OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 1 — Jan. 14, 2013
  • pp: 370–381
« Show journal navigation

Edge control in CNC polishing, paper 2: simulation and validation of tool influence functions on edges

Hongyu Li, David Walker, Guoyu Yu, Andrew Sayle, Wilhelmus Messelink, Rob Evans, and Anthony Beaucamp  »View Author Affiliations


Optics Express, Vol. 21, Issue 1, pp. 370-381 (2013)
http://dx.doi.org/10.1364/OE.21.000370


View Full Text Article

Acrobat PDF (1756 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Edge mis-figure is regarded as one of the most difficult technical issues for manufacturing the segments of extremely large telescopes, which can dominate key aspects of performance. A novel edge-control technique has been developed, based on ‘Precessions’ polishing technique and for which accurate and stable edge tool influence functions (TIFs) are crucial. In the first paper in this series [D. Walker Opt. Express 20, 19787–19798 (2012)], multiple parameters were experimentally optimized using an extended set of experiments. The first purpose of this new work is to ‘short circuit’ this procedure through modeling. This also gives the prospect of optimizing local (as distinct from global) polishing for edge mis-figure, now under separate development. This paper presents a model that can predict edge TIFs based on surface-speed profiles and pressure distributions over the polishing spot at the edge of the part, the latter calculated by finite element analysis and verified by direct force measurement. This paper also presents a hybrid-measurement method for edge TIFs to verify the simulation results. Experimental and simulation results show good agreement.

© 2013 OSA

1. Introduction

Manufacturing segmented mirrors presents its own challenges. Edge mis-figure is regarded as one of the most difficult technical issues, which can dominate the performance of segmented-mirror telescopes. This is because the integrated edge-length in segmented optical system greatly exceeds the equivalent monolithic system. For example, there are nearly 4km of edges in the E-ELT’s primary mirror, and edge mis-figure can be the limiting factor in stray-light and IR-emissivity performance. The traditional technique pioneered by Keck is to oversize the segment during polishing and figuring, after which the segment is cut hexagonal [8

8. T. S. Mast and J. E. Nelson, “The fabrication of large optical surface using a combination of polishing and mirror bending,” Proc. SPIE 1236, 670–681 (1990). [CrossRef]

]. This introduces global distortion, which is rectified using the slow process of ion figuring.

As we pointed out in Paper 1 [1

1. D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, Paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012). [CrossRef] [PubMed]

], other applications for fine edge control include pupil and image slicer optics, datum straight edges in various applications including wafer-steppers. There are other requirements in the semiconductor industry, for example specialist semiconductors that have been diced to final size, and post-polishing is needed to achieve a uniform thickness of a deposited layer.

In Paper 1, we demonstrated that effective edge-control on hexagonal parts could be achieved whilst polishing the global surface, using developments of the ‘Precessions’ process [9

9. D. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003). [CrossRef] [PubMed]

, 10

10. H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub. 6, 1104801–1104806 (2011).

]. Now, when a spherical compressible polishing-bonnet significantly overhangs the edge of the part, it will naturally roll-down the edge. The methodology described was therefore based on the tool-lift method, where the bonnet is progressively raised or lowered (‘Z offset’), delivering polishing spots (‘tool influence functions’ or ‘TIFs’) of variable size. As the tool-path approaches the edge of the part, tool-lift enables the spot to be controlled so that it never overlaps the precise edge at all, or more normally, it overlaps by a small and controlled amount. In Paper 1, the process variables then comprised:

  • 1. Z-offset (and hence spot-size) at each incremental distance from the edge of the part
  • 2. Dwell-time at each incremental distance from the edge of the part

These were empirically optimized using repeated trials and measuring the resulting edge-profiles. Due to the number of possible combinations of parameters (Z-offset, overhang, precess angle, feed-rate, raster-spacing), this proved a tedious and time-consuming process. Whilst amply demonstrating the effectiveness of the method, it does not lend itself directly to process-automation.

This second paper considers how the process can be ruggedized and automated by modeling edge TIFs from basic mechanical data, and then using these edge TIFs to predict the edge-removal. This immediately enables ‘edge control’ experiments to be performed in software rather than in the optics shop, and lends itself to full numerical optimization. The detailed morphology of the TIFs of variable size and edge-overlap then becomes of paramount importance.

