Abstract:
An optical camera three-dimensional coordinate measuring system for use with objects to be measured is described. The system may include a compact, easily moveable, and rotatable, target of known dimensions comprising a spherical surface to be placed in contact with the object to be measured at different points along the object to be measured thereby eliminating the necessity of using a larger extended probe contact tip extending from the target to the object to be measured. At least one or more light emitting source may be located in a known position in the target such as the center of the spherical surface for example. At least two cameras located at different and known coordinate locations for receiving light from the light emitting source from different optical perspectives may be included. The position in three dimensional coordinates of the object to be measured is computed from the images taken by the cameras.

Description:
CROSS REFERENCE  
       [0001]     This application claims the benefit of priority to U.S. Provisional Patent Application Ser. No. 60/670,217, filed Apr. 11, 2005, the entire contents of which are specifically incorporated herein by reference. 
     
    
     BACKGROUND  
       [0002]     There is a class of portable devices that accurately measure three-dimensional coordinates to a range of several tens of meters. Such devices are ordinarily referred to as portable large-scale coordinate-measuring machines (CMMs). One type of portable CMM is the laser tracker. It sends a laser beam to a retroreflector target, which may be a spherically mounted retroreflector (SMR) comprising a cube-corner retroreflector centered within a sphere that is moved over the surface of interest. Alternatively the target may be a retroprobe, which comprises a cube-corner retroreflector positioned near a mirror to form a virtual image of a probe tip (U.S. Pat. No. 5,530,549).  
         [0003]     A second category of portable CMM is the camera and multiple-light probe (U.S. Pat. No. 5,440,392). This device comprises a probe, which contains a probe tip and at least three point sources of light, together with one or more cameras that view the point sources of light. The image pattern on the camera is used to determine the position of the probe tip in space.  
         [0004]     A third category of portable CMM is the laser tracker with a separate but nearby camera. (U.S. Pat. No. 5,973,788). This device comprises the laser tracker, a camera mounted near the laser tracker, and a probe. The probe comprises a probe tip, at least three point sources of light, and a retroreflector. A laser beam from the laser tracker measures the three-dimensional coordinates of the retroreflector. At the same time, the camera measures the three-dimensional coordinates of the light sources on the probe. The information from these measurements allows the coordinates of the probe-tip in space to be determined. A related idea (U.S. Pat. No. 5,973,788) is to embed the camera into a laser tracker that also contains an absolute distance meter.  
         [0005]     Four attributes are desirable in a portable CMM: (1) low price, (2) high accuracy, (3) rapid data collection, and (4) ease-of-use. Today the least expensive of these devices costs nearly $100,000. Some devices collect data too slowly to be used to efficiency determine the coordinates of three-dimensional contours. Other devices have relatively poor accuracy. There is a need today for a new type of instrument that is fast, accurate, and much less expensive than current portable CMMs.  
         [0006]     Some advantages of the present three-dimensional coordinate measuring device compared to prior art are discussed herein, however this is not intended to be a limiting or exhaustive listing of advantages. There are several companies that make camera-based metrology systems. One of the highest accuracy Metronor systems uses two cameras, which can be placed on a factory floor for example. In this respect, the Metronor system is like the present device. However, the Metronor system is based on a probe with a tip that is not illuminated. The find the location of this tip, the Metronor system must be capable of accurately determining the pitch, roll, and yaw angles of the probe from the camera images of multiple LEDs located on the probe. To make possible the required accuracy, Metronor makes their probes large enough to cover a relatively large fraction of the field of view of the cameras. Such large probes are cumbersome to manage. Furthermore, the probes need to be stiff and fixed in length over temperature, which means using expensive composite materials.  
