Abstract

A calibrated and predictive model of the removal function has been established based on the analysis of a magnetorheological finishing (MRF) process. By introducing an efficiency coefficient of the removal function, the model can be used to calibrate the removal function in a MRF figuring process and to accurately predict the removal function of a workpiece to be polished whose material is different from the spot part. Its correctness and feasibility have been validated by simulations. Furthermore, applying this model to the MRF figuring experiments, the efficiency coefficient of the removal function can be identified accurately to make the MRF figuring process deterministic and controllable. Therefore, all the results indicate that the calibrated and predictive model of the removal function can improve the finishing determinacy and increase the model applicability in a MRF process.

© 2010 Optical Society of America

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References

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  1. D. Golini, W. I. Kordonski, P. Dumas, and S. J.Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80-91 (1999).
  2. D. Golini, S. Jacobs, W. Kordonski, and P. Dumas, “Precision optics fabrication using magnetorheological finishing,” Proc. SPIE CR67, 251-274 (1997).
  3. H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90-96 (2003).
  4. F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214-256 (1927).
  5. W. J. Rupp, “The development of optical surfaces during the grinding process,” Appl. Opt. 4, 743-748 (1965).
    [CrossRef]
  6. W. J. Rupp, “Loose-abrasive grinding of optical surfaces,” Appl. Opt. 11, 2797-2810 (1972).
    [CrossRef]
  7. R. A. Jones, “Computer controlled polisher demonstration,” Appl. Opt. 19, 2072-2076 (1980).
    [CrossRef]
  8. R. A. Jones, “Computer-controlled grinding of optical surface,” Appl. Opt. 21, 874-877 (1982).
    [CrossRef]
  9. X. Zhou, “Study on techniques in computer-controlled grinding and polishing for large and medium aspheric surfaces,” Ph.D. dissertation (National University of Defence Technology, 2007), in Chinese.
  10. M. Yu, L. Yang, and Y. Wan, “Optimizing analysis of dwell-time parameters,” Opt. Optoelectron. Technol. 4, 5-7 (2006).
  11. L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precision Eng. 5, 107-112 (2007).
  12. P. M. Shanbhag, M. R. Feinberg, G. Sandri, M. N. Horenstein, and T. G. Bifano, “Ion beam machining of millimeter scale optics,” Appl. Opt. 39, 599-611 (2000).
    [CrossRef]
  13. C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090-4096 (2009).
    [CrossRef]
  14. T. W. Drueding, “Precision ion figuring system for optical components,” Ph.D. dissertation (Boston University, 1995).
  15. M. Buijs and K. Korpel-Van Houten, “A model for lapping of glass,” J. Mater. Sci. 28, 3014-3020 (1993).
    [CrossRef]
  16. J. C. Lambropoulos, S. D. Jacobs, and J. Ruckman, “Material removal from grinding to polishing,” in Finishing of Advanced Ceramics and Glasses, Vol. 102 of Ceramic Glasses, R. Sabia, V. A. Greenhut, and C. G. Pantano, eds. (American Ceramic Society, 1999), pp. 113-128.
  17. T. Izumitani and S. Harada, “Polishing mechanism of optical glasses,” Glass Technol. 12(5), 131-135 (1971).
  18. A. B. Shorey, S. D. Jacobs, W. I. Kordonski, and R. F. Gans, “Experiments and observations regarding the mechanisms of glass removal in magnetorheological finishing,” Appl. Opt. 40, 20-33 (2001).
    [CrossRef]
  19. A. B. Shorey, “Mechanisms of the material removal in magnetorheological finishing (MRF) of glass,” Ph.D. dissertation (University of Rochester, 2000).
  20. C. Miao, S. N. Shafrir, J. C. Lambropoulos, J. Mici, and S. D. Jacobs, “Shear stress in magnetorheological finishing for glasses,” Appl. Opt. 48, 2585-2594 (2009).
    [CrossRef]
  21. J. E. DeGroote, “Surface interactions between nanodiamonds and glass in magnetorheological finishing (MRF),” Ph.D. dissertation (University of Rochester, 2007).
  22. F. Zhang, X. Zhang, J. Yu, Q. Wang, and P. Guo, “Foundation of mathematics model of magnetorheological finishing,” Opt. Technique 26, 190-192 (2000).
  23. X. Peng, Y. Dai, and S. Li, “Material removal model of magnetorheological finishing,” Chin. J. Mech. Eng. 40(04), 67-70 (2004).
  24. F. Shi, Y. Dai, X. Peng, and C. Song, “Three-dimensional material removal model of magnetorheological finishing (MRF),” China Mech. Eng. 20, 644-648 (2009).

