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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 22 — Oct. 25, 2010
  • pp: 22973–22981
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Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing

Hao Hu, Yifan Dai, and Xiaoqiang Peng  »View Author Affiliations


Optics Express, Vol. 18, Issue 22, pp. 22973-22981 (2010)
http://dx.doi.org/10.1364/OE.18.022973


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Abstract

The influence from the regular tool path to micro fabrication errors in deterministic finishing is studied through the simulations and experiments. The random pitch tool path based on the surface error distribution and the process parameters is designed to reduce this residual error when adopting the regular path to achieve the corrective polish. A nucleated glass flat mirror is polished with this method on the experimental installation UPF700-7 developed by ourselves. The surface accuracy is improved from the initial λ/30(RMS, 90%aperture, λ = 632.8nm) to the final λ/200 in 5 minutes and the medium-high spatial frequency errors induced by the regular path is restricted well at the same time. The accuracy of the simulation and the validity of the random pitch tool path are both proved through the experiments.

© 2010 OSA

1. Introduction

Magnetorheological Finishing (MRF®) is a typical deterministic finishing technology commercialized by QED Technologies(R) for fine figuring of flat, spherical and aspheric optical components. It has the advantages of high process precision, good surface quality and high convergence efficiency [1

1. S. D. Jacobs, W. I. Kordonski, D. Golini, I. V. Prokhorov, G. R. Gorodkin, and T. D. Strafford, “Deterministic Magnetorheological Finishing,” US, Patent, 5795212 (1998).

3

3. B. Hallock, B. Messner, C. Hall, and C. Supranowitz, “Improvements in large window and optics production,” Proc. SPIE 6545, 645419 (2007).

]. The MRF® fabrication principle is utilizing the rheological alteration of the MR fluid in the gradient magnetic field to create a flexible and extremely stable “sub-aperture polishing lap” that conforms to the optical surface. The work material is accurately removed and the surface error correction would be attained quickly by this lap based on the theory of computer controlled optics surfacing (CCOS) [4

4. R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16(1), 218–224 (1977). [CrossRef] [PubMed]

] firstly proposed by Itek inc. in 1970s. However, the micro fabrication errors called “fragmentary errors” are increasing in the process of fast surface error removal because that the “lap” size is less than the work piece like all of the other sub-aperture deterministic polishing technologies [5

5. M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008). [CrossRef]

7

7. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-958. [CrossRef] [PubMed]

]. These medium-high frequency errors would be serious in some applications such as in intense laser systems and high resolution image formation systems which have the strict requirements for both of the surface error and medium-high frequency [8

8. J. K. Lawson, D. M. Aikens, and R. E. English, “Power spectral density specifications for high-power laser systems,” Proc. SPIE 2775, 345–356 (1996). [CrossRef]

,9

9. J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998). [CrossRef]

]. This error is mainly affected by the initial surface error distribution (spatial and frequency domain), the removal function characters (profile, removal efficiency and stability) and the adopted paths [10

10. D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).

].

The experiences from the classical smoothing tell us this error would be restricted if the random tool path is adopted. The literature [10

10. D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).

] also gives an explanation why the random tool path is favorable to reduce this kind of error in optics fabrication based on the entropy increase principle. The regular tool-path inevitably leaves respective signature in the surface, so the challenge is how to introduce elements of the randomness associated with the classical smoothing into the deterministic computer numerical controlled (CNC) process. Aiming at this problem, the partial random path which has added a random micro vibration on the vertical direction of the scan orientation is designed [10

10. D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).

], but this method increases the implementation difficulty of the machine and sometimes it is impossible. The pseudo-random tool path is also presented for this problem and it is effective to reduce the error [11

11. C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-23-18942. [CrossRef]

], but is hard to achieve a high precision on the surface error correction because of the difficulty on speed management. In this paper we first analyze the error sources when the regular tool-path is adopted in MRF®, then a series of simulations and experiments are executed to validate the accuracy of the analysis. A process is done finally with the method of random pitch tool-path.

2. Error analysis

The removal depth in the optical surface at one location is the cumulated removal of polishing along the adjacent path lines in the deterministic finishing. The rationale can be approximately explained using the Eq. (1), E is the surface error, r is the removal function and t denotes as the dwell-time. The error will be removed completely if the convolution of the removal function and the dwell time equal to the surface error.

E(x,y)=r(x,y)t(x,y).
(1)

The surface error and the removal function data are both obtained through the interferometer while the dwell-time can be calculated with the various deconvolution algorithms in actual process. Then the CNC machine would control the “polishing lap” to remove the redundant material in the surface dwell point with different feed rate or residence time according to the dwell-time. Usually, this course will be treated for several iterations until the acquired accuracy is achieved finally. There will be no error theoretically if the “lap” is stable, the data is sufficient and the machine implements the correct dwell-time everywhere in the surface, but this cannot be real. The CNC machine will cross the whole surface with the process path and this path is usually a unicursal path. The raster and spiral tool paths shown in Fig. 1
Fig. 1 The typical raster tool path (a) and spiral tool path (b) adopted in MRF® process.
are both the typical unicursal paths adopted in the deterministic finishing such as MRF process [12

12. C. Supranowitz, C. Hall, P. Dumas, and B. Hallock, “Improving surface figure and microroughness of IR materials and diamond turned surfaces with magnetorheological finishing (MRF®),” Proc. SPIE 6545, 64540S (2007).

