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Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 6 — Mar. 24, 2003
  • pp: 624–631
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Novel laser datum system for nanometric profilometry for large optical surfaces

Ho-Soon Yang, Sug-Whan Kim, and David Walker  »View Author Affiliations


Optics Express, Vol. 11, Issue 6, pp. 624-631 (2003)
http://dx.doi.org/10.1364/OE.11.000624


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Abstract

We report a new laser datum system for precision point-by-point profilometry of large curved optical surfaces. The laser datum is sensed by a nulling quadrant photodiode mounted in a flexural system with hybrid actuators, which also carries interferometer reference optics for vertical and horizontal displacement measurement. The flexure characteristics such as cross-talk and hysteresis were investigated. The optimum environmental conditions for the active position-control were studied, and closed-loop control was modeled. The experimental results for compensation accuracy showed a repeatability of ± 4 nm rms, the compensation accuracy of 10 nm (vertical channel) and 20 nm (horizontal channel).

© 2003 Optical Society of America

1. Introduction

Beyond current 8–10m class large astronomical telescopes, there are currently at least three extremely large telescope projects proposed world-wide. They comprise a 30m class telescope (CELT [1

1. CELT, The California Extremely Large Telescope, http://celt.ucolick.org/

]), a 50m class telescope (EURO50 [2

2. National Physical Laboratory, NPL and the EURO50 telescope, http://www.npl.co.uk/length/dmet/euro50.html

]) and a 100m class telescope (OWL [3

3. OWL, 100 m OWL telescope concept, http://www.eso.org/projects/owl/owl_design.html

]). These telescopes are all based on segmented primary mirrors with 1–2m class hexagonal segments. Such telescopes pose significant technical challenges in mass production of a few hundred – if not thousand – 1–2m class precision mirrors over ~5 years. This contrasts to the ~6 month or more delivery times typical for 2m-class mirrors today. If we are to prove the feasibility of constructing such massive telescopes within a reasonable time-scale of ~15 years, prior development of efficient mass fabrication technology comprising rapid processing and testing is essential. As regards the technical requirement for testing, this is illustrated by the primary mirror segments of EURO50, which must handle a sag of ~10mm, a height accuracy of ~40nm, a lateral range of ~2m and a horizontal accuracy of ~1µm [4

4. D.D. Walker et al., “The primary and secondary mirrors for the proposed Euro50 telescope,” Design Study Report (2002).

].

Interferometry has commonly been used during the fine polishing and figuring stages of large optics fabrication. Profilometry has complimentary properties to interferometry. In particular, it enables metrology of aspheric optics independent of the null lenses needed for interferometry; null lenses being a source of uncertainty and error both in their manufacture and alignment. It also handles aspherics for which there is no convenient null lens. In many cases of optical fabrication, a point-by-point measurement (rather than a continuous scan) is adequate to feed back into the polishing process, and gives information on absolute radius of curvature, which an interferometer as normally implemented does not directly provide.

One of the key factors contributing to the restricted vertical accuracy in profilometry has been the reliance on a mechanical datum (e.g. granite beam), providing an accuracy at perhaps the micron level. This is limited by effects such as hysteresis, gravity deflections under varying loads with a moving probe-assembly, and thermal distortions. In order to compensate mechanical systematic errors, a reversal method has commonly been used [5

5. D. J. Whitehouse, Handbook of surface metrology (IOP, 1995), Chap. 4.

,6

6. W.T. Estler, “Calibration and use of optical straightedges in the metrology of precision machines,” Opt. Eng. 24, 372–379 (1985).

]. The swing-arm profilometer of Steward Observatory Mirror Laboratory [7

7. D.S. Anderson and J.H. Burge, “Swing-arm Profilometry of Aspherics,” in Optical manufacturing and testing, V.J. Doherty and H. Stahl, Proc. SPIE2536, 169–179 (1995). [CrossRef]

] attempts to circumvent the limitations of linear mechanical datums by using purely rotational motions, which are usually more accurate. However, this is at the expense of losing absolute information on radius of curvature, which is critical for ensuring that mirror segments will all work together.