This simulation predicts the edge TIFs by i) modeling the surface speed distribution across the TIF, and ii) the pressure distribution at the edge of the part by finite element analysis (FEA). The latter, verified by force measurement, as described in Section 3. To verify the simulation results of the edge TIFs, a hybrid-measurement method to obtain the experimental edge TIFs is presented in Section 4, using both simultaneous phase interferometry and profilometry. The simulation and measurement results show good agreement, and led to a preliminary model which can predict the edge removal profile, with edge-control result shown in Section 5.

2. The strategy of practical edge control-Tool lift

The strategy we adopt is to use comparatively large polishing spots over the bulk surface to give high volumetric removal rates in pre-polishing and early form-correction polishing, followed by smaller spot-sizes. The tool-lift method [1

1. D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, Paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012). [CrossRef] [PubMed]

] then enables the edge-profiles to be optimized at each stage, as described in detail in Paper 1 [1

1. D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, Paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012). [CrossRef] [PubMed]

] and summarized in Fig. 1
Fig. 1 The sketch of the tool lift process for edge control (reproduced from Paper 1)
below.

3. The modeling of edge TIFs

3.1 Theoretical background

The theoretical basis of prediction of material removal in optical surface polishing was presented by Preston in 1927 [11

11. F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).

], as follows:
Δh(x,y)=kν(x,y)p(x,y)
(1)
where:

  • Δh(x,y)- Removal in unit time at point(x,y)
  • k- Preston coefficient, related to the work piece material, polishing-tool, polishing slurry and temperature of work environment
  • ν(x,y)- Instantaneous relative surface velocity of polish pad at point(x,y)
  • p(x,y)- Instantaneous pressure of the polishing pad at point(x,y)

Define the average removal value of surface materialsR(x,y) in unit time T as the tool influence function, i.e.:
R(x,y)=1T0TΔh(x,y)dt=1T0Tkν(x,y)p(x,y)dt
(2)
Define the revolution period of the polishing tool:
T=2π/ω0
(3)
where, ω0 is the angular velocity of the polishing tool. Since, removal function R(r)can be written as:
R(r)=1T0Tkv(x,y)p(x,y)dt=k2πθ0θ0v(x,y)p(x,y)dθ
(4)
where, θ is the rotation angle of the polishing tool.

The removal function R(x,y) can be determined by Eq. (4), if the surface velocity distribution v(x,y) and the pressure distribution p(x,y) can be obtained.

In the ‘Precession’ polishing technique, when the spot extends beyond the edge of the part, the pressure distribution between tool and part is complex. Wagner and Shannon, (1974), used the force equation in conjunction with the torque equation for static equilibrium [12

12. R. E. Wagner and R. R. Shannon, “Fabrication of aspherics using a mathematical model for material removal,” Appl. Opt. 13(7), 1683–1689 (1974). [CrossRef] [PubMed]

]. This model, however, presents an important problem. Whenever the tool centre is near the edge of the part, the minimum pressure can become negative, which means that this model is no longer valid. Jones, (1986), suggested a linear pressure distribution model in 1986 [13

13. R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25(6), 785–790 (1986). [CrossRef]

]. Cordero-Davila et al, (2004), developed this approach further using a non-linear high pressure distribution near the edge of the part; however, they did not report the model’s validity by experimental results [14

14. A. Cordero-Dávila, J. González-García, M. Pedrayes-López, L. A. Aguilar-Chiu, J. Cuautle-Cortés, and C. Robledo-Sánchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt. 43(6), 1250–1254 (2004). [CrossRef] [PubMed]

]. Kim (2009) established a parametric modeling of edge TIFs based on ‘Preston equation’, which is able to predict edge TIFs [15

15. 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). [CrossRef] [PubMed]

]. This model was based on the presumption of linear pressure distribution for the hard tool. However, the cause of edge effect in flexible bonnet tool is different.

In the work presented here, the surface velocity distribution is obtained according to the geometry of the precess tool-motion. The pressure distribution over the polishing spot at the edge of the part is calculated by means of finite element analysis (FEA), the FEA results being verified by direct force measurement.

