Abstract

This study aims to develop a new optical design method of soft multifocal contact lens (CLs) to obtain uniform optical power in large center-distance zone with optimized Non-Uniform Rational B-spline (NURBS). For the anterior surface profiles of CLs, the NURBS design curves are optimized to match given optical power distributions. Then, the NURBS in the center-distance zones are fitted in the corresponding spherical/aspheric curves for both data points and their centers of curvature to achieve the uniform power. Four cases of soft CLs have been manufactured by casting in shell molds by injection molding and then measured to verify the design specifications. Results of power profiles of these CLs are concord with the given clinical requirements of uniform powers in larger center-distance zone. The developed optical design method has been verified for multifocal CLs design and can be further applied for production of soft multifocal CLs.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. E. S. Bennett, “Contact lens correction of presbyopia,” Clin. Exp. Optom. 91(3), 265–278 (2008).
    [Crossref] [PubMed]
  2. L. T. Vu, C. A. Chen, and P. J. T. Shum, “Analysis on multifocal contact lens design based on optical power distribution with NURBS,” Appl. Opt. 56(28), 7990–7997 (2017).
    [Crossref] [PubMed]
  3. S. Wagner, F. Conrad, R. C. Bakaraju, C. Fedtke, K. Ehrmann, and B. A. Holden, “Power profiles of single vision and multifocal soft contact lenses,” Cont. Lens Anterior Eye 38(1), 2–14 (2015).
    [Crossref] [PubMed]
  4. E. Kim, R. C. Bakaraju, and K. Ehrmann, “Power Profiles of Commercial Multifocal Soft Contact Lenses,” Optom. Vis. Sci. 94(2), 183–196 (2017).
    [Crossref] [PubMed]
  5. G. M. Fuerter, “Spline surfaces as means for optical design,” Proc. SPIE 554(118), 0554 (1986).
  6. J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14(04), 619–640 (2004).
    [Crossref]
  7. W. Y. Hsu, Y. L. Liu, Y. C. Cheng, C. H. Kuo, C. C. Chen, and G. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
    [Crossref]
  8. L. T. Vu, C. C. A. Chen, and Y. T. Qiu, “Optimization of aspheric multifocal contact lens by spline curve,” Proc. SPIE.  10021, 100210L (2016).
  9. L.T. Vu, C. C. A. Chen, and Y. T. Qiu, “Progressive multifocal contact lens and producing method thereof,” TW I584022 (2016).
  10. R. T. Marler and J. S. Arora, “Survey of multi-objective optimization methods for engineering,” J. Struct. Multidisc. Optim. 26(6), 369–395 (2004).
    [Crossref]
  11. R. T. Marler and J. S. Arora, “The weighted sum method for multi-objective optimization: new insights,” J. Struct. Multidisc Optim. 41(6), 853–862 (2010).
    [Crossref]
  12. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
    [Crossref] [PubMed]
  13. R. W. Eglese, “Simulated annealing: A tool for Operational Research,” Eur. J. Oper. Res. 46(3), 271–281 (1990).
    [Crossref]
  14. E. S. Bennett and B. A. Weissman, Clinical Contact Lens Practice, 2nd ed. (Lippincott Williams & Wilkins, 2005).
  15. L. A. Piegl and W. Tiller, The NURBS Book (Springer 1997), Chap. 4.
  16. S. Schwartz, Geometrical and Visual Optics (McGraw-Hill Education / Medical, 2nd ed, 2013). Chap. 1.
  17. W. A. Granville, Elements of the Differential and Integral Calculus (Read Books, Revised Edition, 2007). Chap. 14.
  18. Y. W. Hsu, Y. L. Liu, Y. C. Cheng, Y. H. Kuo, C. C. Chen, and C. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
    [Crossref]
  19. C. C. A. Chen and S. W. Chang, “Shrinkage Analysis on Convex Shell by Injection Molding,” Int. Polym. Process. 23(1), 65–71 (2008).
    [Crossref]

2017 (2)

L. T. Vu, C. A. Chen, and P. J. T. Shum, “Analysis on multifocal contact lens design based on optical power distribution with NURBS,” Appl. Opt. 56(28), 7990–7997 (2017).
[Crossref] [PubMed]

E. Kim, R. C. Bakaraju, and K. Ehrmann, “Power Profiles of Commercial Multifocal Soft Contact Lenses,” Optom. Vis. Sci. 94(2), 183–196 (2017).
[Crossref] [PubMed]

2016 (1)

L. T. Vu, C. C. A. Chen, and Y. T. Qiu, “Optimization of aspheric multifocal contact lens by spline curve,” Proc. SPIE.  10021, 100210L (2016).