A profilometer of nanometric height accuracy over its measurement range, and reasonably fast operation, could improve optics fabrication efficiency by providing a single metrology station throughout CNC grinding, loose abrasive lapping, polishing and figuring. Accomplishing this may be divided into four principle challenges: - i) a straightness datum, ii) measurement of height with respect to the datum, iii) measurement of lateral displacement, and iv) measurement speed. In this paper we describe the use of a laser beam in free-air to define the datum.

A laser beam as a profilometric datum has been described elsewhere. The long trace profiler (LTP) [8

8. P.Z. Takacs, S.-N. Qian, and J. Colbert, “Design of a long-trace surface profiler,” in Metrology:Figure and Finish, B.E.Truax, Proc. SPIE749, 59–64 (1987). [CrossRef]

12

12. S. Qian, G. Sostero, and P.Z. Takacs, “Precision calibration and systematic error reduction in the long trace profiler,” Opt. Eng. 39, 304–310 (2000) [CrossRef]

] used a laser beam reflected from a flat mirror. The slope error of the carriage was subtracted from the slope directly measured on the part, giving the corrected slope of the part. Due to the limited size of the lens and detector in the instrument, surface slopes were limited to 4.2 mrad [10

10. S.-N. Qian, W. Jark, and P. Z. Takacs, “The penta-prism LTP: A long-trace-profiler with stationary optical head and moving penta prism,” Rev.Sci.Instrum. 66, 2562–2569 (1995). [CrossRef]

]. Virdee at NPL also used a laser beam in free air as a datum for a non-contact profilometer, but his work was targeted at measuring precision flat surfaces of 300mm in diameter for international standardization of flatness [13

13. M. Virdee, “Non-contacting straightness measurementto nanometer accuracy,” Int. J. Mach. Tools Manufact. 35, 157–164 (1995). [CrossRef]

].

The laser datum system monitors the position of an interferometer component associated with vertical metrology, with respect to the centroid of the laser beam, and compensates the positional variation by a closed-loop two-axis flexure mechanism. In this paper, technical details of the laser datum system is presented and its performance studied both in simulation and experiment.

Fig. 1. Schematic diagram of profilometer test bench.

2. Laser datum system

Neville et al has previously reported the usage of quadrant detectors (QD) and a laser beam for high resolution position-monitoring [14

14. K. S. Lee Neville, Yimin Cai, and Ajay Joneja, “High-resolution multidimensional displacement monitoring system,” Opt. Eng. 36, 2287–2293 (1997). [CrossRef]

,15

15. K. S. Lee Neville, Yimin Cai, S. F. Wong Alfred, and Ajay Joneja, “Ultra-high-resolution optical monitoring system using a noise cancellation technique,” Opt. Eng. 36, 3353–3359 (1997). [CrossRef]

]. With noise-cancellation techniques, his method showed a resolution of better than 2nm. Figure 2 shows our datum system. A stabilised He-Ne laser is located separately from the instrument and feeds via an optical fibre. The fixed horizontal laser injection module is mounted off one end of the granite beam via a Cervit block, and comprises the output end of the fibre, a spatial filter, and a beam-splitter and other components associated with the interferometric measurement of horizontal displacement of the moving carriage. The traveling laser sensor-module comprises a two-axis flexure system with hybrid actuators. This carries a quadrant photodiode to sense the laser-position, and a Cervit block supporting the reference optics for the horizontal and vertical interferometer arms. The mechanism operates through analogue nulling, i.e., the actuators translate the QD (and the interferometer optics with it) so as to equalize the left and right halves (horizontal error), and the upper and lower halves (vertical error). The heart of the vertical probe comprises a vertical contact-stylus mounted to a 10mm Invar shaft, the top of which carries a retro-reflector. After QD nulling, the vertical interferometer therefore measures the displacement of the stylus directly with respect to the laser datum.

