Abstract

In this paper we experimentally demonstrate the proof of concept for predictive control of thermally induced wavefront aberrations in optical systems. On the basis of the model of thermally induced wavefront aberrations and using only past wavefront measurements, the proposed adaptive optics controller is able to predict and to compensate the future aberrations. Furthermore, the proposed controller is able to correct wavefront aberrations even when some parameters of the prediction model are unknown. The proposed control strategy can be used in high power optical systems, such as optical lithography machines, where the predictive correction of thermally induced wavefront aberrations is a crucial issue.

© 2013 OSA

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2013

D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

S. Ravensbergen, P. Rosielle, and M. Steinbuch, “Deformable mirrors with thermomechanical actuators for extreme ultraviolet lithography: Design, realization and validation,” Precis. Eng.37, 353–363 (2013).
[CrossRef]

A. Haber and M. Verhaegen, “Moving horizon estimation for large-scale interconnected systems,” in press, IEEE Trans. Autom. Control (2013).
[CrossRef]

A. Haber, A. Polo, C. S. Smith, S. F. Pereira, P. Urbach, and M. Verhaegen, “Iterative learning control of a membrane deformable mirror for optimal wavefront correction,” Appl. Opt.52, 2363–2373 (2013).
[CrossRef] [PubMed]

M. Kasprzack, B. Canuel, F. Cavalier, R. Day, E. Genin, J. Marque, D. Sentenac, and G. Vajente, “Performance of a thermally deformable mirror for correction of low-order aberrations in laser beams,” Appl. Opt.52, 2909–2916 (2013).
[CrossRef] [PubMed]

A. Haber, A. Polo, S. K. Ravensbergen, H. P. Urbach, and M. Verhaegen, “Identification of a dynamical model of a thermally actuated deformable mirror,” Opt. Lett.38, 3061–3064 (2013).
[CrossRef]

2012

A. Polo, A. Haber, S. F. Pereira, M. Verhaegen, and H. P. Urbach, “An innovative and efficient method to control the shape of push-pull membrane deformable mirror,” Opt. Express20, 27922–27932 (2012).
[CrossRef] [PubMed]

S. Halle, M. Crouse, A. Jiang, Y. van Dommelen, T. Brunner, B. Minghetti, M. Colburn, and Y. Zhang, “Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results,” Proc. SPIE8326, 832607–832607–19 (2012).
[CrossRef]

C. Bikcora, M. Van Veelen, S. Weiland, and W. Coene, “Lens heating induced aberration prediction via nonlinear kalman filters,” IEEE Trans. Semicond. Manuf.25, 384–393 (2012).
[CrossRef]

B. Canuel, R. Day, E. Genin, P. La Penna, and J. Marque, “Wavefront aberration compensation with a thermally deformable mirror,” Classical Quant. Grav.29, 085012 (2012).
[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. SPIE8239, 82390Z–82390Z–9 (2012).
[CrossRef]

2011

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[CrossRef]

2010

2007

K. Liu, Y. Li, F. Zhang, and M. Fan, “Transient thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” Jpn. J. Appl. Phys46, 6568–6572 (2007).
[CrossRef]

2006

2004

2003

E. Fernandez and P. Artal, “Membrane deformable mirror for adaptive optics: performance limits in visual optics.” Opt. Express11, 1056–1069 (2003).
[CrossRef] [PubMed]

Y. Li, K. Ota, and K. Murakami, “Thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” J. Vac. Sci. Tech. B21, 127–129 (2003).
[CrossRef]

2002

2000

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun.175, 275–287 (2000).
[CrossRef]

1999

P. A. Spence, S. E. Gianoulakis, C. D. Moen, M. Kanouff, A. Fisher, and A. K. Ray-Chaudhuri, “System performance modeling of extreme ultraviolet lithographic thermal issues,” J. Vac. Sci. Tech. B17, 3034–3038 (1999).
[CrossRef]

1994

H. Haferkamp and D. Seebaum, “Beam delivery by adaptive optics for material processing applications using high-power co2 lasers,” Proc. SPIE2207, 156–164 (1994).
[CrossRef]

1990

P. Hello and J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. France51, 2243–2261 (1990).
[CrossRef]

1982

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. SPIE8239, 82390Z–82390Z–9 (2012).
[CrossRef]

Andryzhyieuskaya, A.

