Abstract:
A target is provided having a retroreflector. A body is provided having a spherical exterior portion, the body containing a cavity. The cavity is sized to hold the retroreflector, the cavity open to the exterior of the body and having at least one surface opposite the opening, the retroreflector at least partially disposed in the cavity, wherein the retroreflector and at least one surface define a space therebetween. A transmitter is configured to emit an electromagnetic signal. A first actuator is configured to initiate emission of the electromagnetic signal, wherein the transmitter and the first actuator are affixed to the body.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application is a continuation application of U.S. patent application Ser. No. 13/407,983 filed Feb. 29, 2012, which claims the benefit of provisional application No. 61/448,823 filed Mar. 3, 2011, and also further claims the benefit of provisional application No. 61/475,703 filed Apr. 15, 2011 and provisional application No. 61/592,049 filed Jan. 30, 2012, the entire contents of both of which are hereby incorporated by reference. The U.S. patent Ser. No. 13/407,983 is also a continuation of U.S. patent application Ser. No. 13/370,339 filed Feb. 10, 2012, which claims priority to provisional application No. 61/442,452 filed Feb. 14, 2011, the entire contents of which are hereby incorporated by reference. The present application is further a continuation in part of U.S. patent application Ser. No. 12/620,070 filed Nov. 17, 2009, which claims benefit of provisional application No. 61/116,136 filed Nov. 17, 2008, the entire contents of which are hereby incorporated by reference. 
     
    
     FIELD OF INVENTION 
       [0002]    The present invention relates in general to methods for measuring targets and in particular to methods for measuring the center of a spherical target containing a retroreflector. 
       BACKGROUND 
       [0003]    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 absolute distance meter 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. 
         [0004]    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. 
         [0005]    Ordinarily the laser tracker sends a laser beam to a retroreflector target. A common type of retroreflector target is the spherically mounted retroreflector (SMR), which includes a cube-corner retroreflector embedded within a metal sphere. The cube-corner retroreflector includes three mutually perpendicular mirrors. The vertex, which is the common point of intersection of the three mirrors, is located near the center of the sphere. Because of this placement of the cube corner within the sphere, the perpendicular distance from the vertex to any surface on which the SMR rests remains nearly constant, even as the SMR is rotated. Consequently, the laser tracker can measure the 3D coordinates of a surface by following the position of an SMR as it is moved over the surface. Stating this another way, the laser tracker needs to measure only three degrees of freedom (one radial distance and two angles) to fully characterize the 3D coordinates of a surface. 
         [0006]    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. 
         [0007]    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 many 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 because the orientation of the SMR is not known. 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. 
         [0008]    Most of the SMRs in use today contain open-air cube corner retroreflectors. There are some SMRs that use glass cube corner retroreflectors, but 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. The error this produces can be minimized by moving the vertex of the cube corner behind the center of the sphere. An example of the calculations involved in minimizing this error is given in U.S. Pat. No. 7,388,654 to Raab, et al., the contents of which are incorporated by reference. However, there is no one distance of movement that eliminates the tracker errors in using such a retroreflector over the full range of angles of incidence over which light can enter the cube corner. As a result, 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. However, SMRs made with glass cube corners have a significant advantage compared to SMRs made with open-air cube corners: they have a wider acceptance angle. In other words, the light may enter a glass cube corner at a larger angle of incidence without being clipped than an open-air cube corner. Consequently, there is a need for a method of measuring a relatively large SMR containing a glass cube corner with high accuracy. The need is essentially one of finding the center of the SMR spherical surface, regardless of the position of the glass cube corner, and in this respect it is similar to the need described above for SMRs containing open-air cube corners. 
         [0009]    More generally, there is a need for a method of finding the center of a target having a spherical surface and containing a retroreflector, regardless of the type of retroreflector. For example, a different type of retroreflector put into spherical surfaces is the cateye retroreflector. Another example is the photogrammetric dot—a small circle of reflective material—which is sometimes centered in a sphere. There are errors in the centering of cateye retroreflectors and photogrammetric dots in spheres, just as in centering cube corner retroreflectors in spheres. Hence there is a general need for a method of finding the center of a target having a spherical surface and containing a retroreflector. 
       SUMMARY 
       [0010]    According to an embodiment of the present invention, a target is provided having a retroreflector. A body is provided having a spherical exterior portion, the body containing a cavity. The cavity is sized to hold the retroreflector, the cavity open to the exterior of the body and having at least one surface opposite the opening, the retroreflector at least partially disposed in the cavity, wherein the retroreflector and at least one surface define a space therebetween. A transmitter is configured to emit an electromagnetic signal. A first actuator is configured to initiate emission of the electromagnetic signal, wherein the transmitter and the first actuator are affixed to the body. 
         [0011]    According to another embodiment, a target is provided. The target including a body and a contact element having a region of spherical curvature. A retroreflector is provided. A transmitter is configured to emit an electromagnetic signal. A temperature sensor is configured to measure an air temperature and configured to send the measured air temperature to the transmitter, wherein the contact element, the retroreflector, the transmitter, and the temperature sensor are affixed to the body. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]    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: 
           [0013]      FIG. 1  is a perspective view of a laser tracker and an SMR according to an embodiment; 
           [0014]      FIG. 2  is an illustration of a laser tracker, an auxiliary unit, and an external computer according to an embodiment; 
           [0015]      FIG. 3  is a perspective view of a laser tracker and a six-DOF probe according to an embodiment; 
           [0016]      FIG. 4  is a block diagram showing elements in the payload of a laser tracker according to an embodiment; 
           [0017]      FIG. 5  is a perspective view of a cube corner slug and a master element used in retroreflector replication according to an embodiment; 
           [0018]      FIG. 6  is a perspective view of a glass cube corner with non-reflecting portions at intersecting junctions according to an embodiment; 
           [0019]      FIG. 7  is an example of an illumination pattern produced by non-reflecting portions of a retroreflector and impinging on an orientation camera within the laser tracker according to an embodiment; 
           [0020]      FIGS. 8A-C  are perspective, cross-sectional, and front views, respectively, of a target that includes an open-air cube-corner slug embedded within a sphere according to embodiments; 
           [0021]      FIG. 8D  is a perspective view of the target of  FIGS. 8A-C  with additional features according to an embodiment; 
           [0022]      FIGS. 9A-C  are perspective, cross-sectional, and front views, respectively, of a target that includes a glass cube-corner embedded within a sphere according to embodiments; 
           [0023]      FIG. 9D  is a perspective view of the target of  FIGS. 9A-C  with additional features according to an embodiment; 
           [0024]      FIGS. 10A-B  are perspective and front views, respectively, of the target of  FIGS. 9A-C  to which have been added marks on the top surface of the glass prism according to an embodiment; 
           [0025]      FIGS. 11A-C  are perspective views of the target of  FIGS. 8A-C  to which have been added a reflective region, a bar-code pattern, and an RF identification tag, respectively, according to embodiments; 
           [0026]      FIGS. 12A-B  are front and side sectional views, respectively, of an SMR having a cube corner retroreflector not perfectly centered within a sphere; 
           [0027]      FIGS. 13A-C  show a perspective view of a glass cube corner, a sectional view of a spherical six-DOF target, and a perspective view of a spherical six-DOF target, respectively, according to an embodiment; 
           [0028]      FIG. 14  shows a cross sectional view of a spherical six-DOF target and the path of a ray of light outside and inside the glass prism according to an embodiment; 
           [0029]      FIG. 15  shows a cross sectional view of a spherical six-DOF target and projected lines to illustrate the corrections made mathematically to correct for the bending of light; 
           [0030]      FIG. 16A  shows the steps in a method for measuring the center of a sphere into which a retroreflector is embedded according to an embodiment; 
           [0031]      FIG. 16B  shows the steps in a method for measuring a three-dimensional coordinate of a point on a workpiece surface according to an embodiment; 
           [0032]      FIG. 17A  shows a locator camera located on a tracker and surrounded by near lights and a far light according to an embodiment; 
           [0033]      FIG. 17B  shows a tracker aperture with locator cameras and light located to the right and to the left according to an embodiment; 
           [0034]      FIG. 18A  shows a light that illuminates a retroreflector but does not strike a tracker locator camera; 
           [0035]      FIG. 18B  shows a light that illuminates a region of reflective material, producing scattered light that strikes the tracker locator camera; 
           [0036]      FIG. 19  shows electronics and processors within a laser tracker according to an embodiment; 
           [0037]      FIGS. 20A-C  show an exemplary six-DOF target having a probe tip and a probe extension according to an embodiment; 
           [0038]      FIGS. 21A-C  show a six-DOF probe similar to that in  FIGS. 20A-C  except that the probe extension is tilted at an arbitrary angle and locked in place with knob according to an embodiment; and 
           [0039]      FIG. 22  shows the steps in a method for measuring a point on a workpiece using a target having an identifier element according to an embodiment. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0040]    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 spherically mounted retroreflector (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. 