Fig. 2. The diagram of flexure system in the laser datum system.

Hybrid actuators were used because of the difficulty of achieving both nanometric precision and large dynamic range in a single actuator. The dynamic range was required to accommodate the errors of straightness of the granite beam and departures from parallelism with the laser datum. Each hybrid actuator consists of a stacked PZT and a motor mike (hereafter called MM). The MM has a motion range of 25 mm, but its positioning accuracy is a few micrometers at best, due to inherent backlash, friction and inertia. The PZT provided a range of 10 µm and nanometer-level positioning accuracy. Figure 3 shows the concept of the QD electronics, comprising FET-OP amps and differential amps with unity gain. The position signals from the quadrant diode are generated with simple equations as shown in Fig 3.

Fig. 3. Generation of position signal from quardrantdiode electronics: Pvertical=(VA+VC) - (VB+VD), Phorizontal=(VA+VB) - (VC+VD)

3. Flexure subsystem

Ideally, the position of each flexural position should not be affected by that of the other. However, as shown in Fig. 4 (a), the original flexure design caused significant cross-talk and hysteresis between two-axis movements. The horizontal flexure position was affected by 6.7% of the positional change of the vertical flexure, whereas that of the vertical flexure was influenced by about 3.7% of the horizontal flexure travel. Additionally, the motion of the vertical PZT suffered hysterisis of ~30% to the horizontal displacement. The horizontal PZT motion produced less than 0.1% hysteresis in vertical displacement.

Such cross-talk and hysteresis can be interpreted with, first, the arcuate motion of the flexure. Although this effect cannot be removed entirely from this system, precise alignment of the flexure system with respect to the datum reduced the deflection of each flexure and with it the cross-talk. The second contribution is the inherent geometry of the original flexure system as shown in Fig. 2. The horizontal PZT moves with the vertical flexure, whereas the horizontal MM is attached onto the outer frame. This problem was solved by mounting the horizontal MM on the moving platform attached to the frame of the vertical flexure. Cross-talk was then reduced to 1.1% and 1.7% of vertical and horizontal flexure movements respectively (as shown in Fig. 4 (b)), and hysteresis to <20 nm.

Fig. 4. (a) Horizontal (filled square symbol)/vertical (filled circle symbol) displacement of the QD for the vertical (bottom x-axis)/horizontal (top x-axis) flexure movement. (b) Cross-talk and hysteresis of the flexure system after modification.

4. Environmental effects

Air turbulence is detrimental to defining a temporally stable line in space. Table 1 shows the displacement of the laser spot on the quadrant diode monitored under different environmental conditions. Clearly, air leakage from the air bearing affected the local environment, causing thermal fluctuations of refractive index of the air, as its exhaust temperature was measured to be some lower than ambient. Even without the air-bearing pressurized, local ‘seeing’ effects disturbed measurements. However, with a set of mechanical shields between the laser beam path and air bearing, it was demonstrated that fluctuation of the datum position could be <0.02 µm, p-v providing the air-bearing was not operated. It would in principle be possible to preheat the air-bearing supply by a corresponding 0.4°C but this has not been attempted.

Adding to the local seeing effect discussed, the thermal condition can cause a drift in the collimating lens or local bending of the structure in the vicinity of the collimator lens. For example, when looking for 60 nm accuracy of vertical measurement over a meter of travel, the laser beam should be stable to better than 0.06 µrad. Controlling or even measuring such small angular displacement in and around the collimator lens assembly is indeed a very challenging task. This problem can, in principle, be solved with another QD at the opposite end of the granite beam, monitoring any directional instability of the beam. Now, the QD sensitivity is measured to be 42 mV/µm. It follows that the full-scale QD output-signal of 5V, when digitized by a 16-bit ADC, would provide a resolution of ~1.8 nm over the total height displacement of 119 µm. Whilst this method has not yet been implemented, it is clear that the directional instability of the reference laser beam could be compensated well within the target form accuracy of 60 nm.