3.2 Modeling of surface velocity distribution v (x,y)

A sketch of the movement of a precessed bonnet is shown in Fig. 2
Fig. 2 Sketch of space movement of the tool of the precess.
. The velocity relation of any point in the polishing contact zone is shown in Fig. 3
Fig. 3 Velocity relation of any point in contact zone.
.where:

  • P(x,y)is any point in polishing contact zone;
  • ω0is the angular velocity around axis of tool;
  • ω is the angular velocity around a normal work piece;
  • O is the centre of polishing spot;
  • ρ is the process angle;
  • d is the compression value of tool (Z-offset);
  • R is the radius of curvature of the tool

According to the geometry of precess in the polishing area, the velocity component distribution v'p1(x,y)can be expressed as:
v'p1(x,y)=2cosρ(Rd)1s(sα)(sβ)(sγ)ω0
(5)
where:
α=[(Rr)2+x2+y2]1/2;β=(Rd)(cosρ)1;γ=[y2+[(Rd)tgρx]2]1/2;s=12αβγvp2=rω
(6)
vp(x,y)=(v'p1(x,y))2+(vp2(x,y))2+2cosαv'p1(x,y)vp2(x,y)
(7)
Based on Eq. (7), the relative surface velocity distribution function in the polishing zone has been simulated using MatLab code. The parameters in the modeling are: 160mm tool radius of curvature, 2.8mm Z-offset and 10° precess angle. To simplify the modeling process, normalization (scaling magnitude of velocity from 0 to 1) has been applied in the simulation. Figure 4
Fig. 4 Surface velocity distribution normalized simulation results: R160 tool, Z-offset: 2.8mm, Precess angle: 10°.
shows the simulation results for surface velocity distribution; note the absence of zero surface speed anywhere in the tool influence function, unlike a simple rotating tool.

3.3 FEA model for pressure distribution and results

The pressure on the work piece is caused by elastic deformation of the tool. To simplify the problem, a thin layer of polishing cloth is considered to be a second order effect and is neglected in the modelling. A nominal 100mm x 100mm square, 10mm thick, Zerodur part were chosen for the model. The bonnet material was natural rubber (BS-1154: 2003). The material properties for the modeling are listed in Table 1

Table 1. Materials Characteristics for Modeling

table-icon
View This Table
. The R160mm tool, 2.8mm Z-offset and 10° precess angle is chosen for the modeling.

The FEA of the bonnet tool polishing model is defined as a two-body contact. A contact pair is created between the surface of the tool and the polishing surface of the part. During the polishing process, the back surface of the part is fixed on the support system. Thus, all degree of freedom (DOF) of the back surface are constrained with zero displacements. The top surface of the tool is fixed on the polishing machine. The bonnet tool is depressed by the Z-offset to deliver a spot-size along the Z-direction. Thus, the top surface of the tool is constrained with zero displacements along X-axis and Y-axis and −2.8mm displacement along Z-axis. The elements and restraints of the FEA model are shown in Fig. 5
Fig. 5 The elements and the restraints on the FEM model for R160mm tool.
. The pressure distribution simulation result is shown in Fig. 6
Fig. 6 The absolute pressure distribution simulation results (R160mm tool, 2.8mm Z-offset, 60mm spot-size).
, for which the maximum pressure on the Zerodur part is 1.17 x 105 Pa for the case considered.

Figure 7
Fig. 7 The absolute pressure distribution simulation results (Overhang: 5mm, 15mm, 20mm, 25mm).
shows that pressure distribution at the edge of the part with different overhangs (5mm, 15mm, 20mm, 25mm), which can be seen that, when the spot beyond the edge of the part, the pressure applied on the edge becomes extremely high.

3.4 Experimental verification for FEA results of the pressure distribution

The total force f applied on the part should be the same as the integral of the pressure distribution p(x,y) over the part contact area A, which can be described as:
f=Ap(x,y)dxdy
(8)
The pressure distribution simulation results of 2.8mm Z-offset (R160mm tool) are shown in Fig. 6. Thus, the simulated force f R160 can be calculated according to Eq. (8), which is:
fR160=16.43kg
To verify the pressure distribution p(x,y) simulation results, the force f exerted on the part has been measured on the polishing machine. OpTIC Glyndwr has developed a device for force measurement, using three Omega (SN: LCM201) standard load cells whose accuracy is ± 1.0% (linearity, hysteresis and repeatability combined). The sketch of the set-up of the force measurement is shown in Fig. 8
Fig. 8 The sketch of the set-up of the force measurement.
.

The force measurements for R160mm tool were carried out on the machine. Figure 9
Fig. 9 The force with different Z-offset measurement result of R160mm bonnet tool.
shows the force exerted by a R160mm bonnet applied to the part with different Z-offsets. It can be seen that the force on the part is 15.87KgF, when the Z-offset is 2.8mm for R160mm tool (the simulation result is 16.43kg). The simulation error is 3.6% for this tool according to the force measurement results.