         [0041]    The laser tracker  10  is a device that has a device frame of reference  30 . The device frame of reference may have as its origin the gimbal point  22 . The frame of reference may be fixed with respect to the azimuth base  16 , which is typically stationary with respect to the surroundings. The device frame of reference may be represented by a variety of coordinate systems. One type of coordinate system is a Cartesian coordinate system having three perpendicular axes x, y, and z. Another type of coordinate system is a spherical coordinate system. A point  74  within a spherical coordinate 30 may be represented in a spherical coordinate system by one 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 makes measurements in a spherical coordinate system, but a point measured in spherical coordinates may be easily converted to Cartesian coordinates. 
         [0042]    The target  26  has a target frame of reference  40 . The target frame of reference may be represented, for example, using Cartesian coordinates x, y, and z. The x, y, and z axes of the target frame of reference  40  move with the target  26  and are not necessarily parallel to the corresponding device axes x, y, and z of the device frame of reference  30 . The target  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 center of the target  26  using the distance and two angles it has measured. It may also be used to account for a vector offset of the retroreflector reference point (e.g., cube-corner vertex) with respect to the center of the spherical contact surface of the target  26  using methods described herein below. To move from the center of the target to the surface of the workpiece the position of the center point is offset by an amount equal to the radius of the spherical target surface. In an embodiment, the direction of the offset is found by measuring several points near to the contact point  63  to determine the surface normal at the point  63 . 
         [0043]    Laser beam  46  may include one or more laser wavelengths. 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. 
         [0044]    In exemplary laser tracker  10 , locator cameras  52  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  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 has a relatively wide field of view, for example, 30 or 40 degrees. The purpose of the lens is to form an image on the photosensitive array of objects within the field of view of the lens. Usually at least one light source  54  is placed near locator camera  52  so that light from light source  54  is reflected off each retroreflector target  26  onto 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 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. A use of two locator cameras for this purpose is described in U.S. Published Patent Application No. 2010/0128259 to Bridges, et al., the contents of which are herein incorporated by reference. 
         [0045]    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 is omitted and connections are made directly between laser tracker  10  and computer  80 . 
         [0046]    In  FIG. 3 , laser tracker  10  sends a laser beam to six-DOF probe  60 . Six-DOF probe includes a retroreflector (not shown) that returns light  46  back to the tracker  10 , a holder  66 , a probe shaft  64 , and a probe tip  62 . The operator who holds six-DOF probe  60  places the probe tip  62  into contact with the workpiece at a point of interest. The laser tracker  10  in combination with the six-DOF probe  60  determines the three dimensional coordinates of probe tip  62 . Such six-DOF probes are sometimes used to measure points that are not in the line of sight of the laser beam  46  from the laser tracker  10 . For example, the probe tip may be placed behind an object while the retroreflector within six-DOF probe  66  is tracked by the tracker laser beam  46 . 
         [0047]    To determine the three-dimensional coordinates of the probe tip  62 , the tracker measures six degrees of freedom of the probe tip. It measures the three translational degrees of freedom of the retroreflector reference point. For the cube corner retroreflector described hereinabove, the retroreflector reference point is the vertex of the cube corner. For a cateye retroreflector made of a single sphere (for example, using glass with refractive index equals two), the reference point is the center of the cateye sphere. For a cateye retroreflector made of two hemispherical elements, the reference point is centered on the two hemispherical elements on the plane that separates them. For a reflective photogrammetry target in the shape of a flat circle, the reference point is the center of the circle. 
         [0048]    The three translational degrees of freedom may be described in a Cartesian frame of reference with x, y, and z coordinates. Alternatively, the three translational degrees of freedom may be described in a spherical frame of reference with radial distance r, azimuth angle phi, and zenith angle theta. The laser tracker  10  measures a distance r using either an interferometer or an absolute distance meter (ADM). It measures an azimuth angle phi and a zenith angle theta 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. 
         [0049]    As stated herein above, some targets, such as six-DOF probe  60 , require a tracker configured for six-DOF measurements. In addition to measuring the three translational degrees of freedom, the tracker must also be able to measure three orientational degrees of freedom. Together, three translational and three orientational degrees of freedom that produce six independent degrees of freedom fully specify (fully constrain) the position of every point within a rigid body—for example, the rigid body six-DOF probe  60 . 
         [0050]    The three degrees of orientational freedom may be described in a variety of ways. Methods for describing three degrees of orientational freedom include Euler angles and Tait-Bryan angles, the latter of which include the well-known pitch-yaw-roll and heading-elevation-bank descriptions. In the present application, the term three degrees of orientational freedom should be understood to mean three independent degrees of freedom. For example, a rotation about an x axis, a y axis, and a third axis in the x-y plane would represent only two degrees of freedom as the three axes are not independent. In other words, the three axes do not provide a method of specifying the rotation about the z axis and hence do not represent three independent degrees of freedom. 
         [0051]    It is possible to have several interconnected objects that move independently. In such a situation, more than three degrees of freedom may be required to fully specify the motion of the collection of objects. Generally, a six-DOF probe such as probe  60  moves as a unit so that three degrees of orientational freedom are sufficient to fully describe the orientation of every point on the probe structure. 
         [0052]    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. 
         [0053]      FIG. 4  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 absolute distance meter (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. 
         [0054]    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 than transmits the wavelength of light emitted by source element  410  and reflects the wavelength of light emitted by source element  405 . 
         [0055]    Most of the light from beam splitter  420  passes through beam splitters  425  and  430 . A small amount of light is reflected off each of these mirrors and is lost. The light passes through beam expander  435 . The beam expander  435  expands the size of the beam on the way out of the tracker. The laser light  440  leaving the tracker  10  travels to a retroreflector target  26  or a retroreflector probe  60 . A portion of this laser light returns to the tracker. The beam expander reduces the size of the beam on the way back into the tracker. In an embodiment, some of the light reflects off beam splitter  430  and travels to orientation camera  445 . The orientation camera is used to obtain the three degrees of orientational freedom of the six-DOF probe  60  or any other six-DOF device. Orientation camera contains a lens system  446  and a photosensitive array  447 . It may use a motor to adjust the size of the image. The principal of operation of the orientation camera is explained in the &#39;758 patent. 
