Abstract

We present an overview of the engineering design and empirical performance of four stressed-lap polishing tools developed at the University of Arizona. Descriptions of the electromechanical actuators, servo systems, computer interfacing, and attachment of the lap to the polishing machine are provided. The empirical performance of a representative tool is discussed in terms of accuracy, repeatability, and hysteresis. Finally, we estimate the statistical likelihood of aluminum lap-plate failure through a metal-fatigue analysis for a worst-case stress-cycling situation.

© 1994 Optical Society of America

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References

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  1. H. M. Martin, J. R. P. Angel, A. Y. S. Cheng, “Use of an actively stressed lap to polish a 1.8-m paraboloid,” in Proceedings of the European Southern Observatory Conference on Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching-bei-Muchen, Germany, 1988), p. 353.
  2. H. M. Martin, D. S. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, R. S. Young, “Progress in the stressed-lap polishing of a 1.8-m f/1 mirror,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 682–690 (1990).
  3. D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).
  4. D. S. Anderson, J. H. Burge, D. A. Ketelsen, H. M. Martin, S. C. West, G. Poczulp, J. Richardson, W. Wong, “Fabrication and testing of the 3.5-m, f/1.75 WIYN primary mirror,” in Fabrication and Testing of Large Optics, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1994, 193–207 (1993).
  5. S. C. West, J. H. Burge, R. S. Young, D. S. Anderson, C. Murgiuc, D. A. Ketelsen, H. M. Martin, “Optical metrology for two large highly aspheric telescope mirrors,” Appl. Opt. 31, 7191–7197 (1992).
    [Crossref] [PubMed]
  6. J. Lubliner, J. E. Nelson, “Stressed mirror polishing. 1: A technique for producing nonaxisymmetric mirrors,” Appl. Opt. 19, 2332–2340 (1980).
    [Crossref] [PubMed]
  7. J. E. Shigley, C. R. Mischke, Mechanical Engineering Design, 5th ed. (McGraw-Hill, New York, 1989), Chap. 7, pp. 269–303.
  8. S. C. West, W. B. Davison, “Fatigue limits of a 2.2m stressed lap baseplate on the MMT and Columbus mirrors,” Multiple Mirror Telescope Conversion Tech. Mem.92-3 (University of Arizona, Tucson, Ariz., 1992).

1992 (1)

1980 (1)

Anderson, D. S.

S. C. West, J. H. Burge, R. S. Young, D. S. Anderson, C. Murgiuc, D. A. Ketelsen, H. M. Martin, “Optical metrology for two large highly aspheric telescope mirrors,” Appl. Opt. 31, 7191–7197 (1992).
[Crossref] [PubMed]

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

H. M. Martin, D. S. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, R. S. Young, “Progress in the stressed-lap polishing of a 1.8-m f/1 mirror,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 682–690 (1990).

D. S. Anderson, J. H. Burge, D. A. Ketelsen, H. M. Martin, S. C. West, G. Poczulp, J. Richardson, W. Wong, “Fabrication and testing of the 3.5-m, f/1.75 WIYN primary mirror,” in Fabrication and Testing of Large Optics, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1994, 193–207 (1993).

Angel, J. R. P.

H. M. Martin, D. S. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, R. S. Young, “Progress in the stressed-lap polishing of a 1.8-m f/1 mirror,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 682–690 (1990).

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

H. M. Martin, J. R. P. Angel, A. Y. S. Cheng, “Use of an actively stressed lap to polish a 1.8-m paraboloid,” in Proceedings of the European Southern Observatory Conference on Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching-bei-Muchen, Germany, 1988), p. 353.

Burge, J. H.

S. C. West, J. H. Burge, R. S. Young, D. S. Anderson, C. Murgiuc, D. A. Ketelsen, H. M. Martin, “Optical metrology for two large highly aspheric telescope mirrors,” Appl. Opt. 31, 7191–7197 (1992).
[Crossref] [PubMed]

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

D. S. Anderson, J. H. Burge, D. A. Ketelsen, H. M. Martin, S. C. West, G. Poczulp, J. Richardson, W. Wong, “Fabrication and testing of the 3.5-m, f/1.75 WIYN primary mirror,” in Fabrication and Testing of Large Optics, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1994, 193–207 (1993).