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

Arain, M. A.

Artal, P.

Aufmuth, P.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun.175, 275–287 (2000).
[CrossRef]

Baik, K.-H.

D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

Bakker, H.

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

Beak, D. H.

D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

Beems, M.

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

Bekaert, J.

J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[CrossRef]

Bikcora, C.

C. Bikcora, M. Van Veelen, S. Weiland, and W. Coene, “Lens heating induced aberration prediction via nonlinear kalman filters,” IEEE Trans. Semicond. Manuf.25, 384–393 (2012).
[CrossRef]

Bonora, S.

Brunner, T.

S. Halle, M. Crouse, A. Jiang, Y. van Dommelen, T. Brunner, B. Minghetti, M. Colburn, and Y. Zhang, “Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results,” Proc. SPIE8326, 832607–832607–19 (2012).
[CrossRef]

Canuel, B.

Cao, H.

J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[CrossRef]

Cavalier, F.

Choi, J. P.

D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

Coene, W.

C. Bikcora, M. Van Veelen, S. Weiland, and W. Coene, “Lens heating induced aberration prediction via nonlinear kalman filters,” IEEE Trans. Semicond. Manuf.25, 384–393 (2012).
[CrossRef]

Colburn, M.

S. Halle, M. Crouse, A. Jiang, Y. van Dommelen, T. Brunner, B. Minghetti, M. Colburn, and Y. Zhang, “Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results,” Proc. SPIE8326, 832607–832607–19 (2012).
[CrossRef]

Crouse, M.

S. Halle, M. Crouse, A. Jiang, Y. van Dommelen, T. Brunner, B. Minghetti, M. Colburn, and Y. Zhang, “Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results,” Proc. SPIE8326, 832607–832607–19 (2012).
[CrossRef]

Danzmann, K.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun.175, 275–287 (2000).
[CrossRef]

Day, R.

Engblom, P.

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

Fan, M.

K. Liu, Y. Li, F. Zhang, and M. Fan, “Transient thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” Jpn. J. Appl. Phys46, 6568–6572 (2007).
[CrossRef]

Fernandez, E.

Finders, J.

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

Fisher, A.

P. A. Spence, S. E. Gianoulakis, C. D. Moen, M. Kanouff, A. Fisher, and A. K. Ray-Chaudhuri, “System performance modeling of extreme ultraviolet lithographic thermal issues,” J. Vac. Sci. Tech. B17, 3034–3038 (1999).
[CrossRef]

Fritschel, P.

Gemmink, J.-W.

J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[CrossRef]

Genin, E.

Gianoulakis, S. E.

P. A. Spence, S. E. Gianoulakis, C. D. Moen, M. Kanouff, A. Fisher, and A. K. Ray-Chaudhuri, “System performance modeling of extreme ultraviolet lithographic thermal issues,” J. Vac. Sci. Tech. B17, 3034–3038 (1999).
[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. SPIE8239, 82390Z–82390Z–9 (2012).
[CrossRef]

Grunner, T.

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

Haber, A.

Haferkamp, H.

H. Haferkamp and D. Seebaum, “Beam delivery by adaptive optics for material processing applications using high-power co2 lasers,” Proc. SPIE2207, 156–164 (1994).
[CrossRef]

Halle, S.

S. Halle, M. Crouse, A. Jiang, Y. van Dommelen, T. Brunner, B. Minghetti, M. Colburn, and Y. Zhang, “Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results,” Proc. SPIE8326, 832607–832607–19 (2012).
[CrossRef]

Hello, P.

P. Hello and J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. France51, 2243–2261 (1990).
[CrossRef]

Hollink, T.

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

Huang, W.

D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

Hunsche, S.