Table 1. Typical P-V displacements of the laser datum beam on the quadrant diode in three different conditions.

table-icon
View This Table

5. Close-loop compensation model

The sensitivity of the QD depends on the intensity and size of the laser beam. If the laser intensity were uniform over the quadrant diode, it would produce no position-dependent signal. However, the beam profile emerging from the launch optics were near-Gaussian with σ (rms radial fluctuation) = 1.1 mm, i.e., 63% of encircled energy fell within 2.2 mm in diameter, which was smaller than the 3 mm square active area of the quadrant diode. The beam size remained constant at 2.1 ± 0.1 mm over the horizontal travel range of 1m. This ensured that the quadrant diode produced a voltage proportional only to the vertical displacement of the laser beam.

Figure 5 illustrates the MM and PZT control model of the datum beam position. The selection of which actuator was energized depended on the signal from the pre-amplifier. If this signal were above a specified value, the MM was selected, and if below, the PZT. In the latter case, the system transfer function Y(s) is defined as:-

Y(s)=P(s)(1+G(s))
(1)

where P(s) is the disturbance function. The system loop gain G(s) is defined as:-

G(s)=αβK1K2K3
(2)

where α is the expansion coefficient of PZT (µm/V), β is the sensitivity coefficient (V/µm). K1, K2 and K3 take the form of an OP amp transfer function, or:-

K(f)=Adc(1+jff1)
(3)

Here Adc is the amplification of the OP amp at zero frequency, and f1 is the cut-off frequency. Taking cut-off frequencies of K1, K2, and K3 with 4Hz, 0.12 Hz, and 18.3 Hz, and considering that α is 0.14 µm/V, and β is 0.044 V/µm from experiments, the result of closed-loop model simulation is shown in Fig. 6 (a). This is the response of the system to the step function disturbance. The difference between the height of step function disturbance and the height recovered from the PZT compensation was only ~3 nm. Whilst the result implies that the system is under-damped, this simulation predicted that the positional compensation of the datum system could be accomplished well within the measurement requirement of 60 nm.

6. Compensation experiment and results

The position of the quadrant diode was artificially disturbed and then recovered by the closed loop control. Figure 6 shows the model prediction (6a) and the experiment results (6b). The datum system was disturbed vertically by 0.7 microns, before time ‘A’ in Fig. 6 (b). This generated the residual cross-talk of about 0.1–0.2 micron, as explained in Fig. 4 (b). The closed loop control commenced at ‘A’. The overshooting and oscillatory signals are shown in both channels during the position recovery, as expected from the model simulation. This transient response subsided to acceptable levels within ~1 second for both channels (the horizontal being more tolerant for modest surface-slopes).

Fig. 5. Positional compensation model, when the PZT is activated.

The resulting positional accuracies are about 10 nm and 20 nm in the vertical and horizontal channels respectively. These compensation accuracies are larger than the 3 nm expected from the simulation. The discrepancy is believed to be due to the observed residual hysteresis of the demonstration system. The same test was repeated 15 times to assess its repeatability. The measured repeatability of ±4 nm rms in the vertical channel was achieved from the closed loop compensation, thereby demonstrating that the current datum system stays well within the target measurement accuracy of 60 nm.

Fig. 6. (a) Simulated transient response of the PZT (circle points) to the step disturbance (solid line). (b) Experiment results of position compensation of the datum beam at both channels. The dotted lines are the original position.

6. Concluding remarks

Most profilometers conduct a continuous trace, whereas we have reported on a point-by-point measurement system. The ~1 sec settling time for the laser datum would introduce serious errors for a continuous trace. In contrast, it is perfectly satisfactory for a set of discrete samples, as the laser system can settle as the probe is lowered onto the surface prior to the capture of the metrology data. For a nominal 40–80 points across the surface, the down-time due to settling would then be only ~one to two minutes respectively, for the entire measurement. A 40 by 40 grid of points on an off-axis mirror segment (e.g., mounted on a rotary stage) would take ~40 mins, and an 80 by 80 <3 hours. In the context of automated polishing of large optics, this is a very useful development, particularly as texture can be measured separately by readily available commercial instrumentation.