2015 (1)

S. Wagner, F. Conrad, R. C. Bakaraju, C. Fedtke, K. Ehrmann, and B. A. Holden, “Power profiles of single vision and multifocal soft contact lenses,” Cont. Lens Anterior Eye 38(1), 2–14 (2015).
[Crossref] [PubMed]

2012 (2)

W. Y. Hsu, Y. L. Liu, Y. C. Cheng, C. H. Kuo, C. C. Chen, and G. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Y. W. Hsu, Y. L. Liu, Y. C. Cheng, Y. H. Kuo, C. C. Chen, and C. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

2010 (1)

R. T. Marler and J. S. Arora, “The weighted sum method for multi-objective optimization: new insights,” J. Struct. Multidisc Optim. 41(6), 853–862 (2010).
[Crossref]

2008 (2)

C. C. A. Chen and S. W. Chang, “Shrinkage Analysis on Convex Shell by Injection Molding,” Int. Polym. Process. 23(1), 65–71 (2008).
[Crossref]

E. S. Bennett, “Contact lens correction of presbyopia,” Clin. Exp. Optom. 91(3), 265–278 (2008).
[Crossref] [PubMed]

2004 (2)

J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14(04), 619–640 (2004).
[Crossref]

R. T. Marler and J. S. Arora, “Survey of multi-objective optimization methods for engineering,” J. Struct. Multidisc. Optim. 26(6), 369–395 (2004).
[Crossref]

1990 (1)

R. W. Eglese, “Simulated annealing: A tool for Operational Research,” Eur. J. Oper. Res. 46(3), 271–281 (1990).
[Crossref]

1986 (1)

G. M. Fuerter, “Spline surfaces as means for optical design,” Proc. SPIE 554(118), 0554 (1986).

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Arora, J. S.

R. T. Marler and J. S. Arora, “The weighted sum method for multi-objective optimization: new insights,” J. Struct. Multidisc Optim. 41(6), 853–862 (2010).
[Crossref]

R. T. Marler and J. S. Arora, “Survey of multi-objective optimization methods for engineering,” J. Struct. Multidisc. Optim. 26(6), 369–395 (2004).
[Crossref]

Bakaraju, R. C.

E. Kim, R. C. Bakaraju, and K. Ehrmann, “Power Profiles of Commercial Multifocal Soft Contact Lenses,” Optom. Vis. Sci. 94(2), 183–196 (2017).
[Crossref] [PubMed]

S. Wagner, F. Conrad, R. C. Bakaraju, C. Fedtke, K. Ehrmann, and B. A. Holden, “Power profiles of single vision and multifocal soft contact lenses,” Cont. Lens Anterior Eye 38(1), 2–14 (2015).
[Crossref] [PubMed]

Bennett, E. S.

E. S. Bennett, “Contact lens correction of presbyopia,” Clin. Exp. Optom. 91(3), 265–278 (2008).
[Crossref] [PubMed]

Chang, S. W.

C. C. A. Chen and S. W. Chang, “Shrinkage Analysis on Convex Shell by Injection Molding,” Int. Polym. Process. 23(1), 65–71 (2008).
[Crossref]

Chen, C. A.

Chen, C. C.

W. Y. Hsu, Y. L. Liu, Y. C. Cheng, C. H. Kuo, C. C. Chen, and G. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Y. W. Hsu, Y. L. Liu, Y. C. Cheng, Y. H. Kuo, C. C. Chen, and C. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Chen, C. C. A.

L. T. Vu, C. C. A. Chen, and Y. T. Qiu, “Optimization of aspheric multifocal contact lens by spline curve,” Proc. SPIE.  10021, 100210L (2016).

