the axis of symmetry, the operator adjusts the SMR reference ray to obtain the preferred orientation. 
     There are some special cases in which it is not possible to align the axis of symmetry to the beam of light. For example, with the SMR at the home position  17 , it may not be possible to align the axis of symmetry to the beam of light because of mechanical constraints. In this special case, the meaning of the term preferred orientation is modified accordingly to permit for the necessary change in alignment. The special case for alignment at the home position is discussed hereinbelow. 
     A first type of preferred orientation is one in which the SMR reference plane  920  is aligned to the x″-z″ plane of the payload frame of reference  35  as shown in  FIG. 1 . The x″ axis corresponds to the direction of the beam of light, and the z″ axis is perpendicular to the x″ axis and to the y″ (zenith) axis. The x″-z″ plane always includes the z′ vector (of the device frame of reference  30 ), which points out the top of the device  10 . For the device  10  in its normal upright position, the preferred orientation is one in which the SMR reference plane contains a gravity vector as well as the beam of light  46 . However, the more general x″-z″ plane can be used when the gravity vector may not be appropriate, for example, when the tracker is turned on its side with the laser beam pointed straight up. With the first type of preferred orientation, the operator simply holds the SMR so as to place the SMR sphere center and the SMR reference mark in the plane that includes the beam  46  and the axis z′. The operator should also attempt to align the axis of symmetry  840  of the SMR to the direction of the beam of light  46 , as discussed hereinabove with respect to  FIGS. 9C, 9C  and hereinbelow with respect to  FIGS. 12, 13 . With the SMR held in the preferred orientation, software in the processor uses the measured 3D coordinates of the SMR vertex and the SMR compensation parameters to calculate the SMR sphere center, as described hereinabove with respect to  FIGS. 9A-D . 
     A second type of preferred orientation is one in which the SMR reference plane  920  is aligned to the y″-z″ plane of the payload frame of reference  35  as shown in  FIG. 1 . The y″-z″ plane always includes the zenith axis  18  (y″ axis) of the device  10 . If the device  10  is placed in an upright orientation as shown in  FIG. 1 , the azimuth axis  20  is pointed in the vertical direction, and the zenith axis  18 , which rotates about the azimuth axis, lies on a horizontal plane. With the second type of preferred orientation, the operator holds the SMR so as to place the SMR sphere center and the SMR reference mark in a plane that includes the beam  46  and the zenith axis  18  (x″ axis). If the reference mark  930  points radially outward on a collar  905  as shown in  FIG. 9A , then, for the second preferred orientation, the reference mark should be held in a horizontal plane. For the second type of preferred orientation, a preferred position of the SMR reference mark  930  relative to the sphere center  860  needs also to be given—for example, to the right of the sphere center. As stated hereinabove, the operator should attempt to align the axis of symmetry  840  of the SMR to the direction of the beam of light  46 . 
     A third type of preferred orientation is one in which the SMR reference ray  940  is aligned in a prescribed manner to a measurement line to measure a dimensional characteristic of the measurement line. This is discussed further hereinbelow with reference to  FIGS. 19A, 19B . 
     We now discuss with regard to  FIGS. 12A-E  errors associated with misalignment of the axis of symmetry  840  with respect to a beam of light from a device  10 . An SMR in  FIG. 12A  receives a beam of light  1210  having a beam center  1212  and a beam width  1214 , the beam of light  1210  beginning to be clipped by a collar  905  of the SMR. The angle  1215  is the acceptance angle of the SMR for the beam of light  1210 . For an SMR that has a diameter of 1.5 inches and receives a typical beam of red light from a laser tracker  10 , the acceptance angle  1215  is usually about 25 degrees. 
     An SMR in  FIG. 12B  receives a beam of light  1240  that is in line with the axis of symmetry  840 . For  FIG. 12B , an expanded region  1230  near the vertex  820  and sphere center  860  is shown in a magnified view  1  in  FIG. 12C . Because the beam of light  1240  is aligned with the axis of symmetry  840 , the position of the sphere center may be determined with accuracy only limited by the measurement error in finding the 3D coordinates of the SMR vertex—in other words, by the errors in the distance and two angles measured by the device  10 . 
     The SMR  720  in  FIG. 12D  has been rotated about its sphere center by an angle of 10 degrees. As a result of this rotation, the vertex  820  shifts by an amount  1250  to a new vertex position  820 R. The axis of symmetry, which is the axis that is symmetrical with respect to the three intersection junctions, also shifts by 10 degrees from the line  840  to the line  840 R. As a result, rotating the SMR  720  about its center, for example, when the SMR is placed on a kinematic nest, results in a misalignment error vector  1250  in the position of the center after compensation parameters have been applied for the SMR depth error vector and the SMR runout error vector. As shown in  FIG. 12E , the misalignment error  1250  includes a component  1252  along the axis of symmetry  840 R and a component  1254  on a plane perpendicular to the axis of symmetry  840 R. 
     During normal operation, an operator can usually keep the axis of symmetry  840  of a 1.5-inch diameter SMR aligned to the direction of the beam of light  1240  to within about 10 degrees. As shown in  FIG. 12D , a rotation of an SMR about a sphere center  860  by an angle of 10 degrees results in a misalignment error vector  1250  that is relatively small compared to the SMR error vector  885 R. For the case of the 3D coordinates of the SMR being measured by a laser tracker, the beam of light  1240  is the beam  46  as shown in  FIG. 1 . 
     Referring now to  FIGS. 13A-F , methods are described to improve the alignment of the axis of symmetry  840  with the beam of light  46 , thereby minimizing the magnitude of the misalignment error vector  1250 . In a first method shown in  FIG. 13A , an alignment cap  1310  is placed over the collar  905 . The alignment cap includes a ring  1312  onto which is attached an opaque cover  1314  on which is centered marked crosshairs  1317  or a marked circle  1316  having a diameter approximately the same as the light beam  46  from the 3D coordinate measurement device  10 . To align the axis of symmetry  840  with the incoming beam of light  46 , the operator first blocks the beam of light with the alignment cap  1310 , which stops the beam from tracking the SMR  700 . The operator places the alignment cap  1310  over the collar  905  and rotates the SMR to center the incident light beam  1318  in the marked circle  1316 . The operator removes the alignment cap  1310 , which causes the beam to lock onto the SMR. In so doing, the light beam  46  is brought into coincidence with the axis of symmetry  840 . With this method, an alignment accuracy of 2 degrees or better might be expected for a 1.5-inch SMR. 
     In a second method shown in  FIG. 13B , a window  1320  that lets light through to the retroreflector is positioned against the collar  905  so as to align outer marked circle  1324  with the outer edge of the collar. The operator notes the position of incident light  1328  scattered off the window  1320  relative to crosshairs  1317  or an inner marked circle  1326  and rotates the SMR to bring the incident light  1328  into coincidence with the inner marked circle  1326 . In so doing, the incident light beam  46  is brought into coincidence with the axis of symmetry  830 . 
       FIG. 13C  illustrates a method of aligning the SMR by observing a portion  1332  of the incident light beam with a reflective strip  1320 , which might be a strip of cardboard, for example. By moving the strip in relation to the aperture of the SMR, the operator can visually judge the direction in which the SMR should be rotated to improve alignment. 
       FIG. 13D  is like  FIG. 13C  except that a finger  1340  rather than reflective strip  1330  is used to observe a portion  1342  of the incident light. By moving the finger in relation to the aperture of the SMR, the operator can visually judge the direction in which the SMR should be rotated to improve alignment. 
     In a method shown in  FIG. 13E , a reflective cap  1350  is placed over the collar  905 , which is hidden from view in  FIG. 13E . The reflective cap includes a ring  1352  onto which is attached a mirror  1354  designed to receive light  1352  and reflect light  1353  off the mirror&#39;s front surface. Optionally, crosshairs  1317  or a marked circle  1356  is centered on the mirror  1354 . The circle has a diameter approximately equal to that of the light beam from the 3D coordinate measurement device. To align the axis of symmetry  840  with the incoming beam of light  1352 , the operator first blocks the beam of light with the reflective cap  1350 , which stops the beam from tracking the SMR  700 . The operator places the reflective cap over the collar  905  and, if the circle  1356  is present, rotates the SMR to place the beam approximately in the center of the circle. The operator observes the position of the reflected light on or near the 3D coordinate measurement device and, if needed to further improve alignment, rotates the SMR  700  to move the reflected beam of light closer to the emission point from the 3D coordinate measurement machine. In  FIG. 1 , the emission point of the laser tracker  10  is the point at which the beam of light  46  leaves the laser tracker  10 . When the reflected beam of light is close enough to the emission point, the operator removes the mirror cap  1350 , which causes the beam to lock onto the SMR. A typical high quality mirror has a wedge angle of only a few arc minutes, which produces a negligible angular deviation in the reflected beam of light. By reflecting the beam of light so that it strikes the 3D measurement device near the emission point, it is possible to align the axis of symmetry  830  with the beam of light to within a small fraction of a degree. For example, an SMR  700  with reflective cap  1350  is 10 meters from a laser tracker  26 , the axis of alignment  840  is aligned to the emitted light beam  46  to within 1 degree if the reflected laser beam is within about 175 mm, or about 7 inches, of the emission point. 
       FIG. 13F  illustrates a method of causing the 3D coordinate measurement device, such as laser tracker  10 , to emit a beam of light in a rotating pattern  1360  having a diameter equal to that of the SMR, for example, SMR collar  905  or similar feature. The operator aligns the SMR by rotating it until the SMR is aligned to the rotating beam. 
     Previously in reference to  FIGS. 1 and 6 , a method was taught for combining a home position measurement with a reading of barcodes using a device camera. A part of this method was setting the distance meter to a home reference value for the sphere center rather than the vertex of the SMR being used. To convert 3D coordinates from a vertex point to a sphere center, it may be important to know the orientation of the SMR in the home position, as described hereinbelow with reference to  FIG. 22 . Two methods are now given for establishing the orientation of the SMR. 
     As explained hereinabove, establishing a preferred orientation has two aspects. In the usual case, the axis of symmetry of the SMR is aligned as well as possible to the beam of light. In a second aspect, the SMR is rotated about the axis of symmetry to place the reference mark in a preferred orientation. 
     In some cases, it is not possible to completely align the axis of symmetry to the beam of light. For example, at a home position  17  and at some kinds of nests, mechanical constraints may prevent the SMR from being rotated into exact alignment with the beam. In the case of the home position, another type of alignment criterion may be given. For example, a manufacturer may specify that the collar of an SMR is to be placed approximately 2 mm above the nest. The software in the device  10  may then calculate the error vector based on the provided SMR parameters. 
     For the case in which the axis of symmetry is not aligned with the beam of light, the orientation is easily obtained by moving the reference point into the desired orientation (for example, into a vertical plane or a plane that includes the azimuth axis) and then aligning the axis of symmetry in relation to the beam direction as specified (e.g., by moving a collar 2 mm above a nest). Another possibility is to use the camera  56  to determine the orientation of the SMR. With the camera turned to point at the home position, the orientation of the SMR is easily found from the position of the barcode (or any other marker). Use of the camera in this way provides accurate results and is simple for an operator. 
     This camera concept may also be applied for the case of SMRs located at distances of many meters from the device  10  if suitable zoom cameras are provided in the camera. An example of such a zoom camera is described in the &#39;758 patent, discussed above and incorporated by reference. A reflective mark such as the mark  610  of  FIG. 6A  of the present application may be used with such a camera to provide automatic determination of the orientation of an SMR. This method is applicable when a six DOF tracker is used with a three DOF SMR. 