The effect of environmental air turbulence on the datum was reduced to ~20nm by a simple polythene curtain around the table and a polythene shield covering the instrument. However, we did not overcome the deleterious effects of air-bearing leakage. Whilst controlling the input air-temperature to the bearing will undoubtedly mitigate the effect, we would recommend the use of a different linear bearing, such as a plain sliding bearing with weight-relief. In order to monitor and, if needed, to compensate the remaining directional instability of the laser reference beam, a secondary QD at the opposite end of the granite beam to the laser source is also proposed.

The successful control of the laser datum with an accuracy of 10–20 nm provides an attractive approach to profilometric referencing for 1–2m class mirrors, especially as it will provide absolute metrology of base radius-of-curvature as well as aspheric form.

Acknowledgement

The development of SPLOT was funded by the Satellite Technology Research Centre (SaTReC) in the Korea Advanced Institute of Science and Technology (KAIST) and the UK Particle Physics and Astronomy Research Council under an underpinning grant. We acknowledge that the final stage of this research, particularly manuscript preparation, was supported, in part, by Center for Space Astrophysics, under the creative research initiative program of the Ministry of Science and Technology and by Korea Institute of S&T Evaluation and Planning (Grant code M1-0206-00-0014).

References and links

1.

CELT, The California Extremely Large Telescope, http://celt.ucolick.org/

2.

National Physical Laboratory, NPL and the EURO50 telescope, http://www.npl.co.uk/length/dmet/euro50.html

3.

OWL, 100 m OWL telescope concept, http://www.eso.org/projects/owl/owl_design.html

4.

D.D. Walker et al., “The primary and secondary mirrors for the proposed Euro50 telescope,” Design Study Report (2002).

5.

D. J. Whitehouse, Handbook of surface metrology (IOP, 1995), Chap. 4.

6.

W.T. Estler, “Calibration and use of optical straightedges in the metrology of precision machines,” Opt. Eng. 24, 372–379 (1985).

7.

D.S. Anderson and J.H. Burge, “Swing-arm Profilometry of Aspherics,” in Optical manufacturing and testing, V.J. Doherty and H. Stahl, Proc. SPIE2536, 169–179 (1995). [CrossRef]

8.

P.Z. Takacs, S.-N. Qian, and J. Colbert, “Design of a long-trace surface profiler,” in Metrology:Figure and Finish, B.E.Truax, Proc. SPIE749, 59–64 (1987). [CrossRef]

9.

P.Z. Takacs, S.C.K. Feng, E. L. Church, S. -N. Qian, and W. -M. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for optics and large optics, J.B.Arnold and R.E.Parks, Proc. SPIE966, 354–364 (1989). [CrossRef]

10.

S.-N. Qian, W. Jark, and P. Z. Takacs, “The penta-prism LTP: A long-trace-profiler with stationary optical head and moving penta prism,” Rev.Sci.Instrum. 66, 2562–2569 (1995). [CrossRef]

11.

P.Z. Takacs, “Significant Improvements in Long Trace Profiler Measurement Performance,” in Optics for High-brightness synchrotron radiation beamlinseII, L.E.Berman and J.R.Arthur., Proc. SPIE2856, 236–245 (1996). [CrossRef]

12.

S. Qian, G. Sostero, and P.Z. Takacs, “Precision calibration and systematic error reduction in the long trace profiler,” Opt. Eng. 39, 304–310 (2000) [CrossRef]

13.

M. Virdee, “Non-contacting straightness measurementto nanometer accuracy,” Int. J. Mach. Tools Manufact. 35, 157–164 (1995). [CrossRef]

14.

