Both the ASME B and the draft VDI/VDE 2617 have strengths and

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1 Choosing Test Positions for Laser Tracker Evaluation an Future Stanars Development ala Muralikrishnan 1, Daniel Sawyer 1, Christopher lackburn 1, Steven Phillips 1, Craig Shakarji 1, E Morse 2, an Robert riges 3 1 National Institute of Stanars an Technology, Gaithersburg, Marylan Center for Precision Metrology, UNC Charlotte, Charlotte, NC FRO Technologies, Kennett Square, P bstract working group within the ISO TC 213 committee is eveloping a raft ocument [1] for evaluating the performance of laser trackers. The SME Stanar [2] an the raft VDI/VDE 2617 part 1 [3] escribe some useful tests that are incorporate into this new ISO ocument. ut both the SME an VDI/VDE ocuments also have some limitations. The new ISO raft ocument, which is currently uner consieration by the committee, raws from the key attributes of the SME an the raft VDI/VDE 2617 part 1 while eliminating weak or reunant tests. The approach to selecting suitable tests is base on the sensitivity of each test to ifferent geometric misalignments in ifferent tracker esigns. We iscuss the propose ISO raft ocument in this paper. 1. Introuction laser tracker task force within the ISO TC 213 WG1 committee is currently working on a raft ocument for an international Stanar on laser trackers. The task force inclues experts involve in laser tracker metrology from several countries (US, Germany, Japan, ustria, etc). One major topic of iscussion is the number an type of tests to be inclue in the raft ISO ocument. There are at least two excellent ocuments that serve as starting points for this purpose, the SME Stanar an the raft VDI/VDE 2617 part 1. oth the SME an the raft VDI/VDE 2617 have strengths an weaknesses. The task force has attempte to raw from the strengths of the two ocuments while eliminating their weaknesses an reunancies. The working raft, currently out for voting to become a Committee Draft (CD), contains a core set of tests that exhibit sensitivity to ifferent geometric/optical misalignments in laser trackers. This core set of tests was etermine from a sensitivity analysis performe using mathematical error moels for ifferent tracker esigns. In aition to the core set, the proposal contains a require supplemental set; there are two efault options for this supplemental set, one of which is rawn from the Stanar an the other is from the raft VDI/VDE 2617 part 1. Iniviually, each test is comprise of a measurement of a single calibrate reference length. The overall number of propose measure reference lengths is 15, to be consistent with the number of tests in the ISO Stanar [4]. In the following sections, we briefly escribe a sensitivity analysis base metho illustrating the strength of the propose ISO approach an provie examples of its effectiveness; we also point out the strengths an weakness of the SME an the raft VDI/VDE 2617 part Sensitivity nalysis ase pproach There are many ifferent geometric an optical misalignments within a tracker that lea to systematic errors in the measure range an angles of a target. Tracker manufacturers generally inclue geometric error compensation moels within their

2 software to account for some of these errors. The parameters of these moels are etermine from compensation proceures performe prior to a measurement. If the error moels are carefully constructe from a stuy of ifferent tracker error sources, they can also be useful in ientifying laser tracker tests that are sensitive to the ifferent sources of error that constitute the error moel. We have escribe error moels an the sensitivity analysis base metho in [5]; a etaile escription is beyon the scope here. To illustrate how the technique may be useful in etecting tracker errors, we present two examples where through appropriate positioning of the reference lengths the test becomes sensitive to specific geometric misalignment terms. Example 1: n offset beam in a tracker without a beam steering mirror: For an ieally constructe laser tracker, the laser beam emerges from the point of intersection of the staning (vertical) an transit (horizontal) axes of the tracker. ut if the beam emerges with an offset from these axes, there may be an error in the horizontal an vertical angle reaings. We consier the component of the offset in the vertical plane to illustrate our approach, see Fig. 1. Fig. 1 (a) shows a symmetrically place reference length. The ieal beam emerges from O an strikes one en of the length at an the other en at. The offset beam travels to 1 an 1.The errors at ( 1 ) an ( 1 ) are equal in magnitue an sign an therefore there is no net error in the length; the length only appears to be rotate by a small amount. symmetrically place length is therefore not sensitive to an offset beam. Fig. 1 (b) shows an asymmetrically place reference length. In this case, a component of the error 1 is along the (a) (b) O O Offset c Staning axis Staning axis V 1 1 Offset c V length an cancels some of the error at, but there is still a resiual error leaing to some sensitivity to beam offset misalignment. simple calculation may be performe to maximize the sensitivity as shown here. The net error in the length E is given by L L 1 1 Transit axis passes through O an into the plane of the paper Figure 1 (a) symmetrically place vertical reference length () test is not sensitive to offset c because the errors at ( 1 ) an at ( 1 ) are equal in magnitue an sign resulting in a net zero error in the length (b) n asymmetrically positione vertical reference length () test is sensitive to offset c because only a portion of the error at serves to cancel that at resulting in a resiual error.

