Active Optics: stress polishing of toric mirrors for the VLT SPHERE adaptive optics system

Emmanuel Hugot; Marc Ferrari; Kacem El Hadi; Pascal Vola; Jean Luc Gimenez; Gérard R. Lemaitre; Patrick Rabou; Kjetil Dohlen; Pascal Puget; Jean Luc Beuzit; Norbert Hubin

doi:10.1364/AO.48.002932

Applied Optics
Vol. 48,
Issue 15,
pp. 2932-2941
(2009)
•https://doi.org/10.1364/AO.48.002932

Active Optics: stress polishing of toric mirrors for the VLT SPHERE adaptive optics system

Emmanuel Hugot, Marc Ferrari, Kacem El Hadi, Pascal Vola, Jean Luc Gimenez, Gérard R. Lemaitre, Patrick Rabou, Kjetil Dohlen, Pascal Puget, Jean Luc Beuzit, and Norbert Hubin

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Emmanuel Hugot, Marc Ferrari, Kacem El Hadi, Pascal Vola, Jean Luc Gimenez, Gérard R. Lemaitre, Patrick Rabou, Kjetil Dohlen, Pascal Puget, Jean Luc Beuzit, and Norbert Hubin, "Active Optics: stress polishing of toric mirrors for the VLT SPHERE adaptive optics system," Appl. Opt. 48, 2932-2941 (2009)

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Abstract

The manufacturing of toric mirrors for the Very Large Telescope–Spectro-Polarimetric High-Contrast Exoplanet Research instrument (SPHERE) is based on Active Optics and stress polishing. This figuring technique allows minimizing mid and high spatial frequency errors on an aspherical surface by using spherical polishing with full size tools. In order to reach the tight precision required, the manufacturing error budget is described to optimize each parameter. Analytical calculations based on elasticity theory and finite element analysis lead to the mechanical design of the Zerodur blank to be warped during the stress polishing phase. Results on the larger ( $366 mm$ diameter) toric mirror are evaluated by interferometry. We obtain, as expected, a toric surface within specification at low, middle, and high spatial frequencies ranges.

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	Mirror TM1	Mirror TM2	Mirror TM3
Material	Zerodur	Zerodur	Zerodur
Clear aperture diameter	$133.0 mm$	$27.0 mm$	$366.0 mm$
Total diameter mirror + mount	$200 mm$	$50 mm$	$400 mm$
Beam footprint diameter	$116.2 mm$	$6.9 mm$	$353.1 mm$
Field of view (FOV)	$130.1 mm$	$16.4 mm$	$362.3 mm$
Incidence angle	$4.3532 °$	$5.5 °$	$3.7 °$
Horizontal radius of curvature $R_{y}$	$1589.66 mm$	$851.77 mm$	$3608.0 mm$
Vertical radius of curvature $R_{x}$	$1580.51 mm$	$843.95 mm$	$3592.98 mm$
Average radius of curvature $< R >_{m} = 1 / C$	$1585.1 mm$	$847.86 mm$	$3600.5 mm$
Astm 3 coefficient RMS	$1645.3 nm$	$202.4 nm$	$3965.9 nm$
Astm 5 coefficient RMS	$0.4 nm$	$0.0 nm$	$1.5 nm$
Radius of curvature tolerance	$\pm 0.1 %$	$\pm 0.1 %$	$\pm 0.1 %$
Low frequency tolerance ( $σ_{lof}$ )	$17.0 nm$ RMS	$17.0 nm$ RMS	$17.0 nm$ RMS
Middle frequency tolerance ( $σ_{MidF}$ )	$5.0 nm$ RMS	$3.0 nm$ RMS	$5.0 nm$ RMS
High frequency tolerance ( $σ_{hif}$ )	$3.0 nm$ RMS	(overlap with $R_{q}$ )	$3.0 nm$ RMS
Roughness ( $R_{q}$ )	$1.5 nm$ RMS	$1.5 nm$ RMS	$1.5 nm$ RMS
Reflected WFE tolerance	$50 nm$ RMS	$50 nm$ RMS	$50 nm$ RMS