         [0007]     In most cases a different kind of probe such as the embodiments described below which are not currently used by any camera-based system, would be more useful, convenient, and cost effective than an extended probe such as Metronor&#39;s. The simplest such device—the sphere with a light source placed at its center—takes advantage of the fact that the distance from the center to the edge of a sphere is a constant. Thus, the sphere body acts like a spacer of known dimensions between the object to be measured and the light source. Also, the sphere can be turned in any direction. Because of this fact, the spherically mounted light source can be used to measure the contour of almost any object. In some cases, a handle will be also convenient. A similar idea from symmetry leads to the fiducial target, which will typically be put into a pre-established tooling hole. In this case, the light source is located on the rotational axis of symmetry of the target. By measuring the target, it is therefore possible to determine the three-dimensional coordinate of the hole on the tool.  
         [0008]     One thing that all of the targets—sphere, probe-mount, fiducial, wide-angle, or retroprobe target—have in common is that all emit light over a wide angle from a single point in space. All of the prior art camera-based probes use multiple points of light. Thus, it has not been obvious to those skilled in the art that such useful and accurate probes could be devised based on a single point-of-light. Proof of this fact is that people have been making camera-based metrology systems for years and that no one has yet implemented such as system, which arguably can be made less expensively and with equal or higher accuracy.  
       SUMMARY OF INVENTION  
       [0009]     An optical camera three-dimensional coordinate measuring system for use with objects to be measured may comprise a compact, easily moveable, and rotatable, target of known dimensions comprising a spherical surface to be placed in direct contact with the object to be measured at different points along the object to be measured thereby eliminating the necessity of using a larger extended probe contact tip extending from the target to the object to be measured; at least one or more light emitting source located in a known position in the target and wherein the light emitting source is located at the spherical center of the target having a spherical surface; at least two cameras located at different and known coordinate locations for receiving light from the light emitting source from different optical perspectives; and a processor for computing the position in three dimensional coordinates of the object to be measured from images of the light emitting source on the cameras, from the known positions of the cameras, from the known dimensions of the target, and from the known position of the light emitting source in the target.  
         [0010]     Another embodiment, may comprise a Coordinate Measurement Machine (CMM) for use with objects to be measured comprising: a spherical or cylindrical shaped geometric target of known dimensions to be placed in contact with the object to be measured at different points along the object to be measured; at least one or more light emitting diode (LED) light source located at a point of symmetry on the spherical or cylindrical shaped geometric target; at least two photosensitive cameras located at different and known coordinate locations for receiving light from the light emitting diode (LED) light source from different optical perspectives; a processor for computing the position in three dimensional coordinates of the object to be measured from images of the light emitting diode (LED) light source recorded on the cameras, from the known positions of the cameras, from the known dimensions of the spherical or cylindrical shaped geometric target, and from the known position of the light emitting source located in the spherical or cylindrical geometric target; wherein the at least two cameras each include at least one or more photosensitive arrays which are used to determine coordinates of the object to be measured from the recorded images of the light emitting diode (LED) light source on the photosensitive arrays that the light from light emitting diode (LED) light source is incident upon.  
         [0011]     Another embodiment may comprise an optical camera three-dimensional coordinate measuring method for measuring objects comprising: placing a compact, easily moveable, and rotatable, target of known dimensions comprising a spherical surface in direct contact with the object to be measured at different points along the object to be measured thereby eliminating the necessity of using a larger extended probe contact tip extending from the target to the object to be measured; emitting light from the target form at least one or more light emitting source located in a known position in the target; recording images of the light source at least two cameras located at different and known coordinate locations for receiving light from the light emitting source from different optical perspectives; and computing the position in three dimensional coordinates of the object to be measured from images of the light emitting source on the cameras, from the known positions of the cameras, from the known dimensions of the target, and from the known position of the light emitting source in the target.  
