Optical distortion evaluation of an aerodynamically heated window, based on the higher-order singular value decomposition with the influence of elasto-optical effect excluded

Haosu Xiao; Zhile Wang; Zhigang Fan

doi:10.1364/AO.51.003269

Applied Optics
Vol. 51,
Issue 16,
pp. 3269-3278
(2012)
•https://doi.org/10.1364/AO.51.003269

Optical distortion evaluation of an aerodynamically heated window, based on the higher-order singular value decomposition with the influence of elasto-optical effect excluded

Haosu Xiao, Zhile Wang, and Zhigang Fan

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Haosu Xiao, Zhile Wang, and Zhigang Fan, "Optical distortion evaluation of an aerodynamically heated window, based on the higher-order singular value decomposition with the influence of elasto-optical effect excluded," Appl. Opt. 51, 3269-3278 (2012)

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Abstract

The higher-order singular value decomposition (HOSVD) was used to reconstruct the three-dimensional (3D) refractive index field of an aerodynamically heated window. The numerical 3D optical distortion was evaluated for both the reconstructed and the exact refractive index fields of the window, excluding the influence of the elasto-optical effect. The method based on the HOSVD truncation was shown to reduce the refractive index information required to capture the major optical distortion of the window. The refractive index information was reduced by reconstructing the refractive index field of the window using the truncated $n$ -mode singular matrices. The method can also be used to evaluate the optical distortion of the window.

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Physical Properties	Performance Parameters
Density ( $kg \cdot m^{- 3}$ )	4102
Melting point ( $K$ )	1973
Expansion coefficient ( $10^{- 6} K^{- 1}$ )	7.0
Heat capacity ( $J \cdot {kg}^{- 1} \cdot K^{- 1}$ )	470
Young’s modulus ( $10^{9} Pa$ )	74
Thermal conductivity ( $W \cdot m^{- 1} \cdot K^{- 1}$ )	19
Poisson ratio	0.29
Mean strength ( $10^{6} Pa$ )	100

Point	$Δ n_{t}$	$Δ n_{11}$	$Δ n_{22}$	$Δ n_{33}$	$Δ n_{23}$	$Δ n_{31}$	$Δ n_{12}$
1	$3.62 \times 10^{- 3}$	$4.02 \times 10^{- 5}$	$3.45 \times 10^{- 5}$	$3.45 \times 10^{- 5}$	$- 1.09 \times 10^{- 7}$	$5.23 \times 10^{- 9}$	$- 3.29 \times 10^{- 6}$
2	$2.28 \times 10^{- 3}$	$- 7.59 \times 10^{- 5}$	$- 1.59 \times 10^{- 4}$	$1.64 \times 10^{- 4}$	$1.16 \times 10^{- 4}$	$3.78 \times 10^{- 5}$	$- 1.74 \times 10^{- 5}$

Mode- $n$ Matrix Unfoldings	$B_{(1)}$	$B_{(2)}$	$B_{(3)}$
The first-order $n$ -mode singular value	534.958	534.958	534.958
The second-order $n$ -mode singular value	0.055	0.054	0.020
The third-order $n$ -mode singular value	0.052	0.051	0.001

Physical Properties	Performance Parameters
Density ( $kg \cdot m^{- 3}$ )	4102
Melting point ( $K$ )	1973
Expansion coefficient ( $10^{- 6} K^{- 1}$ )	7.0
Heat capacity ( $J \cdot {kg}^{- 1} \cdot K^{- 1}$ )	470
Young’s modulus ( $10^{9} Pa$ )	74
Thermal conductivity ( $W \cdot m^{- 1} \cdot K^{- 1}$ )	19
Poisson ratio	0.29
Mean strength ( $10^{6} Pa$ )	100

Point	$Δ n_{t}$	$Δ n_{11}$	$Δ n_{22}$	$Δ n_{33}$	$Δ n_{23}$	$Δ n_{31}$	$Δ n_{12}$
1	$3.62 \times 10^{- 3}$	$4.02 \times 10^{- 5}$	$3.45 \times 10^{- 5}$	$3.45 \times 10^{- 5}$	$- 1.09 \times 10^{- 7}$	$5.23 \times 10^{- 9}$	$- 3.29 \times 10^{- 6}$
2	$2.28 \times 10^{- 3}$	$- 7.59 \times 10^{- 5}$	$- 1.59 \times 10^{- 4}$	$1.64 \times 10^{- 4}$	$1.16 \times 10^{- 4}$	$3.78 \times 10^{- 5}$	$- 1.74 \times 10^{- 5}$

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Applied Optics