] to correct the surface errors. As shown in the figure, the scan speed v 1 can be continuous on these regular paths while the line feed speed v 2 is not. This is an important source for the medium-high frequency errors.

The surface accuracy can be high in existing fabrication results when the regular tool path is adopted, so we can research the relation between the process parameters and the residual errors to find out the optimal conditions to restrict it without changing these simple paths. The magnitude of the error from the tool path in MRF process is studied on the assumption that the removal function is completely stable and the errors from the measurement are neglectable. As referred previously, the residual ripple errors from the tool path are mainly contributed by the discontinuation of the line feed speed. We can simplify the problem just for thinking the errors on this direction. At the same time, the surface error is expressed using a series of discrete data where the dwell points stay, so we can analyze the problem with the simplified model shown in Fig. 2
Fig. 2 Diagrammatic sketch for the surface removal with the MRF® removal function.
.

Without loss of generalities, this model is established on the uniform material removal. The initial surface S0 is discretized as a series of adjacent data points pi (i = 1…n) and the distance between the dwell point equals to the pitch. The material removal E(p) on dwell point p can be denoted as the Eq. (2). In this expression, r(pi;p) is the material removal on point p when the removal function is staying on point pi, while t(pi) indicates the dwell-time on point pi.

E(p)=i=1nr(pi;p)t(pi).
(2)

The material removal E’(p’) on non-dwell point p’ is expressed with the Eq. (3). Then r(pi;p’) is the material removal on point p’ when the removal function is on point pi.

E'(p')=i=1nr(pi;p')t(pi).
(3)

The dwell points value in polished surface S1 are the same when the removal function passes through the whole surface while the non-dwell points value are not. The residual error height σE(p') between them can be expressed with the Eq. (4).

σE(p')=i=1n|r(pi;p)r(pi;p')|t(pi).
(4)

3. Simulation and experiments analysis

3.1 Simulation analysis

The residual error height σE is mainly associated with the removal function characteristics and magnitude of the dwell-time through the analysis in Eq. (4). We can find that the relationship between the value |r(pi;p) -r(pi;p’)| and the pitch is a direct proportion while the magnitude of dwell-time and the removal depth is also a linear relationship. Aiming at this circumstance, two actual removal functions shown in Fig. 3
Fig. 3 The 2D map (a) and profile (b) of the first removal function for simulation.
and Fig. 4
Fig. 4 The 2D map (a) and profile (b) of the second removal function for simulation.
are adopted to simulate the relationship between the residual error height and these influencing factors.

It is the removal function obtained with the polishing wheel whose diameter is 100mm shown in Fig. 3 and it is with the 200mm diameter wheel shown in Fig. 4. The left side in each figure is the 2D map and the right side is the profile along the north–south direction in the width direction center. Both of the removal functions immerse in the workpiece with the same depth 0.3mm and their peak removal value is also close. The geometry size of the first removal function is about 8mm × 6mm and the second one is about 15mm × 9mm.

3.2 Experiments analysis

3.3 Strategy to reduce the ripple

The medium-high frequency errors caused by the regular tool path cannot be eliminated while could be restricted through the method of reducing the removal depth and pitch according to the simulation and experiment results. So the uniform removal and path pitch can be selected appropriately in response to the distribution of the surface error and process parameters in actual fabrication. The empirical formula that we choose is given as:

σEPV=12i=1n|r(pi)r(pi1)|r(pi)DΔP2σEr.
(5)

D means the removal depth, ΔP is the pitch value and σErmeans the required residual ripple height. This formula is not convenient in practical application and we estimate with another process parameterva generally, which means the actual feed rate. It can be acquired through the specific management with the dwell-time and the identification is denoted as Eq. (6) if the raster path is adopted. The minimal feed speed vmin is based on the actual requirement and CNC machine performance.

va=DΔP/i=1nr(pi)vmin.
(6)

It is favorable to change the pitch real-time according to the surface error distribution, so we can adopt the random pitch path in practical fabrication. The advantages for adopting the spiral path to manufacture the rotation symmetry optics are obvious than using the raster path according to the above analysis. The removal function sweeps the whole surface twice along the spiral path with the equilong pitch if the diameter-scan mode is applied. The actual pitch will be smaller than the spiral path pitch shown in Fig. 12(a)
Fig. 12 Spiral path through the diameter (a) and diagrammatic sketch of random pitch spiral path (b).
and the removal depth is just half of the whole depth every time. Thereby, it is a better choice to adopt the spiral path to polish the rotation symmetry optics. For example, the diagrammatic tool path we choose for the figure error correction is shown in Fig. 12(b). It is a typical pitch-variation tool path.