         [0012]     Another embodiment may be an optical camera three-dimensional coordinate measuring system for use with objects to be measured comprising: a compact, easily moveable, and rotatable, target of known dimensions comprising a cylindrical surface to be placed in at least one or more holes in the object to be measured thereby eliminating the necessity of using a larger extended probe contact tip extending from the target to the object to be measured; at least one or more light emitting sources wherein the light emitting source is located at a known position along an axis of cylindrical symmetry; at least two cameras located at different and known coordinate locations for receiving light from the light emitting source from different optical perspectives; and a processor for computing the position in three dimensional coordinates of the object to be measured from images of the light emitting source on the cameras, from the known positions of the cameras, from the known dimensions of the target, and from the known position of the light emitting source in the target. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0013]     Referring now to the drawings, exemplary embodiments are shown which should not be construed to be limiting regarding the entire scope of the disclosure, and wherein the elements are numbered alike in several FIGURES:  
         [0014]      FIG. 1  is a perspective view of an exemplary three-dimensional measuring device; and  
         [0015]      FIG. 2  is a block diagram of some of the main elements within the exemplary emitter of  FIG. 1 ; and  
         [0016]      FIGS. 3A, 3B , and  3 C are perspective views of three embodiments of exemplary emitter of  FIG. 2 ; and  
         [0017]      FIGS. 4A, 4B , and  4 C are perspective views of transparent spherical shell segments that may be affixed to the three emitter embodiments shown in  FIG. 3  to protect the light sources from dust and dirt; and  
         [0018]      FIG. 5  shows a side view and a cross-sectional view of exemplary spherically mounted wide-angle emitter; and  
         [0019]      FIGS. 6A, 6B , and  6 C show sectional views of the emitter ball within the wide-angle emitter and the path of light rays within the spherical cavity of the emitter ball; and  
         [0020]      FIG. 7  shows a perspective view of exemplary retroprobe emitter; and  
         [0021]      FIG. 8  is a block diagram of some of the main elements of the cameras within the system; and  
         [0022]      FIG. 9  is a perspective view of the a first embodiment of the imaging block within the cameras wherein the images are formed with a beam splitter, cylindrical lenses, and linear photosensitive arrays; and  
         [0023]      FIG. 10  is a perspective view of a second embodiment of the imaging block within the cameras wherein the images are formed with spherical optics and an area photosensitive array; and  
         [0024]      FIG. 11  is a perspective view of a tooling ball and nest. 
     
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS  
       [0025]     Three-dimensional coordinate measuring device  100  shown in  FIG. 1  comprises two or more cameras  400 A,  400 B, computing interface  500 , and emitter  200 , which may be implemented as spherically mounted emitter  210 , probe mounted emitter  220 , fiducial emitter  230 , wide-angle emitter  240 , or retroprobe emitter  260 .  
         [0000]     Emitter  
         [0026]     As shown in  FIG. 2 , emitter  200  comprises light source  202 , rigid probe structure  204 , and wire  206 . The light source preferably emits light over a broad angle from a small spot in space. An example of a light source is a wide-angle light emitting diode (LED) but the invention is not limited to LED light sources as any suitable light source may be used.  
         [0027]     Electronic signaling means  180  comprises power source  182 , pulser  184 , transceiver  185 , antenna  186 , and operator control unit  188 . Power source  182  may be a battery or a plug for AC power. Pulser  184  sends an electronic signal over wire  206  that causes light source  202  to flash. The timing, duration, and intensity of pulses generated by pulser  184  may be controlled in one of three ways: (1) by a signal received through antenna  186 , (2) by a signal initiated when the operator presses a button on operator control unit  188 , or (3) by a predetermined signal pattern. Electronic signaling means  180  may be embedded within rigid probe structure  204 , carried by the operator, or put on the floor. Antenna  186  intercepts electromagnetic energy such as radio frequency (RF) or infrared energy. As an alternative embodiment, antenna  186  may be replaced by a wire connected to a computing device or remote control unit.  
         [0028]      FIG. 3  shows three embodiments of emitter  200 : spherically mounted emitter  210 , probe mounted emitter  220 , and fiducial emitter  230 . Spherically mounted emitter  210  comprises partial sphere  212 , light source  214 , and wire  216 . Partial sphere  212  is a sphere in which a segment has been removed. It is preferably made of steel so that it can be held in place by a magnetic nest. Light source  214  is positioned in the center of partial sphere  212 . Wire  216  connects light source  214  to electronic signaling means  180  (shown in  FIG. 2 ).  
