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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 5 — Mar. 1, 2010
  • pp: 5271–5281
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Measurement of influence function using swing arm profilometer and laser tracker

Hongwei Jing, Christopher King, and David Walker  »View Author Affiliations


Optics Express, Vol. 18, Issue 5, pp. 5271-5281 (2010)
http://dx.doi.org/10.1364/OE.18.005271


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Abstract

We present a novel method to accurately measure 3D polishing influence functions by using a swing arm profilometer (SAP) and a laser tracker. The laser tracker is used to align the SAP and measure the parameters of the SAP setup before measuring the influence function. The instruments and the measurement method are described, together with measurement uncertainty analysis. An influence function deliberately produced with asymmetric form in order to create a challenging test is measured, and compared with that of a commercial 3D profilometer. The SAP result is 48.2μm in PV, 7.271mm3 in volume. The 3D profilometer result is 48.4μm in PV, 7.289mm3 in volume. The forms of the two results show excellent correlation. This gives confidence of the viability of the SAP method for larger influence functions out of range of the commercial instrument.

© 2010 OSA

1. Introduction

Accurate measurement of the influence function of a sub-diameter polishing tool is critical to computer controlled polishing [1

1. D. W. Kim, W. H. Park, S.-W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5656. [CrossRef] [PubMed]

3

3. D. W. Kim and S.-W. Kim, “Static tool influence function for fabrication simulation of hexagonal mirror segments for extremely large telescopes,” Opt. Express 13(3), 910–917 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-910. [CrossRef] [PubMed]

], particularly as input to corrective polishing routines. In some cases, 2D profiles are adequate; but for full 3D correction of surfaces, 3D maps of influence functions are required. The traditional measurement method is to use a profilometer with 3D capability, such as the Taylor Hobson Form Talysurf, which has a 120mm gauge range. However, this limits the size of the influence functions that can reasonably be measured, as a clear unpolished land is required to define an effective datum for measurement.

A Zeeko IRP1600 CNC polishing machine (1.6m capacity) is currently being installed at the National Facility. In this paper we present a novel method for measuring 3D influence functions using a swing arm profilometer (SAP) with 1m capacity, and a laser tracker. This method can therefore easily handle a range of influence functions from small to the ~150mm limit of the IRP1600 polishing machine when used with standard Zeeko polishing bonnets. It also gives the possibility to measure larger influence functions delivered by more traditional polishing laps, which can then be used to model the removal process. Finally, it has the ability to measure deep influence functions (tens of microns and not possible with phase-shifting interferometer) with 12.5nm resolution, fast speed and a large number of data points, for which a coordinate measurement machine (CMM) would not be comparable.

A laser tracker is essentially an optical CMM, measuring spherical coordinates rather than Cartesian coordinates. The tracker uses a distance-measuring interferometer (DMI) and two angular encoders to measure rotation angles. A laser beam is launched and reflected back by a sphere-mounted retro-reflector (SMR). When the SMR is moved, a feed back sensor detects and tracks the motion. The Arizona group have pioneered use of the laser tracker to align and measure large optics, and reported outstanding results [4

4. C. Zhao, R. Zehnder, and J. H. Burge, “Measuring the radius of curvature of a spherical mirror with an interferometer and a laser tracker,” Opt. Eng. 44(9), 090506 (2005). [CrossRef]

,5

5. J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 6676E (2007).

].

The SAP is traditionally used for testing large convex or concave optics [6

6. D. S. Anderson, R. E. Parks, and T. Shao, “A versatile profilometer for aspheric optics,” in Proceedings of OF&T Workshop Technical Digest (Academic, Monterrey, CA 1990), Vol. 11, pp. 119–122.

12

12. H. Jing, C. King, and D. Walker, “Simulation and validation of a prototype swing arm profilometer for measuring extremely large telescope mirror-segments,” Opt. Express 18(3), 2036–2048 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2036. [CrossRef] [PubMed]

]. In contrast, we report the use of the SAP in a novel way to measure large, nominally plano optics with large surface figure errors outside the range of phase-shifting interferometer (tens of microns) with a resolution of 12.5nm. The rotary axis of the arm-bearing is set parallel to the rotary axis of the rotary table. The part is then measured along concentric circular traces. The probe operates in absolute mode instead of comparator mode.