3 E = c(1 cosv), where c is the offset of the beam in the vertical plane. The sensitivity s, given as the ratio of the error in the length to the offset in the beam, is s = E/c = 1-cosV. Clearly, s is largest when V tens to 9 ; therefore for a given length L, it is esirable to place the length as close as possible to the tracker. This test position etects the error that woul appear in a measurement of a large vertical length such as on the tail section of an aircraft. Example 2: Eccentricity in the horizontal angle encoer: ny eccentricity in the mechanical placement of the horizontal angle encoer relative to its axis of rotation will result in systematic errors in the tracker s horizontal angle reaing. The error e(φ) in horizontal angle φ ue to an eccentrically mounte encoer may be given by a cosφ + b sinφ where (a, b) are the eccentricities along x an y [6]. The problem therefore is to ientify a position an orientation for reference length L that maximizes the sensitivity to this misalignment. We will consier just the cosine term here, i.e, e(φ) = a cosφ ; a similar argument applies to the sine term. Clearly, a horizontally place reference length will be sensitive to this error source. Further, a symmetrically place reference length will be preferable since the errors at two ens coul potentially sum to prouce twice the error. Some simple trigonometry from Fig. 2 yiels the error in the length E(θ,φ) as (see [7] for a more etaile explanation) E(θ,φ) = R[e(φ +θ) cosθ - e(φ -θ) cosθ] = R a[cos(φ +θ) cosθ - cos(φ -θ) cosθ] = L a cosθ sinφ. The sensitivity s, given as the ratio of the error in the length to eccentricity in the encoer, is therefore s = E(θ,φ)/a = L cosθ sinφ. (a) Staning axis passes through O into plane of paper (b) y e(φ +θ) O R y θ For an artifact of length L, the sensitivity is largest when φ = 9, an θ is as small as possible. The angle θ cannot be zero since it is half the angle subtene by the length. ut moving the length far away from the tracker will reuce this angle. There will of course be limits to how far away a length can be place. 3 m length place 6 m away, as in the SME R D φ x O Horizontal angle encoer θ φ +θ 2 θ D 1 L L x Figure 2 (a) horizontal reference length test to etect eccentricity in the horizontal angle encoer. The reference length is place so that its bisector makes an angle φ with the x axis. The length subtens an angle 2θ at tracker O (b) iagram showing the calculation of the errors in the length ue to error in the horizontal angle from eccentricity in the encoer, see [7] for more etails.