         [0029]     Probe mounted emitter  220  comprises small partial sphere  222 , light source  223 , wire  224 , probe body  225 , rotating shaft  226 , and locking mechanism  227 . Light source  223  is positioned in the center of small partial sphere  222 . Wire  224  connects light source  223  to electronic signaling means  180  (shown in  FIG. 2 ), which preferably is enclosed within probe body  225 . Power source  182  preferably is a battery and operator control unit  188  preferably is integrated into probe body  225 . Rotating shaft  226  can be turned through a range of angles and locked into place with locking mechanism  227 .  
         [0030]     Fiducial emitter  230  comprises light source  232 , crown  234 , shank  236 , and wire  238 . Light source  232  is positioned along the cylindrical axis of symmetry of shank  236  and crown  234 . Shank  236  sits inside a fiducial tooling hole that is formed in object  140 . The bottom of crown  234  makes contact with the surface of the object  140 . Light source  232  is positioned so that it sits a fixed distance above the surface of object  140 . Wire  238  connects light source  232  to electronic signaling means  180 .  
         [0031]     Portable large-scale CMMs are often used in dirty industrial environments where particulate matter is scattered throughout the air. If a particle settles over one of the light sources in the emitters of  FIG. 3 , it may partially or totally block the light from the light source. To avoid this problem, a symmetrical transparent cover can be centered over the light source. An optional attachment to spherically mounted emitter  210  is transparent spherical shell segment  219  shown in  FIG. 4 . Spherical shell segment  219  is drawn in normal and reversed view to show the internal structure of the shell. The spherical surfaces of spherical shell segment  219  are centered on the center of spherical surface  212  shown in  FIG. 3 . Light emitted by light source  214  then travels in straight rays through spherical shell segment  219 . Spherical shell segment  229  is optionally attached to spherically mounted probe  220  and spherical shell segment  239  is optionally attached to fiducial emitter  230 .  
         [0032]     A fourth embodiment of emitter  200  is the wide-angle emitter  240 , shown in perspective view in  FIGS. 1 and 5  and in cross-sectional view through the center of the emitter in  FIG. 5 . Wide-angle emitter  240  comprises emitter ball  250 , shaft  242 , electronics cavity  244 , spherical base segment  246 , and optional handle  248 . The intensity of light from wide-angle emitter  240  is nearly the same in all directions. Emitter ball  250  is centered on the lower surface of spherical base segment  246 . In other words, the distance from the center of emitter ball  250  to the outer surface of spherical base segment  246  is equal to the radius of spherical base segment  246 .  
         [0033]     Emitter ball  250 , shown in central cross section in  FIG. 6 ( a ), comprises upper transparent hemispherical shell  251 , lower transparent hemispherical shell  252 , and wide-angle light source  255 . Upper and lower hemispherical shells  251  and  252  are joined together with index-matching cement to form hollow spherical cavity  253 . Spherical cavity  253  is covered with a coating  254  comprising multiple thin layers of hard dielectric material that transmits a small fraction of the light from the light source, say one or two percent, and reflects the rest of the light with very little loss. Wide-angle light source  255  is mounted near the bottom of spherical cavity  253 . Electrical wires attached to the light source are routed through opening  259  drilled into lower hemispherical shell  252 .  
