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 (6)

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]

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. SPIE 8683, 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, 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]

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]

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

2012 (5)

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. Express 20, 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. SPIE 8326, 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. SPIE 8239, 82390Z–82390Z–9 (2012).
[Crossref]

2011 (2)

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. SPIE 7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[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. SPIE 7973, 79731G–79731G-13 (2011).
[Crossref]

2010 (1)

2007 (1)

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. Phys 46, 6568–6572 (2007).
[Crossref]

2006 (1)

2004 (1)

2003 (2)

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. B 21, 127–129 (2003).
[Crossref]

E. Fernandez and P. Artal, “Membrane deformable mirror for adaptive optics: performance limits in visual optics.” Opt. Express 11, 1056–1069 (2003).
[Crossref] [PubMed]

2002 (1)

2000 (1)

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 (1)

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. B 17, 3034–3038 (1999).
[Crossref]

1994 (1)

H. Haferkamp and D. Seebaum, “Beam delivery by adaptive optics for material processing applications using high-power co2 lasers,” Proc. SPIE 2207, 156–164 (1994).
[Crossref]

1990 (1)

P. Hello and J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. France 51, 2243–2261 (1990).
[Crossref]

1982 (1)

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–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. SPIE 7973, 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. SPIE 8683, 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. SPIE 7973, 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. SPIE 8683, 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. SPIE 7973, 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. SPIE 7973, 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. SPIE 8326, 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. SPIE 7973, 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. SPIE 8683, 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. SPIE 8326, 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. SPIE 8326, 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. SPIE 7973, 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. Phys 46, 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. SPIE 7973, 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. B 17, 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. SPIE 7973, 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. B 17, 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. SPIE 8239, 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. SPIE 7973, 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. SPIE 2207, 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. SPIE 8326, 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. France 51, 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. SPIE 7973, 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. SPIE 8683, 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. SPIE 7973, 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. SPIE 8326, 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. SPIE 8683, 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. B 17, 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. Phys 46, 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. B 21, 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. Phys 46, 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. SPIE 7973, 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. SPIE 8326, 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. B 17, 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. SPIE 7973, 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. B 21, 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. SPIE 7973, 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. SPIE 8683, 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. SPIE 7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[Crossref]

Nowacki, W.

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. B 21, 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. SPIE 8683, 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. SPIE 8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[Crossref]

Park, T.

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. SPIE 8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[Crossref]

Pereira, S. F.

Phan, M.

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. SPIE 8239, 82390Z–82390Z–9 (2012).
[Crossref]

Poletto, L.

Polo, A.

Ravensbergen, S.

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. B 17, 3034–3038 (1999).
[Crossref]

Reitze, D.

Roddier, F.

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

Rosielle, P.

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]

Ryu, 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. SPIE 8683, Optical Microlithography XXVI, 86831Q–86831Q–8 (2013).
[Crossref]

Seebaum, D.

H. Haferkamp and D. Seebaum, “Beam delivery by adaptive optics for material processing applications using high-power co2 lasers,” Proc. SPIE 2207, 156–164 (1994).
[Crossref]

Sentenac, D.

Sheldon, S. J.

Smith, C. S.

Spence, P. 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. B 17, 3034–3038 (1999).
[Crossref]

Staals, F.

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. SPIE 7973, 79731G–79731G-13 (2011).
[Crossref]

Steinbuch, M.

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]

Tanner, D. B.

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–82390Z–9 (2012).
[Crossref]

Thorne, J. M.

Tyson, R.

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

Urbach, H. P.

Urbach, P.

Vajente, G.

Van Adrichem, P.

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. SPIE 7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[Crossref]

van Dommelen, 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. SPIE 8326, 832607–832607–19 (2012).
[Crossref]

Van Look, L.

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. SPIE 7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[Crossref]

Van Veelen, M.

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]

Vandenberghe, G.

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. SPIE 7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[Crossref]

Vdovin, G.

Verdult, V.

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

Verhaegen, M.

Vinet, J.-Y.

P. Hello and J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. France 51, 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. SPIE 8239, 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. SPIE 7973, 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. SPIE 7973, Optical Microlithography XXIV, 79730V–79730V (2011).
[Crossref]

Zhang, F.

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. Phys 46, 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. SPIE 8326, 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. SPIE 7973, 79731G–79731G-13 (2011).
[Crossref]

Zucker, M.

Appl. Opt. (3)

Classical Quant. Grav. (1)

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]

IEEE Trans. Autom. Control (1)

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

IEEE Trans. Semicond. Manuf. (1)

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 (1)

P. Hello and J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. France 51, 2243–2261 (1990).
[Crossref]

J. Vac. Sci. Tech. B (2)

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. B 21, 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. B 17, 3034–3038 (1999).
[Crossref]

Jpn. J. Appl. Phys (1)

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. Phys 46, 6568–6572 (2007).
[Crossref]

Opt. Commun. (1)

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 (4)

Opt. Lett. (3)

Precis. Eng. (1)

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 (6)

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. SPIE 7973, 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. SPIE 8239, 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. SPIE 2207, 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. SPIE 7973, 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. SPIE 8683, 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. SPIE 8326, 832607–832607–19 (2012).
[Crossref]

Other (9)

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).
[Crossref]

Adaptica Srl, “Saturn user manual,” http://www.adaptica.com/site/en/pages/saturn .

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).

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

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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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