4 Stanar, prouces a sensitivity equal to 97 % of the theoretical maximum sensitivity (which is realize when the length is place infinitely far away) achievable for this 3 m length, an is sufficient for our purpose here in etecting eccentricity errors. The above examples showe how unerstaning error sources an eveloping mathematical error moels can ai in the selection of test positions that are sensitive to the ifferent geometric errors. nother example is iscusse in [7], where the placement of horizontal lengths is stuie to achieve maximum sensitivity to secon orer scale errors in the horizontal angle encoer. We next iscuss the strengths an weaknesses of the SME an the raft VDI/VDE 2617 part SME The SME is the only publishe an available Stanar for laser trackers. The Stanar inclues three types of tests to be performe on trackers ranging tests, length measurement system tests, an two-face system tests. We o not escribe these tests here; a escription may be foun in the Stanar [2] an in other publications [8, 9]. We focus on the strengths an weaknesses of this Stanar here. Strengths: The separation of the ranging tests from the volumetric length tests allow the testing of the ranging unit to its full extent an also allows for a smaller artifact length (such as the 2.3 m length) when testing volumetric performance. The incorporation of two-face tests offers a quick an effective check of the tracker s health. Two-face tests are ieal because they are sensitive to numerous tracker misalignment terms an require no artifact for their performance. Many tests escribe in the Stanar are sensitive to ifferent geometric/optical misalignments within the tracker. s one example, the horizontal length test performe at the four clocking angles (, 9, 18 an ) is sensitive to the eccentricity of the horizontal angle encoer as iscusse in the preceing section. Weaknesses: There are several reunant tests in the Stanar. For example, the vertical length test must be performe at 4 clocking angles (, 9, 18, an ) accoring to the Stanar whereas for the known kinematic errors of current tracker esigns only one position will suffice (the azimuth has no influence on vertical length measurements since it remains fixe uring the measurement). It is not necessary to perform the iagonal length test at both the 3 m an 6 m istance. Higher sensitivity to squareness error is obtaine at the 3 m position. lso the two-face tests at the 3 m istance are not necessary; the tests at 1 m an 6 m position will suffice in capturing the epenence of two-face errors on istance from the target. There is consierable symmetry in the placement of the lengths that result in poor or no sensitivity to numerous geometric misalignment terms in trackers. Examples of terms that show poor or no sensitivity inclue beam offsets an tilt, vertical inex offset, one component of vertical encoer eccentricity, an a component of secon orer scale error in the horizontal an vertical angle encoer. Improvements in the positioning of the reference length, such as introucing some asymmetry in placement, will improve the sensitivity of the test to ifferent geometric

5 misalignments, as we have shown in [5]. The raft ISO ocument has incorporate this concept an inclues the following tests: asymmetric horizontal length tests, asymmetric vertical length tests, asymmetric iagonal length tests, symmetrical horizontal lengths place above the tracker, an a buck-in buck-out test (or a close approximation to it). 4. Draft VDI/VDE 2617 Part 1 The raft VDI/VDE 2617 part 1 proposes testing the tracker in a large volume by measuring ifferent lengths place in ifferent orientations. In recommening these system level tests, the raft ocument treats the tracker as a black box without attempting to isolate errors in each axis. Strengths: The raft requires the measurement of some very large lengths that may more closely resemble a laser tracker s intene application. There are some interesting positions that may be chosen in the measurement volume that are very sensitive to some error sources, such as a horizontal length place 1.5 m away an 1.5 m below or above the tracker height that is sensitive to one component of the vertical angle encoer s eccentricity; this misalignment term is otherwise not easy to etect. nother useful test is to place the tracker insie the measurement volume an sight to two targets at opposite ens an in line with the tracker. This test will be sensitive to any zero error in the trackers ranging unit (bir-bath error) an any offset between the staning an the transit axes. The raft escribes tests to estimate probe size an form error. These are useful tests since spherically mounte retro-reflector (SMR) errors may be large an require testing. Weaknesses: This Stanar allows consierable flexibility in choosing the test lengths. Therefore it is quite possible that a poor choice of lengths will not etect many tracker errors when in fact, the tracker may have large systematic errors. For trackers without a beam steering mirror, even a goo choice of lengths will not be sensitive to collimation error. Monte Carlo simulation suggeste that there is consierable probability of choosing lengths that are not sensitive to beam offset as well. For a tracker with a beam steering mirror, there is high probability of not etecting cover plate offset (see [5, 6] for more information on these geometric misalignment terms). ecause the ranging tests are not separate from the volumetric length tests, there is a nee to perform measurements on some very large lengths. It can be quite teious to calibrate such large lengths. Two-face tests are only suggeste as a fast an intermeiate test of the tracker, an are not require to be performe. In practice, the two-face tests are invaluable in iagnosing a tracker s health an shoul be performe as part of the testing proceure. 5. The Draft ISO Set of Tests We iscuss the tests escribe in the raft ISO ocument in this section. There are 15 reference lengths teste to be consistent with the ISO Stanar for Coorinate Measuring Machines (CMMs). Of these, the ISO ocument contains a core set of 41 tests (see Table 1) esigne to be sensitive to all known optomechanical errors in the ifferent esigns of trackers currently available. The remaining 64 test lengths are user-efine tests. There are two efault options; the first efault option is rawn from the

6 SME an is liste in Table 2, the secon efault option is rawn from the raft VDI/VDE 2617 part 1 an is shown in Figure 4. The user is free to choose any other set of 64 test lengths as well. 5.1 Core Tests It shoul be note that each test position may be sensitive to more than one source of error, an further, the same test may exhibit ifferent sensitivity to the same error source in a ifferent tracker esign. ny justification for the inclusion of a test will therefore involve multiple factors. In this paper we attempt to provie one principal reason for the inclusion of each test here. Fig. 3 shows some of the positions escribe in Table 1. reference length 2.25 m to 2.75 m long may be use for the tests unless specifically inicate in Table 1. Positions 1 an 2 are esigne to test a large fraction of each of the angular axes of the tracker. These are inclue in the spirit of the ISO where each axis is teste for at least 66 % of its range. Further, position 1 also tests for bir-bath error an any offset between the staning an transit axes. Positions 3 to 6 test for the eccentricity in the horizontal angle encoer, position 7 tests for one component of the vertical angle encoer eccentricity, positions 8 to 15 test for squareness between the staning axis an the transit axis, an positions 16 to 19 attempt to isolate the effect of combination of errors (for example, the effect of beam offset, beam tilt, an encoer eccentricity in a tracker with a beam steering mirror). Positions 2 to 23 test for beam offsets along the horizontal irection, position 24 tests for beam offset along the vertical irection, positions 25 to 28 test for collimation error (for example, tilte beam in a tracker without a beam steering mirror), position 29 tests for another component of the vertical angle encoer s eccentricity, positions 3 to 35 test for low even orer harmonics in the horizontal angle encoer s scale [7], an positions 36 to 4 test for ranging error in a tracker. Position 41 is a synthetic length test an is escribe in the raft VDI/VDE 2617 part 1. The purpose of this test is to valiate the temperature compensation capability of the tracker system. This is achieve as follows. long length is realize between two nests an the istance between them is calibrate using an interferometer. The length is reporte at 2 C; let its value be L. It is now assume that there exists a steel block of that length in the room whose temperature is T. Further assume that the thermal coefficient of expansion of the block is exactly 11.5 μm/m/ C. If the temperature of the room T is ifferent from 2 C, the block s length at 2 C can be calculate as Ls = L(1-11.5x1-6 (T-2)). This synthetic length Ls is the calibrate length of the hypothetical steel block at 2 C; for this calculation the temperature T is etermine by placing a temperature sensor on a block of steel that is in equilibrium with the room. The laser tracker is then use to measure the istance between the nests with an expansion coefficient of 11.5 μm/m/ C input in its software. s before, the temperature sensor of the laser tracker is mae to measure the temperature of a block of steel which is in equilibrium with the room. The length obtaine thus is compare against Ls to etermine the error. The 41 tests escribe in Table 1 comprise the core set of tests that is sensitive to known sources of geometric misalignments. It is preferable to have aitional tests for several reasons: The ISO an SME Stanars require three measurements to be performe at each position an