         [0034]      FIG. 6 ( b ) depicts the rays of light  256  that emerge from wide-angle light source  255 . For a wide-angle light source in the form of a light-emitting diode (LED), the emitted light typically has a half-power full angle of about 120 degrees. The wide angular spread of light from light source  255  is shown in  FIG. 6 ( b ). Because the surface of cavity  253  is coated to be highly reflective, only a small amount of light passes through transparent hemispherical shells  251  and  252 . Most of the remaining light is reflected except for a small amount that is absorbed.  FIG. 6 ( c ) shows how a particular ray of light  257 A reflects as rays off the surface of cavity  253  in the following order:  257 B,  257 C, and  257 D. The reflections continue until all of the light has been transmitted through hemispherical shells  251  and  252  or absorbed by the glass or coating. The rays of light  257 A,  257 B,  257 C,  257 D, and so forth cover widely spaced points on the surface of spherical cavity  253 . After reflection, the rays  256  will be dispersed over the surface of spherical cavity  253 . As a result of the wide-angular spread of light from light source  255  and the high reflectance of light from dielectric coating  254 , the power of the light source light per unit area is nearly constant over the surface of spherical cavity  253 . Furthermore, the light rays do not in general strike the surface of cavity  253  at normal incidence. As a result, the light transmitted through cavity surface  253  are refracted in all different directions with respect to the incident beam and again refracted at all different directions by the outer surfaces of hemispherical shells  251  and  252 . To cameras  400 A and  400 B, emitter ball  251  appears as a diffusely illuminated circle having a diameter equal to that of the spherical cavity  253 . The position of the centroid of the illuminated cavity  253  when viewed from the position of either camera will be nearly the same as the geometrical center of the cavity. There will be some slight variation in the position of the centroid as emitter ball  250  is tilted with respect to the cameras.  
         [0035]     To obtain the most accurate measurements with wide-angle emitter  240 , the diameter of cavity  253  should be made as small as practical; a diameter of 1 mm is reasonable. In addition, dielectric coating  254  should be designed to have high reflectance with low loss at the light source wavelength. If the transmittance per pass is 1% and the reflectance is nearly 99%, then the variation in optical power per unit area over the surface of the cavity is small. Using these techniques, it should be possible to build a wide-angle emitter that operates over an angular field-of-view of 230 or 240 degrees with an error in centroid position of not more than about 10 micrometers over the range of angles. Wide-angle emitter  240  is advantageous when multiple cameras are stationed to view a target over a variety of angles. This measurement situation is discussed below. Electronics and battery for wide-angle emitter  240  may be stored in electronics cavity  244  or in handle  248 . Alternatively electronics and power may be provided by a wire from a remote location.  
         [0036]     A fifth embodiment of emitter  200  is the retroprobe emitter  260 , shown in perspective view in  FIGS. 1 and 7 . Retroprobe emitter  260  comprises light source  261 , baffle  262 , light source support  263 , mirror  264 , probe shaft  265 , and probe tip  266 . Light beam  270  emanates from light source  261 , reflects off mirror  264 , and travels as light beam  271  to camera  400 A. Light beam  272  emanates from light source  261 , reflects off mirror  264 , and travels as light beam  273  to camera  400 B. Probe tip  266  is located at the position of the virtual image of light source  261  formed by mirror  264 . In other words, a line drawn between probe tip  266  and light source  261  bisects the reflecting surface of mirror  264  in a right angle. Baffle  262  blocks light from light source  261  from directly reaching camera  400 A or  400 B. The cameras therefore see the light source as emanating from point  266 . This configuration is advantageous because probe tip  266  can reach points for which a light source is not visible to both cameras  400 A,  400 B.  
         [0000]     Camera  
         [0037]     A block diagram of camera  400 A, which is identical to camera  400 B, is shown in  FIG. 8 . Camera  400 A comprises imaging block  410  and electrical block  430 . There are two embodiments of imaging block  410 . The first embodiment is linear imaging block  800  shown in  FIG. 9 . Linear imaging block  800  comprises optical bandpass filter  814 , beam splitter  816 , first and second apertures  820 A,  820 B, first and second cylindrical lens assemblies  830 A,  830 B, and first and second linear photosensitive arrays  840 A,  840 B. The purpose of optical bandpass filter  814  is to eliminate background light outside the wavelength range of light source  202 . This improves the signal-to-noise ratio of photosensitive array  840 A,  840 B. An alternative to optical bandpass filter  814  is to coat the surfaces of first and second lens assemblies  830 A,  830 B to filter out unwanted wavelengths.  