4. The measurement of edge TIFs

When the polishing spot from a bonnet projects beyond the edge of the part, the bonnet material at some level wraps around the edge. The local edge-removal of the TIFs then becomes abnormally high. If not managed, this will turn the edge down. Moreover, the resulting slopes can be beyond the measurement-range of full-aperture interferometry. To obtain the full TIFs data at the edge, we have therefore developed a measurement method using both 3D interferometer and 2D Profilometer data [10

10. H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub. 6, 1104801–1104806 (2011).

]. The sketch of this method is shown in Fig. 10
Fig. 10 The schematic diagram of interpolating 3D TIF at the edge, where (a) 2D scanning and interpolating boundary of TIF (b) Interpolating of 3D in the vicinity of edge of TIF.
. Firstly, the depth data of certain points of the edge were measured by individual 2D scanning. Five 2D scans were then chosen for interpolating the boundary of each TIF, as shown in Fig. 10(a). After the boundary of the TIF was obtained, the 3D topology of the TIF at the edge of the part was then interpolated, as shown in Fig. 10(b).

To verify the simulation results, four TIFs at the edge of the part were interpolated, for which the parameters were the same as in the simulation (R160mm bonnet; precess angle: 10°; off-set: 2.8mm, overhang: 5mm, 15mm, 20mm, 25mm). The stitched results are shown in Fig. 11
Fig. 11 The results of stitched 3D IFs at the edge (Overhang: 5mm, 15mm, 20mm, 25mm).
. Approximately 2mm of the edge-data is lost in the interferometer field, which was recovered with the profilometer.

The 2D comparison of modeling and experimental edge TIFs results is shown in Fig. 12
Fig. 12 Comparison of modeling and experimental results of edge TIFs.
. For simplification of the comparison, experimental results have been normalized (by scaling the magnitude of removal from 0 to 1). This shows that the shape of the simulated edge-TIFs is in reasonable agreement with measurement. The residual error is attributed to the contribution of errors in the pressure distribution calculated by FEA, and to the measurement error.

5. First application of edge modeling result

To predict and optimize the profile of the edge of the part, a simple model has been developed, which effectively co-adds the multiple edge TIFs in the edge zone. An experiment to verify this modeling result was carried out on a 200mm across corners, hexagonal part, using the same process parameters. Figure 13
Fig. 13 Preliminary modelling result of edge removal profile, using modelled TIF data.
shows the comparison of modeling and experimental results (edge to edge). It shows a reasonable agreement. Note that in Fig. 13 of this paper, the edge-modeling results are based on modeling the edge TIFs. In contrast, the preliminary results presented in Fig. 9 of Paper 1 were based on the empirically measured TIFs in the vicinity of edges.

By this means, the tool lift parameters were optimized and the whole process was demonstrated on a 200mm across corners, hexagonal witness part. The final result is shown in Fig. 14
Fig. 14 Edge control results (200mm cross corners, Zerodur hexagonal part).
, from which it can be seen that the PVq (95%) for each of the edges within the 10mm wide trapezoid zone, as previously defined [1

1. D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, Paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012). [CrossRef] [PubMed]

], are approximately 100nm and no edge turn down. The dominant edge-defect remaining in the PV number is the turning-up of the corners. This is because, for a defined maximum spot overlap on the edges, the overlap on the corners is less, simply from geometry. Therefore we are currently developing a local edge rectification method using a small tool, as a final process step. The details of the method and will be published in due course.

6. Conclusion

This paper has reported on the most recent phase of our edge control development, driven by the E-ELT mirror segments, but looking ahead to wider applications. The ‘Precessions’ polishing technique has proved highly competent in addressing aspheres, but raises the challenge of edge-roll when the flexible bonnet overhangs the edge of the part. We have summarized our strategy, as reported in detail in Paper 1, based on shrinking the TIFs in the vicinity of edges using tool-lift. We have then pointed out the limitations of using empirical TIF data in an automated segment serial-production context. This has led to the improved technique reported here, based on modeling TIFs using Preston’s equation. The input data comprised the computed speed-distributions over the polishing spot delivered by a precessed bonnet, combined with the pressure distributions exerted by the bonnet calculated using finite element analysis. The latter has been confirmed by direct force-measurement.

To verify the edge TIFs simulation results, a hybrid-measurement method for edge-TIFs has been described, in which the interferometry and profilometry results are stitched together. The simulation and measurement results showed good agreement. Using these simulated edge TIFs, we have established a model which can predict the edge removal profile. By this means, the edge control parameters have been successfully optimized, for the first time without recourse to empirical TIF data. The method opens up the possibility of locally correcting edges using a tool-path constrained to the edge-zone; the subject of current work.