         [0056]    Part of the 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 detector. 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 with the tracker  10  to keep the returning light beam centered, as nearly as possible, on the position detector  450 . 
         [0057]    As explained in the &#39;758 patent, the orientation camera  445  provides the tracker  10  with one method of measuring the six degrees of freedom of a target. Other methods are possible, and the methods described herein for measuring the center of a spherical target are also applicable to these other methods. 
         [0058]    The traditional SMR  26  includes a body having a spherical exterior portion and a retroreflector. The body contains a cavity sized to hold a cube corner retroreflector, which is attached to the cavity. The spherical exterior portion has a spherical center. 
         [0059]    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. 
         [0060]    Cube corner retroreflectors may be open-air cube corners or glass cube corners. Open-air cube corner retroreflectors have an interior portion of air, while the glass cube corner retroreflectors have an interior portion of glass. The glass cube corner retroreflector is a type of glass prism. One surface of the glass prism called the top surface is distal to the vertex. 
         [0061]    The SMR is designed for use with a laser tracker for measuring three degrees of freedom. A more powerful version of the SMR is the spherical six-DOF target. Some examples of six-DOF targets are shown in  FIGS. 8A-D  and  9 A-D. These will be discussed in more detail hereinafter. 
         [0062]    One type of six-DOF target uses cube corners containing marks or non-reflecting portions, as explained in the &#39;758 patent. Each intersection junction of the cube corner retroreflector may have a non-reflecting portion. The non-reflecting portion does not necessarily suppress all light that it reflects or scatters. Rather the non-reflecting portions are configured to greatly reduce the return of light to the tracker. The reduced return of light may be achieved, for example, by making the non-reflecting portion from (a) an absorbing material such as an absorbing coloration or an absorbing tape, (b) a scattering surface texture or material, (c) a curved reflective surface that results in a diverging pattern of light, or (d) a planar surface that reflects the light away from the laser tracker. Other methods for making the non-reflecting portion achieve a reduced return of light may be utilized in light of the teachings herein, as should be apparent to one of ordinary skill in the art. 
         [0063]    There are at least two common methods for making open-air cube corner retroreflectors: replication and assembly of glass panels.  FIG. 5  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 . For example, the planar reflector faces  512  of the master element  510  may be perpendicular to each of its nearest neighbors 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. 
         [0064]    Usually, the intersection junctions of the master element  510  are not perfectly sharp. One reason for this lack of sharpness is the difficulty of machining such sharp intersection junctions. Another reason is that the intersection junctions tend to chip during repeated replications if the junctions are too sharp. Instead, the intersection junctions are usually rounded with a small fillet or angled with a small bevel. Usually, for cube corners that are placed in spherically mounted retroreflectors used to measure three degrees of freedom, these features are made as small as practical. For example, a fillet applied to the intersection junctions of master element  510  might have a radius of curvature of 0.003 inch. This radius of curvature is transferred to the intersection junctions of slug  520 . The fillet or bevel applied to the cube corner retroreflector is a non-reflecting portion according to the explanation given hereinabove. In other words, very little light will return to the laser tracker after striking a fillet or bevel applied to the intersection junctions of the cube corner retroreflector. 
         [0065]    If the cube corner retroreflector is to be used in conjunction with a system to measure six degrees of freedom similar to that described in the &#39;758 patent, then it may be desirable to broaden the non-reflecting portions observed by the orientation camera within the laser tracker. If a six-DOF target is only a few meters away from the tracker, then the narrow non-reflecting portions commonly present in high quality SMRs may be wide enough to be easily seen by the orientation camera. However, if the six-DOF target is located farther away—for example, up to 30 meters from the laser tracker—then the non-reflecting portions will need to be widened to make them visible on the orientation camera. For example, the non-reflecting portions might need to be about 0.5 mm wide to be clearly seen by the orientation camera. 
         [0066]    In  FIG. 5 , the non-reflecting portion  517  near the vertex  514  is narrower than the non-reflecting portion  516  farther from the vertex. By reproducing this combination of non-reflecting portions  515  on each of the three intersection junctions, a pattern like that of  FIG. 7  is observed on the orientation camera  445  within the laser tracker  10 . The thickness of the non-reflecting portions on the intersecting junctions on the slug  520  may be controlled by adjusting the radii of curvature on the intersecting junctions of the master element  510 . 
         [0067]    The second common method of making open-air cube corner retroreflectors is to join mirror panels into a cube-corner assembly. Three mirror panels are joined together to be mutually perpendicular. There are slight gaps at the intersection regions between glass panels. Light that strikes the gaps is not reflected back to the laser tracker and so represents non-reflecting portions. If thicker lines are desired, these may be obtained, for example, by (a) increasing the width of the gap, (b) coloring (darkening) the mirrors over the desired portions, or (c) attaching low reflection material (e.g., black adhesive tape) at the intersection junctions. 
         [0068]    Referring now to  FIG. 6 , a glass cube corner retroreflector  400  has planar reflectors  612  that are mutually perpendicular. The non-reflecting portions of glass cube corner retroreflector  600  shown in  FIG. 6  are obtained by removing some of the glass along the intersection junctions. The non-reflecting portion  617  near the vertex  614  is thinner than the non-reflecting portion  616  farther from the vertex  614 . A relatively thin non-reflecting portion  617  may be obtained by using a relatively small bevel, and the relatively thick non-reflecting portion  616  corresponds to the relatively large bevel. If desired, the bevels could be replaced by other shapes such as fillets. In general, the non-reflecting portions in the glass cube corner prism  600  are obtained by removing glass at the intersection junctions. This removed material may take such forms as bevels or fillets. In most cases, most of the light scattered off the bevels or fillets will not return to the laser tracker. If desired, loss can be further increased by darkening or otherwise treating the bevels or fillets, or absorptive adhesive material may be applied to the bevels or fillets. 
         [0069]    FIG. 12 of the &#39;758 patent illustrates an image pattern  100  in the prior art appearing on an orientation camera within a laser tracker. The three lines shown in this figure were obtained by illuminating a cube corner retroreflector onto which non-reflecting portions were placed on each of the three intersection junctions of the three planar surfaces of the cube corner retroreflector. The vertex of the cube corner retroreflector corresponds to the intersection point of the lines. Each of the lines in this figure extends on both sides of the intersection (vertex) point because each non-reflecting portion blocks laser light on the way into and on the way out of the cube corner. 
         [0070]    A potential problem with non-reflecting portions placed on a cube corner retroreflector to produce the pattern of FIG. 12 of the &#39;758 patent is that a large amount of light may be lost near the center of the retroreflector where the optical power is the highest. In some cases, the result of the reduced optical power returning to the laser tracker is a decrease in tracking performance and a decrease in the accuracy of distance and angle measurements by the laser tracker. To get around this problem, the non-reflecting portions may be modified to produce an illumination pattern  700  like that shown in  FIG. 7 . Such modifications are possible using the methods already described in conjunction with  FIGS. 5 and 6 . In  FIG. 7 , the lines  710 ,  720 ,  730  adjacent to the vertex point  740  are relatively narrow compared to the lines farther from the vertex. 