This paper is organized as follows. In Section 2, the measurement instruments are described. In Section 3, the measurement uncertainty of the instruments is presented. In Section 4, the detailed measurement procedure is presented. An influence function is measured and the result is compared with that of a 3D Talysurf profilometer, leading to concluding remarks in Section 5.

2. Measurement instruments

The instruments being used to measure influence function are shown in Fig. 1
Fig. 1 Measurement instruments (SAP + Laser Tracker)
. Which comprise the SAP and a Laser Tracker.

The Laser Tracker has two functions in the measurement setup. The first function is to align the SAP to ensure the swinging path of the probe head passes through the rotary axis of the rotary table. By building a coordinate system on the rotary table and measuring the swinging arc of the arm, we can determine whether the swinging path of the probe head passes through the rotary axis of the rotary table and do corresponding adjustment to it. The second function is to measure the length of the arm, i.e. the length of the probe head center to rotation center of arm bearing.

After alignment, the SAP is used to capture the 3D profile data of the influence function by rotating the rotary table and swinging the arm.

The XY coordinates measurement principle is shown in Fig. 2
Fig. 2 XY coordinates measurement principle
. The circle in the left represents the rotary table. Point O represents rotation center of the rotary table. Point S represents rotation center of the arm bearing. The arc crossing point O represents the swinging path of the swinging arm. The 2D coordinate system on the rotary table is XOY.

The X and Y coordinates of P are as follows
X=L×cos(β)×2×(1cos(α))
(1)
Y=L×sin(β)×2×(1cos(α))
(2)
Where L is the length of the arm as determined by Laser Tracker measurement. The angle of α is the swinging angle of the swinging arm, which is measured by an encoder installed on the arm bearing. The angle of β is the rotary angle of the rotary table, which is measured by encoder installed on the rotary table.

The Z coordinate of P can be measured using a high precision contact probe.

3. Measurement uncertainty analysis

The following analysis is based on the current specifications of the instruments: 780.76mm in arm length, 100mm in maximum diameter of influence function, the temperature variation is ± 0.5°C.

3.1 Measurement uncertainty in X and Y coordinates

X and Y coordinates are determined by the length of the arm, angle of rotary table, angle of arm bearing and temperature variation.

According to the statistic data of the arm length measured by the laser tracker, the measurement uncertainty of the arm length is 0.05mm. For the current specifications of the instruments, the max angle of the arm is 3.670°. The uncertainty induced by the length of the arm is

uarmlengthxy=0.05×2×(1cos(3.670))=3.2μm
(3)

According to the statistic data of the radial runout measurement of the rotary table, the measurement uncertainty induced by the radial runout of the rotary table is

uRTxy=0.1μm
(4)

According to the specifications of the arm bearing, the radial runout of the arm bearing is 25nm. The uncertainty induced by the radial runout of the arm bearing is

uarmbearingxy=0.025μm
(5)

According to the NPL measurement uncertainty report, the temperature dependent uncertainty ( ± 0.5°C variation) in XY coordinates is

utempxy=2.51μm
(6)

The combined uncertainty in X and Y coordinates is as follows

ucxy=uarmlengthxy2+uRTxy2+uarmbearingxy2+utempxy2=3.22+0.12+0.0252+2.512=4.1μm
(7)

The expanded uncertainty (k = 2) in X and Y coordinates is as follows

Uxy=k×ucxy=2×4.1μm=8.2μm
(8)

3.2 Measurement uncertainty in Z coordinate

Z coordinate is determined by the Solartron linear encoder LT10, axial runout of rotary table, axial runout of arm bearing and temperature variation.