Overall, the work reported in this paper has provided a sound basis for automating optimization of the process for controlling edges on mirror-segments and in other applications.

Acknowledgments

References and links

1.

D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, Paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012). [CrossRef] [PubMed]

2.

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE 5489, 1–10 (2004). [CrossRef]

3.

H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE 5494, 62–70 (2004). [CrossRef]

4.

H. M. Martin, R. G. Allen, B. Cuerden, J. M. Hill, D. A. Ketelsen, S. M. Miller, J. M. Sasian, M. T. Tuell, and S. Warner, “Manufacture of the second 8.4m primary mirror for the Large Binocular Telescope,” Proc. SPIE 6273, 62730C1 (2006).

5.

J. E. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” Proc. SPIE 4004, 282–289 (2000). [CrossRef]

6.

R. Geyl, M. Cayrel, and M. Tarreau, “Glan Tlescope Canarias optics manufacture: progress report3,” Proc. SPIE 5494, 57–61 (2004). [CrossRef]

7.

A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE 5494, 31–38 (2004). [CrossRef]

8.

T. S. Mast and J. E. Nelson, “The fabrication of large optical surface using a combination of polishing and mirror bending,” Proc. SPIE 1236, 670–681 (1990). [CrossRef]

9.

D. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003). [CrossRef] [PubMed]

10.

H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub. 6, 1104801–1104806 (2011).

11.

F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).

12.

R. E. Wagner and R. R. Shannon, “Fabrication of aspherics using a mathematical model for material removal,” Appl. Opt. 13(7), 1683–1689 (1974). [CrossRef] [PubMed]

13.

R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25(6), 785–790 (1986). [CrossRef]

14.

A. Cordero-Dávila, J. González-García, M. Pedrayes-López, L. A. Aguilar-Chiu, J. Cuautle-Cortés, and C. Robledo-Sánchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt. 43(6), 1250–1254 (2004). [CrossRef] [PubMed]

15.

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). [CrossRef] [PubMed]

OCIS Codes
(110.6770) Imaging systems : Telescopes
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.5450) Optical design and fabrication : Polishing
(230.4040) Optical devices : Mirrors

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: August 16, 2012
Revised Manuscript: November 22, 2012
Manuscript Accepted: November 23, 2012
Published: January 4, 2013

Citation
Hongyu Li, David Walker, Guoyu Yu, Andrew Sayle, Wilhelmus Messelink, Rob Evans, and Anthony Beaucamp, "Edge control in CNC polishing, paper 2: simulation and validation of tool influence functions on edges," Opt. Express 21, 370-381 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-370


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, Paper 1: edges on processing the global surface,” Opt. Express20(18), 19787–19798 (2012). [CrossRef] [PubMed]
  2. R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE5489, 1–10 (2004). [CrossRef]
  3. H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004). [CrossRef]
  4. H. M. Martin, R. G. Allen, B. Cuerden, J. M. Hill, D. A. Ketelsen, S. M. Miller, J. M. Sasian, M. T. Tuell, and S. Warner, “Manufacture of the second 8.4m primary mirror for the Large Binocular Telescope,” Proc. SPIE 6273, 62730C1 (2006).
  5. J. E. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” Proc. SPIE4004, 282–289 (2000). [CrossRef]
  6. R. Geyl, M. Cayrel, and M. Tarreau, “Glan Tlescope Canarias optics manufacture: progress report3,” Proc. SPIE5494, 57–61 (2004). [CrossRef]
  7. A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004). [CrossRef]
  8. T. S. Mast and J. E. Nelson, “The fabrication of large optical surface using a combination of polishing and mirror bending,” Proc. SPIE1236, 670–681 (1990). [CrossRef]
  9. D. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express11(8), 958–964 (2003). [CrossRef] [PubMed]
  10. H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub.6, 1104801–1104806 (2011).
  11. F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol.11, 214–256 (1927).
  12. R. E. Wagner and R. R. Shannon, “Fabrication of aspherics using a mathematical model for material removal,” Appl. Opt.13(7), 1683–1689 (1974). [CrossRef] [PubMed]
  13. R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng.25(6), 785–790 (1986). [CrossRef]
  14. A. Cordero-Dávila, J. González-García, M. Pedrayes-López, L. A. Aguilar-Chiu, J. Cuautle-Cortés, and C. Robledo-Sánchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt.43(6), 1250–1254 (2004). [CrossRef] [PubMed]
  15. D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express17(7), 5656–5665 (2009). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited