Simulation and analysis of a multi-order imaging Fabry–Perot interferometer for the study of thermospheric winds and temperatures

Jonathan J. Makela; John W. Meriwether; Yiyi Huang; Peter J. Sherwood

doi:10.1364/AO.50.004403

Applied Optics
Vol. 50,
Issue 22,
pp. 4403-4416
(2011)
•https://doi.org/10.1364/AO.50.004403

Simulation and analysis of a multi-order imaging Fabry–Perot interferometer for the study of thermospheric winds and temperatures

Jonathan J. Makela, John W. Meriwether, Yiyi Huang, and Peter J. Sherwood

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Jonathan J. Makela, John W. Meriwether, Yiyi Huang, and Peter J. Sherwood, "Simulation and analysis of a multi-order imaging Fabry–Perot interferometer for the study of thermospheric winds and temperatures," Appl. Opt. 50, 4403-4416 (2011)

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Abstract

We describe an analysis procedure for estimating the thermospheric winds and temperatures from the multi-order two-dimensional (2D) interferograms produced by an imaging Fabry–Perot interferometer (FPI) as imaged by a CCD detector. We also present a forward model describing the 2D interferograms. To investigate the robustness and accuracy of the analysis, we perform several Monte Carlo simulations using this forward model for an FPI that has recently been developed and deployed to northeastern Brazil. The first simulation shows that a slight cross-contamination at high temperatures exists between neighboring orders in the interferogram, introducing a bias in the estimated temperatures and increasing errors in both the estimated temperatures and winds when each order is analyzed in full. The second simulation investigates how using less than an entire order in the analysis reduces the cross contamination observed in the first set of simulations, improving the accuracy of the estimated temperatures. The last simulation investigates the effect of the signal-to-noise ratio on the errors in the estimated parameters. It is shown that, for the specific FPI simulated in this study, a signal-to-noise ratio of 1.5 is required to obtain thermospheric wind errors of $5 m / s$ and temperature errors of $20 K$ .

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A	the area illuminated by the FPI on the CCD chip
$f_{o}$	the focal length of the lens on the system
d	the etalon separation
R	the reflectivity of the etalon
μ	the index of refraction in the etalon
$Ω_{i}$	the field of field of the ith spectral element
$θ_{i}$	the angle subtended by the ith spectral element [rad]
$Ψ (λ, θ_{i})$	the instrument function of the instrument
$Q_{i}$	the quantum efficiency of the ith spectral element
$T_{o i}$	the optical transmission of the instrument
$T_{F} (λ)$	the filter transmission function of the filter used to select the emission being studied
$Y (λ)$	the spectral distribution of the source emission being studied
$\bar{Δ λ_{F}}$	the spectral width of the interference filter used in the FPI
$T_{F o}$	the transmission of the filter passband at $λ_{l}$
t	the integration time
$C_{0 j}$	calibration factor for the jth spectral element [ $counts / (s Rayleigh)$ ]

$A_{i}$	the area of the ith annular region
$B_{i}$	the dark count background of the ith annular ring
$r_{i}$	the outer radius of the ith annular ring
$n_{annuli}$	the number of annular regions being considered
$a_{0 i}$ , $a_{n i}$ , and $b_{n i}$	the Fourier coefficients
$λ_{r}$	an arbitrary reference wavelength
$λ_{l}$	the observed wavelength of the Doppler-shifted emission
$λ_{0}$	the wavelength of the emission in the rest frame
$Δ λ_{0}$	the free spectral range (FSR) of the instrument at $λ_{0}$
$K_{laser}$	the number of spectral bins between two consecutive peaks in the laser interferogram (that is, in one FSR)
$K_{sky}$	the number of spectral bins between two consecutive peaks in the sky-emission interferogram (that is, in one FSR)

K	Boltzman's constant
m	the mass of the emitting particle
c	the speed of light
$ℜ_{0}$	the intensity of the $630.0 nm$ emission
$\frac{\partial ℜ}{\partial λ}$	the night sky continuum brightness [ $Rayleigh / Angstrom$ ]
λ	the wavelength of interest ( $630.0 nm$ in our case)
T	the temperature of the emitting region
v	the relative velocity between the receiver and the emitter
$v_{ref}$	a reference velocity measurement with zero-Doppler velocity

Parameter	Value
Etalon gap distance (d)	$1.5 cm$
Etalon gap index of refraction (μ)	1.0
Etalon reflectivity (R)	0.76
System field of view	$1.78 °$

A	the area illuminated by the FPI on the CCD chip
$f_{o}$	the focal length of the lens on the system
d	the etalon separation
R	the reflectivity of the etalon
μ	the index of refraction in the etalon
$Ω_{i}$	the field of field of the ith spectral element
$θ_{i}$	the angle subtended by the ith spectral element [rad]
$Ψ (λ, θ_{i})$	the instrument function of the instrument
$Q_{i}$	the quantum efficiency of the ith spectral element
$T_{o i}$	the optical transmission of the instrument
$T_{F} (λ)$	the filter transmission function of the filter used to select the emission being studied
$Y (λ)$	the spectral distribution of the source emission being studied
$\bar{Δ λ_{F}}$	the spectral width of the interference filter used in the FPI
$T_{F o}$	the transmission of the filter passband at $λ_{l}$
t	the integration time
$C_{0 j}$	calibration factor for the jth spectral element [ $counts / (s Rayleigh)$ ]

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