According to the specifications of Solartron linear encoder LT10, the measurement uncertainty of Solartron linear encoder LT10 is

uprbz=0.5μm
(9)

According to the specifications of the arm bearing, the axial runout of the arm bearing is 25nm. The uncertainty induced by the axial runout of the arm bearing is

uRTz=0.025μm
(10)

According to the statistic data of the axial runout measurement of the rotary table, the measurement uncertainty induced by the axial runout of the rotary table is

uarmbearingz=0.1μm
(11)

According to the NPL measurement uncertainty report, the temperature dependent uncertainty ( ± 0.5°C variation) in Z coordinate is

utempz=0.87μm
(12)

The combined uncertainty in Z coordinate is as follows

ucz=uprbz2+uRTz2+uarmbearingz2+utempz2=0.52+0.0252+0.12+0.872=1μm
(13)

The expanded uncertainty (k = 2) in Z coordinate is as follows

Uz=k×ucz=2×1μm=2μm
(14)

3.3 Summary

The measurement uncertainty of the instruments under current circumstances is summarized as follows

  • Horizontal (X): ± 8.2μm
  • Horizontal (Y): ± 8.2μm
  • Vertical (Z): ± 2μm

From the analysis of the measurement uncertainty, the major contributions of the measurement uncertainty are from the length of the arm and the temperature variation. If we want to improve the measurement accuracy, we should measure the length of the arm more accurately and control the temperature more rigidly.

4. Measurement procedure and results

Before measuring the influence function, an alignment was performed to the instruments using a flat mirror. The alignment procedure are summarized as follows

  • 1. Levelling of the flat mirror. Place the flat mirror on the stage on the rotary table. Position the probe at the edge of the flat mirror and rotate the rotary table. Monitor the probe trace and do corresponding tip/tilt adjustment to the stage to make the probe trace deviation less than 0.5μm.
  • 2. Levelling of the SAP. Stop the rotary table. Swing the arm back and forth. Monitor the probe trace and do corresponding tip/tilt adjustment to the SAP in Y axis to make the probe trace deviation less than 0.5μm.
  • 3. Alignment of the tilt angle of arm bearing of the SAP. Stop the rotary table. Swing the arm back and forth. Monitor the probe trace and adjust the tilt angle of arm bearing to make the probe trace deviation less than 0.5μm.
  • 4. Centering the probe. Measure the plane of the flat mirror, a line along the Y axis of SAP and the rotary axis of rotary table using the laser tracker. Build a coordinate system on the flat mirror, set the origin of the coordinate system to the intersection point of flat mirror and rotary axis of rotary table. Swing the arm back and forth. Scan the swinging arc of the probe using the laser tracker. Check whether the swinging arc passes through the origin of the coordinate system, if not adjust the X stage of SAP. Position the probe at the origin of the coordinate system and set the angle of the table and the angle of the arm to zero.

After the alignment, an influence function sample was measured using the instruments (shown in Fig. 1) described in this paper, the data was acquired by making concentric scans rotating the rotary table and incrementing the arm-angle by 0.02°between scans (as shown in Fig. 3
Fig. 3 Measurement pattern. The arc is the swinging path of the arm. The concentric circles are probe traces of the scans.
).

The data cloud of the SAP measurement is the left one shown in Fig. 4
Fig. 4 Data clouds of SAP (left) and 3D Talysurf profilometer (right)
. To verify this measuring method the same influence function sample was measured using the 3D Talysurf profilometer. The data cloud of the 3D Talysurf profilometer measurement is the right one shown in Fig. 4.

Using the data clouds and Matlab software, the surface under test can be reconstructed. The reconstructed surface of SAP data is shown in Fig. 5
Fig. 5 Reconstructed surface of SAP data (PV: 48.2μm, volume = 7.271mm3)
. The peak to valley value of SAP measurement is 48.2μm. The volume of SAP measurement is 7.271mm3.

The reconstructed surface of 3D Talysurf profilometer data is shown in Fig. 6
Fig. 6 Reconstructed surface of Talysurf profilometer data (PV: 48.4μm, volume = 7.289mm3)
. The peak to valley value of 3D talysurf profilometer measurement is 48.4μm. The volume of 3D Talysurf profilometer measurement is 7.289mm3.

