Abstract

We present a new algorithm for the on-line determination of thicknesses of deposited layers that can be used in the course of coating production with broadband optical monitoring. The proposed algorithm can be considered as a modification of the well-known sequential algorithm. The main idea of the new algorithm is to re-calculate thicknesses of some of the previously deposited layers along with the determination of the thickness of the last deposited layer. The algorithm implies analytical estimations that enable recalculating only those layer thicknesses that can be found with better accuracy than before. Simulation and computational manufacturing experiments confirm high accuracy of the proposed algorithm.

© 2015 Optical Society of America

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Comparison of algorithms used for optical characterization of multilayer optical coatings

Tatiana V. Amotchkina, Michael K. Trubetskov, Vladimir Pervak, Sebastian Schlichting, Henrik Ehlers, Detlev Ristau, and Alexander V. Tikhonravov
Appl. Opt. 50(20) 3389-3395 (2011)

Computational experiments on optical coating production using monochromatic monitoring strategy aimed at eliminating a cumulative effect of thickness errors

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Investigation of the effect of accumulation of thickness errors in optical coating production by broadband optical monitoring

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Appl. Opt. 45(27) 7026-7034 (2006)

References

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  1. B. Vidal, A. Fornier, and E. Pelletier, “Optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 17(7), 1038–1047 (1978).
    [Crossref] [PubMed]
  2. B. Vidal, A. Fornier, and E. Pelletier, “Wideband optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 18(22), 3851–3856 (1979).
    [PubMed]
  3. B. Vidal and E. Pelletier, “Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors,” Appl. Opt. 18(22), 3857–3862 (1979).
    [PubMed]
  4. D. Ristau, H. Ehlers, T. Gross, and M. Lappschies, “Optical broadband monitoring of conventional and ion processes,” Appl. Opt. 45(7), 1495–1501 (2006).
    [Crossref] [PubMed]
  5. D. Ristau, H. Ehlers, S. Schlichting, and M. Lappschies, “State of the art in deterministic production of optical thin films,” Proc. SPIE 7101, 71010C (2008).
    [Crossref]
  6. B. Badoil, F. Lemarchand, M. Cathelinaud, and M. Lequime, “Interest of broadband optical monitoring for thin-film filter manufacturing,” Appl. Opt. 46(20), 4294–4303 (2007).
    [Crossref] [PubMed]
  7. S. Wilbrandt, O. Stenzel, and N. Kaiser, “All-oxide broadband antireflection coatings by plasma ion assisted deposition: design, simulation, manufacturing and re-optimization,” Opt. Express 18(19), 19732–19742 (2010).
    [Crossref] [PubMed]
  8. K. Friedrich, S. Wilbrandt, O. Stenzel, N. Kaiser, and K. H. Hoffmann, “Computational manufacturing of optical interference coatings: method, simulation results, and comparison with experiment,” Appl. Opt. 49(16), 3150–3162 (2010).
    [Crossref] [PubMed]
  9. H. A. Macleod, Thin-Film Optical Filters, 4th ed. (Taylor & Francis, 2010).
  10. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the effect of accumulation of thickness errors in optical coating production by broadband optical monitoring,” Appl. Opt. 45(27), 7026–7034 (2006).
    [Crossref] [PubMed]
  11. H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20(1), 82–89 (1981).
    [Crossref] [PubMed]
  12. P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13(2), 285–290 (1972).
    [Crossref]
  13. H. A. Macleod, “Turning value monitoring of narrow-band alldielectric thin film optical filters,” Opt. Acta (Lond.) 19(1), 1–28 (1972).
    [Crossref]
  14. H. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta (Lond.) 24(9), 907–930 (1977).
    [Crossref]
  15. A. V. Tikhonravov and M. K. Trubetskov, “Automated design and sensitivity analysis of wavelengh-division multiplexing filters,” Appl. Opt. 41(16), 3176–3182 (2002).
    [Crossref] [PubMed]
  16. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the error self-compensation effect associated with broadband optical monitoring,” Appl. Opt. 50(9), C111–C116 (2011).
    [Crossref] [PubMed]
  17. B. T. Sullivan and J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. I. Theoretical description,” Appl. Opt. 31(19), 3821–3835 (1992).
    [Crossref] [PubMed]
  18. T. V. Amotchkina, M. K. Trubetskov, V. Pervak, S. Schlichting, H. Ehlers, D. Ristau, and A. V. Tikhonravov, “Comparison of algorithms used for optical characterization of multilayer optical coatings,” Appl. Opt. 50(20), 3389–3395 (2011).
    [Crossref] [PubMed]
  19. A. V. Tikhonravov and M. K. Trubetskov, “On-line characterization and re-optimization of optical coatings,” Proc. SPIE 5250, 406–413 (2004).
    [Crossref]
  20. H. Ehlers, S. Schlichting, C. Schmitz, and D. Ristau, “Adaptive manufacturing of high precision optics based on virtual deposition and hybrid process control techniques,” Chin. Opt. Lett. 8, 62–66 (2010).
    [Crossref]
  21. S. Wilbrandt, O. Stenzel, N. Kaiser, M. K. Trubetskov, and A. V. Tikhonravov, “In situ optical characterization and reengineering of interference coatings,” Appl. Opt. 47(13), C49–C54 (2008).
    [Crossref] [PubMed]
  22. A. V. Tikhonravov and M. K. Trubetskov, “Computational manufacturing as a bridge between design and production,” Appl. Opt. 44(32), 6877–6884 (2005).
    [Crossref] [PubMed]
  23. A. V. Tikhonravov and M. K. Trubetskov, “Modern design tools and a new paradigm in optical coating design,” Appl. Opt. 51(30), 7319–7332 (2012).
    [Crossref] [PubMed]