     An SMR may be used to measure the coordinates of surface points by bringing the SMR into contact with the surface at a plurality of points. It may also be used to measure the coordinates associated with kinematic nests. In both of these types of measurements, an error in the radius of the SMR can produce an error in the measurements of surface or nest points. As explained hereinabove, methods are available to accurately measure the radius of an SMR. The radius delta, defined as the measured radius minus the nominal radius, may be stored in memory for later access. The measured radius in this case is measured by one of the accurate methods described hereinabove, for example, by using a Cartesian CMM, Talyrond®, or absolute interferometer. The radius delta may also be saved in an information storage device such as a barcode or RFID chip, which in an embodiment is attached to each SMR, and read by a reading device of the 3D coordinate measurement device. 
     For a device  10  used to measure 3D coordinates on a surface with an SMR, the SMR is moved to several locations on the surface, and a collection of 3D coordinates for the sphere centers of the SMR obtained for the corresponding surface contact points. 3D center coordinates in close proximity to one another are used to obtain a vector normal to the collection of 3D points. The normal vector is projected from one point in the collection of contact points or from one point not in the collection but near the collection of points. The 3D coordinates of the contact point corresponding to the one point are obtained by projecting the normal vector from the 3D sphere center coordinates toward the surface being measured. 
     An error in the radius of the SMR will not change the overall shape of a planar surface. However, an error in the radius of an SMR can cause errors in other situations. This can readily be seen by considering the case in which an SMR is used to measure the distance between two planar surfaces, wherein one planar surface is to the left of the SMR and one planar surface is to the right of the SMR. If the true diameter is greater than the nominal diameter or reference diameter and if all other measurements are perfect, then the measured distance will be too small by twice the SMR radius error. 
     An error in SMR radius can also produce errors in measurements made on supports such as kinematic nests.  FIG. 14A  shows an example of a type of kinematic nest  1400 , which in this case includes three spherical balls  1420  each affixed to a top surface  1412  of a base  1410  and separated from the other balls by 120 degrees. A support axis  1430  is an axis perpendicular to the plane that intersects the centers of the three balls  1420 . The support axis  1430  is also equidistant from the centers of the three balls  1420  at any point along the support axis.  FIG. 14B  shows an arrangement  1450  in which a spherical exterior portion of an SMR  700  is placed on the kinematic nest  1400 . As used herein, the term “kinematic” means that the SMR can be removed from and returned to the nest, with the 3D coordinates being nearly the same after the movement as before the movement. As the SMR  700  is rotated, the sphere center remains fixed in place on the support axis  1430 . In some cases, a magnet is included in the base  1410  to hold a steel spherical exterior portion of an SMR firmly against the kinematic nest  1400  and to keep it from falling off the nest. 
     A way to describe the support axis  1430  in mathematical terms is as a locus of sphere centers for spheres of different sizes mounted on the nest. In other words, a sphere with a relatively small radius and a sphere with a relatively large radius will both lie on the support axis  1420 . Of course, there is some minimum and maximum sphere size that will properly fit onto the three balls  1420 , but within the acceptable range of sphere sizes, the locus of sphere centers will lie on the support axis  1430 . 
     SMRs are provided by manufacturers with a nominal radius. Application software performs calculations based on the nominal radius of an SMR, the nominal radius being a numerical value provided by the SMR manufacturer. Differences in values for the nominal radius and the actual radius can result in errors, as is discussed further hereinbelow. 
     A nest, such as nest  14 A, does not in general have a clearly defined reference point. A convenient and consistent reference point for a combination of a particular nest with a particular SMR is an “ideal support position,” which is a position on the support axis  1430 . The ideal support position is defined as the position on the support axis  1430  of the sphere center for a sphere having a radius exactly equal to the nominal radius. An SMR having a radius different than the nominal radius will have a sphere center at a different position on the support axis referred to as the actual support position. 
     Because neither measurement of a radius nor corrections to 3D coordinates based on radius error depend on the internal reflecting mechanism of the retroreflector, the methods for correcting radius discussed herein are not limited to an SMR having an open-air cube corner retroreflector. The methods are equally applicable to an SMR that includes a glass cube corner retroreflector, which is to say, a retroreflector that includes a glass prism having three perpendicular reflecting faces. The methods are also applicable to the case of a cateye retroreflector in which the retroreflector has a glass optical element shaped either as a single sphere or as two hemispheres cemented together, wherein the optical element is placed at least partially within a cavity in a spherical exterior portion. SMRs that include glass prism or cateyes are well known in the art. 
     As stated hereinabove, the measured radius minus the nominal radius is the radius delta. Let the support axis  1430  be positive in a direction from a plane connecting the centers of the three spheres to the sphere center of an SMR held by the nest. In other words, in  FIG. 14A , the direction to the right is considered positive along the support axis  1430 . Then the ideal support position may be found by measuring the 3D coordinates of the sphere center of an SMR in the nest  1400  and translating the 3D coordinates along the support axis in the negative direction by a distance approximately, but not exactly, equal to radius delta. The exact amount of translation also depends on the geometry of the nest  1400 , as explained hereinbelow with reference to  FIG. 15 . A formula may be used to determine the ideal support position as a function of the radius error or delta. Compensation values such as coefficients may be stored in memory for use by the processor, in the device  10  or a separate computer  80 , for example, may be used in determining the 3D coordinates of the ideal support position. 