         [0038]     Optical axis  310  goes through the centers of beam splitter  816 , first aperture  820 A, first cylindrical lens assembly  830 A, and first linear photosensitive array  840 A. The reflection of optical axis  310  off of beam splitter  816  goes through the centers of second aperture  820 B, second cylindrical lens assembly  830 B, and second linear photosensitive array  840 B. Light ray  314  emerges from source of light  202  and travels to linear imaging block  800 , as shown in  FIG. 9 . First aperture  820 A permits only some of the light to enter the first cylindrical lens assembly  840 A. First cylindrical lens assembly  830 A may be composed of from one to several individual lens elements combined in a rigid structure. It is even possible to omit lens assembly  830 A altogether, which results in a type of pinhole camera. Aperture  820 A may be located between or outside the lens elements within cylindrical lens assembly  840 A. First cylindrical lens assembly  830 A has focusing strength in the y direction but not in the x direction. In other words, first cylindrical lens assembly will tend to focus light in the y direction but leave it unaffected in the x direction. Consequently light entering first cylindrical lens assembly  830 A will form line  854 A extending in the x direction.  
         [0039]     Light source  202  is at coordinates (x 0 , y 0 , z 0 ) relative to some global frame of reference within the measurement environment of  FIG. 1 . Ray of light  314  is split by beam splitter  816 . To find the beam images, consider the rays that pass through the optical centers of cylindrical lens assemblies  830 A,  830 B. The centroids of lines of light  854 A,  854 B form at approximately fa y ,fa x  where f is the focal length of cylindrical lens assembly  830 A and a y , a x  are the angles in the y, x directions that ray  314  makes with respect to optical axis  310 . The actual centroids are at slightly different positions than fa y , fa x  because of aberrations in the lens system. Correction values are applied to each point to compensate for these aberrations. The correction values are determined through measurements made one time at the factory.  
         [0040]     It is important to minimize the amount of background light that illuminates linear photosensitive arrays  840 A,  840 B. One method of reducing background light has already been discussed—adding optical bandpass filter  814  or coating cylindrical optical lens assembly  830 A,  830 B to reject unwanted wavelengths. Another method of reducing background light is to synchronize the integration time of linear photosensitive arrays  840 A,  840 B to correspond to the flashing of light source  202 .  
         [0041]     The second embodiment of imaging block  410  is area imaging block  900  shown in  FIG. 10 . Area imaging block  900  comprises optical bandpass filter  914 , aperture  920 , spherical lens assemblies  930 , and area photosensitive array  940 . The purpose of optical bandpass filter  914  is to eliminate background light outside the wavelength range of light source  202 . This improves the signal-to-noise ratio of photosensitive array  940 . An alternative to optical bandpass filter  914  is to coat the surfaces of lens assembly  930  to filter out unwanted wavelengths.  
         [0042]     Optical axis  310  goes through the centers of optical bandpass filter  914 , aperture  920 , spherical lens assembly  930 , and area photosensitive array  940 . Light ray  314  emerges from source of light  202  and travels to area imaging block  900  as shown in  FIG. 10 . Aperture  920  permits only some of the light to enter the spherical lens assembly  930 . Spherical lens assembly  930  may be composed of from one to several individual lens elements combined in a rigid structure. It is even possible to omit lens system  930  altogether, which results in a pinhole camera. Aperture  920  may be located between or outside the lens elements within spherical lens assembly  940 .  
         [0043]     Spherical lens assembly  930  has the same focusing strength in the x and y directions. Consequently light entering spherical lens assembly  930  forms a small spot at point  953  on area photosensitive array  940 . To find the position of point  953 , the ray of light  314  from light source  202  is drawn through the optical center of spherical lens assembly  930 . Usually the distance from camera  400 A,  400 B is much larger than the focal length of the lens systems within the cameras. In this case, the point of light  953  is formed at approximately the focal length f away from the effective center of cylindrical lens system  930 . If the center of photosensitive array  940  is at position (x, y)=(0, 0), then point  953  is located on array  930  at approximately the coordinates (fa x ,fa y ), where a x , a y  are the angles of ray  310  with respect to optical axis  314 . The diameter of aperture  920  is set small enough to minimize aberrations without reducing optical power too much.  
