Lens Heating Induced Aberration Prediction via Nonlinear Kalman Filters

Bikcora, Can; Veelen, Martijn van; Weiland, S.; Coene, W.

doi:10.1109/tsm.2012.2200510

Cited by 13 publications

(3 citation statements)

References 21 publications

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“…Thermally-induced mechanical deformations, wavefront aberrations, and large focal shifts can negatively affect performance and significantly limit the resolution of both refractive and reflective optical systems. For example, thermal phenomena and thermally-induced aberrations can limit the achievable resolution and performance of optical lithography systems, [1][2][3][4][5][6][7][8][9][10] space and ground telescopes, [11][12][13][14][15][16][17][18][19][20][21][22][23] gravitational wave detectors, [24][25][26] high power lasers, [27][28][29] and other optical systems. [30][31][32][33] In the case of refractive optical systems consisting of lenses, absorbed thermal energy and non-uniform temperature distributions across optical elements, induce mechanical deformations and variations of refractive indices.…”

Section: Introductionmentioning

confidence: 99%

Subspace identification of low-dimensional Structural-Thermal-Optical-Performance (STOP) models of reflective optics

Haber¹,

Draganov²,

Krainak³

2022

Preprint

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In this paper, we investigate the feasibility of using subspace system identification techniques for estimating transient Structural-Thermal-Optical Performance (STOP) models of reflective optics. As a test case, we use a Newtonian telescope structure. This work is motivated by the need for the development of model-based datadriven techniques for prediction, estimation, and control of thermal effects and thermally-induced wavefront aberrations in optical systems, such as ground and space telescopes, optical instruments operating in harsh environments, optical lithography machines, and optical components of high-power laser systems. We estimate and validate a state-space model of a transient STOP dynamics. First, we model the system in COMSOL Multiphysics. Then, we use LiveLink for MATLAB software module to export the wavefront aberrations data from COMSOL to MATLAB. This data is used to test the subspace identification method that is implemented in Python. One of the main challenges in modeling and estimation of STOP models is that they are inherently large-dimensional. The large-scale nature of STOP models originates from the coupling of optical, thermal, and structural phenomena and physical processes. Our results show that large-dimensional STOP dynamics of the considered optical system can be accurately estimated by low-dimensional state-space models. Due to their lowdimensional nature and state-space forms, these models can effectively be used for the prediction, estimation, and control of thermally-induced wavefront aberrations. The developed MATLAB, COMSOL, and Python codes are available online.

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Section: Introductionmentioning

confidence: 99%

Subspace identification of low-dimensional Structural-Thermal-Optical-Performance (STOP) models of reflective optics

Haber¹,

Draganov²,

Krainak³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Furthermore, due to a constant demand for higher productivity and less production costs, the power transmitted through the projection optics of lithography machines constantly increases. Consequently, the energy absorbed by projection optics induces wavefront aberrations that can compromise the resolution of the system [8][9][10][11][12]. In the next generation of optical lithography machines, that will use Extreme UltraViolet (EUV) sources, degradation of resolution due to the heating of optical elements will become even more severe [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Predictive control of thermally induced wavefront aberrations

et al. 2013

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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. Baik, "Lens heating impact analysis and controls for critical device layers by computational method," Proc. SPIE 8683, Optical Microlithography

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“…Furthermore, the possibility of transferring an existing imaging solution from a DUV wafer scanner to an EUV tool is usually ruled out because of the inherent physical differences between these two machines. In the scope of imaging quality, the reticle (mask) [4] and elements of the projection optics [5] are primarily responsible for image deteriorations, and despite the altered design in an EUV tool, the significance of these contributors remains intact. In particular, the context of this paper is restricted to the thermally induced deformation of an EUV reticle.…”

mentioning

confidence: 99%

Thermal Deformation Prediction in Reticles for Extreme Ultraviolet Lithography Based on a Measurement-Dependent Low-Order Model

Bikcora

Weiland

Coene

2014

IEEE Trans. Semicond. Manufact.

Self Cite

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In extreme ultraviolet lithography, imaging errors due to thermal deformation of reticles are becoming progressively intolerable as the source power increases. Despite this trend, such errors can be mitigated by adjusting the wafer and reticle stages based on a set of predicted deformation-induced displacements. Since this control scheme operates online, an accurate low-order model is necessary. However, finite element modeling of the reticle and its adjacent components leads to a large-scale thermomechanical model that should be simplified. First, parameters of the model's initial thermal condition are reduced to only a few from which numerous initial conditions can be accurately reconstructed. This entails placement of temperature sensors at the corresponding locations, and for this purpose, the discrete empirical interpolation method (DEIM) is utilized. Then, linear and nonlinear model reductions are performed via the proper orthogonal decomposition method and DEIM, respectively. The resultant model is employed in the Kalman filter to estimate the parameters of the reticle's temperature-dependent coefficient of thermal expansion from several displacement measurements and to subsequently predict the displacements that are used for control. By processing the outputs from the simulated large-scale model, this filter is shown to perform successfully, even in the presence of an unexpected initial condition.Index Terms-Discrete empirical interpolation method, extreme ultraviolet lithography, Kalman filter, proper orthogonal decomposition, reticle heating, sensor placement.

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Lens Heating Induced Aberration Prediction via Nonlinear Kalman Filters

Cited by 13 publications

References 21 publications

Subspace identification of low-dimensional Structural-Thermal-Optical-Performance (STOP) models of reflective optics

Subspace identification of low-dimensional Structural-Thermal-Optical-Performance (STOP) models of reflective optics

Predictive control of thermally induced wavefront aberrations

Thermal Deformation Prediction in Reticles for Extreme Ultraviolet Lithography Based on a Measurement-Dependent Low-Order Model

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