4. Experiment certification

Although the experience in optics fabrication indicates that the more unorderly the path introduce the smaller medium-high frequency errors, it is difficult to implement in MRF. Because the figure error correction convergence is the prime target, the tool-path must be appropriate to actualize the dwell-time. The random pitch path is verified hereinafter through the experiment. First, the nucleated glass flat mirror with 100mm diameter (90% effective aperture) was fabricated using the equilong 1mm pitch spiral path. The process time is about 30 minutes. The initial figure error and the polished surface are shown in Fig. 13
Fig. 13 Initial figure error (a) and the polished surface (b) with 1mm pitch spiral path.
. It is shown that the figure error has been improved from the initial 0.334λ (RMS, λ = 632.8nm) to 0.059λ (RMS) after one iteration. But the periodic structure can be observed obviously on the polished surface map. The strongest peak is also observed on the 1mm−1 spatial frequency in the PSD curve shown in Fig. 14
Fig. 14 PSD for equilong pitch spiral polished region.
. The result shows the same regularity as the raster scan.

Another fabrication on the same work was done with the random pitch spiral tool path along the diameter after the smoothing treatment and the result is shown in Fig. 15
Fig. 15 Initial figure error (a) and the polished surface (b) with the random pitch spiral path.
. The whole process time is about 5 minutes. The figure precision has been improved to λ/200 (RMS). At the same time, there is no obvious ripple on the polished surface shown in Fig. 15 and it can also be found that there is no strong periodic feature in the PSD curve shown in Fig. 16
Fig. 16 PSD for random pitch spiral polished region.
. The experiment has certificate the practicability of the random pitch tool path based on the surface error distribution and process parameters.

5. Conclusion

The rules from the process parameters to the residual errors when adopting the regular tool path are studied through the simulations and experiments. It certificates that the random pitch tool path based on the surface error distribution and parameters can restrict the tool path ripple height while the convergence efficiency would not be reduced.

References and links

1.

S. D. Jacobs, W. I. Kordonski, D. Golini, I. V. Prokhorov, G. R. Gorodkin, and T. D. Strafford, “Deterministic Magnetorheological Finishing,” US, Patent, 5795212 (1998).

2.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999). [CrossRef]

3.

B. Hallock, B. Messner, C. Hall, and C. Supranowitz, “Improvements in large window and optics production,” Proc. SPIE 6545, 645419 (2007).

4.

R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16(1), 218–224 (1977). [CrossRef] [PubMed]

5.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008). [CrossRef]

6.

M. Ghigo, R. Canestrari, D. Spiga, and A. Novi, “Correction of high spatial frequency errors on optical surfaces by means of ion beam figuring,” Proc. SPIE 6671, 667114 (2007). [CrossRef]

7.

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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-958. [CrossRef] [PubMed]

8.

J. K. Lawson, D. M. Aikens, and R. E. English, “Power spectral density specifications for high-power laser systems,” Proc. SPIE 2775, 345–356 (1996). [CrossRef]

9.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998). [CrossRef]

10.

D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).

11.

C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-23-18942. [CrossRef]

12.

C. Supranowitz, C. Hall, P. Dumas, and B. Hallock, “Improving surface figure and microroughness of IR materials and diamond turned surfaces with magnetorheological finishing (MRF®),” Proc. SPIE 6545, 64540S (2007).

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.4610) Optical design and fabrication : Optical fabrication
(220.5450) Optical design and fabrication : Polishing

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: June 8, 2010
Revised Manuscript: September 19, 2010
Manuscript Accepted: September 24, 2010
Published: October 15, 2010

Citation
Hao Hu, Yifan Dai, and Xiaoqiang Peng, "Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing," Opt. Express 18, 22973-22981 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-22-22973


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References

  1. S. D. Jacobs, W. I. Kordonski, D. Golini, I. V. Prokhorov, G. R. Gorodkin, and T. D. Strafford, “Deterministic Magnetorheological Finishing,” US, Patent, 5795212 (1998).
  2. D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999). [CrossRef]
  3. B. Hallock, B. Messner, C. Hall, and C. Supranowitz, “Improvements in large window and optics production,” Proc. SPIE 6545, 645419 (2007).
  4. R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16(1), 218–224 (1977). [CrossRef] [PubMed]
  5. M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008). [CrossRef]
  6. M. Ghigo, R. Canestrari, D. Spiga, and A. Novi, “Correction of high spatial frequency errors on optical surfaces by means of ion beam figuring,” Proc. SPIE 6671, 667114 (2007). [CrossRef]
  7. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-958 . [CrossRef] [PubMed]
  8. J. K. Lawson, D. M. Aikens, and R. E. English, “Power spectral density specifications for high-power laser systems,” Proc. SPIE 2775, 345–356 (1996). [CrossRef]
  9. J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998). [CrossRef]
  10. D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).
  11. C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-23-18942 . [CrossRef]
  12. C. Supranowitz, C. Hall, P. Dumas, and B. Hallock, “Improving surface figure and microroughness of IR materials and diamond turned surfaces with magnetorheological finishing (MRF®),” Proc. SPIE 6545, 64540S (2007).

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