Abstract

We report a method for passive compensation of thermally induced focal shifts and higher-order aberrations of NIR laser processing optics. Theoretical considerations are made on the elimination of aberrations including polarization effects using a multi-stage compensation element with optical flats of both positive and negative dn/dT. A compensation layout is designed and optimized utilizing numerical simulations of thermo-optic effects. Based on these findings, optical elements for compensation of an F-Theta objective are manufactured. By means of wavefront measurements and beam caustic measurements the feasibility of simultaneous passive compensation of focal shifts and higher-order aberrations is demonstrated.

© 2017 Optical Society of America

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References

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  1. A. Kudryashov, V. Samarkin, A. Rukosuev, and A. Alexandrov, “High-power lasers and adaptive optics,” Proc. SPIE 5333, 45–52 (2004).
    [Crossref]
  2. A. Kudryashov, V. Samarkin, A. Alexandrov, J. Sheldakova, and P. Romanov, “Wide aperture (more than 500 mm) deformable mirrors for high power laser beam correction,” Proc. SPIE 8960, 89601G (2014).
    [Crossref]
  3. T. Graf and H. Hügel, Laser in der Fertigung (Vieweg + Teubner, 2009), Chap. 2.
  4. J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Simulation of bulk-absorption thermal lensing in transmissive optics of gravitational waves detectors,” Appl. Phys. B 77(4), 409–414 (2003).
    [Crossref]
  5. J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Class. Quantum Gravity 21(5), S903–S908 (2004).
    [Crossref]
  6. J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “A temperature controlled liquid crystal lens for spherical aberration compensation,” Microsyst. Technol. 13(2), 161–164 (2006).
    [Crossref]
  7. G. Eberle, V. Chiron, and K. Wegener, “Simulation and realization of a focus shifting unit using a tunable lens for 3D laser material processing,” Phys. Procedia 41, 441–447 (2013).
    [Crossref]
  8. M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
    [Crossref]
  9. Scanlab datasheet, “VarioSCAN, VarioSCANdei,” http://www.scanlab.de/sites/default/files/pdf-dateien/data-sheets/varioscanvarioscande-en.pdf (2015).
  10. M. Scaggs and G. Haas, “Thermal lensing compensation optic for high power lasers,” Proc. SPIE 7913, 79130C (2011).
    [Crossref]
  11. S. Piehler, C. Thiel, A. Voss, M. Abdou Ahmed, and T. Graf, “Self-compensation of thermal lensing in optics for high-brightness solid-state lasers,” Proc. SPIE 8239, 82390Z (2012).
    [Crossref]
  12. M. Stubenvoll, B. Schäfer, and K. Mann, “Measurement and compensation of laser-induced wavefront deformations and focal shifts in near IR optics,” Opt. Express 22(21), 25385–25396 (2014).
    [Crossref] [PubMed]
  13. C. Thiel, M. Stubenvoll, B. Schäfer, and T. Krol, „Reliable Beam Positioning for Metal-based Additive Manufacturing by Means of Focal Shift Reduction,” presented at the 2015 Lasers in Manufacturing Conference (LiM), Munich, Germany, 22–25 June 2015.
  14. M. J. Weber, Handbook of Optical Materials (CRC, 2003).
  15. Schott datasheet, “Optical Glass: Data Sheets,” Schott North America Inc. (2013).
  16. M. Stubenvoll, B. Schäfer, K. Mann, A. Walter, and L. Zittel, “Photothermal absorption measurements for improved thermal stability of high-power laser optics,” Proc. SPIE 8885, 88851R (2013).
    [Crossref]
  17. J. C. Wyant and K. Creath, “Basic Wavefront Aberration Theory for Optical Metrology,” in Applied Optics and Optical Engineering, Vol. XI, R. R. Shannon and J. C. Wyant, ed. (Academic, 1992).