To make the differences between the two measurements clearer, a subtraction of the two surfaces was done. Before the subtraction, the radius compensation of the probe head was performed to make the two surfaces comparable because the probe diameter of the Talysurf measurement is 0.5mm, the probe diameter of the SAP measurement is 1.0mm. The difference surface is shown in Fig. 7
Fig. 7 Difference surface of SAP and Talysurf measurement (PV: 2.3μm, rms = 0.3μm)
.

From the difference surface of the two measurements, there are many concentric rings caused by random errors coming from the rotary table and the arm bearing. The maximum differences between the measurements occur at the steepest slopes, which is because the probe radius compensation at the steeper slopes results in larger errors. There are many high frequency errors in the difference surface, due to the difference in the probe diameters used (the smaller Talysurf profilometer probe measured more high frequency data). Comparing the PV and volume values from Fig. 5 and Fig. 6, it is clear that the high frequency contents have no significant effect on the volume measured for the deep influence functions of tens of microns depth. These results can be used as input to the polishing processes in use at the National Facility such as Zeeko precessions. We expect to filter out some of the higher frequencies from the data before doing this and expect to report on the work in a future paper.

Two section profiles (X = 5mm and Y = 0mm) from the reconstructed surfaces are compared. The section profiles in Y = 0mm of the two results are shown in Fig. 8
Fig. 8 Profiles in Y = 0mm
.

A subtraction of the two profiles was done. The difference profile is shown in Fig. 9
Fig. 9 Difference profile in Y = 0mm(PV: 2.0μm, rms = 0.4μm)
.

The section profiles in X = 5mm of the two results are shown in Fig. 10
Fig. 10 Profiles in X = 5mm
.

A subtraction of the two profiles was done. The difference profile is shown in Fig. 11
Fig. 11 Difference profile in X = 5mm(PV: 1.0μm, rms = 0.3μm)
.

5. Conclusions

In this paper we present a novel method to accurately measure the influence function by using a swing arm profilometer and a laser tracker. The laser tracker is used to align the SAP and measure the parameters of the SAP setup before measuring the influence function. The SAP captures the 3D profile data of the influence function by rotating the rotary table and swinging the arm. The measurement uncertainty of the instruments is presented, which is ± 8.2μm in X and Y coordinates, ± 2μm in Z coordinate. The detailed measurement procedure is presented. A sample influence function is measured and the result is compared with that of a 3D profilometer. The SAP result is 48.2μm in PV, 7.271mm3 in volume. The 3D Talysurf profilometer result is 48.4μm in PV, 7.289mm3 in volume. The forms of the two results show considerable resemblance. Two section profiles from each reconstructed surface are extracted and compared. The results of the section profiles in Y = 0mm from SAP measurement and 3D Talysurf profilometer measurement are 42.5μm in PV, 11.3μm in rms and 43.3μm in PV, 11.7μm in rms respectively. The results of the section profiles in X = 5mm from SAP measurement and 3D Talysurf profilometer measurement are 47.3μm in PV, 13.6μm in rms and 47.1μm in PV, 14.1μm in rms respectively. The profiles show good correlation.

Acknowledgments

The work in this paper was done during a sabbatical year that Hongwei Jing spent at the National Facility for Ultra Precision Surfaces, St. Asaph, UK as a visiting scholar, he is indebted to the Chinese Academy of Sciences (CAS) and University College London (UCL) for their support. Christopher King and David Walker acknowledge support from the former UK Particle Physics and Astronomy Research Council. The prototype swing arm profilometer was constructed by the UK National Physical Laboratory (NPL) under National Measurement System Length Programme funding, in collaboration with UCL. The authors gratefully acknowledge the help and assistance of NPL, and in particular, Dr. Andrew Lewis.

References and links

1.

D. W. Kim, W. H. Park, S.-W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5656. [CrossRef] [PubMed]

2.

L. Huang, C. Rao, and W. Jiang, “Modified Gaussian influence function of deformable mirror actuators,” Opt. Express 16(1), 108–114 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-108. [CrossRef] [PubMed]

3.