C. C. A. Chen and S. W. Chang, “Shrinkage Analysis on Convex Shell by Injection Molding,” Int. Polym. Process. 23(1), 65–71 (2008).
[Crossref]

Cheng, Y. C.

Y. W. Hsu, Y. L. Liu, Y. C. Cheng, Y. H. Kuo, C. C. Chen, and C. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

W. Y. Hsu, Y. L. Liu, Y. C. Cheng, C. H. Kuo, C. C. Chen, and G. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Conrad, F.

S. Wagner, F. Conrad, R. C. Bakaraju, C. Fedtke, K. Ehrmann, and B. A. Holden, “Power profiles of single vision and multifocal soft contact lenses,” Cont. Lens Anterior Eye 38(1), 2–14 (2015).
[Crossref] [PubMed]

Eglese, R. W.

R. W. Eglese, “Simulated annealing: A tool for Operational Research,” Eur. J. Oper. Res. 46(3), 271–281 (1990).
[Crossref]

Ehrmann, K.

E. Kim, R. C. Bakaraju, and K. Ehrmann, “Power Profiles of Commercial Multifocal Soft Contact Lenses,” Optom. Vis. Sci. 94(2), 183–196 (2017).
[Crossref] [PubMed]

S. Wagner, F. Conrad, R. C. Bakaraju, C. Fedtke, K. Ehrmann, and B. A. Holden, “Power profiles of single vision and multifocal soft contact lenses,” Cont. Lens Anterior Eye 38(1), 2–14 (2015).
[Crossref] [PubMed]

Fedtke, C.

S. Wagner, F. Conrad, R. C. Bakaraju, C. Fedtke, K. Ehrmann, and B. A. Holden, “Power profiles of single vision and multifocal soft contact lenses,” Cont. Lens Anterior Eye 38(1), 2–14 (2015).
[Crossref] [PubMed]

Fuerter, G. M.

G. M. Fuerter, “Spline surfaces as means for optical design,” Proc. SPIE 554(118), 0554 (1986).

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Holden, B. A.

S. Wagner, F. Conrad, R. C. Bakaraju, C. Fedtke, K. Ehrmann, and B. A. Holden, “Power profiles of single vision and multifocal soft contact lenses,” Cont. Lens Anterior Eye 38(1), 2–14 (2015).
[Crossref] [PubMed]

Hsu, W. Y.

W. Y. Hsu, Y. L. Liu, Y. C. Cheng, C. H. Kuo, C. C. Chen, and G. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Hsu, Y. W.

Y. W. Hsu, Y. L. Liu, Y. C. Cheng, Y. H. Kuo, C. C. Chen, and C. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Kim, E.

E. Kim, R. C. Bakaraju, and K. Ehrmann, “Power Profiles of Commercial Multifocal Soft Contact Lenses,” Optom. Vis. Sci. 94(2), 183–196 (2017).
[Crossref] [PubMed]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Kuo, C. H.

W. Y. Hsu, Y. L. Liu, Y. C. Cheng, C. H. Kuo, C. C. Chen, and G. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Kuo, Y. H.

Y. W. Hsu, Y. L. Liu, Y. C. Cheng, Y. H. Kuo, C. C. Chen, and C. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Liu, Y. L.

Y. W. Hsu, Y. L. Liu, Y. C. Cheng, Y. H. Kuo, C. C. Chen, and C. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

W. Y. Hsu, Y. L. Liu, Y. C. Cheng, C. H. Kuo, C. C. Chen, and G. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Marler, R. T.

R. T. Marler and J. S. Arora, “The weighted sum method for multi-objective optimization: new insights,” J. Struct. Multidisc Optim. 41(6), 853–862 (2010).
[Crossref]

R. T. Marler and J. S. Arora, “Survey of multi-objective optimization methods for engineering,” J. Struct. Multidisc. Optim. 26(6), 369–395 (2004).
[Crossref]

Qiu, Y. T.

L. T. Vu, C. C. A. Chen, and Y. T. Qiu, “Optimization of aspheric multifocal contact lens by spline curve,” Proc. SPIE.  10021, 100210L (2016).

