Abstract:
A method for determining three-dimensional coordinates of an object point on a surface of an object, the method including steps of: sending a beam of light to a diffraction grating; sending a first diffracted beam and a second diffracted beam to an objective lens to form at least two spots of light, which are passed through transparent regions of a plate to produce a first fringe pattern on the surface of the object; imaging the object point illuminated by the first fringe pattern onto a photosensitive array to obtain a first electrical data value; moving the plate to a second position; sending spots through plate to produce a second fringe pattern on the surface of the object; imaging the point onto the array point to obtain a second electrical data value; and calculating the three-dimensional coordinates of the first object point.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims the benefit of U.S. Provisional Patent Application No. 61/507,771, filed on Jul. 14, 2011, the contents of which are hereby incorporated by reference in their entirety. 
    
    
     BACKGROUND 
     The present disclosure relates to a coordinate measuring device. One set of coordinate measurement devices belongs to a class of instruments that measure the three-dimensional (3D) coordinates of a point by projecting a pattern of light to an object and recording the pattern with a camera. 
     A particular type of coordinate-measuring device, sometimes referred to as an accordion-fringe interferometer, forms the projected pattern of light by the interference of light of diverging wavefronts emitted by two small, closely spaced spots of light. The resulting fringe pattern projected onto the object is analyzed to find 3D coordinates of surface points for each separate pixel within the camera. 
     An implementation of an accordion fringe interferometer is one in which a diffraction grating is moved using piezoelectric actuator, a capacitive feedback sensor, a flexure stage, multiple laser sources, and multiple objective lenses. This type of accordion fringe interferometer is relatively expensive to manufacture and relatively slow in performing measurements. What is needed is an improved method of finding 3D coordinates. 
     SUMMARY OF THE INVENTION 
     A method for determining three-dimensional coordinates of a first point on a surface of an object includes the steps of: providing a first source, a projector, and a camera, the projector including a first diffraction grating, an objective lens, and a first plate, the camera including a camera lens and a photosensitive array, the first source producing a first source beam of light, the first plate containing a first transmissive region, a second transmissive region, and at least one opaque region, the projector having a projector perspective center, the camera having a camera perspective center, a line segment between the projector perspective center and the camera perspective center being a baseline, the baseline having a baseline length. The method also includes: sending the first source beam of light to the first diffraction grating; forming with the first diffraction grating at least a first diffracted beam of light and a second diffracted beam of light; sending the first diffracted beam of light and the second diffracted beam of light to the objective lens; forming with the objective lens at least a first spot of light and a second spot of light, the first spot of light arising from the first diffracted beam of light and the second spot of light arising from the second diffracted beam of light; placing the first plate in a first position near the first spot of light and the second spot of light. The method further includes: passing first light from the first spot of light through a first thickness of glass in the first transmissive region and passing second light from the second spot of light through a second thickness of glass in the second transmissive region while keeping other light from passing the first plate, a difference in the first thickness and the second thickness equal to a first thickness difference; combining the first light and the second light to produce a first fringe pattern on the surface of the object; imaging the first object point illuminated by the first fringe pattern onto an array point on a photosensitive array to obtain a first electrical data value from the photosensitive array; moving the first plate to a second position; passing third light from the first spot of light through a third thickness of glass in the first transmissive region and passing fourth light from the second spot of light through a fourth thickness of glass in the second transmissive region while keeping other light from passing the first plate, a difference in the third thickness and the fourth thickness equal to a second thickness difference, the second fringe difference not equal to the first fringe difference; combining the third light and the fourth light on the surface of the object to produce a second fringe pattern on the surface of the object, the first fringe pattern and the second fringe pattern having a first fringe pitch at the first object point; imaging the first object point illuminated by the second fringe pattern onto the array point to obtain a second electrical data value from the photosensitive array; calculating the three-dimensional coordinates of the first object point based at least in part on the first electrical data value, the second electrical data value, and the baseline length; and storing the three-dimensional coordinates of the first object point. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       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: 
         FIG. 1  is a schematic diagram illustrating the triangulation principle of operation of a 3D measuring device; 
         FIG. 2  is a block diagram showing elements of an exemplary projector in accordance with an embodiment of the present invention; 
         FIG. 3  is a schematic diagram showing the main elements of an exemplary projector in accordance with an embodiment of the present invention; 
         FIGS. 4 ,  4 A, and  4 B are drawings showing a front view, first sectional view, and second sectional view, respectively, of a phase shifter and pinhole object; 
         FIG. 5  is a schematic drawing showing elements of a motorized stage that moves a phase/fringe adjuster in accordance with an embodiment of the present invention; 