K. S. Lee Neville, Yimin Cai, and Ajay Joneja, “High-resolution multidimensional displacement monitoring system,” Opt. Eng. 36, 2287–2293 (1997). [CrossRef]

15.

K. S. Lee Neville, Yimin Cai, S. F. Wong Alfred, and Ajay Joneja, “Ultra-high-resolution optical monitoring system using a noise cancellation technique,” Opt. Eng. 36, 3353–3359 (1997). [CrossRef]

OCIS Codes
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

ToC Category:
Research Papers

History
Original Manuscript: February 19, 2003
Revised Manuscript: March 18, 2003
Published: March 24, 2003

Citation
Ho-Soon Yang, Sug-Whan Kim, and David Walker, "Novel laser datum system for nanometric profilometry for large optical surfaces," Opt. Express 11, 624-631 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-6-624


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References

  1. CELT, The California Extremely Large Telescope, <a href="http://celt.ucolick.org/">http://celt.ucolick.org/</a>
  2. National Physical Laboratory, NPL and the EURO50 telescope, <a href="http://www.npl.co.uk/length/dmet/euro50.html">http://www.npl.co.uk/length/dmet/euro50.html</a>
  3. OWL, 100 m OWL telescope concept, <a href="http://www.eso.org/projects/owl/owl_design.html">http://www.eso.org/projects/owl/owl_design.html</a>
  4. D.D.Walker et al., �??The primary and secondary mirrors for the proposed Euro50 telescope,�?? Design Study Report (2002).
  5. D. J. Whitehouse, Handbook of surface metrology (IOP, 1995), Chap. 4.
  6. W.T.Estler, �??Calibration and use of optical straightedges in the metrology of precision machines,�?? Opt. Eng. 24, 372-379 (1985).
  7. D.S.Anderson, J.H.Burge, �??Swing-arm Profilometry of Aspherics,�?? in Optical manufacturing and testing, V.J.Doherty and H.Stahl, Proc. SPIE 2536, 169-179 (1995). [CrossRef]
  8. P.Z.Takacs, S.-N. Qian and J. Colbert, �??Design of a long-trace surface profiler,�?? in Metrology:Figure and Finish, B.E.Truax, Proc. SPIE 749, 59-64 (1987). [CrossRef]
  9. P.Z.Takacs, S.C.K. Feng, E. L. Church, S. -N. Qian, W. -M. Liu, �??Long trace profile measurements on cylindrical aspheres,�?? in Advances in Fabrication and Metrology for optics and large optics, J.B.Arnold and R.E.Parks, Proc. SPIE 966, 354-364 (1989). [CrossRef]
  10. S.-N. Qian, W.Jark, P. Z. Takacs, �??The penta-prism LTP: A long-trace-profiler with stationary optical head and moving penta prism,�?? Rev. Sci. Instrum. 66, 2562-2569 (1995). [CrossRef]
  11. P.Z.Takacs, �??Significant Improvements in Long Trace Profiler Measurement Performance,�?? in Optics for High-brightness synchrotron radiation beamlinseII, L.E.Berman and J.R.Arthur., Proc. SPIE 2856, 236- 245 (1996). [CrossRef]
  12. S.Qian, G.Sostero, P.Z.Takacs, �??Precision calibration and systematic error reduction in the long trace profiler,�?? Opt. Eng. 39, 304-310 (2000) [CrossRef]
  13. M. Virdee, �??Non-contacting straightness measurementto nanometer accuracy,�?? Int. J. Mach. Tools Manufact. 35, 157-164 (1995). [CrossRef]
  14. K. S. Lee Neville, Yimin Cai, Ajay Joneja, �??High-resolution multidimensional displacement monitoring system,�?? Opt. Eng. 36, 2287-2293 (1997). [CrossRef]
  15. K. S. Lee Neville, Yimin Cai, S. F. Wong Alfred, Ajay Joneja, �??Ultra-high-resolution optical monitoring system using a noise cancellation technique,�?? Opt. Eng. 36, 3353-3359 (1997). [CrossRef]

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