J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[CrossRef]

Jiang, A.

S. Halle, M. Crouse, A. Jiang, Y. van Dommelen, T. Brunner, B. Minghetti, M. Colburn, and Y. Zhang, “Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results,” Proc. SPIE8326, 832607–832607–19 (2012).
[CrossRef]

Kang, Y. S.

D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

Kanouff, M.

P. A. Spence, S. E. Gianoulakis, C. D. Moen, M. Kanouff, A. Fisher, and A. K. Ray-Chaudhuri, “System performance modeling of extreme ultraviolet lithographic thermal issues,” J. Vac. Sci. Tech. B17, 3034–3038 (1999).
[CrossRef]

Kasprzack, M.

Knight, L. V.

Korth, W. Z.

La Penna, P.

B. Canuel, R. Day, E. Genin, P. La Penna, and J. Marque, “Wavefront aberration compensation with a thermally deformable mirror,” Classical Quant. Grav.29, 085012 (2012).
[CrossRef]

Lawrence, R.

Li, Y.

K. Liu, Y. Li, F. Zhang, and M. Fan, “Transient thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” Jpn. J. Appl. Phys46, 6568–6572 (2007).
[CrossRef]

Y. Li, K. Ota, and K. Murakami, “Thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” J. Vac. Sci. Tech. B21, 127–129 (2003).
[CrossRef]

Lim, R.

M. Phan, R. Lim, and R. Longman, “Unifying Input-Output and State-Space Perspectives of Predictive Control,” Princeton University, Department of Mechanical and Aerospace Engineering Technical Report No. 3044 (1998).

Liu, K.

K. Liu, Y. Li, F. Zhang, and M. Fan, “Transient thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” Jpn. J. Appl. Phys46, 6568–6572 (2007).
[CrossRef]

Loktev, M.

Longman, R.

M. Phan, R. Lim, and R. Longman, “Unifying Input-Output and State-Space Perspectives of Predictive Control,” Princeton University, Department of Mechanical and Aerospace Engineering Technical Report No. 3044 (1998).

Lück, H.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun.175, 275–287 (2000).
[CrossRef]

Mack, C.

C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (Wiley, 2008).

Malacara, D.

D. Malacara, Optical shop testing (Wiley-Interscience, 2007).
[CrossRef]

Marque, J.

Martin, R. M.

Maslow, M.

J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[CrossRef]

Minghetti, B.

S. Halle, M. Crouse, A. Jiang, Y. van Dommelen, T. Brunner, B. Minghetti, M. Colburn, and Y. Zhang, “Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results,” Proc. SPIE8326, 832607–832607–19 (2012).
[CrossRef]

Moen, C. D.

P. A. Spence, S. E. Gianoulakis, C. D. Moen, M. Kanouff, A. Fisher, and A. K. Ray-Chaudhuri, “System performance modeling of extreme ultraviolet lithographic thermal issues,” J. Vac. Sci. Tech. B17, 3034–3038 (1999).
[CrossRef]

Mueller, G.

Mulkens, J.

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

Müller, K.-O.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun.175, 275–287 (2000).
[CrossRef]

Murakami, K.

Y. Li, K. Ota, and K. Murakami, “Thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” J. Vac. Sci. Tech. B21, 127–129 (2003).
[CrossRef]

Nachtwein, A.

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

Nam, Y. S.

D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

Neumann, J.

J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[CrossRef]

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W. Nowacki, Dynamic Problems of Thermoelasticity (Springer, 1975).

Ota, K.

Y. Li, K. Ota, and K. Murakami, “Thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” J. Vac. Sci. Tech. B21, 127–129 (2003).
[CrossRef]

Ottaway, D.

Park, C.-H.

D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

Park, K.-Y.

D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

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D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

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M. Phan, R. Lim, and R. Longman, “Unifying Input-Output and State-Space Perspectives of Predictive Control,” Princeton University, Department of Mechanical and Aerospace Engineering Technical Report No. 3044 (1998).