2009 (3)

2007 (1)

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precision Eng. 5, 107-112 (2007).

2006 (1)

M. Yu, L. Yang, and Y. Wan, “Optimizing analysis of dwell-time parameters,” Opt. Optoelectron. Technol. 4, 5-7 (2006).

2004 (1)

X. Peng, Y. Dai, and S. Li, “Material removal model of magnetorheological finishing,” Chin. J. Mech. Eng. 40(04), 67-70 (2004).

2003 (1)

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90-96 (2003).

2001 (1)

2000 (2)

P. M. Shanbhag, M. R. Feinberg, G. Sandri, M. N. Horenstein, and T. G. Bifano, “Ion beam machining of millimeter scale optics,” Appl. Opt. 39, 599-611 (2000).
[CrossRef]

F. Zhang, X. Zhang, J. Yu, Q. Wang, and P. Guo, “Foundation of mathematics model of magnetorheological finishing,” Opt. Technique 26, 190-192 (2000).

1999 (1)

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

1997 (1)

D. Golini, S. Jacobs, W. Kordonski, and P. Dumas, “Precision optics fabrication using magnetorheological finishing,” Proc. SPIE CR67, 251-274 (1997).

1993 (1)

M. Buijs and K. Korpel-Van Houten, “A model for lapping of glass,” J. Mater. Sci. 28, 3014-3020 (1993).
[CrossRef]

1982 (1)

1980 (1)

1972 (1)

1971 (1)

T. Izumitani and S. Harada, “Polishing mechanism of optical glasses,” Glass Technol. 12(5), 131-135 (1971).

1965 (1)

1927 (1)

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

Bifano, T. G.

Buijs, M.

M. Buijs and K. Korpel-Van Houten, “A model for lapping of glass,” J. Mater. Sci. 28, 3014-3020 (1993).
[CrossRef]

Dai, Y.

F. Shi, Y. Dai, X. Peng, and C. Song, “Three-dimensional material removal model of magnetorheological finishing (MRF),” China Mech. Eng. 20, 644-648 (2009).

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precision Eng. 5, 107-112 (2007).

X. Peng, Y. Dai, and S. Li, “Material removal model of magnetorheological finishing,” Chin. J. Mech. Eng. 40(04), 67-70 (2004).

DeGroote, J. E.

J. E. DeGroote, “Surface interactions between nanodiamonds and glass in magnetorheological finishing (MRF),” Ph.D. dissertation (University of Rochester, 2007).

Drueding, T. W.

T. W. Drueding, “Precision ion figuring system for optical components,” Ph.D. dissertation (Boston University, 1995).

Dumas, P.

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

D. Golini, S. Jacobs, W. Kordonski, and P. Dumas, “Precision optics fabrication using magnetorheological finishing,” Proc. SPIE CR67, 251-274 (1997).

Feinberg, M. R.

Fess, E. M.

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90-96 (2003).

Gans, R. F.

Golini, D.

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

D. Golini, S. Jacobs, W. Kordonski, and P. Dumas, “Precision optics fabrication using magnetorheological finishing,” Proc. SPIE CR67, 251-274 (1997).

Guo, P.

F. Zhang, X. Zhang, J. Yu, Q. Wang, and P. Guo, “Foundation of mathematics model of magnetorheological finishing,” Opt. Technique 26, 190-192 (2000).

Harada, S.

T. Izumitani and S. Harada, “Polishing mechanism of optical glasses,” Glass Technol. 12(5), 131-135 (1971).

Hogan, S. J.

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

Horenstein, M. N.

Izumitani, T.

T. Izumitani and S. Harada, “Polishing mechanism of optical glasses,” Glass Technol. 12(5), 131-135 (1971).

Jacobs, S.