     The amount of shift in the sphere center  860  is now calculated for the case of an SMR  700  supported by a kinematic nest  1400  having three balls  1420  separated by 120 degrees.  FIG. 15  shows line segments corresponding to elements of the nest  1400  and SMR  700  of  FIG. 14B . Each of the three spheres  1420  has a center  1510 , with any two of the centers  1510  separated by a base distance  1525 , which is given a mathematical symbol a. A cross section drawn through the centers of each ball shows an outline  1515 . Each of the balls contacts the spherical exterior portion  720  of the SMR  700  at a tangent point  1520 . A line drawn from the sphere center  860  through a tangent point  1520  passes through the center  1510  of a ball  1420 . The SMR has a reference or nominal radius R and a radius error e so that the actual radius of the SMR is R+e. The three lines  1525  form base of a triangular pyramid  1540 . The lines  1530 , which extend from the ball centers  1510  to the sphere center  860 , form the edges of the triangular pyramid. The radius of each ball is r so that the edges of the triangular pyramid have length R+e+r. The altitude segment  1550  of the pyramid, which has a height h, extends from a base center  1545 , which lies on the plane connecting the three ball centers  1510 , to the sphere center  860 . Each of the vertices  1510  of the base has an angle of 60 degrees, and so a line drawn from a ball center  1510  to the base center  1545  has length b=a/√{square root over (3)}. By the Pythagorean Theorem, the height of the altitude segment is h=√{square root over ((R+e+r) 2 −b 2 )}. Let the edge length be R 0  and the height be h 0  for a radius error of e=0. Using the binomial approximation, it can be shown that, to good accuracy, the change in the height h as a result of an error e is δh=eR 0 /h 0 . Because the height h 0  is smaller than the edge length R 0 , the change in height δh is somewhat larger than the radius error e. For example, for a radius error of 1 micrometer, the change in height δh is 1.048 micrometers. The reason that the change in height is larger than the radius error is that a larger SMR  700  intersects the balls  1420  slightly farther away from the base that connects the ball centers  1510 . 
     In general, the change in height δh depends on the construction (geometry) of the SMR nest  1400  and is different for different types of nests. In order to correct as accurately as possible for the effect of the radius error on the change in height, it is necessary to know both the amount of radius error and the type of nest being used with the SMR. To get an approximate correction for the effect of the radius error on the change in height, the radius error e may be used without considering the geometry of the nest. For the example given in the last paragraph, the relative error in the calculated height resulting from not considering the geometry of the nest  1400  was 4.8%. 
     An example is now given of the effect of SMR radius errors on measurements made with SMRs in nests.  FIGS. 16A, 16B  show front and side views, respectively, of a first SMR  700 A and a second SMR  700 B held by a first nest  1400 A and a second nest  1400 B, respectively. In an ideal case in which the radius of both  700 A and  700 B is equal to the reference radius, the length between the SMR centers is indicated in  FIG. 16C  by the arrow  1672 . Consider next a case in which the sphere radius of the first SMR  700 A is equal to the reference radius while the sphere radius of the second SMR  700 B is larger than the reference radius. For the SMR  700 B, the sphere center is pushed upwards, as indicated by the arrow  1674 . Consequently, the measured 3D coordinates lead to the vector  1676 . If the length of the vector  1672  is L 1  and the length of the vector  1674  is δh, then the difference in the lengths  1672  and  1676  is ΔL=√{square root over (L 1   2 +δh 2 )}−L 1 , which after applying the binominal approximation, is given to good accuracy as ΔL=δ h 2 /2L 1 . Taking as an example δh=2 micrometers and L 1 =2 meters, the resulting error is 10 −6  micrometers, which is negligible. 
     In contrast,  FIGS. 17A, 17B  show the situation in which the first SMR  700 A and first nest  1400 A are aligned as in  FIG. 16B , while the second nest  1400 B is oriented perpendicular to the line connecting the sphere centers of  700 A,  700 B. In an ideal case in which the radii of both  700 A and  700 B are equal to the reference radius, the length between the SMR centers is indicated in  FIG. 17B  by the arrow  1752 . Consider next a case in which the sphere radius of the first SMR  700 A is equal to the reference radius while the sphere radius of the second SMR  700 B is larger than the reference radius. For the SMR  700 B, the sphere center is pushed to the left, as indicated by the arrow  1754 . Consequently, the measured 3D coordinates lead to the vector  1756 , which is too short by the offset value  1754 . The offset value  1754  depends both on the delta (or radius error) and on the geometry of the nest, as explained hereinabove. In this case, if the sphere radius of  700 B is too large by 2 micrometers and the nest geometry is the same as that given in the previous example, the measured distance between the two SMRs will be too small by 2.096 micrometers. In other words, for the situation in  FIGS. 16A , B, the error in the measured length between the SMRs was not affected by a diameter error in one of the SMRs while, for the situation in  FIGS. 17A , B, the error in the measured length between SMRs is directly affected by a diameter error in one of the SMRs. 
     It is clear from the discussion hereinabove that in many situations the direction of the support axes  1430  of two nests can have a large effect on the uncorrected distance measured between SMRs placed in the nests. There are several ways that a direction of a support axis  1430  can be obtained. First, the operator may indicate the direction of the support axis in application software. Second, a nest may be mounted directly on an object having surfaces known in a CAD model, from which the direction of the support axes  1430  may be determined. Third, measurements may be made to an inspection plan that includes the direction of the support axis  1430  of each nest used in the inspection. Fourth, the operator may measure features of the nest to determine the direction of the support axis  1430 . For example, in the case of the nest  1400  of  FIG. 14A , the operator may use the device  10  with an SMR to measure 3D coordinates of points on the top surface  1412 . These 3D point coordinates are fit to a plane from which the perpendicular support axis  1430  is found. 
     In general, to correct for errors for measurements made with SMRs placed in nests, both the direction of the support axis  1430  and the magnitude of the radius delta is needed. A more accurate correction is possible if the geometry of the nest is also taken into account as discussed with reference to  FIG. 15 . 
     A procedure described with reference to  FIG. 18  is useful whenever the same SMR positions must be measured with a tracker moved to multiple locations. For example, a calibration procedure may require that a distance between two SMRs  700 A,  700 B be measured with the tracker set away from the SMRs by two different locations  10 A,  10 B as shown in  FIG. 18 . In other cases, the tracker may be required to measure three or more nests from multiple locations as a way of putting tracker measurements made from different locations into a common frame of reference. 