         [0044]     The position of the centroid of point of light  953  is calculated from the pixel response of area photosensitive array  940 . In general, it is necessary to correct this position to account for the effect of optical aberrations. The correction values are determined through measurements made one time at the factory.  
         [0045]     It is important to minimize the amount of background light that illuminates area photosensitive array  940 . One method of reducing background light has already been discussed—adding optical bandpass filter  914  or coating spherical optical lens assembly  930  to reject unwanted wavelengths. Another method of reducing background light is to synchronize the integration time of area photosensitive array  940  to correspond to the flashing of light source  202 .  
         [0046]     Electrical block  430  in  FIG. 8  comprises conditioner  432  and computing means  434 . The main purpose of conditioner  432  is to produce digital signals suitable for processing by computing means  434 . If photosensitive array  420  is a CCD array, then conditioner  432  will probably contain an analog-to-digital converter and support circuitry. If photosensitive array  420  is a CMOS array, then conditioner  432  will probably not require an analog-to-digital converter and may contain only a buffer/line-driver. Data is transferred from conditioner  432  to computing means  434 , which may contain a digital signal processor (DSP), field-programmable gate array (FPGA), microprocessor, or similar computing device. The purpose of computing means  434  is to process the images on photosensitive array according to the prescription given above—finding the centroid, applying the appropriate correction factors, and performing the best-fit calculations.  
         [0047]     Computing interface  500  comprises computing means  510 , user interface  520 , transceiver  530 , and antenna  540 . Data is sent from computing means  434  to computing means  510 . At the same time, data is sent from the corresponding computing means in camera  400 B. These two cameras provide information on the angles to light source  202 .  
         [0048]     Coordination is required between the pulsing of light source  202 , the exposure and reading of data from photosensitive array  840 A,  840 B, or  940 , and the computation by computing means  434  and  510 . The timing signals for this coordination may be triggered in one of three ways: (1) by a signal received through antenna  186  or a wire that takes the place of antenna  186 , (2) by a signal initiated when the operator presses a button on operator control unit  188 , or (3) by a predetermined signal pattern.  
         [0000]     Calculations  
         [0049]     The objective of three-dimensional coordinate measuring device  100  is to determine the position of the moving emitter  200 . This is done in two phases—the resection phase and the intersection phase. In the resection phase, the position and orientation of the cameras is determined. One of the two cameras is taken to be at the origin (x, y, z)=(0, 0, 0) with orientation angles (pitch, roll, and yaw) equal to zero. The position and orientation of the second camera is found by measuring points of light having a known distance between the points. This is done several times with the points located at different distances and positions relative to the cameras. It is necessary to measure points separated by known distances in the resection phase to establish the scale of the camera. This is conveniently done with an artifact made of a low CTE material such as composite material or Invar. Two or more light sources are mounted on the artifact. In the intersection phase, the coordinates of the emitter are determined at the frame rate of the camera as the emitter is moved from point to point.  
         [0050]     In both resection and intersection measurements, best-fit mathematics are used to determine the required coordinates and orientations. These mathematical techniques are well known to workers in photogrammetry and surveying. Numerous books and papers have been written on this subject, so further discussion is not given here.  
         [0000]     Measurement  
         [0051]     Most of the important dimensional characteristics of object  140  can be measured with coordinate measuring device  100 . The surface contours of object  140  can be determined by moving spherically mounted light source  210  over the surface of object  140  while light source  214  flashes rapidly at regular intervals. Because light source  214  is located in the center of partial sphere  212 , the distance from light source  214  to the surface of object  140  is constant, regardless of the pitch, yaw, or roll angle of spherically mounted light source  210 . The constant distance is removed from the coordinate readings to determine the coordinates of the surface. By measuring the surface contour of a flat object, it is possible to determine the flatness of the object—in other words, how much the surface deviates from an ideal plane. By measuring two flat objects, it is possible to determine the angle between the surface planes. By measuring a spherical surface, it is possible to determine the center and diameter of the sphere. Probe-mounted emitter  220  can be used to measure the surface contour of a small object or an object with fine detail.  
         [0052]     A convenient method of making measurements over a large footprint (say, 15 meters on a side) is to use wide-angle emitter  240  in combination with multiple fixed cameras each having a wide field-of-view. As wide-angle emitter  240  is moved, it is viewed continually by the cameras. The operator measures on all sides of the object without the need to relocate the cameras or perform additional resection procedures.  
         [0053]     It is common practice to place fiducial points on tools used the assembly and characterization of automobiles, airplanes, scientific structures, and similar objects. One use of the fiducial points is to monitor whether the object dimensions change over time. Such dimensional changes may result from mechanical shock or from changes in ambient temperature. One way to establish fiducial points is to drill holes in the object at appropriate locations. Probes, such as tooling ball  160  or fiducial emitter  230 , are placed in the hole. Tooling ball  160 , shown in FIGS.  1  and  11 , comprises sphere  162 , crown  164 , and shank  166 . When shank  166  is placed in a fiducial tooling hole, the center of sphere  162  is a fixed distance above the top of the hole. Spherically mounted light source  210  or probe-mounted light source  220  can be used to measure the contour of sphere  162 . From this, the center of the tooling hole can be determined. Fiducial emitter  230  has already been described. Light source  232  is located at the position corresponding to the center of sphere  162 . Because of this, the location of the tooling hole can be determined and is not affected by the orientation of fiducial emitter  230  in the tooling hole.  
         [0054]     Another way to establish fiducial points is to attach nests to objects or their surroundings. Magnetic nest  150  is shown in  FIGS. 1 and 11 . It comprises the nest body (shown in  FIG. 11 ), three spherical point contacts (not shown) within the nest body and a magnet (not shown) within the nest body. A spherical surface, when placed on the three spherical point contacts, can be rotated to any desired pitch, yaw, and roll angles about the center of the sphere. If spherically mounted light source  210  that is made of steel is placed in magnetic nest  150 , the magnet within the nest will hold the light source  210  securely in contact with the three spherical point contacts while allowing light source  210  to be rotated to any desired position. Nest  150  can be attached to an object or its surroundings by means such as screws or hot glue.  
         [0055]     Sometimes it is necessary to measure a feature that is obscured from the direct view of one or more cameras  400 A,  400 B. The retroprobe emitter  260  permits probing of such hidden features.  
         [0000]     Speed, Accuracy, and Cost  
         [0056]     Imaging block  800  provides high speed and accuracy for low cost. Consider a CCD linear array with 5000 pixels and 100% fill factor with a camera having a field-of-view of 50 degrees=0.87 radian. If the subpixel accuracy of the system is 100:1 and the geometry of the cameras produces a reduction in three-dimensional accuracy relative to angular measurements of two, then the expected three-dimensional accuracy is 0.87*2/(5000*100)=3.5 parts per million, which is as good or better than that available from any other three dimensional measurement system available today. Measurement speed is 10,000 Hz, which is higher than most measurement systems available today.  
         [0057]     Area imaging block  900  also provides high speed and accuracy for low cost. Consider a CCD linear array with 1000 pixels and 100% fill factor with a camera having a field-of-view of 50 degrees=0.87 radian. If the subpixel accuracy of the system is 200:1 and the geometry of the cameras produces a reduction in three-dimensional accuracy relative to angular measurements of two, then the expected three-dimensional accuracy is 0.87*2/(1000*200)=8.7 parts per million, which comparable to the best three-dimensional portable coordinate-measuring machines available today. Measurement speed is about 100 Hz, which is sufficient for almost all applications as long as the light is flashed to freeze the motion of a moving emitter.  
         [0058]     Of course, there are many ways to construct the claimed displays using the principles taught herein. The specific embodiments we describe are only a few among the set of all possible constructions that fall within the scope of the claims.  
         [0059]     While the invention has been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims. Moreover, the use of the terms first, second, etc. do not denote any order or importance, but rather the terms first, second, etc. are used to distinguish one element from another. Furthermore, the use of the terms a, an, etc. do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced item.