Santosa, F.

J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14(04), 619–640 (2004).
[Crossref]

Shum, P. J. T.

Su, C. D.

Y. W. Hsu, Y. L. Liu, Y. C. Cheng, Y. H. Kuo, C. C. Chen, and C. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Su, G. D.

W. Y. Hsu, Y. L. Liu, Y. C. Cheng, C. H. Kuo, C. C. Chen, and G. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Vu, L. T.

L. T. Vu, C. A. Chen, and P. J. T. Shum, “Analysis on multifocal contact lens design based on optical power distribution with NURBS,” Appl. Opt. 56(28), 7990–7997 (2017).
[Crossref] [PubMed]

L. T. Vu, C. C. A. Chen, and Y. T. Qiu, “Optimization of aspheric multifocal contact lens by spline curve,” Proc. SPIE.  10021, 100210L (2016).

Wagner, S.

S. Wagner, F. Conrad, R. C. Bakaraju, C. Fedtke, K. Ehrmann, and B. A. Holden, “Power profiles of single vision and multifocal soft contact lenses,” Cont. Lens Anterior Eye 38(1), 2–14 (2015).
[Crossref] [PubMed]

Wang, J.

J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14(04), 619–640 (2004).
[Crossref]

Appl. Opt. (1)

Clin. Exp. Optom. (1)

E. S. Bennett, “Contact lens correction of presbyopia,” Clin. Exp. Optom. 91(3), 265–278 (2008).
[Crossref] [PubMed]

Cont. Lens Anterior Eye (1)

S. Wagner, F. Conrad, R. C. Bakaraju, C. Fedtke, K. Ehrmann, and B. A. Holden, “Power profiles of single vision and multifocal soft contact lenses,” Cont. Lens Anterior Eye 38(1), 2–14 (2015).
[Crossref] [PubMed]

Eur. J. Oper. Res. (1)

R. W. Eglese, “Simulated annealing: A tool for Operational Research,” Eur. J. Oper. Res. 46(3), 271–281 (1990).
[Crossref]

Int. J. Adv. Manuf. Technol. (2)

Y. W. Hsu, Y. L. Liu, Y. C. Cheng, Y. H. Kuo, C. C. Chen, and C. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

W. Y. Hsu, Y. L. Liu, Y. C. Cheng, C. H. Kuo, C. C. Chen, and G. D. Su, “Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description,” Int. J. Adv. Manuf. Technol. 63(1), 225–233 (2012).
[Crossref]

Int. Polym. Process. (1)

C. C. A. Chen and S. W. Chang, “Shrinkage Analysis on Convex Shell by Injection Molding,” Int. Polym. Process. 23(1), 65–71 (2008).
[Crossref]

J. Struct. Multidisc Optim. (1)

R. T. Marler and J. S. Arora, “The weighted sum method for multi-objective optimization: new insights,” J. Struct. Multidisc Optim. 41(6), 853–862 (2010).
[Crossref]

J. Struct. Multidisc. Optim. (1)

R. T. Marler and J. S. Arora, “Survey of multi-objective optimization methods for engineering,” J. Struct. Multidisc. Optim. 26(6), 369–395 (2004).
[Crossref]

Math. Models Methods Appl. Sci. (1)

J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14(04), 619–640 (2004).
[Crossref]

Optom. Vis. Sci. (1)

E. Kim, R. C. Bakaraju, and K. Ehrmann, “Power Profiles of Commercial Multifocal Soft Contact Lenses,” Optom. Vis. Sci. 94(2), 183–196 (2017).
[Crossref] [PubMed]

Proc. SPIE (2)

G. M. Fuerter, “Spline surfaces as means for optical design,” Proc. SPIE 554(118), 0554 (1986).

L. T. Vu, C. C. A. Chen, and Y. T. Qiu, “Optimization of aspheric multifocal contact lens by spline curve,” Proc. SPIE.  10021, 100210L (2016).

