Simultaneous Position and Angular Error Measurement of a XY- stage using Miniature Interferometer with Step-size Variation 1 Dut ta , S ., 2 Pati, C., 3 Sen, R. 1 Scientist, PE&M Group, CSIR-CMERI Durgapur-9 Email: [email protected]2 PA, CSIR-CMERI Durgapur-9 Email: [email protected]3 Chief Scient ist , PE& M Group, CS IR-CME RI Dur gap ur-9 Email: [email protected]Abstract: Positional and angular errors in precision m easurement tools are predominantly affect the accuracy of the measurement system. Error measurement by laser interferometers are now necessary for precision machine tools. In this work, a measurement system with miniature interferometers of size 33mmX139mmX94mm with 0.1 nm linear resolution and 0.002 arcsec angular resolution has been employed to measure the positional and angular errors of a XY-stage of Talysurf non-cont act surface profiler. The measurement has been taken with varying stepsize as 1µm, 10µm, 100µm and 5mm. A variation of error propagation with the change of stepsize has also been presented in this study. Keywords: Miniature interferometer, Error measurement, Stepsize variation, XY-stage 1. INTRODUCTION With the advent of micromanufacturing and precision manufacturing, the measurement system necessitates the error free system. For that purpose error measurement and error compensation techniques are in a path of research advancement over the time. Schwenke et al. [1] reviewed and updated the trend of error measurement and error compensation systems. They have inferred that the laser based m easurem ent unit has been used successfully for measuring the geometric errors. Ta n et al. [2] develo p ed an volum e tric er r or model for a XY sta ge an d a lso e stimate d e rrors offline using radial basis function network. Also they have proposed an error compensation method for reducing the error from 160µm to 55µm. They tested thei r algorithm in a 100m m X100m m XY stage wi th 2.5 µm ste psi ze. A s a dvancem ent, they used a multi-layered NN algorithm to speed up their previously developed RBF network for error modeling for forward and reverse direction to com pe ns at e th e e rrors in a XY sta ge with on-line tuning [3]. Hwang et al. [4] measured and analyzed the ge om etri c errors of a scan ni ng type XY sta ge driven by linear motor and compensated linear error and yaw error with a novel configuration usi ng a m as ter an d a slave actu ators i n Y - di rection. Barm an a nd Sen [5] com pens ated the X, Y and Z- axes positional errors of a CNC-machine tools using a commercial software. Dutta et al. [6] studied the maximum hysteresis point for a ultra high resolution single-axis translational stage and also they concluded that the stepsize and velocity of movement affect the accuracy of the stage. Wang et al. [7] used a sequential multi-lateration me asureme nt method to m easure the geome tr ic errors of a milling machine and grinding machine using a laser tracker and then they separated the errors for each axis. However, the variation of error distribution with the variation of stepsize in case of error measurement is predominant in micomachine tools for their necessity in microaccuracy purpose. This problem has not been reported in any research. Th u s t he autho r s ha v e employed a study of e r ror
Transcript
7/29/2019 Simultaneous Position and Angular Error Measurement of a XY-stage using Miniature Interferometer with Step-size Variation 1Dutta, S., 2Pati, C., 3Sen, R.
Abstract: Positional and angular errors in precision measurement tools are predominantlyaffect the accuracy of the measurement system. Error measurement by laserinterferometers are now necessary for precision machine tools. In this work, ameasurement system with miniature interferometers of size 33mmX139mmX94mm with0.1 nm linear resolution and 0.002 arcsec angular resolution has been employed tomeasure the positional and angular errors of a XY-stage of Talysurf non-contact surfaceprofiler. The measurement has been taken with varying stepsize as 1µm, 10µm, 100µmand 5mm. A variation of error propagation with the change of stepsize has also beenpresented in this study.
With the advent of micromanufacturing andprecision manufacturing, the measurement systemnecessitates the error free system. For that purposeerror measurement and error compensationtechniques are in a path of research advancementover the time. Schwenke et al. [1] reviewed and
updated the trend of error measurement and errorcompensation systems. They have inferred that thelaser based measurement unit has been usedsuccessfully for measuring the geometric errors. Tan et al. [2] developed an volumetric error modelfor a XY stage and also estimated errors offlineusing radial basis function network. Also they haveproposed an error compensation method forreducing the error from 160µm to 55µm. Theytested their algorithm in a 100mmX100mm XYstage with 2.5 µm stepsize. As advancement, theyused a multi-layered NN algorithm to speed uptheir previously developed RBF network for error
modeling for forward and reverse direction tocompensate the errors in a XY stage with on-line
tuning [3]. Hwang et al. [4] measured and analyzedthe geometric errors of a scanning type XY stagedriven by linear motor and compensated linearerror and yaw error with a novel configurationusing a master and a slave actuators in Y-direction.Barman and Sen [5] compensated the X, Y and Z-axes positional errors of a CNC-machine toolsusing a commercial software. Dutta et al. [6]studied the maximum hysteresis point for a ultrahigh resolution single-axis translational stage andalso they concluded that the stepsize and velocityof movement affect the accuracy of the stage.Wang et al. [7] used a sequential multi-laterationmeasurement method to measure the geometricerrors of a milling machine and grinding machineusing a laser tracker and then they separated theerrors for each axis.
However, the variation of error distributionwith the variation of stepsize in case of errormeasurement is predominant in micomachine toolsfor their necessity in microaccuracy purpose. Thisproblem has not been reported in any research. Thus the authors have employed a study of error
7/29/2019 Simultaneous Position and Angular Error Measurement of a XY-stage using Miniature Interferometer with Step-size Variation 1Dutta, S., 2Pati, C., 3Sen, R.
distribution of a XY-stage by varying the stepsize.Also a miniature interferometer with the facility of simultaneous measurement of positional andangular error has been employed in this researchfor facilitating the compact measurement purpose.
2. EXPERIMENTAL METHODOLOGY
A miniature interferometer has been involvedto measure the errors of the XY-translational stageof a Talysurf correlation coherence interferometry(CCI) Lite surface profiler by varying the stepsize. The experimental set up has been shown in Fig. 1.
Fig. 1 Experimental set up
2.1 Experimental set up
A double beam plane mirror miniatureinterferometer made by SIOS GmbH has been usedto measure the positional and angular errors of theXY-stage. The principle of plane mirror laserinterferometer has been explained in Fig. 2.
Fig.2 Basic interferometer principle
Laser beam delivered from a laser source hasbeen splitted by a beam splitter. Then the beam W1
goes to a plane mirror M and reflects back todetector. Another beam W2 went to detector as a
reference beam. Thus the path difference betweenW1 and W2 creates fringe by interference. Fromthe fringe information the movement of the mirroror position of the mirror can be determined. Theequation of interference of two beams withintensity
1I and
2I is stated in Eq. 1:
1 2 1 2
0
22 cos( . . . )I I I I I ni s
π γ
λ = + + + (1)
where, I , γ ,0
λ , n, i andsare the resultant
intensity distribution, phase angle beforemeasurement, wavelength of laser source (here632.5nm for HeNe laser), refractive index of ambient air, an optical interpolation factor and pathlength to be measured, respectively. This way, thes can be calculated by knowing the order of interference, δ as stated in Eq. (2):
0.
.s i n
δ λ = (2)
In this work a miniature double beaminterferometer has been used to measure theposition and angular error, simultaneously [8]. Theprinciple of this interferometer has been given inFig. 3.
Fig. 3 Principle of double beam plane mirrorinterferometer
In this interferometer, the linear resolution has
been reached to 0.1 nm by incorporating anelectronic interpolation factor, e , which is thenumber of pulses forming a signal period. Thelinear resolution of this interferometer is stated asEq. 3.
0.
. .Ls
ei n
δ λ = (3)
The refractive index of the ambient air, n, isdependent upon the air temperature, pressure andhumidity. For retaining the n as constant foraccurate measurement a pressure sensor and atemperature sensor has been incorporated in the
measuring system. Edlen's equation incorporatingwith interferometric software helped to compensate
7/29/2019 Simultaneous Position and Angular Error Measurement of a XY-stage using Miniature Interferometer with Step-size Variation 1Dutta, S., 2Pati, C., 3Sen, R.
the effect of pressure and temperature variationduring measurement. The principle angular tiltmeasurement is shown in Fig. 4.
Fig. 4 Principle of angular tilt measurement
The angular error obtained is given in Eq. 4.
tans
Lα
∆= (4)
where, α , s∆ and Lare the angular tilt, differencein path length traversed by beams, B1 and B2, andlateral separation between B1 and B2, respectively. Thus this system allows to measure the positionand angular tilt simultaneously, which is shown inFig. 5.
Fig. 5 Simultaneous measurement of positionand angular tilt
The compactness of this interferometers isanother beauty of this measuring system. Thebeamsplitters are incorporated within a box of size33mmX139mmX94mm for its compactness. Thesystem inside the box is shown schematically inFig. 6. Jäger et al. [9] utilized the compactness of this miniature interferometer for development of ahigh resolution nanopositioning andnanomeasuring machine. The specification of thisminiature interferometer is given in Table 1. Table2 shows the specifications of the XY-stage of Talysurf CCI (Correlation CoherenceInterferometry) Lite surface profiler. The vertical
resolution of the profiler is 0.1Å. This Talysurf
system is used to evaluate the 3D surface profile of miniature components.
Fig. 6 Compactness of double beam planemirror miniature interferometer
(Made by SIOS GmbH)Measurement range (linear) 2mLinear resolution 0.1nmMeasurement range (angular) ±2arcminAngular resolution 0.002arcsecInterferometer software INFASDimension of the interferometerbox
33mm3139mm394mm
Beam separation 12.7mmFlatness of the plane mirror 0.15µm
Table 2. Specifications of XY-stage Travel range in X-axis 150mm Travel range in Y-axis 150mmLinear resolution 1µm
2.2 Methodology
The XY -stage of Talysurf CCI Lite surfaceprofiler is mainly used to position different
components ranging from micrometer to millimeterdimension. Thus the accuracy of the positioningcapability in both the terms of linear and angularshould be inspected for highly accuratemeasurement purpose by varying the stepsize of thestage. By taking this objective in mind, the errordistribution has been studied for varying stepsize,because knowing the error distributions at 1µm and100µm stepsizes are important for positioning of micro-scale and meso-scale parts, respectively. Inthis work, error distribution (both linear andangular) of the stage has been inspected at 1µm,10µm, 100µm and 5mm stepsize with a measuring
range of 51mm in both X and Y axes. At the timeof measurement, 1µm, 10µm, 100µm and 5mm
7/29/2019 Simultaneous Position and Angular Error Measurement of a XY-stage using Miniature Interferometer with Step-size Variation 1Dutta, S., 2Pati, C., 3Sen, R.
stepsizes have been taken for 0 to 10µm, 11 to100µm, 100µm to 1mm and 1mm to 51mm,respectively for both forward and reverse direction.
3. RESULTS AND DISCUSSIONS
The maximum and minimum errors for themeasurement of each range and the total errorrange has been reported in Table 3 for both forwardand reverse measurement.
Table 3. Results of error measurementPosition Error Measurement
It can be seen from the Table 3 that positionalerror range of X-axis is 0.6µm to 1µm, 0.7µmto 1.7µm, 1.6µm to 2.8µm and 129µm to 138µmfor the stepsizes of 1µm, 10µm, 100µm and 5mm,respectively. The percentage of error range withrespect to measurement range are 10%, 1.7%,
0.28% and 0.27% for the measuring range 10µm,100 µm, 1mm and 51mm, respectively in X-axis.Similarly, the positional error range of Y-axisis 0.8µm to 1.5µm, 2.2µm to 6.2µm, 1.8µm to3.9µm and 135µm to 148µm for the stepsizes of 1µm, 10µm, 100µm and 5mm, respectively. Thepercentage of error range with respect tomeasurement range are 15%, 6.2%, 0.39% and0.29% for the measuring range 10µm, 100 µm,1mm and 51mm, respectively in Y-axis. It can alsobe seen from the Table 3 that angular tilt errorrange of X-axis is 0.18arcsec to 0.65arcsec,0.31arcsec, 0.38arcsec to 0.82arcsec and 7.7arcsec
to 8arcsec for the stepsizes of 1µm, 10µm, 100µmand 5mm, respectively. The percentage of errorrange with respect to measurement range are 6.5%,0.31%, 0.08% and 0.016% for the measuring range10µm, 100 µm, 1mm and 51mm, respectively in X-axis. Similarly, the angular tilt error range of
Y-axis are 0.5rcsec to 1.9arcsec, 0.5arcsecto 0.7arcsec, 0.7arcsec to 1arcsec and 18arcsec forthe stepsizes of 1µm, 10µm, 100µm and 5mm,respectively. The percentage of error range withrespect to measurement range are 19%, 0.7%, 0.1%and 0.036% for the measuring range 10µm, 100µm, 1mm and 51mm, respectively in X-axis. It can
be seen from the results that the error percentage isdecreasing as the measuring range as well as stepsize is increasing for the position error as well asfor angular tilt. For better understanding, the errorshas been plotted in Figs. 7, 8, 9, 10, 11, 12, 13 and14 against the position of respective axis. X and Y-axis position errors are denoted as posxe and posye,respectively. The angular errors or yaw errors of Xand Y-axes are denoted asεx andεy, respectively.