Cheng, A. Y. S.

H. M. Martin, J. R. P. Angel, A. Y. S. Cheng, “Use of an actively stressed lap to polish a 1.8-m paraboloid,” in Proceedings of the European Southern Observatory Conference on Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching-bei-Muchen, Germany, 1988), p. 353.

Davison, W. B.

S. C. West, W. B. Davison, “Fatigue limits of a 2.2m stressed lap baseplate on the MMT and Columbus mirrors,” Multiple Mirror Telescope Conversion Tech. Mem.92-3 (University of Arizona, Tucson, Ariz., 1992).

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

DeRigne, S. T.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

Hille, B. B.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

Ketelsen, D. A.

S. C. West, J. H. Burge, R. S. Young, D. S. Anderson, C. Murgiuc, D. A. Ketelsen, H. M. Martin, “Optical metrology for two large highly aspheric telescope mirrors,” Appl. Opt. 31, 7191–7197 (1992).
[Crossref] [PubMed]

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

D. S. Anderson, J. H. Burge, D. A. Ketelsen, H. M. Martin, S. C. West, G. Poczulp, J. Richardson, W. Wong, “Fabrication and testing of the 3.5-m, f/1.75 WIYN primary mirror,” in Fabrication and Testing of Large Optics, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1994, 193–207 (1993).

Kittrell, W. C.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

Lubliner, J.

Martin, H. M.

S. C. West, J. H. Burge, R. S. Young, D. S. Anderson, C. Murgiuc, D. A. Ketelsen, H. M. Martin, “Optical metrology for two large highly aspheric telescope mirrors,” Appl. Opt. 31, 7191–7197 (1992).
[Crossref] [PubMed]

H. M. Martin, D. S. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, R. S. Young, “Progress in the stressed-lap polishing of a 1.8-m f/1 mirror,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 682–690 (1990).

H. M. Martin, J. R. P. Angel, A. Y. S. Cheng, “Use of an actively stressed lap to polish a 1.8-m paraboloid,” in Proceedings of the European Southern Observatory Conference on Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching-bei-Muchen, Germany, 1988), p. 353.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

D. S. Anderson, J. H. Burge, D. A. Ketelsen, H. M. Martin, S. C. West, G. Poczulp, J. Richardson, W. Wong, “Fabrication and testing of the 3.5-m, f/1.75 WIYN primary mirror,” in Fabrication and Testing of Large Optics, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1994, 193–207 (1993).

Mischke, C. R.

J. E. Shigley, C. R. Mischke, Mechanical Engineering Design, 5th ed. (McGraw-Hill, New York, 1989), Chap. 7, pp. 269–303.

Murgiuc, C.

Nagel, R. H.

H. M. Martin, D. S. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, R. S. Young, “Progress in the stressed-lap polishing of a 1.8-m f/1 mirror,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 682–690 (1990).

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

Nelson, J. E.

Poczulp, G.

D. S. Anderson, J. H. Burge, D. A. Ketelsen, H. M. Martin, S. C. West, G. Poczulp, J. Richardson, W. Wong, “Fabrication and testing of the 3.5-m, f/1.75 WIYN primary mirror,” in Fabrication and Testing of Large Optics, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1994, 193–207 (1993).

Richardson, J.

D. S. Anderson, J. H. Burge, D. A. Ketelsen, H. M. Martin, S. C. West, G. Poczulp, J. Richardson, W. Wong, “Fabrication and testing of the 3.5-m, f/1.75 WIYN primary mirror,” in Fabrication and Testing of Large Optics, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1994, 193–207 (1993).

Shigley, J. E.

J. E. Shigley, C. R. Mischke, Mechanical Engineering Design, 5th ed. (McGraw-Hill, New York, 1989), Chap. 7, pp. 269–303.

Trebisky, T. J.

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

West, S. C.