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. SPIE8239, 82390Z–82390Z–9 (2012).
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Polo, A.

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S. Ravensbergen, P. Rosielle, and M. Steinbuch, “Deformable mirrors with thermomechanical actuators for extreme ultraviolet lithography: Design, realization and validation,” Precis. Eng.37, 353–363 (2013).
[CrossRef]

S. Ravensbergen, “Adaptive optics for extreme ultraviolet lithography : actuator design and validation for deformable mirror concepts,” Ph.D. thesis, Technische Universiteit Eindhoven (2012).

Ravensbergen, S. K.

Ray-Chaudhuri, A. K.

P. A. Spence, S. E. Gianoulakis, C. D. Moen, M. Kanouff, A. Fisher, and A. K. Ray-Chaudhuri, “System performance modeling of extreme ultraviolet lithographic thermal issues,” J. Vac. Sci. Tech. B17, 3034–3038 (1999).
[CrossRef]

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F. Roddier, Adaptive optics in astronomy (Cambridge University Press, 1999).
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S. Ravensbergen, P. Rosielle, and M. Steinbuch, “Deformable mirrors with thermomechanical actuators for extreme ultraviolet lithography: Design, realization and validation,” Precis. Eng.37, 353–363 (2013).
[CrossRef]

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D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

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H. Haferkamp and D. Seebaum, “Beam delivery by adaptive optics for material processing applications using high-power co2 lasers,” Proc. SPIE2207, 156–164 (1994).
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P. A. Spence, S. E. Gianoulakis, C. D. Moen, M. Kanouff, A. Fisher, and A. K. Ray-Chaudhuri, “System performance modeling of extreme ultraviolet lithographic thermal issues,” J. Vac. Sci. Tech. B17, 3034–3038 (1999).
[CrossRef]

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F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

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S. Ravensbergen, P. Rosielle, and M. Steinbuch, “Deformable mirrors with thermomechanical actuators for extreme ultraviolet lithography: Design, realization and validation,” Precis. Eng.37, 353–363 (2013).
[CrossRef]

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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. SPIE8239, 82390Z–82390Z–9 (2012).
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Tyson, R.

R. Tyson, Principles of Adaptive Optics, Third Edition, Series in Optics and Optoelectronics Series (CRC Press-INC, 2010).
[CrossRef]

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Urbach, P.

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J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[CrossRef]

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S. Halle, M. Crouse, A. Jiang, Y. van Dommelen, T. Brunner, B. Minghetti, M. Colburn, and Y. Zhang, “Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results,” Proc. SPIE8326, 832607–832607–19 (2012).
[CrossRef]

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J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
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C. Bikcora, M. Van Veelen, S. Weiland, and W. Coene, “Lens heating induced aberration prediction via nonlinear kalman filters,” IEEE Trans. Semicond. Manuf.25, 384–393 (2012).
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J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
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M. Verhaegen and V. Verdult, Filtering and System Identification: A Least Squares Approach (Cambridge University Press, 2007).
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P. Hello and J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. France51, 2243–2261 (1990).
[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. SPIE8239, 82390Z–82390Z–9 (2012).
[CrossRef]

Weiland, S.

C. Bikcora, M. Van Veelen, S. Weiland, and W. Coene, “Lens heating induced aberration prediction via nonlinear kalman filters,” IEEE Trans. Semicond. Manuf.25, 384–393 (2012).
[CrossRef]

Willekers, R.

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
[CrossRef]

Williams, L. F.

Wolf, A.

J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[CrossRef]

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K. Liu, Y. Li, F. Zhang, and M. Fan, “Transient thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” Jpn. J. Appl. Phys46, 6568–6572 (2007).
[CrossRef]

Zhang, Y.

S. Halle, M. Crouse, A. Jiang, Y. van Dommelen, T. Brunner, B. Minghetti, M. Colburn, and Y. Zhang, “Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results,” Proc. SPIE8326, 832607–832607–19 (2012).
[CrossRef]

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (2011).
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Appl. Opt.

