Concept and modeling analysis of a high fidelity multimode deformable mirror

Chao Zhou; Yun Li; Anding Wang; Tingwen Xing

doi:10.1364/AO.54.005436

Applied Optics
Vol. 54,
Issue 17,
pp. 5436-5443
(2015)
•https://doi.org/10.1364/AO.54.005436

Concept and modeling analysis of a high fidelity multimode deformable mirror

Chao Zhou, Yun Li, Anding Wang, and Tingwen Xing

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Chao Zhou, Yun Li, Anding Wang, and Tingwen Xing, "Concept and modeling analysis of a high fidelity multimode deformable mirror," Appl. Opt. 54, 5436-5443 (2015)

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Abstract

Conventional deformable mirrors (DM) cannot meet the requirement of aberration controlling for advanced lithography tools. This paper illustrates an approach using the property that deformation of a thin plate is similar to optical modes to realize a high fidelity multimode deformable mirror whose deformation has characteristics of optical aberration modes. The way to arrange actuators is also examined. In this paper, a 36-actuator deformable mirror is taken as an example to generate low-order Zernike modes. The result shows that this DM generates the fourth fringe Zernike mode (Z4) defocus, and primary aberration Z5–Z8 with an error less than 0.5%, generates the fifth-order aberration Z10–Z14, and generates the seventh-order aberration Z17–Z20 with an error less than 1.1%. The high fidelity replication of the Zernike mode indicates that the DM satisfies the demand of controlling aberrations corresponding to the first 20 Zernike modes in an advanced lithography tool.

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Equations (11)

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Primary	Third Order	Fifth Order	Seventh Order	Ninth Order
$A_{20} r^{2}$ Z4:Curv1	$A_{40} r^{4}$ Z9:Sph 3	$A_{60} r^{6}$ Z16:Sph 5	$A_{80} r^{8}$ Z25:Sph7	$A_{10,0} r^{10}$ Z36:Sph 9
$A_{11} r \cos θ$ Z2:Tilt 1	$A_{31} r^{3} \cos θ$ Z7:Coma 3	$A_{51} r^{5} \cos θ$ Z14:Coma5	$A_{71} r^{7} \cos θ$ Z23:Coma 7	$A_{91} r^{9} \cos θ$ Z34:Coma 9
	$A_{22} r^{2} \cos 2 θ$ Z5:Astm 3	$A_{42} r^{4} \cos 2 θ$ Z12:Astm 5	$A_{62} r^{6} \cos 2 θ$ Z21:Astm 7	$A_{82} r^{8} \cos 2 θ$ Z32:Astm 9
		$A_{33} r^{3} \cos 3 θ$ Z10:Tref 5	$A_{53} r^{5} \cos 3 θ$ Z19:Tref 7	$A_{73} r^{7} \cos 3 θ$ Z30:Tref 9
			$A_{44} r^{4} \cos 4 θ$ Z17:Sqr7	$A_{64} r^{6} \cos 4 θ$ Z28:Sqr 9
				$A_{55} r^{5} \cos 5 θ$ Z26:Pent 9

Property	Value
Mirror material	Fused silicon
Young’s modulus	77.8 GPa
Poisson’s ratio	0.17
Diameter of mirror	400 mm
Diameter of clear aperture	200 mm
Thickness of mirror	20 mm
Mirror support	Fixed
Inner ring radius	150 mm
Number of actuators on inner ring	18
Outer ring radius	175 mm
Number of actuators on outer ring	18
Convection coefficient	$1 W / m^{2} \cdot K$
Thermal expansion coefficient (22°C)	5E-7/°C

Primary	Third Order	Fifth Order	Seventh Order	Ninth Order
$A_{20} r^{2}$ Z4:Curv1	$A_{40} r^{4}$ Z9:Sph 3	$A_{60} r^{6}$ Z16:Sph 5	$A_{80} r^{8}$ Z25:Sph7	$A_{10,0} r^{10}$ Z36:Sph 9
$A_{11} r \cos θ$ Z2:Tilt 1	$A_{31} r^{3} \cos θ$ Z7:Coma 3	$A_{51} r^{5} \cos θ$ Z14:Coma5	$A_{71} r^{7} \cos θ$ Z23:Coma 7	$A_{91} r^{9} \cos θ$ Z34:Coma 9
	$A_{22} r^{2} \cos 2 θ$ Z5:Astm 3	$A_{42} r^{4} \cos 2 θ$ Z12:Astm 5	$A_{62} r^{6} \cos 2 θ$ Z21:Astm 7	$A_{82} r^{8} \cos 2 θ$ Z32:Astm 9
		$A_{33} r^{3} \cos 3 θ$ Z10:Tref 5	$A_{53} r^{5} \cos 3 θ$ Z19:Tref 7	$A_{73} r^{7} \cos 3 θ$ Z30:Tref 9
			$A_{44} r^{4} \cos 4 θ$ Z17:Sqr7	$A_{64} r^{6} \cos 4 θ$ Z28:Sqr 9
				$A_{55} r^{5} \cos 5 θ$ Z26:Pent 9

Property	Value
Mirror material	Fused silicon
Young’s modulus	77.8 GPa
Poisson’s ratio	0.17
Diameter of mirror	400 mm
Diameter of clear aperture	200 mm
Thickness of mirror	20 mm
Mirror support	Fixed
Inner ring radius	150 mm
Number of actuators on inner ring	18
Outer ring radius	175 mm
Number of actuators on outer ring	18
Convection coefficient	$1 W / m^{2} \cdot K$
Thermal expansion coefficient (22°C)	5E-7/°C

Abstract

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Figures (9)

Tables (2)

Equations (11)

Applied Optics