         [0071]    A cube corner retroreflector having non-reflecting portions may be embedded in a sphere, as shown in  FIGS. 8A-D  and  9 A-D, or in a probe, as shown in FIG. 1 of the &#39;758 patent.  FIG. 8A  shows a spherical six-DOF target  800  including a spherical body  802 , an open-air cube corner retroreflector  804  with non-reflecting portions, a collar  806 , and a reference mark, or feature,  801 . A cavity in the spherical body  802  is sized to accept the cube corner retroreflector  804 . The cube corner retroreflector  804  is at least partially disposed in spherical body  802 , possibly with adhesive. The collar  806  provides protection for the cube corner retroreflector  804  and provides a convenient grip. The reference mark, or feature,  801  is used to establish a coarse reference orientation for the target  800 . The reference feature  801  may also be a textural feature such as a dimple or bump. The reference feature may be any feature that enables the user to distinguish a particular position or orientation of the retroreflector  804 .  FIG. 8B  shows a cross sectional view taken through the center of the spherical six-DOF target  800 . The cross section reveals the open-air cube corner  804  to be of the replicated type, but a cube corner retroreflector formed of three mirror panels could equally well be used. The retroreflector  804  is at least partially disposed within the cavity  815 .  FIG. 8C  shows a front view of the spherical six-DOF target  800 . The three intersection junctions  809  are visible about vertex  808 . 
         [0072]    The coarse orientation of the retroreflector is determined when there is an ambiguity in the orientation of the retroreflector because of the symmetry of the retroreflector. For example, in a cube corner retroreflector, the three intersecting lines  710 ,  720 ,  730  formed by the three reflecting surfaces, as shown in  FIG. 7 , extend on both sides of the center point  740 . For the case in which the axis of symmetry is aligned with the direction of the laser beam  46  from the laser tracker  10 , the lines  710 ,  720 , and  730  are separated by 60 degrees. In this case, there is a six-fold degeneracy, which is to say that the six lines cannot be assigned to the particular physical lines on the cube corner. To eliminate the degeneracy, a method is used to establish a coarse orientation by which a particular line of a cube corner retroreflector is associated with a particular line that appears in an image on an orientation camera within a laser tracker. Although the example given here is for a method of measuring six degrees of freedom using a target that includes a cube corner retroreflector, the measurement made with an orientation camera included in a laser tracker, the principle may be applied more generally to other types of retroreflectors, other types of targets, and other methods of determining the six degrees of freedom of a target. 
         [0073]      FIG. 9A  shows a spherical six-DOF target  900  including a spherical body  902 , a glass cube corner retroreflector prism  904  with non-reflecting portions, a collar  906 , and a reference mark, or feature,  901 . A cavity in the spherical body  902  is sized to accept the cube corner retroreflector  904 . The cube corner retroreflector  904  is at least partially disposed in the cavity. The collar  906  provides protection for the cube corner retroreflector  904  and provides a convenient grip. The reference mark, or feature,  901  is used to establish a coarse reference orientation for the spherical six-DOF target  900 .  FIG. 9B  shows a cross sectional view taken through the center of the spherical six-DOF target  900 . The retroreflector  904  is at least partially disposed within the cavity  915 .  FIG. 9C  shows a front view of the spherical six-DOF target  900 . The three intersection junctions  909  are beneath the top surface of the glass prism and so are shown as dashed lines about the vertex  908 . 
         [0074]      FIG. 8D  shows an interface component  820  attached to spherical six-DOF target  800  to produce an enhanced spherical six-DOF target  810 . Interface component  820  may contain a number of optional elements. One such optional element is a reference feature  822 , which may be a reference mark, a retroreflector (e.g., a small glass cube corner retroreflector), a region of reflective material, or a target light (e.g., an LED). The retroreflector or region of reflective material may be illuminated by a light from the laser tracker and the image captured by a locator camera in the laser tracker to determine the coarse orientation of the target  810 . Alternatively, the target light may be illuminated and the image captured by a locator camera on the laser tracker to determine the coarse orientation of the target  810 . The reference feature  822  may be left off altogether in which case the interface component  820  may itself serve as a reference mark, or feature. In this case, the operator aligns the target  810  in a prescribed orientation which is understood to be the coarse orientation. 
         [0075]    Another optional element of interface component  820  is identifier element  824 . The identifier element  824  may take the form of a bar-code pattern or radio-frequency identification (RFID) tag, for example. In an embodiment, the bar code has a one-dimensional pattern that includes a series of parallel lines of differing thicknesses and spacings. In another embodiment, the bar code has a two-dimensional pattern that includes a series of dots or squares spaced in a two-dimensional pattern. The tracker may read the contents of the bar code using a locator camera placed, for example, on the front of the tracker or with an orientation camera. The tracker may read the identity of the RFID tag by illuminating the RFID tag with radio frequency (RF) energy. The identifier element  824  may contain a serial number that identifies the particular target  810 . Alternatively, the identifier element may contain one or more parameters that characterize the target  810 . A serial number could include letters or other symbols as well as numbers and is intended to identify a particular target. Parameters could provide any information about any aspect of the device—for example, geometrical characteristics or thermal characteristics. A serial number may be used by a processor to gain access to parameters associated with a particular target. 
         [0076]    Another optional element of interface component  820  is antenna  830 . Antenna  830  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 that is powered by a small battery  828  that fits inside interface component  820 . The small circuit board may be made of rigid-flex material which permits a very compact circuit to be enclosed within the interface component. 
         [0077]    The identification function performed by identifier element  824  may instead be carried by saving the identification information, which might be a serial number or one or more parameters, in the electrical components of the circuit board within the interface component  820  and then transmitting the identification information to the laser tracker with an RF signal from the antenna  830  or with an optical signal from the target light at  822 . RF and optical signals are two examples of electromagnetic signals that might be used to transmit identification information. As used here, optical signals may include ultraviolet, visible, infrared, and far infrared wavelengths. 
         [0078]    The interface component  820  may also be provided with one or more optional actuator buttons  826 . The actuator buttons  826  may be used to start and stop measurements or to initiate a variety of other actions. These buttons may be used in combination with indicator lights on the laser tracker to ensure that the tracker has received the intended commands. 
         [0079]    The interface component  820  may also contain a temperature sensor  832  mounted within the target—for example, on the spherical body  802  or cube corner retroreflector  804 . As the spherical body  802  and cube corner retroreflector  804  are heated or cooled, the position of the vertex  808  may shift since in general the spherical body  802  and cube corner retroreflector  804  may be made of different materials having different coefficients of thermal expansion (CTEs). By tracking the temperature of the target  810 , compensation may be performed to shift the position of the vertex  808  by an appropriate amount. 
         [0080]    The interface component may include an air temperature sensor assembly  834  comprising a temperature sensor  836 , protector  838 , and insulation (not shown). The temperature sensor may be a thermistor, RTD, thermocouple, or any other device capable of measuring temperature. It may be placed in a protector structure, which might be a hollow cylinder, for example. The purpose of the protector is to keep the temperature sensor from being damaged and to keep heat sources away from the temperature sensor. The protector is open at the end and may contain perforations to increase exposure of the temperature sensor to air. Insulation is provided between the body  802  and the air temperature sensor  836 . The insulation keeps the sensor from being exposed to the metal of the target, which may be at a different temperature than the surrounding air. 