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Other (5)

E. S. Bennett and B. A. Weissman, Clinical Contact Lens Practice, 2nd ed. (Lippincott Williams & Wilkins, 2005).

L. A. Piegl and W. Tiller, The NURBS Book (Springer 1997), Chap. 4.

S. Schwartz, Geometrical and Visual Optics (McGraw-Hill Education / Medical, 2nd ed, 2013). Chap. 1.

W. A. Granville, Elements of the Differential and Integral Calculus (Read Books, Revised Edition, 2007). Chap. 14.

L.T. Vu, C. C. A. Chen, and Y. T. Qiu, “Progressive multifocal contact lens and producing method thereof,” TW I584022 (2016).

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Figures (10)

Fig. 1
Fig. 1 Illustration of the soft multifocal CLs design with center-distance.
Fig. 2
Fig. 2 The illustration of the power distributions [2].
Fig. 3
Fig. 3 Fitting the NURBS design curves with spherical/aspheric curves in center-distance zone.
Fig. 4
Fig. 4 a) Injection molds for shell molds; b) Shell mold for casting soft CLs.
Fig. 5
Fig. 5 The power profiles: a) requirements of Case 1 to Case 4, b) initial power designs of Case 1 to Case 4.
Fig. 6
Fig. 6 The simulated power distributions of the initial designs for Case 1 and Case 2.
Fig. 7
Fig. 7 The simulated power distributions of the initial designs for Case 3 and Case 4.
Fig. 8
Fig. 8 The measured power distributions of the soft multifocal contact lens samples of Case 1 to Case 4.
Fig. 9
Fig. 9 The power error curves between the original requirements and measurement results of a) Case 1 and Case 2, b) Case 3 and Case 4.
Fig. 10
Fig. 10 The power profile of the modified Case 4-V2 based on the requirements after clinical

Tables (4)

Tables Icon

Table 1 The required parameters of the soft (Oculfilcon D 55%) contact lenses

Tables Icon

Table 2 The setting parameters of the initial designs for Case 1 to Case 4

Tables Icon

Table 3 Optimization results of Case 1 to Case 4

Tables Icon

Table 4 The additional optical powers in the center-distance zones of the multifocal CLs samples of Case 1 to Case 4

Equations (17)

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

Pw ¯ (x)= P distance +12Add 1 (D op 2 x c ) 2π 0 x e 9 (2t D op ) 2 2 ( D op 2 x c ) 2 dt
C(u)= i=0 h N i,p (u) w i P i i=0 h N i,p (u) w i
U={ 0,...,0 p+1 , u p+2 ,..., u h+1 , 1,...,1 p+1 }
N i,0 (u)={ 1 if u i u u i+1 0 otherwise N i,p (u)= u u i u i+p u i N i,p1 (u)+ u i+p+1 u u i+p+1 u i+1 N i+1,p1 (u)
k= | C'(u)×C''(u) | | C'(u) | 3
R= 1 k
CC(u)=C(u)+R(u)N(u)
N(u)= C'(u)×( C"(u)×C'(u) ) C'(u) C"(u)×C'(u)
Pw=(1n) k b + (n1) k f 1 t c (1 1 n ) k f
J power = ( i=1 m ( Pw i Pw i ¯ ) 2 m ) 1/2 OR J power = ( i=1 m ( ( (1n) k b i + (n1) k f i 1 t c (1 1 n ) k f i ) Pw i ¯ ) 2 m ) 1/2
y= x 2 / R o 1+ 1(1+ k c ) x 2 / R o 2
k AS = y" (1+y ' 2 ) 3/2
{ CCx ¯ =x y'(1+y ' 2 ) y" CCy ¯ =y+ 1+y ' 2 y"
or J fitting_center = i=1 s ( ( x j x j ¯ ) 2 + ( y j y j ¯ ) 2 ) 1/2 / s J fitting_center = i=1 s | D j D ¯ j |/ s ; (j=1:s)
J cc_center = j=1 s ( ( CC x j CC x j ¯ ) 2 + ( CC y j CC y j ¯ ) 2 ) 1/2 / s
J obj =α J power +β J fitting_center +γ J cc-center Min
J obj =0.1* J power +0.45 J fitting_center +0.45* J cc-center Min

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