Classical Quant. Grav.

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[CrossRef]

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A. Haber and M. Verhaegen, “Moving horizon estimation for large-scale interconnected systems,” in press, IEEE Trans. Autom. Control (2013).
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C. Bikcora, M. Van Veelen, S. Weiland, and W. Coene, “Lens heating induced aberration prediction via nonlinear kalman filters,” IEEE Trans. Semicond. Manuf.25, 384–393 (2012).
[CrossRef]

J. Phys. France

P. Hello and J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. France51, 2243–2261 (1990).
[CrossRef]

J. Vac. Sci. Tech. B

Y. Li, K. Ota, and K. Murakami, “Thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” J. Vac. Sci. Tech. B21, 127–129 (2003).
[CrossRef]

P. A. Spence, S. E. Gianoulakis, C. D. Moen, M. Kanouff, A. Fisher, and A. K. Ray-Chaudhuri, “System performance modeling of extreme ultraviolet lithographic thermal issues,” J. Vac. Sci. Tech. B17, 3034–3038 (1999).
[CrossRef]

Jpn. J. Appl. Phys

K. Liu, Y. Li, F. Zhang, and M. Fan, “Transient thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography,” Jpn. J. Appl. Phys46, 6568–6572 (2007).
[CrossRef]

Opt. Commun.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun.175, 275–287 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Precis. Eng.

S. Ravensbergen, P. Rosielle, and M. Steinbuch, “Deformable mirrors with thermomechanical actuators for extreme ultraviolet lithography: Design, realization and validation,” Precis. Eng.37, 353–363 (2013).
[CrossRef]

Proc. SPIE

F. Staals, A. Andryzhyieuskaya, H. Bakker, M. Beems, J. Finders, T. Hollink, J. Mulkens, A. Nachtwein, R. Willekers, P. Engblom, T. Grunner, and Y. Zhang, “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 na immersion scanner,” Proc. SPIE7973, 79731G–79731G-13 (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. SPIE8239, 82390Z–82390Z–9 (2012).
[CrossRef]

H. Haferkamp and D. Seebaum, “Beam delivery by adaptive optics for material processing applications using high-power co2 lasers,” Proc. SPIE2207, 156–164 (1994).
[CrossRef]

J. Bekaert, L. Van Look, G. Vandenberghe, P. Van Adrichem, M. Maslow, J.-W. Gemmink, H. Cao, S. Hunsche, J. Neumann, and A. Wolf, “Characterization and control of dynamic lens heating effects under high volume manufacturing conditions,” Proc. SPIE7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[CrossRef]

D. H. Beak, J. P. Choi, T. Park, Y. S. Nam, Y. S. Kang, C.-H. Park, K.-Y. Park, C.-H. Ryu, W. Huang, and K.-H. Baik, “Lens heating impact analysis and controls for critical device layers by computational method,” Proc. SPIE8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[CrossRef]

S. Halle, M. Crouse, A. Jiang, Y. van Dommelen, T. Brunner, B. Minghetti, M. Colburn, and Y. Zhang, “Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results,” Proc. SPIE8326, 832607–832607–19 (2012).
[CrossRef]

Other

M. Phan, R. Lim, and R. Longman, “Unifying Input-Output and State-Space Perspectives of Predictive Control,” Princeton University, Department of Mechanical and Aerospace Engineering Technical Report No. 3044 (1998).

S. Ravensbergen, “Adaptive optics for extreme ultraviolet lithography : actuator design and validation for deformable mirror concepts,” Ph.D. thesis, Technische Universiteit Eindhoven (2012).

F. Roddier, Adaptive optics in astronomy (Cambridge University Press, 1999).
[CrossRef]

R. Tyson, Principles of Adaptive Optics, Third Edition, Series in Optics and Optoelectronics Series (CRC Press-INC, 2010).
[CrossRef]

C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (Wiley, 2008).