2014 (2)

A. Kudryashov, V. Samarkin, A. Alexandrov, J. Sheldakova, and P. Romanov, “Wide aperture (more than 500 mm) deformable mirrors for high power laser beam correction,” Proc. SPIE 8960, 89601G (2014).
[Crossref]

M. Stubenvoll, B. Schäfer, and K. Mann, “Measurement and compensation of laser-induced wavefront deformations and focal shifts in near IR optics,” Opt. Express 22(21), 25385–25396 (2014).
[Crossref] [PubMed]

2013 (2)

M. Stubenvoll, B. Schäfer, K. Mann, A. Walter, and L. Zittel, “Photothermal absorption measurements for improved thermal stability of high-power laser optics,” Proc. SPIE 8885, 88851R (2013).
[Crossref]

G. Eberle, V. Chiron, and K. Wegener, “Simulation and realization of a focus shifting unit using a tunable lens for 3D laser material processing,” Phys. Procedia 41, 441–447 (2013).
[Crossref]

2012 (1)

S. Piehler, C. Thiel, A. Voss, M. Abdou Ahmed, and T. Graf, “Self-compensation of thermal lensing in optics for high-brightness solid-state lasers,” Proc. SPIE 8239, 82390Z (2012).
[Crossref]

2011 (2)

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

M. Scaggs and G. Haas, “Thermal lensing compensation optic for high power lasers,” Proc. SPIE 7913, 79130C (2011).
[Crossref]

2006 (1)

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “A temperature controlled liquid crystal lens for spherical aberration compensation,” Microsyst. Technol. 13(2), 161–164 (2006).
[Crossref]

2004 (2)

A. Kudryashov, V. Samarkin, A. Rukosuev, and A. Alexandrov, “High-power lasers and adaptive optics,” Proc. SPIE 5333, 45–52 (2004).
[Crossref]

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Class. Quantum Gravity 21(5), S903–S908 (2004).
[Crossref]

2003 (1)

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Simulation of bulk-absorption thermal lensing in transmissive optics of gravitational waves detectors,” Appl. Phys. B 77(4), 409–414 (2003).
[Crossref]

Abdou Ahmed, M.

S. Piehler, C. Thiel, A. Voss, M. Abdou Ahmed, and T. Graf, “Self-compensation of thermal lensing in optics for high-brightness solid-state lasers,” Proc. SPIE 8239, 82390Z (2012).
[Crossref]

Alexandrov, A.

A. Kudryashov, V. Samarkin, A. Alexandrov, J. Sheldakova, and P. Romanov, “Wide aperture (more than 500 mm) deformable mirrors for high power laser beam correction,” Proc. SPIE 8960, 89601G (2014).
[Crossref]

A. Kudryashov, V. Samarkin, A. Rukosuev, and A. Alexandrov, “High-power lasers and adaptive optics,” Proc. SPIE 5333, 45–52 (2004).
[Crossref]

Aschwanden, M.

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

Blair, D.

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Class. Quantum Gravity 21(5), S903–S908 (2004).
[Crossref]

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Simulation of bulk-absorption thermal lensing in transmissive optics of gravitational waves detectors,” Appl. Phys. B 77(4), 409–414 (2003).
[Crossref]

Blum, M.

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

Büeler, M.

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

Chiron, V.

G. Eberle, V. Chiron, and K. Wegener, “Simulation and realization of a focus shifting unit using a tunable lens for 3D laser material processing,” Phys. Procedia 41, 441–447 (2013).
[Crossref]

Degallaix, J.

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Class. Quantum Gravity 21(5), S903–S908 (2004).
[Crossref]

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Simulation of bulk-absorption thermal lensing in transmissive optics of gravitational waves detectors,” Appl. Phys. B 77(4), 409–414 (2003).
[Crossref]

Eberle, G.

G. Eberle, V. Chiron, and K. Wegener, “Simulation and realization of a focus shifting unit using a tunable lens for 3D laser material processing,” Phys. Procedia 41, 441–447 (2013).
[Crossref]

Graf, T.

S. Piehler, C. Thiel, A. Voss, M. Abdou Ahmed, and T. Graf, “Self-compensation of thermal lensing in optics for high-brightness solid-state lasers,” Proc. SPIE 8239, 82390Z (2012).
[Crossref]

Grätzel, C.

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

Haas, G.

M. Scaggs and G. Haas, “Thermal lensing compensation optic for high power lasers,” Proc. SPIE 7913, 79130C (2011).
[Crossref]

Hain, M.

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “A temperature controlled liquid crystal lens for spherical aberration compensation,” Microsyst. Technol. 13(2), 161–164 (2006).
[Crossref]

Ju, L.

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Class. Quantum Gravity 21(5), S903–S908 (2004).
[Crossref]

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Simulation of bulk-absorption thermal lensing in transmissive optics of gravitational waves detectors,” Appl. Phys. B 77(4), 409–414 (2003).
[Crossref]

Knittel, J.

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “A temperature controlled liquid crystal lens for spherical aberration compensation,” Microsyst. Technol. 13(2), 161–164 (2006).
[Crossref]

Kudryashov, A.

