Effect and suppression of secondary fringes in FATWindII

Chunmin Zhang; Haishan Dai; Tingkui Mu; Yan Qu

doi:10.1364/AO.51.004186

Applied Optics
Vol. 51,
Issue 18,
pp. 4186-4195
(2012)
•https://doi.org/10.1364/AO.51.004186

Effect and suppression of secondary fringes in FATWindII

Chunmin Zhang, Haishan Dai, Tingkui Mu, and Yan Qu

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Chunmin Zhang, Haishan Dai, Tingkui Mu, and Yan Qu, "Effect and suppression of secondary fringes in FATWindII," Appl. Opt. 51, 4186-4195 (2012)

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Abstract

By considering the instrument as a complex operator on the incident electric field, a model to calculate secondary fringes of the Field-widened, Achromatic, Temperature-compensated Wind Imaging Interferometer (FATWindII) has been built. The distribution of secondary fringes on a charge coupled device detector has been plotted. The effects of secondary fringes on inversion errors of temperature and wind velocity have been presented. The results show that antireflection coating on the air/glass interface cannot meet the accuracy requirement of FATWindII. A theoretical method for calculating the optimal wedge angles of compensating glasses is derived to suppress the secondary fringes while preserving the primary ones. By adopting both methods, coating with antireflection film and shaping wedge compensating glasses, the relative intensity of secondary fringes is reduced to below 2.5% and the inversion errors of temperature and wind velocity introduced by the effects of secondary fringes can be minimized to about 0.05 K and $0.045 {ms}^{- 1}$ , respectively.

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	Material	Refractive Indexa	Thickness (mm)	Optical Path (mm)b
Beam splitter	BK7	$n_{1} / 1.51509$	$g_{0} / 50.8000$	153.8413
Compensating glasses 1	N-LaF21	$n_{2} / 1.78454$	$g_{1} / 65.2867$	232.9132
Compensating glasses 2	LF5	$n_{0} / 1.57851$	$g_{3} / 60.7636$	191.7264
Air gap	Air	1.00000	$g_{2} / 1.91000$	3.8148
Thermal compensation	$65.248 \times 10^{- 6} mm / K$

Original OPD ( $S_{k}$ )		Transmittance ( $T_{k}$ )	OPD Modification Factor ( $a_{k}$ )
$S_{1}$	$Δ$	$1 / ε_{0} c \cdot t_{1} t_{2}$	$2 [(n_{1} - 2) α - (n_{2} - 1) β]$
$S_{2}$	$2 d_{1}$	$1 / ε_{0} c \cdot t_{1}^{'} t_{1}^{''}$	$- 4 α$
$S_{3}$	$d_{1}$	$1 / ε_{0} c \cdot (t_{1} t_{1}^{'} + t_{1} t^{''})$	$- 2 α$
$S_{4}$	$Δ - d_{1}$	$1 / ε_{0} c \cdot t_{1}^{'} t_{2}$	$2 [(n_{1} - 1) α - (n_{2} - 1) β]$
$S_{5}$	$Δ + d_{1}$	$1 / ε_{0} c \cdot t_{1}^{''} t_{2}$	$2 [(n_{1} - 3) α - (n_{2} - 1) β]$

	Material	Refractive Indexa	Thickness (mm)	Optical Path (mm)b
Beam splitter	BK7	$n_{1} / 1.51509$	$g_{0} / 50.8000$	153.8413
Compensating glasses 1	N-LaF21	$n_{2} / 1.78454$	$g_{1} / 65.2867$	232.9132
Compensating glasses 2	LF5	$n_{0} / 1.57851$	$g_{3} / 60.7636$	191.7264
Air gap	Air	1.00000	$g_{2} / 1.91000$	3.8148
Thermal compensation	$65.248 \times 10^{- 6} mm / K$

Original OPD ( $S_{k}$ )		Transmittance ( $T_{k}$ )	OPD Modification Factor ( $a_{k}$ )
$S_{1}$	$Δ$	$1 / ε_{0} c \cdot t_{1} t_{2}$	$2 [(n_{1} - 2) α - (n_{2} - 1) β]$
$S_{2}$	$2 d_{1}$	$1 / ε_{0} c \cdot t_{1}^{'} t_{1}^{''}$	$- 4 α$
$S_{3}$	$d_{1}$	$1 / ε_{0} c \cdot (t_{1} t_{1}^{'} + t_{1} t^{''})$	$- 2 α$
$S_{4}$	$Δ - d_{1}$	$1 / ε_{0} c \cdot t_{1}^{'} t_{2}$	$2 [(n_{1} - 1) α - (n_{2} - 1) β]$
$S_{5}$	$Δ + d_{1}$	$1 / ε_{0} c \cdot t_{1}^{''} t_{2}$	$2 [(n_{1} - 3) α - (n_{2} - 1) β]$

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Applied Optics