Gravity unloading of a very large spaceborne monolithic SiC mirror

Fuxiang Tian; Fuxiang Tian; Feng Zhang; Jiang Guo; Lei Zhu; Hao Wang

doi:10.1364/AO.509617

Applied Optics
Vol. 63,
Issue 3,
pp. 838-845
(2024)
•https://doi.org/10.1364/AO.509617

Gravity unloading of a very large spaceborne monolithic SiC mirror

Fuxiang Tian, Feng Zhang, Jiang Guo, Lei Zhu, and Hao Wang

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Fuxiang Tian, Feng Zhang, Jiang Guo, Lei Zhu, and Hao Wang, "Gravity unloading of a very large spaceborne monolithic SiC mirror," Appl. Opt. 63, 838-845 (2024)

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Abstract

We formulated a gravity unloading strategy for a monolithic silicon carbide (SiC) mirror with a $\Phi {3}\,\rm m$ aperture in space. Employing the finite element analysis (FEA) technique, a rapid solution analytical approach for determining optimal support forces during gravity unloading is introduced. This method demonstrates enhanced efficiency and accuracy compared to conventional approaches. A quantitative evaluation methodology for the gravity release error, grounded in the minimum-energy mode, is delineated. The adverse impacts could be expeditiously computed by assessing the maximum deflection of minimum-energy modes generated by various errors. The analytical findings revealed that compliance with the stipulated gravity release error criterion of less than 6 nm (root-mean-square) necessitated the gravity unloading force error to fall within the range of $\pm {0.1}\;{\rm N}$. Additionally, the gravity unloading support position error was required to be within $\Phi {0.5}\;{\rm mm}$, and the measurement error pertaining to the rib thickness of the actual mirror blank had to be within $\pm {0.02}\;{\rm mm}$.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Item	Value
Density ( $g / {c m}^{3}$ )	$3.0 \pm 0.02$
Young‘s modulus (Gpa)	$\geq 350$
Bending strength (Mpa)	$\geq 360$
Fracture toughness (Mpa)	$\geq 4.0$
Coefficient of thermal expansion @10–100 °C ( $10^{- 6} / K$ )	$2.6 \pm 0.2$
Thermal conductivity ( $W / m \cdot K$ )	$\geq 140$

Item	Value
Diameter (mm)	3040
Height in center (mm)	215
Radius of the curvature (mm)	14807
Mass (kg)	656.96
Area density ( $k g / m^{2}$ )	90.5
Thickness of the front face (mm)	7
Thickness of the back face (mm)	7
Thickness of the high ribs (mm)	4
Thickness of the low ribs (mm)	3
Thickness of the outer ring (mm)	5

Item	Active Optics Method	Modified Active Optics Method	$Δ$ ^a
F1 (N)	90.33	90.65	0.32
F2 (N)	91.98	92.55	0.57
F3 (N)	94.48	92.89	−1.59
F4 (N)	88.64	89.06	0.42
F5 (N)	91.16	98.25	7.09
F6 (N)	96.60	97.03	0.43
F7 (N)	96.99	95.74	−1.25
F8 (N)	109.45	105.59	−3.86
F9 (N)	112.21	113.91	1.7
F10 (N)	117.60	108.82	−8.78
F11 (N)	90.91	105.53	14.62
F12 (N)	85.41	84.91	−0.5
F13 (N)	17.39	56.32	38.93
F14 (N)	76.69	52.13	−24.56
F15 (N)	64.13	65.12	0.99
PV (nm)	21.23	14.22	−
RMS (nm)	3.44	3.07	−

	First Modes	Second Modes	Third Modes	Fourth Modes
PV/nm	120.5	122.1	6.8	25.6
RMS/nm	27.1	27.3	1.5	5.5
$Δ R / µ m$	−0.28	−0.42	−7.59	−0.04

	Support Force Error $\pm 1 N$	Support Position Error $Φ 1 m m$	Rib Thickness Error $\pm 0.1 m m$
PV/nm	122.1	10.64	115.35
RMS/nm	27.3	2.26	26.22

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Applied Optics