7 orientation of the reference length. There is no analogous repeatability measurement in our core set. The first efault option in the supplemental set inclues such repeatability tests. It is possible that the intene use of a tracker may be consierably ifferent from any of the tests escribe in the core set. For example, the tracker may primarily perform long length measurements far away from the tracker. Therefore, the user may require such a measurement as part of the supplemental set. The secon efault option inclues such long length measurements. There may be other sources of systematic error in a tracker not relate to optical or geometric misalignments. itional tests are therefore useful in etecting these errors. Table 1 Core set of tests in the raft ISO ocument Position number Distance from tracker Description of reference length position 1 s close as 2 s close as Horizontal, centere (i.e., the ens of the reference length are equiistant from the tracker), an at tracker height. This tests 66 % of the horizontal angle measurement axis of the tracker (see Fig. 3(a)). Vertical, center of the length is at tracker height (ens of the reference length are equiistant from the tracker). This tests 66 % of the vertical angle measurement axis of the tracker (see Fig. 3(b)) m Horizontal, centere (i.e., the ens of the reference length are equiistant from the tracker), an at tracker height (see Fig. 3(a)). 7 3 m Vertical, center of the length is at tracker height (ens of the reference length are equiistant from the tracker) (see Fig. 3(b)) m Right iagonal, centere (i.e., the ens of the reference length are equiistant from the tracker), an the center of the length is at tracker height (see Fig. 3(g)) m Left iagonal, centere (i.e., the ens of the reference length are equiistant from the tracker), an the center of the length is at tracker height (see Fig. 3()) m Horizontal, centere (i.e., the ens of the reference length are equiistant from the tracker), an at tracker height (see Fig. 3(a)) s close as 24 s close as s close as Horizontal, not-centere (i.e, the tracker is irectly in front of one en of the length), an at tracker height (see Fig. 3(e)). Vertical, not-centere (i.e, the tracker is irectly in front of one en of the length) (see Fig. 3(c)). Diagonal, one en is below or above the point irectly in front of the tracker, the other en is at tracker height an to the right or left of the point irectly in front of the tracker. The range to the two ens of the length is equal (see Fig. 3(f)). Horizontal angle(s) with respect to the tracker ( ) at any azimuth at any azimuth 29 Horizontal, centere irectly above (as much as that is possible) the laser tracker itself (see Fig. 3(h)) Long 1 Horizontal, centere (i.e., the ens of the reference length are equiistant from the tracker), at tracker height (see Fig. 3(a))., 3, 6, 9, 12, test This tests 66 % of the ranging axis of the tracker. istances 41 Synthetic length test 1 In the special long case, a longer reference length (e.g., 8 m) is measure at a longer istance (e.g., 8 m) from the tracker. For all other tests escribe above, the reference length coul be relatively small, 2.25 m to 2.75 m.

8 (a) (b) (c) () (e) (f) (g) (h) Figure 3 (a) Symmetrically place horizontal reference length (b) Symmetrically place vertical reference length (c) symmetrically place vertical reference length () Left iagonal reference length (e) symmetrically place horizontal reference length (f) symmetrically place iagonal reference length (g) Right iagonal reference length (g) Symmetrical horizontal reference length place above the tracker 5.2 Supplemental Positions: Option 1 The first efault option for the supplemental positions inclue in the raft ISO ocument is mostly rawn from the SME Stanar, see Table 2. ny test specifie in the SME that was not inclue as part of the core set has been inclue here. In aition, some asymmetric positions that were not part of the core set are also inclue here. These mirror positions, positions 19 to 3, are useful because some error sources prouce length errors that change in sign from a nominal position to a corresponing mirror position. Thus, these tests serve as valuable iagnostic tools to etect specific tracker errors. The value of mirror positions is escribe in [5]. nother aition in the supplemental set are the repeatability measurements escribe in positions 42 to Supplemental Positions: Option 2 The secon efault option for the supplemental positions inclue in the raft ISO ocument is mostly rawn from the raft VDI/VDE 2617 part 1. In this alternative, the laser tracker is positione centrically in front of the longest sie of the measuring volume at a istance of 1.5 m in such a way that the measuring hea is approximately equiistant from the upper an lower ege of the measuring volume. The positions are etermine by eight ifferent measurement lines as iscusse in the raft. Figure 4 shows a possible arrangement of these eight measurement lines. Other arrangements are also permitte. For the remaining 64 positions, a measuring volume of 1 m x 6 m x 3 m (length x breath x height) is recommene. If the laser tracker is use to measure small parts, a measuring volume of 5 m x 3 m x 2 m is recommene. However, other measuring volumes are permitte. In every measurement line, at least three ifferent test lengths must be measure.

9 The raft ISO ocument recommens that 64 lengths be measure from the 8 measurement lines, an that these 64 lengths also sample the ifferent azimuth positions of the tracker. That is, some of the 64 lengths may be measure with the tracker reaing when facing the measurement volume, some lengths may be measure with the tracker reaing 12, an the remaining may be measure with the tracker reaing 24 when facing the measurement volume. The shortest test length shoul amount to at least 1/1 of the shortest sie of the specifie measuring volume. In each measurement line, the largest reference length has to be chosen in such a way that it is not shorter than 2/3 of the length which is maximally possible in the measurement line within the measuring volume. Table 2 Supplemental positions Position number Distance from tracker Description of reference length position m Vertical, centere (i.e., the ens of the reference length are equiistant from the tracker), an the center of the length is at tracker height (see Fig. 3(b)) m Vertical, center of the length at tracker height (ens of the reference length are equiistant from the tracker) (see Fig. 3(b)) m Right iagonal, centere (i.e., the ens of the reference length are equiistant from the tracker), an the center of the length is at tracker height (see Fig. 3(f)) m Left iagonal, centere (i.e., the ens of the reference length are equiistant from the tracker), an the center of the length is at tracker height (see Fig. 3()) s close as Vertical, not-centere (i.e, the tracker is irectly in front of s close as s close as 27-3 s close as one en of the length) (see Fig. 3(c)). Horizontal, not-centere (i.e, the tracker is irectly in front of one en of the length), an at tracker height. This is the mirror position corresponing to positions 2-23 in Table 4 (If the tracker were previously irectly in front of target as in Fig. 3(e), then, the tracker must now be positione irectly in front of target ) (see Fig. 3(e)). Vertical, not-centere (i.e, the tracker is irectly in front of one en of the length). This is the mirror position corresponing to positions 24 in Table 4 an positions in this Table (If the tracker were previously irectly in front of target as in Fig. 3(c), then, the tracker must now be positione irectly in front of target ) (see Fig. 3(c)). Diagonal, one en is below or above the point irectly in front of the tracker, the other en is at tracker height an to the right or left of the point irectly in front of the tracker. The range to the two ens of the length is equal. This is the mirror position corresponing to positions in Table 4 (If the tracker were previously irectly below target as in Fig. 3(f), then, the tracker must now be positione irectly above target ) (see Fig. 3(f)) Horizontal, centere irectly above (as much as that is possible) the laser tracker itself (see Fig. 3(h)) m oy iagonal of a cube. User efine efault position 2 of the Stanar s close as Diagonal, centere (i.e., the ens of the reference length are equiistant from the tracker), an the center of the length is at tracker height. Horizontal angle(s) with respect to the tracker ( ) 9, 18, 9, 18, 9, 18,

10 Table 2 continue: Repeatability measurements Position number Distance from tracker Description of reference length position Distance approximately equal to half the reference length Distance approximately equal to twice the reference length 5-53 Distance approximately equal to half the reference length Distance approximately equal to twice the reference Horizontal, centere (i.e., the ens of the reference length are equiistant from the tracker), an at tracker height. Repeat the measurement 4 times. This tests the repeatability of the horizontal angle measurement capability at the near position. Horizontal, centere (i.e., the ens of the reference length are equiistant from the tracker), an at tracker height. Repeat the measurement 4 times. This tests the repeatability of the horizontal angle measurement capability at the far position. Vertical, center of the length at tracker height (ens of the reference length are equiistant from the tracker). Repeat the measurement 4 times. This tests the