2012 (1)

2011 (2)

2010 (3)

2008 (2)

S. Wilbrandt, O. Stenzel, N. Kaiser, M. K. Trubetskov, and A. V. Tikhonravov, “In situ optical characterization and reengineering of interference coatings,” Appl. Opt. 47(13), C49–C54 (2008).
[Crossref] [PubMed]

D. Ristau, H. Ehlers, S. Schlichting, and M. Lappschies, “State of the art in deterministic production of optical thin films,” Proc. SPIE 7101, 71010C (2008).
[Crossref]

2007 (1)

2006 (2)

2005 (1)

2004 (1)

A. V. Tikhonravov and M. K. Trubetskov, “On-line characterization and re-optimization of optical coatings,” Proc. SPIE 5250, 406–413 (2004).
[Crossref]

2002 (1)

1992 (1)

1981 (1)

1979 (2)

1978 (1)

1977 (1)

H. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta (Lond.) 24(9), 907–930 (1977).
[Crossref]

1972 (2)

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13(2), 285–290 (1972).
[Crossref]

H. A. Macleod, “Turning value monitoring of narrow-band alldielectric thin film optical filters,” Opt. Acta (Lond.) 19(1), 1–28 (1972).
[Crossref]

Amotchkina, T. V.

Badoil, B.

Bousquet, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13(2), 285–290 (1972).
[Crossref]

Cathelinaud, M.

Dobrowolski, J. A.

Ehlers, H.

T. V. Amotchkina, M. K. Trubetskov, V. Pervak, S. Schlichting, H. Ehlers, D. Ristau, and A. V. Tikhonravov, “Comparison of algorithms used for optical characterization of multilayer optical coatings,” Appl. Opt. 50(20), 3389–3395 (2011).
[Crossref] [PubMed]

H. Ehlers, S. Schlichting, C. Schmitz, and D. Ristau, “Adaptive manufacturing of high precision optics based on virtual deposition and hybrid process control techniques,” Chin. Opt. Lett. 8, 62–66 (2010).
[Crossref]

D. Ristau, H. Ehlers, S. Schlichting, and M. Lappschies, “State of the art in deterministic production of optical thin films,” Proc. SPIE 7101, 71010C (2008).
[Crossref]

D. Ristau, H. Ehlers, T. Gross, and M. Lappschies, “Optical broadband monitoring of conventional and ion processes,” Appl. Opt. 45(7), 1495–1501 (2006).
[Crossref] [PubMed]

Fornier, A.

Friedrich, K.

Gross, T.

Hoffmann, K. H.

Kaiser, N.

Kowalczyk, R.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13(2), 285–290 (1972).
[Crossref]

Lappschies, M.