         [0081]    A possible use of air temperature assembly  834  is to measure the temperature of the air as a function of position within the measurement volume. This may be important because measured distance and measured angles depend on the temperature of the air. For example, to get the distance from the tracker to a target, one of the tracker processors calculates the distance by dividing the uncorrected measured distance (as measured by the tracker interferometer or ADM) by the average index of refraction of the air over the path from the tracker to the target. The index of refraction, which is found using the Edlin equation or the Ciddor equation, finds the index of refraction of the air based on the temperature, pressure, and humidity of the air measured by sensors attached to the tracker. The resulting corrected distance value is the distance the tracker interferometer or ADM would have measured if the air were replaced by vacuum. Unlike pressure and humidity, which tend to be relatively constant over a measurement volume, the temperature often varies significantly over the measurement volume. Ordinarily, the temperature of the air in a measurement volume is estimated by placing a temperature sensor at a particular location and assuming that the air temperature has the same value at all positions within the measurement volume. A more accurate way to correct for temperature over the measurement volume would be to move the target  810  from a starting position at the tracker to an ending position near the measurement region, keeping track of the temperature at all distances and calculating the average temperature over those distances. The time constant of the air temperature sensor  836  should be set fast enough to enable the sensor to respond to changes in temperature as the operator carries the target  810  to different positions within the measurement volume. An alternative is to take the average of a first air temperature read by an air temperature sensor near the tracker and a second air temperature read by the air temperature sensor  832  on the target. 
         [0082]      FIG. 9D  shows an interface component  920  attached to spherical six-DOF target  900  to produce an enhanced spherical six-DOF target  910 . Interface component  920  may contain a number of optional elements, which are analogous to the optional elements in the interface component  820 . The optional elements  922 ,  924 ,  930 ,  928 ,  926 , and  932  have the same description as the optional elements  822 ,  824 ,  830 ,  828 ,  826 , and  932 . Because of this, the descriptions will not be repeated here. 
         [0083]      FIG. 10A  is a perspective view of a spherical six-DOF target  1000 , which includes glass cube corner  1004 , spherical body  1002 , and collar  1006 . One or more non-reflecting marks  1008  are placed on the top surface, which is the surface distal to the vertex, of the glass cube corner  1004 . A possible reason for using such marks is to provide a way of determining the three degrees of orientational freedom even when the target is tilted to an extreme angle. In  FIG. 10A , three such marks  1008  are provided to enable the spherical six-DOF target  1000  to be tilted to an extreme angle in any direction. The optional marks  1010  provide a way to more accurately determine the roll angle of the target  1000 .  FIG. 10B  is a front view of spherical six-DOF target  1000 . 
         [0084]      FIGS. 11A-C  depict three embodiments of spherical six-DOF targets. In  FIG. 11A , the spherical six-DOF target  1100  includes a spherical body  1102 , a cube corner retroreflector  1104 , and a collar  1106 . A region of reflecting material  1110  is placed on the front surface of collar  1106 . This region of reflecting material  1110  is illuminated by light from the laser tracker and its position is determined by a locator camera within the tracker. The position of the region  1110  is used to find the coarse orientation of the spherical six-DOF target  1100 . In  FIG. 11B , the spherical six-DOF target  1120  includes the same elements as spherical six-DOF target  1100  except that the region of reflecting material  1110  is replaced by a bar code pattern  1130 . The bar code pattern  1130  may serve to provide an identification of the target  1120  and it may also act as a region of reflecting material to provide a coarse orientation of the target  1120 . If desired, the bar code pattern may extend around the entire circumference of the collar lip rather than only a portion of the lip as shown in  FIG. 11B . If desired, the type of bar code pattern known as a radial pattern may be used. In  FIG. 11C , the spherical six-DOF target  1140  includes the same elements as spherical six-DOF target  1100  except that the region of reflecting material  1110  is replaced by an RF identification chip  1150 . This chip may be interrogated by an RF transmitter/receiver to obtain information about the spherical six-DOF target  1140 . This information may be a serial number or one or more parameters of the target  1140 . 
         [0085]      FIG. 12A  shows a front view of a target  1200 , which may be an SMR or a spherical six-DOF target. The body  1220  has a spherical exterior portion represented by the outer circle. The retroreflector  1210  is represented by the inner circle and the three intersection junctions are represented by three intersecting lines. The three lines intersect at the vertex  1212 . The spherical exterior portion has a sphere center  1222 , indicated in  FIG. 12A  by a + sign surrounded by a circle. If the target  1200  is placed in a nest and rotated, the center  1222  will remain fixed, but the vertex will be rotated in a circular pattern about the center. The resulting circular pattern is called a runout pattern  1232  that may be said to have a runout radius or runout diameter. The three planar reflectors that intersect in the intersection junctions of the retroreflector have an axis of symmetry. If  FIG. 12A  is oriented so that the axis of symmetry is perpendicular to the viewing direction, then the plane of the paper may be called the transverse plane and directions within the transverse plane may be called transverse directions. The front view of  FIG. 12A  shows the errors in the positioning of the retroreflector vertex  1212  in the transverse plane. These errors are shown as dy and dz in  FIG. 12A  and are referred to as the transverse errors  1282  and  1283 , respectively. A two dimensional transverse error vector may be drawn from the sphere center  1222  in a y-z plane. The error vector will map out a circle having a radius equal to the runout radius. 
         [0086]      FIG. 12B  shows a side sectional view taken through the vertex  1212 . In this view, the axis of symmetry lies in the plane of the paper. The error in direction of the axis of symmetry is called the depth  1281  and is shown as dx. 
         [0087]    A three dimensional error vector may be drawn from the sphere center  1222  to the vertex  1212 . The three errors dx, dy, and dz are called the vector length components. It is also possible to decompose the error vector into other directions. For example, it would be possible to select dx to be off the axis of symmetry, and the components dy and dz may be taken perpendicular to dx. 
         [0088]    The error vector has three length components dx, dy, dz in  FIGS. 12A-B . It is possible to measure these three length components of a target  1200  before the targets are used with tracker  10 . By measuring the three orientational degrees of freedom with a six-DOF tracker, it is the possible to correct the measured position of the vertex to obtain a corrected position for the center of the sphere. In this way, the accuracy of tracker readings can be improved. Similarly, this capability brought about by six-DOF measurements makes it possible to use inexpensive spherical six-DOF targets whose center, though off the retroreflector reference point (e.g., vertex) by a considerable distance, can be found with relatively high accuracy nonetheless. 
         [0089]    The target  1200  is given a target frame of reference. For example, such a frame of reference is given in  FIGS. 12A-B . The x, y, and z directions are shown in these figures. The user may select the sphere center  1222  or the vertex  1212  to be the origin of the target frame of reference, as desired. The device, which might be a laser tracker, also has a device frame of reference. To transform the vertex position  1212  into the sphere center  1222 , the rotational transformation is performed to make the axes of the target frame of reference parallel to the corresponding axes of the device frame of reference. This may be done using rotation matrices, quaternions, or other methods that are well known to those of ordinary skill in the art. These well-known methods will not be discussed further. After the target and device frames of reference are aligned, the measured vertex position is shifted in the target frame of reference by the vector length components to get corrected three-dimensional sphere center coordinates. 
         [0090]    Measurements are performed on targets  1200  to obtain the vector length components. For the alignment shown in  FIGS. 12A-B , the two vector length components dy, dz are called the transverse lengths  1282 ,  1283 , respectively, and the vector length component dx is called the depth  1281 . There are many ways to find the two transverse lengths and the depth. One method is to have the target  1200  measured by an accurate Cartesian coordinate measuring machine (CMM). With such methods, the position of the vertex relative to the sphere center can be found to a fraction of a micrometer. Once a measurement has been accurately performed on a target  1200 , the target may be treated as a master so that relative measurements can be performed optically. One method is to use a very accurate absolute distance meter to compare the depth of the target to the depth of the master target just calibrated with the Cartesian CMM. The difference in readings can be added to the error reported for the master target to find the depth in the target under test. The transverse lengths can be measured using a microscope without reference to a master target. A microscope can be used to see runout radii of about a micrometer, and the direction of the vertex in relation to the sphere center can also be determined. 