D. Golini, S. Jacobs, W. Kordonski, and P. Dumas, “Precision optics fabrication using magnetorheological finishing,” Proc. SPIE CR67, 251-274 (1997).

Jacobs, S. D.

C. Miao, S. N. Shafrir, J. C. Lambropoulos, J. Mici, and S. D. Jacobs, “Shear stress in magnetorheological finishing for glasses,” Appl. Opt. 48, 2585-2594 (2009).
[CrossRef]

A. B. Shorey, S. D. Jacobs, W. I. Kordonski, and R. F. Gans, “Experiments and observations regarding the mechanisms of glass removal in magnetorheological finishing,” Appl. Opt. 40, 20-33 (2001).
[CrossRef]

J. C. Lambropoulos, S. D. Jacobs, and J. Ruckman, “Material removal from grinding to polishing,” in Finishing of Advanced Ceramics and Glasses, Vol. 102 of Ceramic Glasses, R. Sabia, V. A. Greenhut, and C. G. Pantano, eds. (American Ceramic Society, 1999), pp. 113-128.

Jiao, C.

C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090-4096 (2009).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precision Eng. 5, 107-112 (2007).

Jones, R. A.

Kordonski, W.

D. Golini, S. Jacobs, W. Kordonski, and P. Dumas, “Precision optics fabrication using magnetorheological finishing,” Proc. SPIE CR67, 251-274 (1997).

Kordonski, W. I.

A. B. Shorey, S. D. Jacobs, W. I. Kordonski, and R. F. Gans, “Experiments and observations regarding the mechanisms of glass removal in magnetorheological finishing,” Appl. Opt. 40, 20-33 (2001).
[CrossRef]

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

Korpel-Van Houten, K.

M. Buijs and K. Korpel-Van Houten, “A model for lapping of glass,” J. Mater. Sci. 28, 3014-3020 (1993).
[CrossRef]

Lambropoulos, J. C.

C. Miao, S. N. Shafrir, J. C. Lambropoulos, J. Mici, and S. D. Jacobs, “Shear stress in magnetorheological finishing for glasses,” Appl. Opt. 48, 2585-2594 (2009).
[CrossRef]

J. C. Lambropoulos, S. D. Jacobs, and J. Ruckman, “Material removal from grinding to polishing,” in Finishing of Advanced Ceramics and Glasses, Vol. 102 of Ceramic Glasses, R. Sabia, V. A. Greenhut, and C. G. Pantano, eds. (American Ceramic Society, 1999), pp. 113-128.

Li, S.

C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090-4096 (2009).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precision Eng. 5, 107-112 (2007).

X. Peng, Y. Dai, and S. Li, “Material removal model of magnetorheological finishing,” Chin. J. Mech. Eng. 40(04), 67-70 (2004).

Miao, C.

Mici, J.

Peng, X.

F. Shi, Y. Dai, X. Peng, and C. Song, “Three-dimensional material removal model of magnetorheological finishing (MRF),” China Mech. Eng. 20, 644-648 (2009).

X. Peng, Y. Dai, and S. Li, “Material removal model of magnetorheological finishing,” Chin. J. Mech. Eng. 40(04), 67-70 (2004).

Pollicove, H. M.

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90-96 (2003).

Preston, F. W.

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

Ruckman, J.

J. C. Lambropoulos, S. D. Jacobs, and J. Ruckman, “Material removal from grinding to polishing,” in Finishing of Advanced Ceramics and Glasses, Vol. 102 of Ceramic Glasses, R. Sabia, V. A. Greenhut, and C. G. Pantano, eds. (American Ceramic Society, 1999), pp. 113-128.

Rupp, W. J.

Sandri, G.

Schoen, J. M.

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90-96 (2003).

Shafrir, S. N.

Shanbhag, P. M.

Shi, F.

F. Shi, Y. Dai, X. Peng, and C. Song, “Three-dimensional material removal model of magnetorheological finishing (MRF),” China Mech. Eng. 20, 644-648 (2009).

Shorey, A. B.