Fig. 7 Position error distributions in forwardmovement of X-axis
7/29/2019 Simultaneous Position and Angular Error Measurement of a XY-stage using Miniature Interferometer with Step-size Variation 1Dutta, S., 2Pati, C., 3Sen, R.
Error distribution for stepsize 1µm for X-axisforward motion is behaving in random manner. Noparticular distribution has been seen from Figs.7(a). However, the errors for stepsizes 10µm and100µm are behaving periodically as seen in Figs.7(b), 7(c), 8(b) and 8(c) for both forward and
reverse motions of X-axis. However, the errordistribution tends to linear for increasing stepsizeas can be seen in Figs. 7(c) and 8(b). Errordistribution for 5mm stepsize is completely linearwhich can be seen from the adjusted R2 values of linear fit given in Figs 7(d) and 8(a) for X-axis.
Fig. 8 Position error distributions in reversemovement of X-axis
Fig. 9 Position error distribution for forward
movement of Y-axis
Fig. 10 Position error distribution for reversemovement of Y-axis
Figs. 9 and 10 are showing the position errordistribution of Y -axis movement in forward andreverse directions, respectively. The error
distribution for 1µm stepsize are more prone torandom nature as seen in Figs 9(a) and 10(d). Theerror distribution for 10µm stepsize is showingperiodic phenomenon for forward movement of Y-axis as per Fig. 9(b). The error distributions for 100µm and 5mm stepsizes are tends to linear fromperiodic and completely linear, respectively as seenin Figs 9(c), 9(d), 10(a) and 10(b).
Fig. 11 Yaw or angular error of X-axis forforward motion
Fig. 12 Yaw or angular error of X-axis forreverse motion
There is a linearly increasing trend of yawerror or angular error for X-axis during forwardand reverse motion for 5mm stepsize as shown inFigs. 11(d) and 12(a). However a periodic butincreasing trend of yaw error can be observed for10µm stepsize for both forward and reversemovement. The trends for 1µm and 100µmstepsizes are not showing similar trends for forwardand reverse movement of X-axis as shown in Figs11 and 12. On the other hand, a linearly increasing
7/29/2019 Simultaneous Position and Angular Error Measurement of a XY-stage using Miniature Interferometer with Step-size Variation 1Dutta, S., 2Pati, C., 3Sen, R.
trend of angular error for Y -axis movement forboth forward and reverse motion has been observedin Figs 13(c), 13(d), 14(a) and 14(b) for 100µm and5mm stepsizes. The yaw error distribution isbehaving quite periodic in nature for 1µm and10µm stepsizes for Y -axis as seen in Figs. 13(a),
13(b), 14(c) and 14(d).
Fig. 13 Yaw error plots for forward motion of Y-axis
Fig. 14 Yaw error plots for reverse motion of Y-axis
4. CONCLUSIONS
It can be seen from the results that the errorsfor smaller stepsizes with smaller are showingmore random or periodic phenomenon and largerstepsizes are showing linearly increasing trends forboth positional and angular error. It may beconcluded from this that major errors can bedetermined by taking larger stepsize for errormeasurement where small errors can be detected bytaking smaller stepsize. Knowing the errordistributions will also be helpful for errorcompensation purpose.
Also a compact measurement system has beenpresented in this study using the facility of
miniature interferometer. Simultaneousmeasurement of position and angular error has beenutilized for fast measurement capability withoutchanging the experimental set-up.
ACKNOWLDGEMENT
Authors are thankful to Department of Scienceand Technology (DST), India for funding thisresearch. Authors are also acknowledging Prof. G.Biswas, Director, CSIR-CMERI for his continuousinspiration.
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