A. Kudryashov, V. Samarkin, A. Alexandrov, J. Sheldakova, and P. Romanov, “Wide aperture (more than 500 mm) deformable mirrors for high power laser beam correction,” Proc. SPIE 8960, 89601G (2014).
[Crossref]

A. Kudryashov, V. Samarkin, A. Rukosuev, and A. Alexandrov, “High-power lasers and adaptive optics,” Proc. SPIE 5333, 45–52 (2004).
[Crossref]

Mann, K.

M. Stubenvoll, B. Schäfer, and K. Mann, “Measurement and compensation of laser-induced wavefront deformations and focal shifts in near IR optics,” Opt. Express 22(21), 25385–25396 (2014).
[Crossref] [PubMed]

M. Stubenvoll, B. Schäfer, K. Mann, A. Walter, and L. Zittel, “Photothermal absorption measurements for improved thermal stability of high-power laser optics,” Proc. SPIE 8885, 88851R (2013).
[Crossref]

Piehler, S.

S. Piehler, C. Thiel, A. Voss, M. Abdou Ahmed, and T. Graf, “Self-compensation of thermal lensing in optics for high-brightness solid-state lasers,” Proc. SPIE 8239, 82390Z (2012).
[Crossref]

Richter, H.

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “A temperature controlled liquid crystal lens for spherical aberration compensation,” Microsyst. Technol. 13(2), 161–164 (2006).
[Crossref]

Romanov, P.

A. Kudryashov, V. Samarkin, A. Alexandrov, J. Sheldakova, and P. Romanov, “Wide aperture (more than 500 mm) deformable mirrors for high power laser beam correction,” Proc. SPIE 8960, 89601G (2014).
[Crossref]

Rukosuev, A.

A. Kudryashov, V. Samarkin, A. Rukosuev, and A. Alexandrov, “High-power lasers and adaptive optics,” Proc. SPIE 5333, 45–52 (2004).
[Crossref]

Samarkin, V.

A. Kudryashov, V. Samarkin, A. Alexandrov, J. Sheldakova, and P. Romanov, “Wide aperture (more than 500 mm) deformable mirrors for high power laser beam correction,” Proc. SPIE 8960, 89601G (2014).
[Crossref]

A. Kudryashov, V. Samarkin, A. Rukosuev, and A. Alexandrov, “High-power lasers and adaptive optics,” Proc. SPIE 5333, 45–52 (2004).
[Crossref]

Scaggs, M.

M. Scaggs and G. Haas, “Thermal lensing compensation optic for high power lasers,” Proc. SPIE 7913, 79130C (2011).
[Crossref]

Schäfer, B.

M. Stubenvoll, B. Schäfer, and K. Mann, “Measurement and compensation of laser-induced wavefront deformations and focal shifts in near IR optics,” Opt. Express 22(21), 25385–25396 (2014).
[Crossref] [PubMed]

M. Stubenvoll, B. Schäfer, K. Mann, A. Walter, and L. Zittel, “Photothermal absorption measurements for improved thermal stability of high-power laser optics,” Proc. SPIE 8885, 88851R (2013).
[Crossref]

Sheldakova, J.

A. Kudryashov, V. Samarkin, A. Alexandrov, J. Sheldakova, and P. Romanov, “Wide aperture (more than 500 mm) deformable mirrors for high power laser beam correction,” Proc. SPIE 8960, 89601G (2014).
[Crossref]

Somalingam, S.

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “A temperature controlled liquid crystal lens for spherical aberration compensation,” Microsyst. Technol. 13(2), 161–164 (2006).
[Crossref]

Stubenvoll, M.

M. Stubenvoll, B. Schäfer, and K. Mann, “Measurement and compensation of laser-induced wavefront deformations and focal shifts in near IR optics,” Opt. Express 22(21), 25385–25396 (2014).
[Crossref] [PubMed]

M. Stubenvoll, B. Schäfer, K. Mann, A. Walter, and L. Zittel, “Photothermal absorption measurements for improved thermal stability of high-power laser optics,” Proc. SPIE 8885, 88851R (2013).
[Crossref]

Thiel, C.

S. Piehler, C. Thiel, A. Voss, M. Abdou Ahmed, and T. Graf, “Self-compensation of thermal lensing in optics for high-brightness solid-state lasers,” Proc. SPIE 8239, 82390Z (2012).
[Crossref]

Tschudi, T.