A. B. Shorey, S. D. Jacobs, W. I. Kordonski, and R. F. Gans, “Experiments and observations regarding the mechanisms of glass removal in magnetorheological finishing,” Appl. Opt. 40, 20-33 (2001).
[CrossRef]

A. B. Shorey, “Mechanisms of the material removal in magnetorheological finishing (MRF) of glass,” Ph.D. dissertation (University of Rochester, 2000).

Song, C.

F. Shi, Y. Dai, X. Peng, and C. Song, “Three-dimensional material removal model of magnetorheological finishing (MRF),” China Mech. Eng. 20, 644-648 (2009).

Wan, Y.

M. Yu, L. Yang, and Y. Wan, “Optimizing analysis of dwell-time parameters,” Opt. Optoelectron. Technol. 4, 5-7 (2006).

Wang, Q.

F. Zhang, X. Zhang, J. Yu, Q. Wang, and P. Guo, “Foundation of mathematics model of magnetorheological finishing,” Opt. Technique 26, 190-192 (2000).

Xie, X.

C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090-4096 (2009).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precision Eng. 5, 107-112 (2007).

Yu, J.

F. Zhang, X. Zhang, J. Yu, Q. Wang, and P. Guo, “Foundation of mathematics model of magnetorheological finishing,” Opt. Technique 26, 190-192 (2000).

Yu, M.

M. Yu, L. Yang, and Y. Wan, “Optimizing analysis of dwell-time parameters,” Opt. Optoelectron. Technol. 4, 5-7 (2006).

Zhang, F.

F. Zhang, X. Zhang, J. Yu, Q. Wang, and P. Guo, “Foundation of mathematics model of magnetorheological finishing,” Opt. Technique 26, 190-192 (2000).

Zhang, X.

F. Zhang, X. Zhang, J. Yu, Q. Wang, and P. Guo, “Foundation of mathematics model of magnetorheological finishing,” Opt. Technique 26, 190-192 (2000).

Zhou, L.

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precision Eng. 5, 107-112 (2007).

Zhou, X.

X. Zhou, “Study on techniques in computer-controlled grinding and polishing for large and medium aspheric surfaces,” Ph.D. dissertation (National University of Defence Technology, 2007), in Chinese.

Appl. Opt. (8)

Chin. J. Mech. Eng. (1)

X. Peng, Y. Dai, and S. Li, “Material removal model of magnetorheological finishing,” Chin. J. Mech. Eng. 40(04), 67-70 (2004).

China Mech. Eng. (1)

F. Shi, Y. Dai, X. Peng, and C. Song, “Three-dimensional material removal model of magnetorheological finishing (MRF),” China Mech. Eng. 20, 644-648 (2009).

Glass Technol. (1)

T. Izumitani and S. Harada, “Polishing mechanism of optical glasses,” Glass Technol. 12(5), 131-135 (1971).

J. Mater. Sci. (1)

M. Buijs and K. Korpel-Van Houten, “A model for lapping of glass,” J. Mater. Sci. 28, 3014-3020 (1993).
[CrossRef]

J. Soc. Glass Technol. (1)

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

Nanotechnol. Precision Eng. (1)

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precision Eng. 5, 107-112 (2007).

Opt. Optoelectron. Technol. (1)

M. Yu, L. Yang, and Y. Wan, “Optimizing analysis of dwell-time parameters,” Opt. Optoelectron. Technol. 4, 5-7 (2006).

Opt. Technique (1)

F. Zhang, X. Zhang, J. Yu, Q. Wang, and P. Guo, “Foundation of mathematics model of magnetorheological finishing,” Opt. Technique 26, 190-192 (2000).

Proc. SPIE (3)

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

D. Golini, S. Jacobs, W. Kordonski, and P. Dumas, “Precision optics fabrication using magnetorheological finishing,” Proc. SPIE CR67, 251-274 (1997).

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90-96 (2003).

Other (5)

X. Zhou, “Study on techniques in computer-controlled grinding and polishing for large and medium aspheric surfaces,” Ph.D. dissertation (National University of Defence Technology, 2007), in Chinese.

T. W. Drueding, “Precision ion figuring system for optical components,” Ph.D. dissertation (Boston University, 1995).

J. C. Lambropoulos, S. D. Jacobs, and J. Ruckman, “Material removal from grinding to polishing,” in Finishing of Advanced Ceramics and Glasses, Vol. 102 of Ceramic Glasses, R. Sabia, V. A. Greenhut, and C. G. Pantano, eds. (American Ceramic Society, 1999), pp. 113-128.