     In a first step of a method, two or more SMRs  700 A,  700 B are rotated in supports  1400 A,  1400 B to align the axis of symmetry  840  of each SMR to a 3D measurement instrument located at a first position having 3D coordinates (x 1 , y 1 , z 1 ) within a frame of reference  1810 . At this first position, the tracker is given reference number  10 A. This alignment may be achieved, for example, using one of the alignment methods of  FIGS. 13A-F . The tracker at  10 A measures the SMRs  700 A,  700 B and at least one additional retroreflector  700 C, which need not be aligned to the tracker  10 A. In a second step, the same 3D measurement instrument is designated as  10 B when located at a second position having 3D coordinates (x 2 , y 2 , z 2 ). In this step, the SMRs  700 A,  700 B are not further rotated but left in their initial orientations. The tracker  10 B measures the 3D coordinates of the vertex of  700 A,  700 B, and  700 C. The 3D coordinates of the vertices of SMRs  700 A,  700 B as measured by the 3D measurement instrument  10 B are mathematically corrected to account for the misalignment of the vertex  820  with respect to the sphere center  860  of each of the SMRs  700 A,  700 B. 
     The mathematical method for doing this is easy to understand. Using the measured values for the retroreflector vertices for  700 A,  700 B,  700 C, the tracker  10 B is put into the frame of reference of the tracker at  10 A. This is done using optimization methods in which the six degrees of freedom (for example, x, y, z, pitch, roll, yaw) of tracker  10 B are adjusted until the 3D coordinates for  700 A,  700 B, and  700 C measured by tracker  10 A and  10 B match as closely as possible. The usual optimization method is one in which the sum of the squared residual errors is minimized. 
     The transformation matrix needed to 3D coordinates measured by  10 B into the frame of reference of  10 A can be used to transform the SMR error vectors for  700 A,  700 B in  10 A into the error vectors for  700 A,  700 B in  10 B. In this way, the step of realigning the SMRs  700 A,  700 B prior to measurement by tracker  10 B can be eliminated. 
     It should be understood that the method of establishing a transformation matrix by measuring the 3D coordinates of at least three retroreflector targets from at least two locations may be carried out even in the absence of SMRs. In other words, cube corner retroreflectors or other types of retroreflectors may be affixed to any sort of object. It should also be understood that the method described herein may be used to correct the 3D coordinates of a single SMR or multiple SMRs when viewed from two or more stations. 
     As explained hereinabove, a type of preferred orientation of an SMR is one in which the SMR reference ray  940  is aligned in a prescribed manner to a measurement line as a way of minimizing error in measuring a dimensional characteristic associated with the measurement line. A case is now considered in which the dimensional characteristic of interest is a length between two points. 
     In a measurement shown in  FIGS. 19A, 19B , nests  1400 A,  1400 B have SMR runout reference angles  950  of zero. The nest  1400 A is mounted directly above the nest  1400 B, and a 3D coordinate measurement device such as tracker  10  is used to measure the vertical distance between an SMR  700 A placed in nest  1400 A and an SMR  700 B placed in nest  1400 B. In  FIG. 19A , the SMR  700 A is rotated within the nest  1400 A so as to place its runout reference line  1910  in the vertical direction toward the top of the SMR  700 A. The SMR  700 B is rotated within the nest  1400 B so as to place its runout reference line  1920  in the vertical direction toward the bottom of the SMR  700 B. The true distance between the sphere center of SMR  700 A and the sphere center of SMR  700 B is indicated by the line  1902 . The SMR runout error vector for SMR  700 A is indicated by the vector  1904  and the SMR runout error vector for SMR  700 B is indicated by the vector  1906 . The resulting measurement of the length between the sphere centers is off by an amount equal to the sum of the magnitudes of the vectors  1904  and  1906 . These errors appear in the measured length represented by the length  1908 . 
     In  FIG. 19B , the SMR  700 C is the same as the SMR  700 A, but the SMR  700 A is rotated to place the runout reference line in the horizontal position, which is the position at which it is perpendicular to the line connecting the centers of the SMRs in the nests  1400 A and  1400 B. The SMR  700 D is the same as the SMR  700 B, but the SMR  700 D is rotated to place the runout reference line in the horizontal position. The true distance between the sphere center of SMR  700 C and the sphere center of SMR  700 D is indicated by the line  1952 . The SMR runout error vector for SMR  700 C is indicated by the vector  1954  and the SMR runout error vector for the SMR  700 D is indicated by the vector  1956 . The resulting length  1958  has a length that is close to the true length  1952 . The error resulting from the calculation of the length  1958  is known as a cosine error which is often negligible, as shown in the example given for  FIG. 16 . 
     The error in the measurement of  FIG. 19A  could have been made smaller if the runout reference lines for  700 A,  700 B had both been aligned either up or down; however, the results in general are much better if the runout reference lines are rotated perpendicular to the line connecting the sphere centers of the two SMRs. This is true not only for a vertical direction but for any direction connecting two SMRs. 
     To simplify the alignment of the SMR runout, it is convenient for the operator to know the direction of the maximum runout error vector component. This is easily accomplished if the reference point is aligned to the maximum runout error vector component, in other words, if the SMR runout reference angle is set to zero. Alternatively, it could be set to 180 degrees or another easily understood value such as +90 or −90 degrees. This angle is a preferred and predetermined angle in the sense that each SMR produced by a manufacturer has the reference point at the same position relative to the maximum runout error vector. 
     The method of aligning a reference mark can also be applied to minimize errors in dimensional measurements in addition to the measurement of length. An example of a dimensional measurement of a small displacement in the positions of the first SMR  1982 ,  1983  in the direction x′. The orientation of the reference mark  932  shown in  FIG. 19C  is still correct for this case. In other words, were the objective to sensitively measure small displacements of either the first nest or second nest along the direction x′, the nest reference marks should be oriented as shown in  FIG. 19C  On the other hand, if the objective were to sensitively measure small displacement of either the first nest or second nest along the direction z′, the optimum position for the reference mark  932  would be different. In this case, the SMR runout error component should be perpendicular to the direction to be measured. As shown in  FIG. 19D , the SMR reference ray  940  should be oriented perpendicular to the beam direction but in the x′-y′ plane. There are two possible orientations in this case, to the left of the beam as in  1987  or to the right of the beam as  1988 . The SMR reference may be oriented to minimize error in the measurement of other dimensional quantities, as will be clear to one of ordinary skill in the art. 