repeatability of the vertical angle measurement capability at the near position. Vertical, center of the length is at tracker height (ens of the reference length are equiistant from the tracker). Repeat the measurement 4 times. This tests the repeatability of the vertical angle measurement capability at the far position. length m long the raial irection so that the near en of the length is 4 m away from the tracker. Repeat the measurement 4 times. This tests the repeatability of the range measurement capability m long the raial irection so that the near en of the length is 6 m away from the tracker. Repeat the measurement 3 times. This tests the repeatability of the range measurement capability. Horizontal angle(s) with respect to the tracker ( ) Figure 4 Possible arrangements of the 8 measurement lines for efault option 2 (source [3])

11 5.4 Probe Tests an Two-face Tests The raft ISO ocument inclues the performance of probe size an probe form error tests, which are similar to those escribe in the raft VDI/VDE 2617 part 1. sphere of calibrate iameter is measure at ifferent locations in the measurement volume at less than 2 m istance from the tracker, an at a istance of about 1 m or more than 75 % of its range. Twenty five ata points are measure on the sphere. The SMR probe is rotate so that a ifferent point on the SMR contacts the calibrate sphere for each measurement point. ny eviation in size an form from the calibrate values are attribute to the optical misalignments an geometry of the SMR. The raft ISO ocument also requires the performance of two-face tests, which are inclue as probe location tests. The tests are recommene in the VDI/VDE 2617 part 1 an, are similar to those escribe in the SME , except that the tests at the 3 m position have been remove because it is reunant. 6. Comparing the SME , the raft VDI/VDE 2617 part 1, an the raft ISO Sensitivity to geometric errors: s we have pointe out earlier, several length tests escribe in the SME are sensitive to ifferent geometric misalignments in trackers, but there are still some reunancies an weaknesses. There is consierable symmetry in the placement of the lengths which cause reuce or no sensitivity to several geometric misalignments. The raft VDI/VDE 2617 part 1 allows consierable flexibility in the placement of the lengths an therefore it is possible to have a combination that has very limite sensitivity to ifferent geometric misalignments. We believe that the core set of tests in the raft ISO ocument aresses this problem by being sensitive to known sources of geometric misalignments in trackers. Number of tests: The SME requires the performance of 15 length tests, 18 twoface tests, an 18 ranging tests (if there are more than one measurement evices within the tracker, there will be 18 ranging tests for each). The raft VDI/VDE 2617 part 1 requires the performance of 15 length tests, a synthetic length test, an three probe tests which involve measurement of a sphere of known iameter an form (if more than one probe (SMR) is use, the probe tests have to be performe for each probe). The raft also recommens 18 two-face interim tests that may perioically be performe on the tracker. The raft ISO ocument contains 15 length tests (incluing the synthetic length test an ranging tests), 18 probe location tests (two-face tests), an two probe size tests. Similarity to the ISO 136-2: The SME Stanar is similar to the ISO in its testing philosophy in that calibrate artifacts are employe along the principal irections to capture specific sources of error. In ISO 136-2, calibrate lengths are place along the three principal irections x, y, an z, an along iagonals to capture errors associate with the motion of a single axis or combination of axes. For a laser tracker, the three principal axes are the ranging axis an the two angular axes. The ranging tests in the capture errors along the ranging axis. Errors associate with the two angular axes, or combination of all three axes, are measure by placing calibrate lengths along the ifferent irections. For example, the horizontal length test captures errors associate with the horizontal angle axis of the tracker.