         FIG. 6  is a drawing that shows the geometry of a ray of light passing through a tilted and wedged window; 
         FIG. 7  is a drawing showing the geometry of rays of light passing through an assembly that includes three wedged windows in accordance with an embodiment of the present invention; 
         FIG. 8  is a drawing showing the geometry of rays of light passing through an assembly that includes three wedged windows in accordance with an embodiment of the present invention; 
         FIG. 9  is a schematic diagram showing the elements of an assembly that changes phase and fringe pitch using a single element; 
         FIGS. 10A-D  are drawings that show front, first sectional, second sectional, and top views, respectively, of a phase and fringe adjuster window in accordance with an embodiment of the present invention; and 
         FIGS. 11A and 11B  are front and top views, respectively, of an assembly capable of adjusting phase and fringe pitch in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     An exemplary 3D measuring device  100  that operates according to the principle of accordion fringe interferometry is shown in  FIG. 1 . A projector  160  under control of an electronics unit  150  produces two small spots of light  112 ,  114 . These spots of light produce a pattern of fringes on the surface of a workpiece  130 . The irradiance at a particular point  124  is determined by the interference of the two rays of light  120 ,  122  at the point  124 . At various points on the surface of the workpiece  130 , the light rays  120 ,  122  interfere constructively or destructively, thereby producing the fringe pattern. A camera  140  includes a lens system  142  and a photosensitive array  146 . The camera  140  forms an image on photosensitive array  146  of the pattern of light on the workpiece  130 . The light from the point  124  may be considered to pass through a perspective center  144  of a lens system  142  to form an image point  128  on the photosensitive array. A particular pixel  128  of the photosensitive array  146  receives light scattered from a small region  124  of the surface of the workpiece  130 . The two angles that define the direction to this small region with respect to the perspective center  144  are known from the geometrical properties of the camera  140 , including the lens system  142 . 
     The light falling onto the photosensitive array  146  is converted into digital electrical signals, which are sent to electronics unit  150  for processing. The electronics unit  150 , which includes a processor, calculates the distance from the perspective center  144  to each point on the surface of the workpiece  130 . This calculation is based at least in part on a known distance  164  from the camera  140  to the projector  160 . For each pixel in the camera  140 , two angles and a calculated distance are known, as explained herein above. By combining the information obtained from all the pixels, a three dimensional map of the workpiece surface is obtained. 
       FIG. 2  shows the elements of an exemplary projector  200  according to an embodiment. A light source  210  sends light to a grating  220  that causes the light to split into multiple beams each traveling at a different angle. The grating may be blazed to maximize the size of the +1 and −1 orders generated in relation to other orders such as the 0, +3, −3, +5, −5 orders. If more than one light source and more than one grating are used, the light emanating from the more than one grating may be combined in a beam combiner  230 . In an embodiment, the beam combiner  230  is a glass beam splitter. The beams of light are sent through an objective lens  240  that focuses the light into two small spots  270 . The spots  270  may be real or virtual, the real spots formed by an objective lens system having a positive power and the virtual spots by an objective lens system having a negative power. A pinhole plate  250  has a region that allows the +1 and −1 orders of the light pass through while blocking the other orders. The pinhole plate is placed near the plane to which the spots  270  are focused. An optional phase/fringe adjuster  260  is also placed near the plane to which the spots  270  are focused. In an embodiment, the pinhole plate  250  and fringe/phase adjuster  260  are integrated into one optical component. Interference occurs in the overlap region  275  and is observed as fringes at points on a workpiece surface. 
       FIG. 3  shows specific elements of an exemplary projector  300  that contains elements corresponding to the generic elements of  FIG. 2 . Light source  310 A provides light that might come from a laser, a superluminescent diode, LED or other source. In an embodiment, the light from the light source  310 A travels through an optical fiber  312 A to a fiber launch  320 A that includes a ferrule  322 A and a lens  324 A. Alternatively, light from light source  310 A may travel through free space to reach lens  324 A. Collimated light  380 A that leaves the fiber launch  320 A passes through grating  330 A, the grating producing beams of light that travel in different directions. The orders of light produced may include 0, ±1, ±3, and ±5. The light passes through beam splitter  340 . In an embodiment, the beam splitter  340  is a non-polarizing beam splitter that transmits 50% of the light and reflects 50% of the light, so that half of the optical power is lost. In another embodiment, the light beams  380 A,  380 B are orthogonally polarized and the beam splitter  340  is a polarizing beam splitter configured to transmit nearly the entire light beam  380 A and reflect nearly the entire light beam  380 B. Light source  310 B provides light that, in an embodiment, travels through an optical fiber  312 B to a fiber launch  320 B that includes a ferrule  322 B and a lens  324 B. Collimated light  380 B that leaves the fiber launch  320 B passes through grating  330 B, the grating producing beams of light that travel in different directions. The light reflects off mirror  335  and reflects off beam splitter  340 . The light transmitted through the beam splitter  340  and the light reflected by the beam splitter  340  travels along the same beam path  390 . The light sources  322 A,  322 B are turned on one at a time so that there is no interference between the beams of light  380 A,  380 B as they exit the beam splitter  340 . 