D. Ristau, H. Ehlers, S. Schlichting, and M. Lappschies, “State of the art in deterministic production of optical thin films,” Proc. SPIE 7101, 71010C (2008).
[Crossref]

D. Ristau, H. Ehlers, T. Gross, and M. Lappschies, “Optical broadband monitoring of conventional and ion processes,” Appl. Opt. 45(7), 1495–1501 (2006).
[Crossref] [PubMed]

Lemarchand, F.

Lequime, M.

Macleod, H.

H. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta (Lond.) 24(9), 907–930 (1977).
[Crossref]

Macleod, H. A.

H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20(1), 82–89 (1981).
[Crossref] [PubMed]

H. A. Macleod, “Turning value monitoring of narrow-band alldielectric thin film optical filters,” Opt. Acta (Lond.) 19(1), 1–28 (1972).
[Crossref]

Pelletier, E.

Pervak, V.

Ristau, D.

T. V. Amotchkina, M. K. Trubetskov, V. Pervak, S. Schlichting, H. Ehlers, D. Ristau, and A. V. Tikhonravov, “Comparison of algorithms used for optical characterization of multilayer optical coatings,” Appl. Opt. 50(20), 3389–3395 (2011).
[Crossref] [PubMed]

H. Ehlers, S. Schlichting, C. Schmitz, and D. Ristau, “Adaptive manufacturing of high precision optics based on virtual deposition and hybrid process control techniques,” Chin. Opt. Lett. 8, 62–66 (2010).
[Crossref]

D. Ristau, H. Ehlers, S. Schlichting, and M. Lappschies, “State of the art in deterministic production of optical thin films,” Proc. SPIE 7101, 71010C (2008).
[Crossref]

D. Ristau, H. Ehlers, T. Gross, and M. Lappschies, “Optical broadband monitoring of conventional and ion processes,” Appl. Opt. 45(7), 1495–1501 (2006).
[Crossref] [PubMed]

Roche, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13(2), 285–290 (1972).
[Crossref]

Schlichting, S.

T. V. Amotchkina, M. K. Trubetskov, V. Pervak, S. Schlichting, H. Ehlers, D. Ristau, and A. V. Tikhonravov, “Comparison of algorithms used for optical characterization of multilayer optical coatings,” Appl. Opt. 50(20), 3389–3395 (2011).
[Crossref] [PubMed]

H. Ehlers, S. Schlichting, C. Schmitz, and D. Ristau, “Adaptive manufacturing of high precision optics based on virtual deposition and hybrid process control techniques,” Chin. Opt. Lett. 8, 62–66 (2010).
[Crossref]

D. Ristau, H. Ehlers, S. Schlichting, and M. Lappschies, “State of the art in deterministic production of optical thin films,” Proc. SPIE 7101, 71010C (2008).
[Crossref]

Schmitz, C.

H. Ehlers, S. Schlichting, C. Schmitz, and D. Ristau, “Adaptive manufacturing of high precision optics based on virtual deposition and hybrid process control techniques,” Chin. Opt. Lett. 8, 62–66 (2010).
[Crossref]

Stenzel, O.

Sullivan, B. T.

Tikhonravov, A. V.

A. V. Tikhonravov and M. K. Trubetskov, “Modern design tools and a new paradigm in optical coating design,” Appl. Opt. 51(30), 7319–7332 (2012).
[Crossref] [PubMed]

T. V. Amotchkina, M. K. Trubetskov, V. Pervak, S. Schlichting, H. Ehlers, D. Ristau, and A. V. Tikhonravov, “Comparison of algorithms used for optical characterization of multilayer optical coatings,” Appl. Opt. 50(20), 3389–3395 (2011).
[Crossref] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the error self-compensation effect associated with broadband optical monitoring,” Appl. Opt. 50(9), C111–C116 (2011).
[Crossref] [PubMed]

S. Wilbrandt, O. Stenzel, N. Kaiser, M. K. Trubetskov, and A. V. Tikhonravov, “In situ optical characterization and reengineering of interference coatings,” Appl. Opt. 47(13), C49–C54 (2008).
[Crossref] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the effect of accumulation of thickness errors in optical coating production by broadband optical monitoring,” Appl. Opt. 45(27), 7026–7034 (2006).
[Crossref] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “Computational manufacturing as a bridge between design and production,” Appl. Opt. 44(32), 6877–6884 (2005).
[Crossref] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “On-line characterization and re-optimization of optical coatings,” Proc. SPIE 5250, 406–413 (2004).
[Crossref]

A. V. Tikhonravov and M. K. Trubetskov, “Automated design and sensitivity analysis of wavelengh-division multiplexing filters,” Appl. Opt. 41(16), 3176–3182 (2002).
[Crossref] [PubMed]

Trubetskov, M. K.