S. C. West, J. H. Burge, R. S. Young, D. S. Anderson, C. Murgiuc, D. A. Ketelsen, H. M. Martin, “Optical metrology for two large highly aspheric telescope mirrors,” Appl. Opt. 31, 7191–7197 (1992).
[Crossref] [PubMed]

S. C. West, W. B. Davison, “Fatigue limits of a 2.2m stressed lap baseplate on the MMT and Columbus mirrors,” Multiple Mirror Telescope Conversion Tech. Mem.92-3 (University of Arizona, Tucson, Ariz., 1992).

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

H. M. Martin, D. S. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, R. S. Young, “Progress in the stressed-lap polishing of a 1.8-m f/1 mirror,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 682–690 (1990).

D. S. Anderson, J. H. Burge, D. A. Ketelsen, H. M. Martin, S. C. West, G. Poczulp, J. Richardson, W. Wong, “Fabrication and testing of the 3.5-m, f/1.75 WIYN primary mirror,” in Fabrication and Testing of Large Optics, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1994, 193–207 (1993).

Wong, W.

D. S. Anderson, J. H. Burge, D. A. Ketelsen, H. M. Martin, S. C. West, G. Poczulp, J. Richardson, W. Wong, “Fabrication and testing of the 3.5-m, f/1.75 WIYN primary mirror,” in Fabrication and Testing of Large Optics, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1994, 193–207 (1993).

Young, R. S.

S. C. West, J. H. Burge, R. S. Young, D. S. Anderson, C. Murgiuc, D. A. Ketelsen, H. M. Martin, “Optical metrology for two large highly aspheric telescope mirrors,” Appl. Opt. 31, 7191–7197 (1992).
[Crossref] [PubMed]

H. M. Martin, D. S. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, R. S. Young, “Progress in the stressed-lap polishing of a 1.8-m f/1 mirror,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 682–690 (1990).

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

Appl. Opt. (2)

Other (6)

J. E. Shigley, C. R. Mischke, Mechanical Engineering Design, 5th ed. (McGraw-Hill, New York, 1989), Chap. 7, pp. 269–303.

S. C. West, W. B. Davison, “Fatigue limits of a 2.2m stressed lap baseplate on the MMT and Columbus mirrors,” Multiple Mirror Telescope Conversion Tech. Mem.92-3 (University of Arizona, Tucson, Ariz., 1992).

H. M. Martin, J. R. P. Angel, A. Y. S. Cheng, “Use of an actively stressed lap to polish a 1.8-m paraboloid,” in Proceedings of the European Southern Observatory Conference on Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching-bei-Muchen, Germany, 1988), p. 353.

H. M. Martin, D. S. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, R. S. Young, “Progress in the stressed-lap polishing of a 1.8-m f/1 mirror,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 682–690 (1990).

D. S. Anderson, J. R. P. Angel, J. H. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, R. S. Young, “Stressed-lap polishing of 3.5-m f/1.5 and 1.8-m f/1.0 mirrors,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 260–269 (1991).

D. S. Anderson, J. H. Burge, D. A. Ketelsen, H. M. Martin, S. C. West, G. Poczulp, J. Richardson, W. Wong, “Fabrication and testing of the 3.5-m, f/1.75 WIYN primary mirror,” in Fabrication and Testing of Large Optics, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1994, 193–207 (1993).

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Figures (11)

Fig. 1
Fig. 1

Side schematic of a single actuator for the 60-cm stressed lap. By the application of tension to the steel bands with an electromechanical actuator, a bending moment is produced in the plate. Motor torque is converted into linear force at the bands by a ball screw and a lever arm. A parallelogram linkage attached to the fulcrum ensures not only that the force application height is constant throughout the dynamic range, but also that the tension bands do not twist. The plastic layer gives the pitch surface the proper average curvature.

Fig. 2
Fig. 2

Top view of the 60-cm stressed lap; 12 actuators are attached to the periphery of the plate, and twisting and bending moments are produced by the arrangement of the tension bands in sets of equilateral triangles.

Fig. 3
Fig. 3

Schematic for the stressed-lap tension servo system. Force commands are loaded into each actuator by the strobing of a 12-bit word into a registered digitial-to-analog coverter (DAC) from a data bus. The shape-update rate is over 1 kHz. The servo bandwidth and damping coefficient are set to yield a maximum 0.1° shape-phase lag error at 10-rpm lap rotation rate.