         [0091]      FIG. 13A  is a perspective view of a glass cube corner retroreflector  1330 . It is a prism that has three planar reflectors  1332  that are mutually perpendicular and meet at a vertex  1334 . The reflective surfaces of the prisms may be coated with a reflective film to enable reflection even when the cube corner is tilted at large angles of incidence (where total internal reflection no longer takes place.) The top surface  1338  is perpendicular to a line, or axis, of symmetry  1360  relative to the three perpendicular surfaces  1332 . The edges  1340  of the prism are shaped into a cylinder, which produces a scalloped effect as the cylinder intersects with the planar reflectors  1332 . To maximize the angle over which light can be received by the cube corner retroreflector  1330 , the top surface  1338  is made nearly tangent to the uppermost point of the scalloped portions. 
         [0092]      FIG. 13C  is a spherical six-DOF target  1300 . It includes a body  1310  that has a spherical external surface  1312 , and it contains a cavity sized to hold the cube corner retroreflector  1330  and a collar  1320 . Cube corner retroreflector  1330  is at least partially disposed within the cavity.  FIG. 13B  is a cross section of the target  1300  of  FIG. 13C  through the plane A-A in that figure. The dashed line  1342  in  FIG. 13A  shows where the section slice passes through the cube corner retroreflector  1330 . The spherical external surface  1312  has a sphere center  1314 , which in general is at a different point than the vertex  1334 . In the embodiment shown in  FIGS. 13A-C ,  14 , and  15 , the spherical external surface  1312  has a diameter of 1.5 inches=38.1 mm. The top surface  1338  of the cube corner retroreflector  1330  has a diameter of 1 inch=25.4 mm, and a height 0.707 times this value, or 17.96 mm. 
         [0093]      FIG. 14  is an orthogonal view of cross section A-A of  FIG. 13C . The hatch marks have been omitted to improve clarity. The sphere center  1314  is 1.3 mm below vertex  1334 . The cube corner retroreflector  1330  has an altitude length  1346  corresponding to the line segment that extends from the vertex  1334  to the point  1344  at which the line, or axis, of symmetry  1360  intersects the top surface  1338 . The top surface has a normal vector  1348 , which in this case is parallel to the line, or axis, of symmetry  1360  but may not be parallel to the axis of symmetry in the general case. The top surface  1338  is placed slightly outside the sphere used to create the body  1310  (before material is removed to obtain the cavity that holds the retroreflector  1330 ). This has the advantage of providing a large contact region for the spherical exterior portion  1312 . 
         [0094]    The central ray  1372  from a beam of light emitted by the laser tracker  10  or other device intersects the cube corner at point  1374 , bends and travels to the vertex  1334 . The position detector  450  in  FIG. 4 , in combination with the motors and servo system of the laser tracker  10 , keeps the beam approximately centered on the vertex  1334 , even if the target  1300  is moved. At the point of intersection  1374 , a line  1376  is constructed perpendicular to the top surface  1338 . The central ray  1372  lies in the plane of the paper (the plane of cross section A-A). The angle of incidence a I  is the angle from the normal  1376  to the central ray  1372 . The angle between the normal  1376  and the refracted ray of light  1373  is the angle of refraction a R . The angle of refraction can be found from Snell&#39;s law, which is n air  sin(a I )=n glass  sin(a R ). In this instance, the glass is selected to have an index of refraction of 1.85. For an angle of incidence of 46 degrees, the angle of refraction is approximately 23 degrees. The larger the angle of incidence the farther from the center  1344  of the top surface is the point of intersection  1374 , which increases the chance of clipping the beam of light entering the retroreflector. In the instance shown in  FIG. 14 , the point of intersection is 5 mm from the edge of the top surface. Projected onto the direction of travel of the incident laser beam, the distance is about 3.5 mm, which means that a beam having a diameter of 7 mm can enter the retroreflector in the geometry shown in  FIG. 14  without clipping. 
         [0095]      FIG. 14  illustrates important advantages of the method taught herein for correcting the position of the center of a glass retroreflector. The acceptance angle, which is twice the largest allowable angle of incidence, is over 90 degrees in this case. This is a much larger acceptance angle than is possible with an open-air cube corner. 
         [0096]    Because the light incident on the glass cube corner bends as it enters the glass, the position of the vertex will be improperly measured unless calculations take the bending of the light into account. It is possible to account for the bending of the light if the three orientational degrees of freedom of the glass cube corner are known. Since the target and the device both have a frame of reference, the three degrees of orientational freedom can be given for the target frame of reference as viewed within the device frame of reference. 
         [0097]    In the &#39;758 patent, equations were given in columns 14 and 15 for relating the pitch, yaw, and roll angles of an open-air cube corner to the slopes of the three lines observed on the photosensitive array of the orientation camera. The equations were compared to three dimensional rotations performed in CAD software to demonstrate their validity. In the &#39;758 patent, the term slope is used in the usual way to indicate a change in ordinate (y) value divided by a corresponding change in the abscissa (x) value. It should be understood that other definitions for slope may be used (for example, the change in abscissa divided by the change in ordinate) if the relevant equations are modified correspondingly. 
         [0098]    There are many computational methods that can be used to relate the orientational angles of the glass cube corner to the slopes of the lines that appear on the photosensitive array of the orientation camera. One method is described here. Three orientational angles are assumed. These may be described in terms of pitch, roll, yaw, or other orientational parameters. Each of the three lines corresponding to the intersection junctions are projected until they intersect a plane that includes the upper surface. These three points can be found using the altitude length and geometry of the cube corner. These three dimensional coordinates of these three points and of the vertex are transformed by a three dimensional rotation matrix, based on the three orientational degrees of freedom, to get new three dimensional coordinates for each. These transformed intersection points are called the junction points at the top surface. A normal vector to the upper surface may be constructed using a first point at the center of the upper surface and a second point of unit length that is perpendicular to the upper surface. These two points are transformed by the three dimensional rotation matrix to get a new normal vector. The light projected from the device in the device frame of reference makes an angle with respect to the new normal vector. The direction of the refracted light is found using vector mathematics. Since the light must intersect the vertex of the glass cube corner, the point of intersection of the central ray of light with the top surface can be found. This point of intersection with the top surface may be referred to as the apparent vertex. The lines that will be displayed on the orientation camera can now be obtained by connecting the apparent vertex with each of the three junction points at the top surface and then projecting these lines to be perpendicular to the direction of propagation of light back to the device. The lines may be drawn on both sides of the apparent vertex since the non-reflecting portions block light both on the way into and the way out of the retroreflector. The slopes of the lines from the calculations are compared to the slopes of the lines observed on the orientation camera. An optimization procedure is carried out to iteratively select parameters to minimize the least squared error until the best values for roll, pitch, and yaw are obtained. A coarse measurement, described in more detail below, is performed to get a good starting value for the calculations. 