A. V. Tikhonravov and M. K. Trubetskov, “Modern design tools and a new paradigm in optical coating design,” Appl. Opt. 51(30), 7319–7332 (2012).
[Crossref] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the error self-compensation effect associated with broadband optical monitoring,” Appl. Opt. 50(9), C111–C116 (2011).
[Crossref] [PubMed]

T. V. Amotchkina, M. K. Trubetskov, V. Pervak, S. Schlichting, H. Ehlers, D. Ristau, and A. V. Tikhonravov, “Comparison of algorithms used for optical characterization of multilayer optical coatings,” Appl. Opt. 50(20), 3389–3395 (2011).
[Crossref] [PubMed]

S. Wilbrandt, O. Stenzel, N. Kaiser, M. K. Trubetskov, and A. V. Tikhonravov, “In situ optical characterization and reengineering of interference coatings,” Appl. Opt. 47(13), C49–C54 (2008).
[Crossref] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the effect of accumulation of thickness errors in optical coating production by broadband optical monitoring,” Appl. Opt. 45(27), 7026–7034 (2006).
[Crossref] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “Computational manufacturing as a bridge between design and production,” Appl. Opt. 44(32), 6877–6884 (2005).
[Crossref] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “On-line characterization and re-optimization of optical coatings,” Proc. SPIE 5250, 406–413 (2004).
[Crossref]

A. V. Tikhonravov and M. K. Trubetskov, “Automated design and sensitivity analysis of wavelengh-division multiplexing filters,” Appl. Opt. 41(16), 3176–3182 (2002).
[Crossref] [PubMed]

Vidal, B.

Wilbrandt, S.

Appl. Opt. (15)

B. Vidal, A. Fornier, and E. Pelletier, “Optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 17(7), 1038–1047 (1978).
[Crossref] [PubMed]

B. Vidal, A. Fornier, and E. Pelletier, “Wideband optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 18(22), 3851–3856 (1979).
[PubMed]

B. Vidal and E. Pelletier, “Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors,” Appl. Opt. 18(22), 3857–3862 (1979).
[PubMed]

D. Ristau, H. Ehlers, T. Gross, and M. Lappschies, “Optical broadband monitoring of conventional and ion processes,” Appl. Opt. 45(7), 1495–1501 (2006).
[Crossref] [PubMed]

B. Badoil, F. Lemarchand, M. Cathelinaud, and M. Lequime, “Interest of broadband optical monitoring for thin-film filter manufacturing,” Appl. Opt. 46(20), 4294–4303 (2007).
[Crossref] [PubMed]

K. Friedrich, S. Wilbrandt, O. Stenzel, N. Kaiser, and K. H. Hoffmann, “Computational manufacturing of optical interference coatings: method, simulation results, and comparison with experiment,” Appl. Opt. 49(16), 3150–3162 (2010).
[Crossref] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the effect of accumulation of thickness errors in optical coating production by broadband optical monitoring,” Appl. Opt. 45(27), 7026–7034 (2006).
[Crossref] [PubMed]

H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20(1), 82–89 (1981).
[Crossref] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “Automated design and sensitivity analysis of wavelengh-division multiplexing filters,” Appl. Opt. 41(16), 3176–3182 (2002).
[Crossref] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the error self-compensation effect associated with broadband optical monitoring,” Appl. Opt. 50(9), C111–C116 (2011).
[Crossref] [PubMed]

B. T. Sullivan and J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. I. Theoretical description,” Appl. Opt. 31(19), 3821–3835 (1992).
[Crossref] [PubMed]

T. V. Amotchkina, M. K. Trubetskov, V. Pervak, S. Schlichting, H. Ehlers, D. Ristau, and A. V. Tikhonravov, “Comparison of algorithms used for optical characterization of multilayer optical coatings,” Appl. Opt. 50(20), 3389–3395 (2011).
[Crossref] [PubMed]

