Actuator patterns for unimorph and bimorph deformable mirrors

Sven Verpoort; Ulrich Wittrock

doi:10.1364/AO.49.000G37

Applied Optics
Vol. 49,
Issue 31,
pp. G37-G46
(2010)
•https://doi.org/10.1364/AO.49.000G37

Actuator patterns for unimorph and bimorph deformable mirrors

Sven Verpoort and Ulrich Wittrock

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Sven Verpoort and Ulrich Wittrock, "Actuator patterns for unimorph and bimorph deformable mirrors," Appl. Opt. 49, G37-G46 (2010)

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Abstract

The actuator pattern of an adaptive mirror determines the amplitudes and the fidelities of the mirror deformations that can be achieved. In this study, we analyze and compare different electrode patterns of piezoelectric unimorph deformable mirrors using a numerical finite element model. The analysis allows us to determine the optimum actuator pattern, and it is also applicable to bimorph mirrors. The model is verified by comparing its predictions with experimental results of our prototype of a novel unimorph deformable mirror.

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Component	Property	Value
Piezo disk	Material	PIC255
	Disk thickness ( $μm$ )	200
	Disk diameter (mm)	10–25
	Maximum voltage (V)	$- 60 / + 100$
	Poisson ratio $v_{p}$	0.36
	Young’s modulus $E_{p}$ (GPa)	62.9
	Piezoelectric strain constant $d_{31} ({mV}^{- 1})$	$- 174 \times 10^{- 12}$
	Piezoelectricity $e (C m^{- 2})$ (stress-charge form)	$e_{31} = - 7.15$
		$e_{33} = 13.7$
		$e_{15} = 11.90$
	Relative permittivity $ε_{r}$	$ε_{T, 11} = 1649$
	Relative permittivity $ε_{r}$	$ε_{T, 33} = 1750$
	Compliance $S (m^{2} N^{- 1})$	$s_{E, 11} = 1.590$
		$s_{E, 33} = 2.097$
		$s_{E, 55} = 4.492$
		$s_{E, 12} = - 5.699$
		$s_{E, 13} = - 7.376$
		$s_{E, 44} = 4.492$
		$s_{E, 66} = 4.319$
Elastic support ring	Material	Polyurethane
	Width (mm)	2.5
	Thickness ( $μm$ )	$\sim 300$
	Young’s modulus $E_{e} (GPa)$	$\sim 0.6$
Passive glass disk	Material	BK10
	Disk thickness ( $μm$ )	100
	Disk diameter (mm)	10..25
	Poisson ratio $v_{g}$	0.208
	Young’s modulus $E_{g} (GPa)$	72

Abstract

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Applied Optics