         [0099]    After the three orientational degrees of freedom have been found, the results are used to correct the distance and two angles read by the laser tracker. In the absence of other knowledge, the device will believe that the vertex  1334  lies at position  1380  of  FIG. 15 . The direction of the vertex  1334  appears to lie along the direction of the central ray  1372  from the device. The device would measure the distance to the vertex as farther than the true distance because the light is traveling through glass, which has a higher index of refraction than air. The greater index of refraction causes the light to travel more slowly. Since distance meters such as interferometers and ADMs judge distance based on the time of flight of the light, a greater time spent in transit by the light results in the device judging the distance to be greater. Let the distance from the intersection point  1374  to the vertex  1334  be represented by the symbol T and let the index of refraction be represented by the symbol n. The distance measured by the tracker too large by T (n−1), which in this case is T (1.85−1)=0.85 T, since 1.85 was assumed to be the index of refraction. Usually, the index of refraction is the phase index of refraction for interferometers and the group index of refraction for absolute distance meters 
         [0100]    Once the three orientational degrees of freedom are known, the distance T can be found. If the normal vector  1348  is parallel to the axis of symmetry, then the distance T is found by dividing the altitude height by the cosine of the angle of refraction. If the normal vector  1348  is not parallel to the axis of symmetry, then the distance T is found using vector mathematics, the use of which is well known to one of ordinary skill in the art. To find the coordinates of the vertex  1334  in the device frame of reference, two steps are taken. First, the distance measured by the device is reduced by T (n−1), which moves the point  1380  to a new point  1382  on the line  1375 . Next the intersection point  1374  is found by moving back along the line  1375  an additional distance T. The line  1375  is rotated about the calculated intersection point  1374  by an angle aI−aR, which causes the point  1382  to move to the vertex  1334 . 
         [0101]    To find the sphere center  1314 , the target frame of reference of the target  1300  is rotated to make its axes parallel to those of the device frame of reference. The vertex position is then adjusted by the depth along the direction of the axis of symmetry to get the three dimensional coordinates of the sphere center. 
         [0102]    As in the case of the open-air cube corner illustrated in  FIGS. 12A-B , the vertex of the glass cube corner may be offset from the sphere center, not only in depth, but also in the two transverse directions perpendicular to the line, or axis, of symmetry  1360 . This is done in the same manner as with the open-air cube corners by rotating the target frame of reference to make its axes parallel to the corresponding axes of the device frame of reference. The coordinates of the vertex are then shifted by appropriate depth and transverse length values to obtain the three dimensional coordinates of the sphere center in the target frame of reference. 
         [0103]      FIG. 16  describes a method  1600  for measuring the center of a spherical target. In step  1610 , a first retroreflector is selected. The retroreflector may be a cube corner retroreflector, a cateye retroreflector, a photogrammetry target, or any other type of retroreflector. In step  1620 , a length is provided for at least one component of the vector that extends from the sphere center to the reference point of the retroreflector. Each of the at least one length is called a vector length component. In a three dimensional space, there are three independent vector length components. For example, the vector length component may be the depth, which is a component along the axis of symmetry of the vector. It might also be a transverse length, which is by definition perpendicular to the axis of symmetry. In step  1630 , a beam of light from the device illuminates the first retroreflector. For example, a laser beam from a laser tracker might illuminate a cube corner retroreflector within a spherical six-DOF target. 
         [0104]    In step  1640 , three orientational degrees of freedom are found. The method for doing this for open-air cube corner retroreflectors was explained in detail in the &#39;758 patent. The method for doing this for a glass cube corner is explained in the present application. In step  1650 , the device measures a first distance and a first set of two angles. For example, a laser tracker might measure an ADM or interferometer distance, a zenith angle, and an azimuth angle, each taken from a point on the tracker to a retroreflector reference point. 
         [0105]    In step  1660 , three dimensional coordinates are calculated for a sphere center of the target. One way to do this, as described above, is to rotate the target frame of reference to make the axes parallel to the corresponding axes of the device frame of reference. The retroreflector reference point of the retroreflector is then shifted by a specified amount in one or more directions. The values obtained for the three dimensional coordinates are the desired result. In step  1670 , this result is saved—for example in a processor or processor memory. 
         [0106]    Although the methods described hereinabove have mostly dealt with the case of cube corner retroreflectors, they are applicable to any type of retroreflector for which three orientational degrees of freedom can be obtained. A method of putting marks on or in the vicinity of the retroreflector target can be used with retroreflectors such as cateye retroreflectors and photogrammetric targets. A cateye retroreflector contains a top transmissive spherical surface and a bottom reflective spherical surface. The top and bottom spherical surfaces may have the same or different radii. One way to make a six-DOF target from a cateye is to place marks on the top spherical surface and an intermediate layer—for example a planar layer that separates an upper and a lower hemisphere of the cateye. Such marks would be decoded in a manner similar to that used with cube corner retroreflectors—by working out suitable mathematical formulas to relate the observed patterns to the three orientational degrees of freedom. In a similar manner, marks may be put on a photogrammetric dot held within a sphere. Such marks may be made on two or more levels to improve the sensitivity of the system for detecting tilt. 
         [0107]    Some types of retroreflectors have symmetries that need to be resolved before a calculation can be completed to determine the three orientational degrees of freedom. For example, a cube corner retroreflector having intersection junctions marked with identical non-reflecting portions appears to have six-fold symmetry when viewed along the axis of symmetry. A three-fold symmetry in the intersection junctions can be seen in the front views of  FIGS. 8C and 9C . Note that the lines are separated by 120 degrees. This three-fold symmetry turns into a six-fold symmetry in the light reflected by the cube corner because the light is blocked by the non-reflecting portions of the intersection junctions both for light entering and leaving the cube corner. As soon as the cube corner is tilted so that it is not viewed along the axis of symmetry, the six-fold symmetry is broken, but the requirement remains to associate at least one of the six marks in the image of the cube corner retroreflector with one of the physical intersection junctions. For example, in the pattern of  FIG. 7 , which represents the pattern of non-reflecting regions that might be seen in an orientation camera, at least one of the six non-reflecting marks must be identified as corresponding to one of the physical intersection junctions of the cube corner retroreflector. 
         [0108]    The association between the physical marks and the pattern reflected by the retroreflector is found from the coarse orientation of the target. The association may be determined by a variety of methods, five of which are described here. A first method uses a reference mark, or feature, such as the mark  801  or  901  shown  FIGS. 8A and 9A , respectively. At the start of a measurement, the operator holds the reference mark, or feature, in a prescribed orientation. For example, the reference mark, or feature, might be held horizontal with the retroreflector pointed straight toward the tracker. The device notes the position of the non-reflecting portions and relates these to the prescribed orientation to establish a coarse orientation in the device frame of reference. This coarse orientation enables software within the device to match a particular line seen on the photosensitive array to a particular intersection junction of the cube corner. With this method, the operator is notified if the coarse orientation is lost, so that the target can be again held in the prescribed orientation to re-establish a new coarse orientation. The operator may be made aware of the need to re-establish a coarse orientation by a flashing light on the device, emitting an audible sound, or using a variety of other methods. 
         [0109]    A second method for establishing a coarse orientation uses a small reference retroreflector in the vicinity of the larger retroreflector. Such a reference retroreflector is shown as element  1708  in FIG. 17 of the &#39;758 patent. A reference retroreflector may be located in a variety of positions near a larger retroreflector. In the present application, for example, a reference retroreflector may be located in position  822  of  FIG. 8D  or position  922  of  FIG. 9D . 
         [0110]    One mode for using a reference retroreflector to establish a coarse orientation is to simultaneously illuminate both the reference retroreflector and the larger retroreflector. This may be done, for example, by flashing the light sources  54  near orientation cameras  52 . If the laser tracker  10  is relatively close to the target, the locator camera will be able to distinguish the relative positions of the two light sources, thereby establishing the coarse orientation. 