Description	RMS [nm]	Description	RMS [nm]	Description	RMS [nm]
Piston 1	0.0	X Tetrafoil 7	1.7	X Pentafoil 9	1.0
X Tilt 1	0.0	Y Tetrafoil 7	1.0	Y Pentafoil 9	0.7
Y Tilt 1	0.0	X Trefoil 7	1.5	X Tetrafoil 9	3.1
Focus 1	35.5	Y Trefoil 7	0.3	Y Tetrafoil 9	0.9
X Astig 3	3976.7	X Astig 7	7.2	X Trefoil 9	0.7
Y Astig 3	0.2	Y Astig 7	1.0	Y Trefoil 9	0.4
X Coma 3	5.9	X Coma 7	0.5	X Astig 9	4.0
Y Coma 3	3.2	Y Coma 7	0.1	Y Astig 9	0.6
Spherical 3	80.1	Spherical 7	1.6	X Coma 9	0.2
X Trefoil 5	6.8			Y Coma 9	0.6
Y Trefoil 5	6.2			Spherical 9	4.6
X Astig 5	8.6
Y Astig 5	0.7
X Coma 5	1.0
Y Coma 5	0.7
Spherical 5	29.7

Description	Unmounted, Horizontal RMS Value [nm]	Mounted, Vertical RMS Value [nm]
X Astig 3	3976.7	3963.4
X Coma 3	5.9	10.4
Sphe 3	80.1	78.1
Sphe 5	29.7	29.5
Sphe 7	1.6	0.9
Sphe 9	4.6	4.7

Error term	$σ_{num}$	$σ_{def}$	$σ_{sup}$	$σ_{pol}$	$σ_{mnt}$	$σ_{mes}$	σ
RMS value [nm]	$< 1.0$	64.0	$< 2.0$	56.6	$< 2.0$	$< 2.0$	85.7
Error term				$σ_{LoF}$	$σ_{MidF}$	$σ_{HiF}$	σ
RMS value [nm]				85.4	6.1	3.8	85.7

	Mirror TM1	Mirror TM2	Mirror TM3
Material	Zerodur	Zerodur	Zerodur
Clear aperture diameter	$133.0 mm$	$27.0 mm$	$366.0 mm$
Total diameter mirror + mount	$200 mm$	$50 mm$	$400 mm$
Beam footprint diameter	$116.2 mm$	$6.9 mm$	$353.1 mm$
Field of view (FOV)	$130.1 mm$	$16.4 mm$	$362.3 mm$
Incidence angle	$4.3532 °$	$5.5 °$	$3.7 °$
Horizontal radius of curvature $R_{y}$	$1589.66 mm$	$851.77 mm$	$3608.0 mm$
Vertical radius of curvature $R_{x}$	$1580.51 mm$	$843.95 mm$	$3592.98 mm$
Average radius of curvature $< R >_{m} = 1 / C$	$1585.1 mm$	$847.86 mm$	$3600.5 mm$
Astm 3 coefficient RMS	$1645.3 nm$	$202.4 nm$	$3965.9 nm$
Astm 5 coefficient RMS	$0.4 nm$	$0.0 nm$	$1.5 nm$
Radius of curvature tolerance	$\pm 0.1 %$	$\pm 0.1 %$	$\pm 0.1 %$
Low frequency tolerance ( $σ_{lof}$ )	$17.0 nm$ RMS	$17.0 nm$ RMS	$17.0 nm$ RMS
Middle frequency tolerance ( $σ_{MidF}$ )	$5.0 nm$ RMS	$3.0 nm$ RMS	$5.0 nm$ RMS
High frequency tolerance ( $σ_{hif}$ )	$3.0 nm$ RMS	(overlap with $R_{q}$ )	$3.0 nm$ RMS
Roughness ( $R_{q}$ )	$1.5 nm$ RMS	$1.5 nm$ RMS	$1.5 nm$ RMS
Reflected WFE tolerance	$50 nm$ RMS	$50 nm$ RMS	$50 nm$ RMS

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Applied Optics