W. Nowacki, Dynamic Problems of Thermoelasticity (Springer, 1975).

M. Verhaegen and V. Verdult, Filtering and System Identification: A Least Squares Approach (Cambridge University Press, 2007).
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Figures (5)

Fig. 1:
Fig. 1:

(a) Experimental setup consisting of two DMs that was used to demonstrate the performance of the predictive control algorithm; (b) Past, present and future.

Fig. 2:
Fig. 2:

(a) Performance of the unconstrained predictive controller; (b) Calculated control input. Negative values of the control channels are set to zero.

Fig. 3:
Fig. 3:

(a) Performance of the constrained predictive controller; (b) The performance of the unconstrained predictive controller for several values of past horizon p.

Fig. 4:
Fig. 4:

(a) Performance of the unconstrained predictive controller for different values of γ; (b) Convergence of an arbitrary channel of the unconstrained predictive control input.

Fig. 5:
Fig. 5:

The performance of the predictive controller when unknown disturbance input is estimated.

Equations (26)

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

Φ ( x , y , k ) = i = 1 36 α i ( k ) Z i ( x , y )
y T ( k ) = [ α 2 ( k ) α 10 ( k ) ] T
x ( k + 1 ) = A x ( k ) + B v
y T ( k ) = C x ( k )
y M ( k ) = M u ( k ) , u ( k ) = [ q 1 2 ( k ) q 2 2 ( k ) q 48 2 ( k ) ] T
y ( k ) = y T ( k ) + y M ( k )
x ( k + 1 ) = A x ( k ) + B v
y ( k ) = C x ( k ) + M u ( k )
v p = [ v v v ] p entries of v , u p = [ u ( k p ) u ( k p + 1 ) u ( k ) ] , y p = [ y ( k p ) y ( k p + 1 ) y ( k ) ]
v f = [ v v v ] f entries of v , u f = [ u ( k + 1 ) u ( k + 2 ) u ( k + f ) ] , y f = [ y ( k + 1 ) y ( k + 2 ) y ( k + f ) ]
O _ p x ( k p ) = y p I _ p v p D _ p u p
O _ p = [ C C A C A p ] , I _ p = [ 0 0 C B 0 C A B C B 0 C A p 1 B C A p 2 B C B ] , D _ p = [ M 0 0 0 0 M 0 0 0 0 M 0 0 0 M ] p + 1 blocks
x ( k p ) = O _ p ( y p I _ p v p D _ p u p )
x ( k ) = A p x ( k p ) + R _ p 1 v p
x ( k ) = A p O _ p y p A p O _ p D _ p u p + ( R _ p 1 + A p O _ p I _ p ) v p
y f = O _ f 1 A x ( k ) + I _ ¯ f v f + D _ f 1 u f
O _ f 1 = [ C C A C A f 1 ] , I _ ¯ f = [ C B 0 C A B C B 0 C A f 1 B C A f 2 B C B ] , D _ f 1 = [ M 0 0 0 0 M 0 0 0 0 M 0 0 0 M ] f blocks
y f = O _ f 1 A p + 1 O _ p y p O _ f 1 A p + 1 O _ p D _ p u p O _ f 1 A p + 1 O _ p I _ p v p The effect of the initial state x ( k p ) + O _ f 1 A R _ p 1 v p + I ¯ _ f v f + D _ f 1 u f
y f = s + D _ f 1 u f
s = O _ f 1 A p + 1 O _ p y p O _ f 1 A p + 1 O _ p D _ p u p + O _ f 1 A ( R _ p 1 A p O _ p I _ p ) v p + I ¯ _ f v f
min u f { y f T y f + u f T W u f }
W = γ Q Q T , Q = [ I I 0 0 I I 0 0 I I 0 I ]
u ^ f = ( D _ f 1 T D _ f 1 + W ) 1 D _ f 1 T s
min u f { y f T y f + u f T W u f } subject to a 1 u f a 2
b = L w , w = [ x ( k p ) v ] where b = y p D _ p u p , L = [ O _ p I _ p q ] , q = [ 1 1 1 ] T p entries
min w { ( b L w ) T ( b L w ) }

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