       FIG. 20A  shows a schematic representation  3000  of the azimuth axis  20  and zenith axis  18  described in  FIG. 1 . Also shown are the azimuth mechanical axis (axle)  20  and the zenith mechanical axis (axle)  23  corresponding to the azimuth axis  20  and zenith axis  18 , respectively. The azimuth mechanical axis  24  rotates about the azimuth axis  20  by an angle  21 . The azimuth axis  20  corresponds to a centerline  27  of the azimuth mechanical axis  24 . The zenith mechanical axis  23  rotates about the zenith axis by an angle  19 . A perpendicular line  28  is drawn between the azimuth axis and the zenith axis at the point of closest approach of the two axes. The perpendicular line  28  intersects the centerline  27  in a point  22 . The length  29  of the perpendicular line between the azimuth axis  20  and zenith axis  18  is the axis offset (AXOF) length  29 . Because in the mechanical arrangement of  FIG. 1 , the payload  15  rotates about the zenith mechanical axis, while the zenith mechanical axis rotates about the azimuth mechanical axis, which is attached to the fixed base, it follows that there the intersection point  22  is stationary with respect to the device frame of reference  30  of  FIG. 1 . For this reason, the point  22  may be considered to be the gimbal point of the device  10 , that is to say the point about which the azimuth and zenith mechanical axes rotate. Notice, however, that the zenith axis  18  does not exactly rotate about the gimbal point  22 . However, mathematical compensations can be made so that all rotations are referenced to the gimbal point. After making small compensations for beam offset and beam tilt, the beam of light  46  appears to emerge from a beam rotation point on the zenith axis  18 . 
     To summarize, it is mathematically convenient and customary in the art to select a gimbal point  22  as a stationary point within the device  10  and to refer 3D coordinates measured by the device  10  back to this point. This means that mathematical compensations are made to account for non-ideal aspects of real-world mechanical axes. One such non-ideal aspect is the axis offset  29 . Another non-ideal aspect of the mechanical axes is axis non-squareness. In an ideal mechanical system, the azimuth and zenith axis are exactly perpendicular. In a real system, there is small deviation from perpendicularity, which is an angular value called the axis non-squareness value. To get the measured 3D coordinates, mathematical methods are used to correct the distance and two angles measured by the device  10  to refer these values to the gimbal point  22 . 
     In a similar manner, in an ideal device  10 , the beam of light  46  passes virtually through the gimbal point  22 . In a real system, the beam of light is offset from the gimbal point  22  first by an axis offset distance  29 . In addition, the beam of light  46  is offset from the beam rotation point (on the zenith axis  18 ). The offset is a small distance value in y″ and z″ in the y″-z″ plane of the payload frame of reference  35  shown in  FIG. 1 . 
     In an ideal device  10 , the beam of light  46  emerges from the device in a direction perpendicular to both the azimuth axis and the zenith axis. In a real device  10 , the beam of light  46  emerges slightly off this idea angle. To move measured distance and two angles to coordinates with the tracker frame of reference, with the gimbal point as the origin, parameters may be used to mathematically account for these effects and reference all measurements to the origin. For example, in the type of beam steering mechanism described in device  10  of  FIG. 1 , the parameters TX, TY may account for beam offsets, and the parameters RX, RY may account for the beam tilts (with respect to the ideal). It should be understood that other beam steering mechanisms, for example, mechanisms that use mirrors, will have different methods of compensating for the mechanical and optical imperfections in the system, but that the general principles discussed herein are applicable to all such beam steering mechanisms. 
     It is necessary to provide a reference distance for the distance meter within the device  10 . Since the beam of light from the distance meter appears to emerge from the beam rotation point, it is necessary to provide a way to refer any measured distances to this point. Methods for doing this are discussed in detail hereinbelow. 
     The frontsight mode of the device  10  is its usual mode of operation. The device illustrated in  FIG. 20A  is in the frontsight mode. In the figure shown, the zenith axis  18  is in front of the azimuth axis  20 , but it could equally well have been on the other side of (in back of) the azimuth axis. The term frontsight mode simply indicates that this is the normal mode of operation of the device as defined by the device manufacturer. 
     Another mode of operation of the device is the backsight mode. To get into the backsight mode, starting from the frontsight mode, the payload is rotated about the azimuth axis by 180 degrees and rotated about the zenith axis to point the beam of light  46  back at the retroreflector target. As shown in  FIG. 20B , an effect of putting the device  10  in to backsight mode is to place the zenith mechanical axis on the opposite side of the azimuth mechanical axis. In other words, if the axis offset parameter is positive in the frontsight mode, it will be negative in the backsight mode, and vice versa. For the case in which a vertex  820  of an SMR  700  is placed in line with the line of closest approach  28  as in  FIGS. 20A and 20B , the backsight distance  47 ′ minus the frontsight distance  47  is equal to twice the axis offset value. 
       FIG. 20C  shows a schematic representation  3040  of the device  10  sending a beam of light to an SMR  700  for the case in which the SMR is placed in a home measurement nest  17  of  FIG. 1 . The beam of light  46 ″ is emitted from the beam rotation point. In an embodiment, the distance meter is set to have a distance of zero at the point  18  in the frontsight mode. It reads a distance  3042  when the SMR  700  is placed in the home position nest  17 . The distance read by the device  10  with respect to the gimbal point  22  (following compensations), however, is a distance  48  from the gimbal point  22  to the vertex point  820 . 