S. Wilbrandt, O. Stenzel, N. Kaiser, M. K. Trubetskov, and A. V. Tikhonravov, “In situ optical characterization and reengineering of interference coatings,” Appl. Opt. 47(13), C49–C54 (2008).
[Crossref] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “Computational manufacturing as a bridge between design and production,” Appl. Opt. 44(32), 6877–6884 (2005).
[Crossref] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “Modern design tools and a new paradigm in optical coating design,” Appl. Opt. 51(30), 7319–7332 (2012).
[Crossref] [PubMed]

Chin. Opt. Lett. (1)

H. Ehlers, S. Schlichting, C. Schmitz, and D. Ristau, “Adaptive manufacturing of high precision optics based on virtual deposition and hybrid process control techniques,” Chin. Opt. Lett. 8, 62–66 (2010).
[Crossref]

Opt. Acta (Lond.) (2)

H. A. Macleod, “Turning value monitoring of narrow-band alldielectric thin film optical filters,” Opt. Acta (Lond.) 19(1), 1–28 (1972).
[Crossref]

H. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta (Lond.) 24(9), 907–930 (1977).
[Crossref]

Opt. Express (1)

Proc. SPIE (2)

D. Ristau, H. Ehlers, S. Schlichting, and M. Lappschies, “State of the art in deterministic production of optical thin films,” Proc. SPIE 7101, 71010C (2008).
[Crossref]

A. V. Tikhonravov and M. K. Trubetskov, “On-line characterization and re-optimization of optical coatings,” Proc. SPIE 5250, 406–413 (2004).
[Crossref]

Thin Solid Films (1)

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13(2), 285–290 (1972).
[Crossref]

Other (1)

H. A. Macleod, Thin-Film Optical Filters, 4th ed. (Taylor & Francis, 2010).

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Figures (3)

Fig. 1
Fig. 1 Physical thicknesses (a) and spectral characteristic (b) of the 40-layer hot mirror design
Fig. 2
Fig. 2 Comparison of levels of characterization errors: (a): Modified S-algorithm (red bars) and S-algorithm (blue bars), (b): Modified S-algorithm (red bars) and T-algorithm (green bars).
Fig. 3
Fig. 3 Levels of errors in the case of Modified S-algorithm (red bars) and S-algorithm (blue bars): (a) errors in thicknesses of deposited coatings, (b) characterization errors.

Tables (1)

Tables Icon

Table 1 Numbers of layers which thicknesses are determined at various algorithm steps for two different values of the coefficient c in Eq. (10): c = 0.5 and c = 1.0.

Equations (13)

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

δ T m e a s j ( λ ) = T m e a s j ( λ ) T j ( d 1 a ,     ,   d j a ,   λ )
F j =   1 L { λ } [ T j ( d 1 ,   ,   d j ,   λ )   T m e a s j ( λ ) ] 2
T j ( d 1 ,   ,   d j ,   λ ) = T j ( d 1 a ,     ,   d j a ,   λ ) + i = 1 j T j d i h i  
F j =   1 L { λ } [ i = 1 j T j d i h i     δ T m e a s j ( λ ) ] 2
F j =   1 L { λ } [ T j d i h i   + l = 1 l i j T j d l h l   δ T m e a s j ( λ ) ] 2
h i = [ 1 L { λ } T j d i δ T m e a s j ( λ ) l = 1 l i j ( 1 L { λ } T j d i T j d l ) h l ] / [ 1 L { λ } ( T j d i ) 2 ]
b i j ( λ ) = T j d i / { λ } ( T j d i ) 2 , c i l j =   { λ } T j d i T j d l / { λ } ( T j d i ) 2
h i = { λ } b i j ( λ )   δ T m e a s j ( λ )   + l = 1 ,   l i j c i l j h l
σ j ( h i ) = [ ( B i j ) 2 σ m e a s 2   +   ( C i j ) 2 σ 2 ] 1 2
B i j = 1 / [ { λ } ( T j d i ) 2 ] 1 2 , C i j = [ l = 1 ,   l i j ( { λ } T j d i T j d l ) 2 ] 1 2 / [ { λ } ( T j d i ) 2 ] 1 2
σ j ( h i ) = A i j   σ   ,
A i j = [ α 2 ( B i j ) 2     +   ( C i j ) 2 ] 1 2
A i j < c min 1 k j 1 A i k

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