Fig. 4
Fig. 4

Electronic system diagram of stressed-lap operation. Lap shapes are determined at the calibration station and used to generate a high-density lookup table of actuator value versus mirror position. During polishing, the VME-based computer reads the encoders on the polishing machine and updates the lap shape at 1-kHz rates with the lookup table.

Fig. 5
Fig. 5

Upper plot shows the shape accuracy of the 1.2-m stressed lap produced by calibration for the 3.5-m f/1.5 U.S. Air Force mirror (solid points) versus the distance of the lap center from the vertex of the mirror (X). Also shown are the rms errors that are produced by the random accessment of these shapes and their comparison with the calibration. This is the most severe test of shape reproducibility and includes all effects from mechanical hysteresis, kinematic attachment, and servo errors. The lower plot shows the corresponding moment amplitudes (peak mode force times the post height) introduced by the actuators for defocus, coma, and astigmatism. At X = 1.52 m, these correspond to 360, 129, and 170 μm of plate deflection, respectively. Plate theory (solid curve) underestimates the actual moments (dashed curves) because of plate stiffening at the lap periphery caused by the steel attachment brackets of the actuators (shown in Fig. 2).

Fig. 6
Fig. 6

Highly exaggerated stressed-lap hysteresis plots derived from the data set used to produce Fig. 5. In each case a contour map is computed by the subtraction of two shapes derived from moving the lap in opposite directions. The top plot shows the difference map produced by moving the lap from the center to the edge of the mirror and back again with no rotation. The two shapes produced at the 50% zone of the mirror are subtracted and displayed. The bottom plot shows hysteresis produced at the mirror edge by subtracting shapes produced by rotating the lap in opposite directions. In each case the difference maps have errors of less than 1.5 μm rms and 4 μm peak to valley over the full 1.2-m diameter of the lap.

Fig. 7
Fig. 7

One measure of the time stability of the stressed-lap tension servo system shows histograms of the sensor rms errors relative to the reference shape at t = 0. Any electronic or uncompensated mechanical drift will look like a shape change and cause the error distribution to translate along the abscissa. Clearly, instability of the stressed-lap electronics is not measurable in 1-h time periods.

Fig. 8
Fig. 8

Two views of the passive mechanical linkage used to connect the 1.2-m stressed lap to the polishing-machine spindle. The upper view depicts the layout of the three four-bar linkages and shows how torque is transmitted to the lap plate. The lower view shows the details of a single four-bar linkage. Each linkage is connected to the midplane of the lap plate by a ball joint that precludes bending moments, produced by the lateral dragging force, from deforming the plate. The linkages passively eliminate unwanted pressure gradients caused by drag and accommodate tilt and piston as the lap is moved over the surface of the mirror. Although the linkages partially compensate for overturning moments, complete cancellation requires active control.

Fig. 9
Fig. 9

SN diagrams for 7075 and 6061 Al alloys with T6 temper. The solid curves show the unmodified fatigue strength, and the dashed curves show fatigue strength modified appropriately for the plate machining, surface finish, and environment.

Fig. 10
Fig. 10

Modified Goodman relations for Al alloys of 7075-T6 (solid curves) and 6061-T6 (dashed curves) for log N = 6 (thick curves) and log N = 7 (thin curves). The alternating and mean stresses of a 2.2-m plate are shown for the center (triangle) and periphery (square) of the plate. They were determined by a finite-element analysis that modeled polishing strokes.

Fig. 11
Fig. 11

Azimuthal variation of the peripheral plate stresses for models of a 2.2-m stressed-lap plate on the Multiple Mirror Telescope (MMT) and Columbus primary mirrors as a function of the distance of the lap center from the mirror vertex (X). The mirror vertex is toward an azimuth of 180°. The upper curve represents the preload stress, and the lower two curves show plate stress around the periphery when the lap center is near the mirror edge.

Tables (2)

Tables Icon

Table 1 Stressed Laps Built to Date

Tables Icon

Table 2 Strength Properties of Various Al Alloys

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