     The light beam traveling along the beam path  390  travels to an objective lens  350  that focuses the light into two small spots  290 . An optical element  360  is placed near the two small spots  390 . In an embodiment, the optical element  360  is a combination phase adjuster and pinhole plate. The pinhole plate blocks small spots created by beams that might be, for example, of orders 0, ±3, and ±5. The phase adjuster adjusts the phase, for example to phase values of 0, 120, and 240 degrees. Interference occurs in the overlap region  395  and is observed as fringes at points on a workpiece surface. 
     The method of calculating distances using accordion fringe interferometry according to the system  100  shown in  FIG. 1  is to shift the relative phase of the two spots  112 ,  114 , which has the effect of moving the fringes on the workpiece. Each pixel of the camera measures the level of light obtained from equal exposures for each of the three phase shifts. At least three measured light levels are used by the processor within the electronics unit  150  to calculate the distance to points on the surface of the workpiece. Therefore to calculate 3D coordinates, the systems shown in  FIGS. 1-3  need the ability to shift the relative phases of the points  112 ,  114 , the points  270 , and the points  390 , respectively. 
     If the range of distances measured by the scanner is relatively large, it will also need the ability to resolve ambiguities in the measured distances. Because the fringe pitch is relatively small, it turns out that there are several possible valid distance solutions based on the images collected by the camera. This ambiguity can be removed by changing the spacing (pitch) between fringes by a known amount. In the embodiment of  FIG. 3 , two different fringe spacings are obtaining by using two sources of light that pass through two corresponding gratings  330 A,  330 B, the gratings  330 A,  330 B having different pitch values. To calculate 3D coordinates, the systems shown in  FIGS. 1-3  in most cases need the ability to change the fringe pitch to at least two values. 
     In an embodiment, the combination pinhole and phase shifter  360  is the optical element  400  shown in  FIG. 4 . The optical element  400  includes a glass plate  405  made of a high quality material such as fused silica. Regions are etched into the glass in a pattern that produces three different relative phase shifts in light passing through the striped areas  410  and  412 . Alternatively, different thicknesses may be created by applying coatings of varying thickness over the glass plate  405 . If coatings are used, care should be taken to minimize differences in the amount of light transmitted by each different layer as differences in transmitted power can cause errors in the calculated distances. In an exemplary embodiment shown in  FIG. 4 , the striped area  410  has a recessed section  432  as shown in section A-A, and the striped area  412  has a recessed section  444  as shown in section B-B. The light passing through striped areas  410  and  412  have three different relative optical path lengths (OPLs), according to the vertical position on the optical element  400  through which the light passes. These three different OPLs produce three different relative phase shifts of the spots of light  390 . On the workpiece, the effect of this phase shift will be a sideways shift of the fringe lines. Many other etched patterns are possible to obtain three different phase shifts. In addition, in some cases, it may be desirable to obtain more than three phase shifts so that additional etched regions may be needed. It should be understood that the pattern shown in  FIG. 4 ,  4 A,  4 B are simply suggestive and not limiting in terms of the types of patterns that might be used. 
     The pinhole function of the optical element  400  is to block unwanted light having orders other than ±1. The order 0 is blocked by an opaque coating  422 , which might be a chrome coating. The orders ±3, ±5 are blocked by the opaque regions  420 ,  424 . In an embodiment, the regions  420 ,  422 , and  424  are in the form of stripes rather than true pinholes. The term pinhole is commonly used to describe the function of blocking unwanted beams and so is used here, even though a striped form of the beam blocker is used in the illustrated embodiment. Other patterns of opaque and transparent regions may be applied to the optical element  400 . 