     To establish the beam rotation point as the zero point for the distance meter, a separate procedure is carried out as is now described with reference to  FIGS. 21A-C . In a first step illustrated in schematic representation  3100  of  FIG. 21A , a distance is measured between two SMR center positions. One way to measure this distance is to align a gimbal point  3112  of a laser tracker to a line that connects the centers of the two SMRs. The sphere center of the SMR  3120  when placed in the nest  3130  may be referred to, for the purpose of this discussion, as the first nest center. The sphere center of the SMR  3120 ′ when moved to the second nest  3130 ′ may be referred to as the second nest center. A line connecting the first nest center and the second nest center may be called the sphere center line. That portion of the sphere center line that lies between the first sphere center and the second sphere center is called the interior portion of the sphere center line, and that portion of the sphere center line excluding the interior portion is the exterior portion. 
     The gimbal point  3112  of the device  3110  is placed at a point on the exterior portion. The distance  3124  of the beam of light  3114  from the gimbal point  3112  to the vertex point  3122  of the SMR in the first nest is measured. The SMR is moved to the second nest  3130 ′. The distance  3126  of the beam of light  3116  from the gimbal point to the vertex point  3122 ′ of the SMR in the second nest is measured. The distance  3126  minus the distance  3124  is the distance between the vertex point  3122  and the vertex point  3122 . However, for the geometry of  FIG. 21A , the SMR depth error is common mode and cancels out for the two length measurements. Hence the difference in the distances  3126  and  3124  is also the distance between the sphere centers of the SMRs  3120  and  3120 ′. 
     Two additional steps illustrated in  FIGS. 21B, 21C  may be carried out to set the distance  3042  to set the distance meter to have a distance of zero at the beam rotation point (on the zenith axis  18 ). In a first step illustrated in schematic representation  3140 , the device in its frontsight mode is placed so that a gimbal point  3112 ′ of the device  3110 ′ is on the interior portion. The distance meter measures the distance  3142  from the gimbal point  3112 ′ to the vertex of the SMR  3120 ′ and the distance  3144  from the gimbal point  3112 ′ to the vertex of the SMR  3120 ″. In a second step illustrated in the schematic representation  3170  of  FIG. 21C , the device  3110 ″ is placed in backsight mode. The measurements to the two SMRs are repeated to obtain distances  3172  and  3174 . 
     The distance  3126  should equal the sum of distances  3142  and  3144  if the distance meter is correctly zeroed to the beam rotation point (on the zenith axis  18 ). To correct for any discrepancy from the ideal, an offset distance is calculated using the formula offset distance=(distance  3126 −(distance  3142 +distance  3144 ))/2. The offset distance is added to each distance reading. Equivalently, we can consider that the offset distance is set to zero the beam rotation point. 
     There are two different types of distance meters—absolute and incremental—that are reset somewhat differently. In the case of an incremental distance meter such as an interferometer, the distance is set to a known value at a given point. For example, it could be that a laser beam sent to an SMR sent to a home position nest is expected to have a distance reading of 0.167 meters based on measurements made in a factory or laboratory. For an incremental distance meter, a beam of light is sent to the SMR in the home position and set to read a value of 0.167 meter. Afterwards, the device may count the number of wavelengths shift in waves of light and multiply these by the wavelength of the light in question (in the local air medium) to get the total change in distance. This change in distance is added to the original distance to get the distance at any later time. 
     In the case of an absolute distance meter (ADM), a beam of light may again be sent to a distance meter, but in this case the distance read by the distance meter is compared to the known distance, which might again be 0.167 meter. One or more parameters associated with the measurement of the ADM, such as a phase offset parameter, for example, are adjusted to give the expected reading of 0.167 meter. Thereafter the adjusted parameter(s) continues to be used in making corrections to the ADM readings. 
     Although the way of resetting a distance meter is somewhat different in the two cases—resetting to a distance for the incremental distance meter and resetting parameters for the ADM—in both cases, it is necessary to send the beam of light from the device to the vertex of the SMR before making the necessary compensations. 
       FIG. 21C  is a schematic representation  3170  that illustrates a way to determine the axis offset value  29 . With the device in the backsight mode, the distance meter measures distances  3172  and  3174 . The axis offset value is calculated with the formula axis offset value=((distance  3142 +distance  3144 )−(distance  3172 +distance  3174 ))/4. The axis offset value is used in transforming the measured distance and two angles into a 3D coordinates in a coordinate system  30  centered on the gimbal point  22 . 
     The methods for setting the zero distance value for the distance meter in the device  10  discussed hereinabove have shown the distances measured by the distance meter taken with respect to the SMR vertex points  820 . However, each SMR has its own depth error, which means that the method of  FIG. 21  will give different results depending on the SMR or SMRs used. A way around this problem is to use SMR compensation parameters to measure to the SMR sphere center(s) rather than the sphere vertex. For the case shown in  FIG. 21B , it is usually the case that the axis of symmetry of the SMRs  3120 ′ and  3120 ″ can be aligned to the beams of light from the device  3110 ′. In this case, the effect of the runout error is negligible. For example, suppose that the SMR runout error for the SMR  3120 ″ is 12 micrometers, with the distance from the gimbal point  3112 ′ equal to 2 meters. The error in the measured length is √{square root over (2 2 +(12·10 −6 ) 2 )}−2 m=3.6·10 −5  μm, which is a negligible value. As long as the axis of symmetry of the SMRs  3120 ′ and  3120 ″ can be well aligned to the beams from the device  3110 ′, it is only necessary to increase or decrease the measured distances  3142 ,  3144  to account for the SMR depth error. By making this correction, the method described above with reference to  FIGS. 21A-21C  will be accurate regardless of the SMR depth error. 
     Some variations are possible in the procedures described in reference to  FIGS. 21A-C . The method of  FIG. 21  may be modified by obtaining a reference artifact having a known distance between nests. The distance between spheres placed on the nests  3130  and  3130 ′ may be measured once using a Cartesian CMM or interferometer. If testing is done in a constant temperature environment, say at 20° C., then the distance between the nests would not be expected to change, especially if the artifact is made of a material having a low coefficient of thermal expansion (CTE). For example, the artifact may be made of carbon fiber composite material having a low CTE, or it may be made of Invar or Super-Invar. 