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “A temperature controlled liquid crystal lens for spherical aberration compensation,” Microsyst. Technol. 13(2), 161–164 (2006).
[Crossref]

Voss, A.

S. Piehler, C. Thiel, A. Voss, M. Abdou Ahmed, and T. Graf, “Self-compensation of thermal lensing in optics for high-brightness solid-state lasers,” Proc. SPIE 8239, 82390Z (2012).
[Crossref]

Walter, A.

M. Stubenvoll, B. Schäfer, K. Mann, A. Walter, and L. Zittel, “Photothermal absorption measurements for improved thermal stability of high-power laser optics,” Proc. SPIE 8885, 88851R (2013).
[Crossref]

Wegener, K.

G. Eberle, V. Chiron, and K. Wegener, “Simulation and realization of a focus shifting unit using a tunable lens for 3D laser material processing,” Phys. Procedia 41, 441–447 (2013).
[Crossref]

Zhao, C.

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Class. Quantum Gravity 21(5), S903–S908 (2004).
[Crossref]

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Simulation of bulk-absorption thermal lensing in transmissive optics of gravitational waves detectors,” Appl. Phys. B 77(4), 409–414 (2003).
[Crossref]

Zittel, L.

M. Stubenvoll, B. Schäfer, K. Mann, A. Walter, and L. Zittel, “Photothermal absorption measurements for improved thermal stability of high-power laser optics,” Proc. SPIE 8885, 88851R (2013).
[Crossref]

Appl. Phys. B (1)

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Simulation of bulk-absorption thermal lensing in transmissive optics of gravitational waves detectors,” Appl. Phys. B 77(4), 409–414 (2003).
[Crossref]

Class. Quantum Gravity (1)

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Class. Quantum Gravity 21(5), S903–S908 (2004).
[Crossref]

Microsyst. Technol. (1)

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “A temperature controlled liquid crystal lens for spherical aberration compensation,” Microsyst. Technol. 13(2), 161–164 (2006).
[Crossref]

Opt. Express (1)

Phys. Procedia (1)

G. Eberle, V. Chiron, and K. Wegener, “Simulation and realization of a focus shifting unit using a tunable lens for 3D laser material processing,” Phys. Procedia 41, 441–447 (2013).
[Crossref]

Proc. SPIE (6)

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

M. Scaggs and G. Haas, “Thermal lensing compensation optic for high power lasers,” Proc. SPIE 7913, 79130C (2011).
[Crossref]

S. Piehler, C. Thiel, A. Voss, M. Abdou Ahmed, and T. Graf, “Self-compensation of thermal lensing in optics for high-brightness solid-state lasers,” Proc. SPIE 8239, 82390Z (2012).
[Crossref]

A. Kudryashov, V. Samarkin, A. Rukosuev, and A. Alexandrov, “High-power lasers and adaptive optics,” Proc. SPIE 5333, 45–52 (2004).
[Crossref]

A. Kudryashov, V. Samarkin, A. Alexandrov, J. Sheldakova, and P. Romanov, “Wide aperture (more than 500 mm) deformable mirrors for high power laser beam correction,” Proc. SPIE 8960, 89601G (2014).
[Crossref]

M. Stubenvoll, B. Schäfer, K. Mann, A. Walter, and L. Zittel, “Photothermal absorption measurements for improved thermal stability of high-power laser optics,” Proc. SPIE 8885, 88851R (2013).
[Crossref]

Other (6)

J. C. Wyant and K. Creath, “Basic Wavefront Aberration Theory for Optical Metrology,” in Applied Optics and Optical Engineering, Vol. XI, R. R. Shannon and J. C. Wyant, ed. (Academic, 1992).

T. Graf and H. Hügel, Laser in der Fertigung (Vieweg + Teubner, 2009), Chap. 2.

C. Thiel, M. Stubenvoll, B. Schäfer, and T. Krol, „Reliable Beam Positioning for Metal-based Additive Manufacturing by Means of Focal Shift Reduction,” presented at the 2015 Lasers in Manufacturing Conference (LiM), Munich, Germany, 22–25 June 2015.

M. J. Weber, Handbook of Optical Materials (CRC, 2003).

Schott datasheet, “Optical Glass: Data Sheets,” Schott North America Inc. (2013).

Scanlab datasheet, “VarioSCAN, VarioSCANdei,” http://www.scanlab.de/sites/default/files/pdf-dateien/data-sheets/varioscanvarioscande-en.pdf (2015).