D. W. Kim and S.-W. Kim, “Static tool influence function for fabrication simulation of hexagonal mirror segments for extremely large telescopes,” Opt. Express 13(3), 910–917 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-910. [CrossRef] [PubMed]

4.

C. Zhao, R. Zehnder, and J. H. Burge, “Measuring the radius of curvature of a spherical mirror with an interferometer and a laser tracker,” Opt. Eng. 44(9), 090506 (2005). [CrossRef]

5.

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 6676E (2007).

6.

D. S. Anderson, R. E. Parks, and T. Shao, “A versatile profilometer for aspheric optics,” in Proceedings of OF&T Workshop Technical Digest (Academic, Monterrey, CA 1990), Vol. 11, pp. 119–122.

7.

D. S. Anderson and H. James, “Burge, “Swing arm Profilometry of Aspherics,” Proc. SPIE 2356, 269–279 (1995).

8.

P. Su, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM for aspherics,” Proc.SPIE 7426, 74260J–74260J −8 (2009).

9.

A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry - traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, Mexico, 2006), pp. 101–105.

10.

A. Efstathiou, Design considerations for a hybrid swing arm profilometer to measure large aspheric optics (Ph.D thesis, London, 2007)

11.

A. Lewis, Uncertainty budget for the NPL-UCL swing arm profilometer operating in comparator mode (HMSO and Queen’s printer, London, 2008).

12.

H. Jing, C. King, and D. Walker, “Simulation and validation of a prototype swing arm profilometer for measuring extremely large telescope mirror-segments,” Opt. Express 18(3), 2036–2048 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2036. [CrossRef] [PubMed]

OCIS Codes
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(220.4840) Optical design and fabrication : Testing

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: December 22, 2009
Revised Manuscript: February 4, 2010
Manuscript Accepted: February 24, 2010
Published: February 26, 2010

Citation
Hongwei Jing, Christopher King, and David Walker, "Measurement of influence function using swing arm profilometer and laser tracker," Opt. Express 18, 5271-5281 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-5271


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References

  1. D. W. Kim, W. H. Park, S.-W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5656 . [CrossRef] [PubMed]
  2. L. Huang, C. Rao, and W. Jiang, “Modified Gaussian influence function of deformable mirror actuators,” Opt. Express 16(1), 108–114 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-108 . [CrossRef] [PubMed]
  3. D. W. Kim and S.-W. Kim, “Static tool influence function for fabrication simulation of hexagonal mirror segments for extremely large telescopes,” Opt. Express 13(3), 910–917 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-910 . [CrossRef] [PubMed]
  4. C. Zhao, R. Zehnder, and J. H. Burge, “Measuring the radius of curvature of a spherical mirror with an interferometer and a laser tracker,” Opt. Eng. 44(9), 090506 (2005). [CrossRef]
  5. J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 6676E (2007).
  6. D. S. Anderson, R. E. Parks, and T. Shao, “A versatile profilometer for aspheric optics,” in Proceedings of OF&T Workshop Technical Digest (Academic, Monterrey, CA 1990), Vol. 11, pp. 119–122.
  7. D. S. Anderson and H. James, “Burge, “Swing arm Profilometry of Aspherics,” Proc. SPIE 2356, 269–279 (1995).
  8. P. Su, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM for aspherics,” Proc.SPIE 7426, 74260J–74260J −8 (2009).
  9. A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry - traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, Mexico, 2006), pp. 101–105.
  10. A. Efstathiou, Design considerations for a hybrid swing arm profilometer to measure large aspheric optics (Ph.D thesis, London, 2007)
  11. A. Lewis, Uncertainty budget for the NPL-UCL swing arm profilometer operating in comparator mode (HMSO and Queen’s printer, London, 2008).
  12. H. Jing, C. King, and D. Walker, “Simulation and validation of a prototype swing arm profilometer for measuring extremely large telescope mirror-segments,” Opt. Express 18(3), 2036–2048 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2036 . [CrossRef] [PubMed]

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