     In another case, different SMRs may be placed in the nests  3130  and  3130 ′ rather than shifting one SMR between nests. Using two SMRs in this way may save time in an automated procedure. In this case, the depth error of each SMR is accounted for separately in determining setting the distance meter to zero at the beam rotation point. 
     The discussion with regard to  FIGS. 21A-C  had to do with methods for setting the distance meter to read correct values or for applying compensation or correction values to distance readings. An important aspect of these corrections is to account for SMR depth error so that distance meter compensation is accurate regardless of the SMR depth error. In the case of a device  10  that has a home position nest  17 , the end result of the procedures of  FIGS. 21A-C  is a numerical value called the home reference distance, defined as the distance from the rotation point (on the zenith axis  18 ) to the center of an SMR (of given diameter) placed in the home position nest. 
     For a device that does not have a home position nest, the end result of the procedures of  FIGS. 21A-C  is a correction to the distance meter itself. In other words, the processing of the distance meter is changed following the procedure to make the sum of the distance readings  3142  and  3144  equal the difference in the distance readings  3126  and  3124 . Afterwards, this reset distance reading may be used to set a distance to a retroreflector fixed to the device. Such a fixed retroreflector may be measured whenever desired to remove drift from the distance meter 
     As stated in the preceding paragraph, for a device having a nest that holds an SMR, the end result of the procedures of  FIGS. 21A-C  is a home reference distance, which is a numerical value. In an embodiment, this numerical value is made more accurate by correcting for SMR depth error. The home reference distance is saved within the memory of the device. 
     In routine use of the device  10 , the home reference distance is used to correct the distance reading of an SMR placed at the home position nest  17 . Such routine correction may be useful in correcting drift in the distance meter, which may occur over time and as a result of temperature changes and mechanical shocks. As explained in  FIG. 20C  and shown again in  FIG. 22 , a beam  46  may be sent to a vertex point  820  of an SMR  700  in a home position nest  17 . If possible, the axis of symmetry of the SMR is aligned to the beam of light from the device. When this is possible, the distance meter may be set a distance  3042  to the vertex  820  based on the home reference distance and the SMR depth error without considering the SMR runout error vector component. For example, suppose that the SMR has a sphere radius of 0.75 inch=19.05 mm, with its sphere vertex  820  a distance of 0.167 meter from the beam rotation point on the zenith axis  18 . Further suppose that the SMR runout error is 0.0005 inch=12.7 micrometers. The SMR runout error produces an error in the measured distance of √{square root over (0.167 2 +(12.7·10 −6 ) 2 )}−0.167 m=4.83·10 −10  m, which is negligible. 
     In some cases, it is not possible to align the axis of symmetry of the SMR  700  with the beam direction  46 . For example, in  FIG. 22  the collar  905  cannot be aligned to the axis of symmetry with having the collar come into contact with the nest surface. Such contact is to be avoided as it can cause the SMR to rise off the nest contact points, thereby causing an error. 
     In this case, it is advisable to account for the effects of the SMR runout error vector component as well as the SMR depth error. This may be done in two steps. In a first step, the SMR is placed in the nest with the collar a certain distance off the nest surface. For example, a prescription might be to lower the collar until it touches the nest surface and then raise the nest by 2 mm. Assuming that the operator can adjust the collar to within one millimeter of the desired value for an SMR having a radius of 19.05 mm, alignment is obtained to within about ±3 degrees. In a second step, the SMR is aligned to place the reference point  932  at a specified orientation. For example, the prescription might be to reference point  932  at the uppermost SMR position. The calculations discussed hereinabove with respect to  FIGS. 9C, 9D and 12A, 12D  can then be carried out to correct the distance reading to account for the vector error. In other words, the home reference distance, which is a value intended for the sphere center of an SMR in the home position nest  17  is adjusted for the vector error to set the distance for the SMR vertex point, which is the actual point measured by the device  10 . An alternative way to carry out the second step is to use the camera  56  of  FIG. 1  to determine the orientation of the SMR, as discussed hereinabove. 
       FIG. 23  shows electrical and computing components  2000  within and outside the laser tracker  10 , which is representative of a device used to measure an SMR. These electrical and computing components are merely representative, and it should be understood that other configurations are possible. A master processor  2070  sends and receives data messages to processors within the laser tracker. These messages may be sent over a wired, optical, or wireless device bus  2030 . Processing may be independently carried out for functions within the laser tracker  10 . For example, there may be a position detector processor  2012 , azimuth encoder processor  2014 , zenith encoder processor  2016 , ADM processor  2020 , interferometer processor  2022 , locator cameras processor  2024 , indicator lights processor  2018 , temperature electronics processor  2025 , azimuth (AZ) and zenith (ZE) motor processor, and RFID and wireless processor  2028 . The RFID and wireless processor  2028  may be connected to an antenna  2029  for emitting or receiving radio frequency (RF) signals. The term processor as used herein is intended to include not only computing devices, which might include microprocessors, FPGAs, and DSPs, but also electronic circuitry to perform functions needed to condition the signals to be sent to a computing device or memory. Such electronic circuitry might include, for example, analog-to-digital converters or temperature determination electronics. The master processor  2070  may be enclosed in a box such as the interface box  70  of  FIG. 2 . Alternatively, it may be integrated into the electronics internal to the tracker body. The signals from the master processor may go to an external computer  25  or be connected to a network  2044 ,  2042 . 
     An electrical memory component within  2000  may be used to store information. Such information may be used by the processor or may be transmitted to a remote processor by wired or wireless means. The information may include a serial number and SMR parameters as discussed hereinabove. 
     While the description above refers to particular embodiments of the present invention, it will be understood that many modifications may be made without departing from the spirit thereof. The accompanying claims are intended to cover such modifications as would fall within the true scope and spirit of the present invention. 
     The presently disclosed embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims, rather than the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.