         [0111]    A second mode for using a reference retroreflector to establish a coarse orientation is to begin by moving the laser beam from the tracker to a first steering angle (comprising a first azimuth angle and a first zenith angle) to center the laser beam on the larger retroreflector. The tracker then moves the beam away from the center of the retroreflector by the distance from the larger target to the smaller target. The laser tracker does this by moving the laser beam by an angle in radians equal to a distance, known in advance from the target dimensions, divided by the distance from the tracker to the retroreflector target. After the laser beam has been moved away from the center, it is rotated in a circular pattern about the initial center point until the smaller retroreflector is intercepted. The laser beam is then centered on the smaller target to obtain a second steering angle (comprising a second azimuth angle and a second zenith angle). The coarse orientation is determined from the relative values of the first and second steering angles. This second mode for using a reference retroreflector is useful when the distance to the target is too large to be accurately measured with the locator cameras  52 . 
         [0112]    A third method for establishing a coarse orientation is to use a target light, which might be an LED, located in position  822  or  922 . Such a target light is illuminated to enable a locator camera, such as the locator camera  52 , to view the position of the target light relative to the retroreflector. In this way, the location of a feature of the retroreflector, such as an intersection junction, for example, may be tagged by the target light. 
         [0113]    A fourth method for establishing a coarse orientation is to use a region of reflective material, which may be located at positions  822  or  922 , for example. In general, most reflective materials do not reflect light in so narrow a beam width as a retroreflector such as a cube corner or high quality cateye. Because of this disparity in reflectance, the reflective material may require a much larger exposure than would a cube corner or cateye. Such a long exposure may result in blooming of the image on the photosensitive array of the locator camera. To get around this problem, at least one light may be placed relatively near to the lens system of the locator camera  52  and at least one light may be placed relatively far from the lens system. As shown in FIGS. 17A-C of the &#39;758 patent, a light must be placed relatively close to the locator camera for the light to be captured by the locator camera. On the other hand, because reflective materials, even those that are intended to be highly reflective or “retroreflective”, reflect light at a relatively large angle, a light that is relatively far from a locator camera will succeed in reflecting light off the reflective material and into the locator camera. Such an arrangement is shown in  FIGS. 17A-B .  FIG. 17A  shows a locator camera/illumination system  1700  that includes a locator camera/illumination system  1710  and a more distance light source  1720 . The locator camera/illumination system  1710  includes a locator camera  1712  and at least one light source  1714 . The locator camera may include a lens system (not shown) and a photosensitive array (not shown).  FIG. 17B  shows two locator camera/illumination systems  1700  placed on the two sides of the entrance/exit aperture  1760  of the device. 
         [0114]      FIGS. 18A-B  depict the principle behind the method described hereinabove. In  FIG. 18A , light from a light source  1810  is reflected off retroreflector  1820 , which might be any type of retroreflector. For a high quality retroreflector such as a cube corner retroreflector, each ray of light results in a parallel ray of light reflected backwards. If a ray of light is incident on the retroreflector, but offset with respect to the retroreflector reference point (e.g., vertex), then the reflected ray of light will be offset by the same amount on the other side of the retroreflector reference point. Hence, as shown in  FIG. 18A , a light source  1810  located far from the locator camera  1830  cannot illuminate a retroreflector  1820  in a way that causes reflected light to be captured by the lens  1832  and photosensitive array  1836 . On the other hand, as shown in  FIG. 18B , a light source  1810  located far from the locator camera  1830  can illuminate a region of reflective material  1860  in a way that causes reflected light to be captured by the lens  1832  and photosensitive array  1836 . Hence by flashing a light close to the tracker, the position of the retroreflector can be identified. By flashing a light far from the tracker, the position of the reflective region can be identified. In the latter case, the illumination can be left on as long as desired since the light from the cube corner retroreflector will not be present to saturate the locator camera and cause blooming. 
         [0115]    In general, it is only necessary to determine the coarse orientation when the laser tracker has stopped measuring a target for a period of time. During continuous measurement, the position of the retroreflector is known to relatively high accuracy based on the previous measurement, and so a coarse measurement is not needed. 
         [0116]      FIG. 19  shows electrical and computing components within and outside the laser tracker  10 . These electrical and computing components are merely representative, and it should be understood that other configurations are possible. A master processor  1970  sends and receives data messages to processors within the laser tracker. These messages may be sent over a wired, optical, or wireless device bus  1930 . Processing may be independently carried out for functions within the laser tracker. For example, there may be a position detector processor  1912 , azimuth encoder processor  1914 , zenith encoder processor  1916 , ADM processor  1920 , interferometer processor  1922 , locator and orientation cameras processor  1924 , six-DOF processor  1926 , indicator lights processor  1918 , and RFID and wireless processor  1928 . The RFID and wireless processor  1928  may be connected to an antenna  1929  for emitting or receiving radio frequency (RF) signals. The master processor  1970  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  1944 ,  1942 . 
         [0117]    Many of the elements described in  FIGS. 8D and 9D  can be similarly applied to a target having a probing extension.  FIGS. 20A-C  depict an exemplary six-DOF target, or probe assembly  2000 , having a probe tip  2060  and a probe extension  2050 . A housing  2010  holds a retroreflector  2020 . Housing  2010  may contain a reference feature  2030  such as a reference mark, a reference retroreflector, a region of reflective material, or a target light source. It may contain a battery (not shown) connected to a compact circuit board holding electrical components (not shown). An antenna  2090  or light source may be connected to the circuit board to enable transmission of wireless messages using electromagnetic signals. Actuator buttons  2040 ,  2042  may be connected to the circuit board to enable the operator to send wireless messages to the laser tracker or other device. 
         [0118]    A material temperature sensor  2080  attached to the circuit board may be connected to the retroreflector  2020  or housing  2010  to measure the temperature and use this information to correct the measured position of  2060  to account for thermal expansion or thermal changes in the index of refraction. An air temperature sensor assembly  2070  may be used to measure the temperature of the air as a function of location within the measurement volume. The air temperature assembly  2070  includes an air temperature sensor  2072 , a protector  2074 , and an insulator  2076 . The temperature sensor may be a thermistor, RTD, thermocouple, or any other device capable of measuring temperature. It may be placed in a protector structure, which might be a hollow cylinder, for example. The purpose of the protector is to keep the temperature sensor from being damaged and to keep heat sources away from the temperature sensor. The protector is open at the end and may contain perforations to increase exposure of the temperature sensor to air. Insulation  2076  is provided between the housing  2010  and the air temperature sensor  2072 . The insulation keeps the sensor from being exposed to the metal of the target, which may be at a different temperature than the surrounding air. The uses of the air temperature sensor are similar to those described hereinabove with regard to  FIGS. 8D and 9D . 
         [0119]    An electrical memory component on the electrical circuit board may be used as an identifier to send information stored on the memory component to a transmitter on the electrical circuit board that sends the information over the antenna  2090  or over a light source. Such information might include a serial number to identify the target or at least one parameter. The parameter may indicate, for example, geometrical, optical, or thermal properties of the target. Alternatively, identification information may be stored on a bar-code pattern or an RFID tag. The bar-code pattern may be read by a locator camera disposed on the tracker and the RFID tag may be read by an RF reader on the laser tracker or other device. 
         [0120]      FIGS. 21A-C  depict another embodiment for a six-DOF target, or probe assembly  2100 . This probe is similar to that described hereinabove with regard to  FIGS. 20A-C  except that the probe extension  2150  is tilted at an arbitrary angle and locked in place with knob  2160 . The components  2120 ,  2130 ,  2140 ,  2142 ,  2170 ,  2180 ,  2190 , and  2195  perform the same function as the components  2020 ,  2030 ,  2040 ,  2042 ,  2070 ,  2080 ,  2090 , and  2095 , respectively, as described hereinabove. 
         [0121]    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. 
         [0122]    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.