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Figures (8)

Fig. 1
Fig. 1 Layout of a compensation scheme for focal shifts and higher-order aberrations of an F-Theta objective. The compensating elements are split into two symmetric sections with a 90° rotation of the polarization in between.
Fig. 2
Fig. 2 Left: Simulated wavefront deformation induced by a laser beam (dL = 6 mm, PL = 120 W) in an N-PK51 sample of the dimensions 35 × 35 × 70 mm3. Center: Polynomial fits in the central area of the simulated wavefront deformation in x and y directions on a diameter of 7 mm. Right: Parameterized coefficient a (cf. Equation (5)) by fitting Eq. (6) to thickness-dependent coefficients determined through numerical simulations.
Fig. 3
Fig. 3 Model for the simulation of thermo-optic aberrations within the half-wave plates and the individual fused silica lenses of an F-Theta objective approximated as plane elements (all dimensions in mm).
Fig. 4
Fig. 4 RMS wavefront deformation of the entire compensation system minimized according to Eq. (8) with respect to lN-PK51 (red) and corresponding thickness lBK7 (blue).
Fig. 5
Fig. 5 Top: Simulated wavefront deformations (λL = 1070 nm, dL = 6 mm, PL = 120 W) of the F-Theta objective with optimized compensation system (wRMS = 1.03 nm), as displayed in Fig. 1. Bottom: Simulated wavefront deformations of the uncompensated F-Theta objective for comparison (wRMS = 12.82 nm).
Fig. 6
Fig. 6 Setup for wavefront measurements of the compensated/uncompensated F-Theta objective.
Fig. 7
Fig. 7 Experimentally determined wavefront deformations plotted as differential images of measurements with and without compensation (PL ≈75 W, dL = 6 mm, λL = 1070 nm). Wavefront (a) was captured without the two half-wave plates (wRMS = 3.23∙10−5 mm), while wavefront (b) was measured with the half-wave plates inserted (wRMS = 8.89∙10−6 mm).
Fig. 8
Fig. 8 Measured focal shifts of an F-Theta objective for x (hollow markers) and y (solid) directions using different compensation layouts.

Equations (8)

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

w comp R ( r, l k )= k=1 K m w k,m R ( l k ) r 2m + m w opt,m R r 2m . w comp T ( r, l k )= k=1 K m w k,m T ( l k ) r 2m + m w opt,m T r 2m
w comp RMS ( l 1 ,..., l K )= w comp RMS,R ( l 1 ,..., l K ) 2 /2 + w comp RMS,T ( l 1 ,..., l K ) 2 /2
Δ w comp = w comp R ( r ) w comp T ( r ) = k=1 K w k R ( r ) w k T ( r )+ w opt R ( r ) w opt T ( r ) = k=1 K n k 3 2 ( B rrrr k + B rrtt k )( σ tt k σ rr k )+ n opt 3 2 ( B rrrr opt + B rrtt opt )( σ tt opt σ rr opt )
Δ w comp = k=1 K 1 w k R ( r ) w k T ( r ) + k= K 1 +1 K w k T ( r ) w k R ( r ) + w opt T ( r ) w opt R ( r ) = k=1 K 1 n k 3 2 ( B rrrr k + B rrtt k )( σ tt k σ rr k ) k= K 1 +1 K n k 3 2 ( B rrrr k + B rrtt k )( σ tt k σ rr k ) n opt 3 2 ( B rrrr opt + B rrtt opt )( σ tt opt σ rr opt )
w ||, =a r 6 +b r 4 +c r 2 +d
a,b,c( l )= s a,b,c p a,b,c l+1 q a,b,c l+1 l.
w comp ( r, l NPK , l BK )= w 1,|| BK ( l BK ) r 2 + w 1,|| NPK ( l NPK ) r 2 before rotation of polarization + w 1, BK ( l BK ) r 2 + w 1, NPK ( l NPK ) r 2 after rotation of polarization + w 1 obj r 2 objective + w 2,|| BK ( l BK ) r 4 + w 2,|| NPK ( l NPK ) r 4 + w 2, BK ( l BK ) r 4 + w 2, NPK ( l NPK ) r 4 + w 2 obj r 4 + w 3,|| BK ( l BK ) r 6 + w 3,|| NPK ( l NPK ) r 6 + w 3, BK ( l BK ) r 6 + w 3, NPK ( l NPK ) r 6 + w 3 obj r 6
w comp,RMS = 1 r L 0 r L w comp ( r, l NPK , l BK ) 2 dr = ! min.

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