Imaging quality evaluation of aerodynamically heated optical dome using ray tracing

Haosu Xiao; Zhigang Fan

doi:10.1364/AO.49.005049

Applied Optics
Vol. 49,
Issue 27,
pp. 5049-5058
(2010)
•https://doi.org/10.1364/AO.49.005049

Imaging quality evaluation of aerodynamically heated optical dome using ray tracing

Haosu Xiao and Zhigang Fan

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Haosu Xiao and Zhigang Fan, "Imaging quality evaluation of aerodynamically heated optical dome using ray tracing," Appl. Opt. 49, 5049-5058 (2010)

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Abstract

An irregular grid model was employed to describe the refractive index distribution of an aerodynamically heated optical dome according to the theories of thermo-optical and elasto-optical effects. Optical transmission through the dome was simulated using the ray-tracing program based on a fourth-order Runge–Kutta algorithm. Two kinds of imaging quality evaluation parameters were presented, wave aberration of the exit pupil and a modulation transfer function. To validate the ray-tracing program, a ray trace through a regular gradient medium was performed. Results were compared with those obtained from the analytic solution. The program was shown to possess great accuracy by using the appropriate parameters.

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Physical Properties	Performance Parameters
Density ( $kg \cdot m^{- 3}$ )	3980
Melting point ( $° C$ )	2050
Expansion coefficient ( $10^{- 6} K^{- 1}$ )	5.3
Heat capacity ( $J \cdot {kg}^{- 1} \cdot K^{- 1}$ )	750
Young’s modulus ( $10^{9} Pa$ )	344
Thermal conductivity ( $W \cdot m^{- 1} \cdot K^{- 1}$ )	36
Poisson ratio	0.27
Mean strength ( $10^{6} Pa$ )	300

	Time
	$3 s$	$6 s$	$9 s$	$12 s$	$15 s$
$Δ n_{e}$	$6.81 \times 10^{- 4}$	$1.42 \times 10^{- 3}$	$2.10 \times 10^{- 3}$	$2.74 \times 10^{- 3}$	$3.35 \times 10^{- 3}$
$Δ n_{o}$	$6.05 \times 10^{- 4}$	$1.26 \times 10^{- 3}$	$1.87 \times 10^{- 3}$	$2.43 \times 10^{- 3}$	$2.97 \times 10^{- 3}$
$Δ n_{2}$	$- 8.20 \times 10^{- 7}$	$- 1.30 \times 10^{- 5}$	$- 2.53 \times 10^{- 5}$	$- 3.71 \times 10^{- 5}$	$- 4.85 \times 10^{- 5}$
$Δ n_{3}$	$5.66 \times 10^{- 6}$	$- 4.93 \times 10^{- 6}$	$- 1.57 \times 10^{- 5}$	$- 2.66 \times 10^{- 5}$	$- 3.71 \times 10^{- 5}$
$Δ n_{4}$	$3.67 \times 10^{- 6}$	$1.15 \times 10^{- 5}$	$1.90 \times 10^{- 5}$	$2.65 \times 10^{- 5}$	$3.38 \times 10^{- 5}$
$Δ n_{6}$	$- 1.69 \times 10^{- 6}$	$4.90 \times 10^{- 6}$	$1.18 \times 10^{- 5}$	$1.83 \times 10^{- 5}$	$2.46 \times 10^{- 5}$
$Δ n_{1}$	$1.75 \times 10^{- 6}$	$2.74 \times 10^{- 6}$	$3.55 \times 10^{- 6}$	$4.52 \times 10^{- 6}$	$5.53 \times 10^{- 6}$
$Δ n_{5}$	$- 3.05 \times 10^{- 6}$	$- 2.31 \times 10^{- 6}$	$- 1.26 \times 10^{- 6}$	$- 2.76 \times 10^{- 7}$	$6.16 \times 10^{- 7}$