12 iagonal length test captures the squareness between the two angular axes. These ieas are illustrate in Fig. 5. Fig. 5 (a) shows some testing positions accoring to the ISO with the artifact aligne along the x axis, the y axis, the z axis, an along a space iagonal. Fig. 5 (b) shows some testing positions accoring to the SME with calibrate lengths along the ranging axis, along the horizontal an vertical irections to test the two angular axes, an along a iagonal to test for squareness. The raft VDI/VDE 2617 part 1 is similar to the ISO Stanar in its approach to specifying the limiting values of the errors. The ISO allows the limiting value of the length measurement error to be a single quantity (a constant) or a simple formula (of the form +L) an must be complie for any length over the entire volume. The SME on the other han allows manufacturers to provie any formula of their choosing to etermine the limiting value of the length measurement error; common formulas provie by manufacturers are inee elaborate. The raft VDI/VDE 2617 part 1 aopts the ISO approach by allowing either a single quantity or a simple +L type formula for this purpose. The core set of the raft ISO ocument is similar to the ISO in that errors in each axis are teste by careful positioning of the reference lengths to achieve maximum sensitivity. The limiting values of the errors will be a formula; whether they will be a simple formula of the type +L or a more complicate one is still uner iscussion. 7. Conclusions oth the SME an the raft VDI/VDE 2617 part 1 provie some excellent tests for the performance evaluation of laser trackers. ut, as pointe out, there are some limitations as well. The symmetrical positioning of the lengths in the SME an the (a) (b) y x H R V Figure 5 (a) Some testing positions accoring to the ISO (b) some testing positions accoring to the SME flexibility in the positioning of the lengths in the raft VDI/VDE 2617 part 1 result in reuce or poor sensitivity to ifferent geometric misalignments in trackers. The ISO raft ocument aresses these concerns by introucing consierable asymmetry in the positioning of the lengths an introucing both a core set of fixe positions an a supplemental set of user-efine flexible positions. The raft ISO ocument also has the inclusion of the two-face tests because they are simple, quick an highly efficient way of etecting tracker error sources. itionally, the raft ISO ocument inclues probe (SMR)

13 tests that are similar to the VDI/VDE 2617 part 1 testing proceure. test that is currently not inclue in the raft ISO ocument but may be consiere is the repeate measurement of a horizontally oriente length, but with the tracker rotate about the azimuth by a small amount (say,.3 ) between measurements. The purpose of this test is to etect uncompensate high frequency perioic errors in the horizontal angle encoer. Two other aspects not yet aresse in the ISO ocument are the inclusion of any ynamic tests as escribe in the Chinese raft Stanar [1] an interim tests such as a bunle ajust proceure [11]. oth are excellent tests an worthy of consieration. References 1. ISO Working Draft: Geometrical Prouct Specifications (GPS) cceptance an reverification tests for coorinate measuring systems (CMS) Part 1: Laser Trackers for measuring point-to-point istances. 2. SME Stanar - Performance Evaluation of Laser- ase Spherical Coorinate Measurement Systems, 3. Draft VDI/VDE 2617 part 1, ccuracy of coorinate measuring machines - Characteristics an their checking - cceptance an reverification tests of lasertrackers, 4. ISO 136-2:29, Geometrical prouct specifications (GPS) -- cceptance an reverification tests for coorinate measuring machines (CMM) -- Part 2: CMMs use for measuring linear imensions, Muralikrishnan, D. Sawyer, C. lackburn, S. Phillips,. orchart, W. T. Estler, SME performance evaluation tests an geometric misalignments in laser trackers, NIST Journal of Research, 114, p , Raimun Loser, Stephen Kyle, lignment an fiel check proceures for the Leica Laser Tracker LTD 5, oeing Large Scale Optical Metrology Seminar, Muralikrishnan, C. lackburn, D. Sawyer, S. Phillips, an R. riges, Measuring Scale Errors in a Laser Tracker s Horizontal ngle Encoer through Simple Length Measurement an Two-face System Tests, submitte to the Journal of Research of the NIST 8. W.T. Estler, D.S. Sawyer,. orchart, an S.D. Phillips, Large- Scale Metrology Instrument Performance Evaluations at NIST, The Journal of the CMSC, Vol 1, No. 2, 26, pp D. Sawyer,. orchart, S.D. Phillips, C. Fronczek, W.T. Estler, W. Woo, an R.W Nickey, Laser Tracker Calibration System, Proc. Meas. Sci. Conf., naheim, C, Draft China Laser Tracker Stanar, Calibration Specification of Laser- ase Spherical Coorinate Measurement Systems 11. Raimun Loser, Laser tracker accuracy certification for large-volume measurements, Journal of the CMSC, 4 (2), utumn 29, pp