     A motorized mechanism  500  shown in  FIG. 5  can be used to provide linear motion to the phase adjuster  400  of  FIG. 4 . The stage  500  includes a ball slide with a hole at its center. Commercially available ball slides of this type have a specified straightness of 0.00008 m/m. A phase/fringe adjuster, which might be for example adjuster  400 , is attached to position  520 . Motion is provided by an actuator  530 , which in an embodiment is a voice coil actuator. The actuator  530  pushes a driver element  532  to move the ball slide. Position feedback is provided by a sensor  540 , which in an embodiment is a linear encoder. Electronics unit  550  provides electronics support for the actuator  530  and feedback sensor  540 . Electronics unit  550  may contain a processor to provide computational support. 
     A method for changing fringe pitch is now considered.  FIG. 6  shows the geometry of a ray of light traveling through a wedged window  600  having a wedge angle ε and an angle of incidence α at the first surface  612 . The wedged window  600  has a first angle of refraction β, a second angle of incidence γ, and a second angle of refraction δ. We are interested in finding the angle of the final ray leaving the wedged window with respect to the initial ray entering the wedged window. In particular, we are interested in how this angular change varies with the angle of incidence α for the case in which α is close to zero. 
     The change in the beam angle at the first interface is β−α, and the change in the beam angle at the second interface is γ−δ. The second angle of incidence is given by
 
γ+βε,  (1)
 
and the total change ζ in beam angle is
 
ζ=β−α+δ−γ=−α+ a  sin( n  sin(γ))−ε,  (2)
 
     For an angle of incidence α=0, Eq. (2) simplifies to
 
ζ= a  sin( n  sin(ε))−ε.  (3)
 
     Eq. (3) can be used to calculate the desired wedge angle. For example, if the index of refraction of the glass is n=1.5 and if the desired angle of deviation is ζ=1.3 milliradians, Eq. (3) can be solved numerically to find the wedge angle ε=2.5 milliradians. 
     To produce three different angles that give the desired distances between the spots at the output of a 3D measurement device, an arrangement of wedged windows can be combined in an assembly  700  as shown in  FIG. 7 . The main direction of each beam is set by a grating element as explained below with reference to  FIG. 9  discussed below. The purpose of the assembly  700  is to make small changes in the angles between the two separated beams to produce desired small changes in fringe pitch. This is conveniently done by placing an unwedged window  712  in the center of the assembly and placing oppositely angled wedged windows  710  and  714  on either side. 
     To produce the desired angles of deviation, the assembly  700  of  FIG. 7  is moved up and down in the plane of the paper. This will produce a consistent angular deviation in each of the three elements  710 ,  712 , and  714 , but there will be a different phase shift in each case, and this phase shift will depend on the position of the assembly  1200  in its up and down movement. 
     To avoid an undesirable shift in phase with variations in the thickness of the glass as the assembly is moved, the wedges may be arranged as in assembly  1300 ,  1350  of  FIGS. 8A ,  8 B. When seen in the top view of  FIG. 8A , the assembly extends out of the plane of the paper. A single beam  1330  enters one of the three sections  1310 ,  1315 ,  1320 . The wedge angle of the glass section  1315 ,  1311 ,  1320  determines the direction of the exiting beams of light  1340 ,  1350 ,  1345 , respectively. For the beam  1330  entering the unwedged section  1310 , the beam  1340  leaves the assembly along the original direction. For the other two sections  1315 ,  1320 , the beam is bent toward the leading edge of the glass, in accordance with  FIG. 6 . An important aspect of the design of the assembly  1300  ( 1350 ) is that the phase of the beam does not change in any one of the sections  1310 ,  1315 ,  1320  as the assembly is moved along. This is true as long as the sections  1310 ,  1315 ,  1320  are properly aligned so that the glass thickness does not change during movement. 
     An arrangement that uses a single optical element to adjust both phase and fringe pitch is shown in  FIG. 9 . Light source  910  provides light that might come from a laser, a superluminescent diode, LED or other source. In an embodiment, the light from the light source  910  travels through an optical fiber  912  to a fiber launch  920  that includes a ferrule  922  and a lens  924 . Alternatively, light from light source  910  may travel through free space to reach lens  924 . Collimated light  980  leaving the fiber launch  920  travels to grating  930  which splits the light into a several beams of light traveling in different directions. Later in the optical path all of the different orders of diffracted light are focused into spots, all of which, except for the ±1 orders, are removed by an opaque mask. The beam  987  reflects off mirror  933 , reflects off mirror  932 , and passes through phase/fringe adjuster  940  that adjusts both phase and fringe spacing at the output of the assembly  900 . The light passes through a first portion of a beam combiner  952  that transmits the light. 