	Time
	$3 s$	$6 s$	$9 s$	$12 s$	$15 s$
$Δ n_{e}$	$6.15 \times 10^{- 4}$	$1.30 \times 10^{- 3}$	$1.90 \times 10^{- 3}$	$2.46 \times 10^{- 3}$	$2.97 \times 10^{- 3}$
$Δ n_{o}$	$5.46 \times 10^{- 4}$	$1.15 \times 10^{- 3}$	$1.69 \times 10^{- 3}$	$2.18 \times 10^{- 3}$	$2.64 \times 10^{- 3}$
$Δ n_{3}$	$2.77 \times 10^{- 5}$	$5.31 \times 10^{- 5}$	$7.52 \times 10^{- 5}$	$9.48 \times 10^{- 5}$	$1.12 \times 10^{- 4}$
$Δ n_{2}$	$1.91 \times 10^{- 5}$	$3.75 \times 10^{- 5}$	$5.37 \times 10^{- 5}$	$6.85 \times 10^{- 5}$	$8.26 \times 10^{- 5}$
$Δ n_{6}$	$- 1.68 \times 10^{- 5}$	$- 3.28 \times 10^{- 5}$	$- 4.69 \times 10^{- 5}$	$- 5.95 \times 10^{- 5}$	$- 7.11 \times 10^{- 5}$
$Δ n_{5}$	$- 1.32 \times 10^{- 5}$	$- 2.55 \times 10^{- 5}$	$- 3.60 \times 10^{- 5}$	$- 4.53 \times 10^{- 5}$	$- 5.35 \times 10^{- 5}$
$Δ n_{4}$	$- 1.07 \times 10^{- 5}$	$- 2.07 \times 10^{- 5}$	$- 2.96 \times 10^{- 5}$	$- 3.78 \times 10^{- 5}$	$- 4.56 \times 10^{- 5}$
$Δ n_{1}$	$3.82 \times 10^{- 6}$	$7.55 \times 10^{- 6}$	$1.07 \times 10^{- 5}$	$1.35 \times 10^{- 5}$	$1.60 \times 10^{- 5}$

Physical Properties	Performance Parameters
Density ( $kg \cdot m^{- 3}$ )	3980
Melting point ( $° C$ )	2050
Expansion coefficient ( $10^{- 6} K^{- 1}$ )	5.3
Heat capacity ( $J \cdot {kg}^{- 1} \cdot K^{- 1}$ )	750
Young’s modulus ( $10^{9} Pa$ )	344
Thermal conductivity ( $W \cdot m^{- 1} \cdot K^{- 1}$ )	36
Poisson ratio	0.27
Mean strength ( $10^{6} Pa$ )	300

	Time
	$3 s$	$6 s$	$9 s$	$12 s$	$15 s$
$Δ n_{e}$	$6.81 \times 10^{- 4}$	$1.42 \times 10^{- 3}$	$2.10 \times 10^{- 3}$	$2.74 \times 10^{- 3}$	$3.35 \times 10^{- 3}$
$Δ n_{o}$	$6.05 \times 10^{- 4}$	$1.26 \times 10^{- 3}$	$1.87 \times 10^{- 3}$	$2.43 \times 10^{- 3}$	$2.97 \times 10^{- 3}$
$Δ n_{2}$	$- 8.20 \times 10^{- 7}$	$- 1.30 \times 10^{- 5}$	$- 2.53 \times 10^{- 5}$	$- 3.71 \times 10^{- 5}$	$- 4.85 \times 10^{- 5}$
$Δ n_{3}$	$5.66 \times 10^{- 6}$	$- 4.93 \times 10^{- 6}$	$- 1.57 \times 10^{- 5}$	$- 2.66 \times 10^{- 5}$	$- 3.71 \times 10^{- 5}$
$Δ n_{4}$	$3.67 \times 10^{- 6}$	$1.15 \times 10^{- 5}$	$1.90 \times 10^{- 5}$	$2.65 \times 10^{- 5}$	$3.38 \times 10^{- 5}$
$Δ n_{6}$	$- 1.69 \times 10^{- 6}$	$4.90 \times 10^{- 6}$	$1.18 \times 10^{- 5}$	$1.83 \times 10^{- 5}$	$2.46 \times 10^{- 5}$
$Δ n_{1}$	$1.75 \times 10^{- 6}$	$2.74 \times 10^{- 6}$	$3.55 \times 10^{- 6}$	$4.52 \times 10^{- 6}$	$5.53 \times 10^{- 6}$
$Δ n_{5}$	$- 3.05 \times 10^{- 6}$	$- 2.31 \times 10^{- 6}$	$- 1.26 \times 10^{- 6}$	$- 2.76 \times 10^{- 7}$	$6.16 \times 10^{- 7}$

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Tables (3)

Equations (20)

Applied Optics