J. E. DeGroote, “Surface interactions between nanodiamonds and glass in magnetorheological finishing (MRF),” Ph.D. dissertation (University of Rochester, 2007).

A. B. Shorey, “Mechanisms of the material removal in magnetorheological finishing (MRF) of glass,” Ph.D. dissertation (University of Rochester, 2000).

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Figures (9)

Fig. 1
Fig. 1

Simulations with different efficiency coefficients of removal function: (a) initial surface error, (b) removal function, (c) simulated residual error, (d) actual residual error ( γ = 0.6 ) , (e) actual residual error ( γ = 0.8 ) , (f) actual residual error ( γ = 0.9 ) , (g) actual residual error ( γ = 1.1 ) , (h) actual residual error ( γ = 1.2 ) , and (i) actual residual error ( γ = 1.4 ) .

Fig. 2
Fig. 2

MRF platform KDMRF-1000.

Fig. 3
Fig. 3

Photo of Zygo interferometer.

Fig. 4
Fig. 4

Surface error distribution map of flat optics measured with a Zygo interferometer: (a) initial surface error, (b) residual error after first polishing, (c) residual error after second polishing.

Fig. 5
Fig. 5

Residual error distribution maps of flat optics by simulating (a)  residual error in the first finishing and (b)  residual error in the second finishing.

Fig. 6
Fig. 6

Photos of the lightweight thin SiC mirror.

Fig. 7
Fig. 7

Surface error distribution maps of the lightweight thin flat SiC mirror: (a) initial surface error, (b) residual error after first MRF, (c) simulated residual error in the first process of MRF.

Fig. 8
Fig. 8

(a) Predicted removal function and (b) the actual removal function.

Fig. 9
Fig. 9

Final surface error distribution map of the lightweight thin SiC mirror measured with a Zygo interferometer.

Tables (1)

Tables Icon

Table 1 Identification Results with Different Efficiency Coefficient of Removal Function

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

h ( x , y ) = α β r ( x α , y β ) · d ( α , β ) d α d β + e ( x , y ) ,
γ = r ' ( x , y ) / r ( x , y ) ,
r ' ( x , y ) = γ r ( x , y ) .
e ( x , y ) = h ( x , y ) α β r ( x α , y β ) · d ( α , β ) d α d β .
e ' ( x , y ) = h ( x , y ) γ α β r ( x α , y β ) · d ( α , β ) d α d β .
e ' ( x , y ) = h ( x , y ) γ ( h ( x , y ) e ( x , y ) ) = ( 1 γ ) h ( x , y ) + γ e ( x , y ) .
e RMS = 1 i n 1 j n ( e ( x i , y j ) S ) 2 / n 2 ,
S = 1 i n 1 j n e ( x i , y j ) / n 2 .
S ' = 1 i n 1 j n e ' ( x i , y j ) / n 2 .
S ' = ( 1 γ ) 1 i n 1 j n h ( x i , y j ) / n 2 + γ 1 i n 1 j n e ( x i , y j ) / n 2 .
S ' = ( 1 γ ) H + γ S .
e RMS ' = 1 i n 1 j n ( e ' ( x i , y j ) S ' ) 2 / n 2 .
e RMS ' 2 = ( 1 γ ) 2 h RMS 2 + γ 2 e RMS 2 + 2 γ ( 1 γ ) C=cov ( h , e ) ,
[ h RMS 2 + e RMS 2 2 · c ov ( h , e ) ] · γ 2 + [ 2 · c ov ( h , e ) 2 · h RMS 2 ] · γ + h RMS 2 e RMS ' 2 = 0 ,
γ 1 = ( a 2 · d 2 a 2 · b 2 + b 2 · d 2 + c 2 2 · c · d 2 ) c + a 2 a 2 + b 2 2 · c , γ 2 = ( a 2 · d 2 a 2 · b 2 + b 2 · d 2 + c 2 2 · c · d 2 ) c + a 2 a 2 + b 2 2 · c .

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