     The light  982  reflects off mirror  934  and reflects off a second region  954  of beam combiner  956 . The two beams of light  985 ,  989  that emerge from beam combiner  956  intersect at position  990 . An afocal beam expander  960 , which in an embodiment includes two positive lens elements  962 ,  964 , is positioned so that the focal length of the first lens element  962  is placed a distance equal to the focal length f 1  of the first lens element  962  away from the intersection point  990 . The two collimated beams of light  985 ,  989  are focused by the first lens element  962  to two spots of light  996  at a distance f 1  from the first lens  962 . The distance between the lenses  962  and  964  is equal to f 1 +f 2  so that the two spots within the beam expander are a distance f 2  from the second lens element  962 . Two collimated beams of light  991 ,  993  emerge from the beam expander  960 . The size of the emerging beams  991 ,  993  equals the transverse magnification M of the beam expander times the size of the incident beams, where the magnification is M=f 2 /f 1 . The angle between the two emerging laser beams is reduced by a factor of 1/M compared to the angle between the incident laser beams  991 ,  993 . As an example, suppose that the diameter of each incident laser beam  985 ,  989  is 0.7 mm, with the beams having a separation angle of 13 milliradians (mrad). Also suppose that the transverse magnification of the beam expander  960  is M=10. The emerging laser beams  991 ,  993  then each have a diameter of 7 mm and an angle of separation of 1.3 mrad. The collimated beams of light  991 ,  993  emerging from the beam expander  960  intersect at position  992 . The objective lens  970 , which might be a 40× microscope objective having a focal length of f O =4.5 mm and a numerical aperture of NA=0.65, for example, is placed so that the distance from the front focal position of the objective lens  970  from the intersection point  992  is equal to the focal length f O  of the objective lens  970 . The objective lens  970  focuses the collimated beams  991 ,  993  into two small spots  994 . A pinhole plate  946 , which includes alternating opaque and transparent stripes, is positioned near the spots  994  to block all orders of diffracted light from the grating  930  except for the +1 and −1 orders. In an alternative embodiment, a plate at the position of the spots  996  contain alternating stripes of opaque and transparent regions to block all orders of light diffracted by the grating except for the +1 and −1 orders. 
       FIG. 10  shows a phase/fringe adjuster  1000  that may be used as the element  940  in  FIG. 9 . The phase/fringe adjuster  1000  includes a glass wedged window that has an entrance face not parallel to an exit face. In the adjuster  1000 , the face  1012  is not parallel to the face  1020 . In addition, the phase/fringe adjuster  1000  includes two small sections  1014 ,  1016  etched into the glass. The difference in the optical path length (OPL) between the top area  1012  and either of the two sections  1014 ,  1016  is equal to the difference in thickness between the top area  1012  and the section multiplied by the quantity n−1, where n is the index of refraction of the glass. The corresponding phase shift is equal to the difference in OPL multiplied by 2π/λ, where λ is the wavelength of light from the light source. So, for example, for a wavelength of 658 nm, an index of refraction of n=1.5, and a first desired phase shift of 120 degrees=2π/3 radians, the section  1014  should be etched to a depth d of d=λ/3(n−1)=658 nm/3(1.5−1)=438.7 nm. If a 240 degree phase shift is desired for the section  1016 , the etching depth should be doubled to 877.3 nm. An alternative approach to etching the glass to a given depth is to coat the glass to a given height at the desired sections. 
     To obtain three different fringe pitches, three glass windows can be stacked, as shown in  FIGS. 11A ,  11 B. A simple way to combine three wedged elements in an assembly is to set the central element to have a wedge angle of zero (parallel entrance and exit surfaces) and the two outside windows to have equal, but oppositely directed, wedge angles. 
     As an example, suppose that the desired separations of the spots  994  in  FIG. 9  are a={46, 52, 58} micrometers. If the focal length of the objective lens  970  is 4.5 mm, then the angles of separation between the beams  991 ,  993  are θ=a/f O ={10.22, 11.56, 12.89} milliradians. If the transverse magnification of the beam expander  996  is M=10, the angles of separation between the beams  985 ,  989  are {102.2, 115.6, and 128.9} milliradians. The mirrors  932 ,  934  are set to produce an angular separation between the beams  985 ,  989  of 115.6 milliradians when the beam  987  passes through the central window  1110  of the phase/fringe adjuster  940 . In this case, the central window  1110  has a wedge angle of zero; in other words, it is a window with parallel sides. The windows  1000  and  1112  are manufactured to have a wedge angle equal to 128.89−115.56=115.55−102.22=13.3 milliradians. The wedged windows  1000 ,  1112  are mounted in opposite directions so that the wedge angles of +13.3 milliradians deflect the beam of light in opposite directions. 
     While the invention has been described with reference to example 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.