Simulation and application of the emission line O19P18 of O2(a1Δg) dayglow near 1.27 μm for wind observations from limb-viewing satellites

Kuijun Wu; Di Fu; Yutao Feng; Juan Li; Xiongbo Hao; Faquan Li

doi:10.1364/OE.26.016984

1. Introduction

Satellite remote sensing has remarkable advantages in global and long-term monitoring the dynamical state of the atmosphere [1, 2]. Both the Thermosphere, Ionosphere, Mesosphere, Energetics and Dynamics (TIMED) Doppler Interferometer (TIDI) [3] and the Wind Imaging Interferometer (WINDII) [4] prove that accurate wind profile observation is achievable by measuring the Doppler shift of airglow emissions. Molecular oxygen (O₂) emissions are among the brightest features of the airglow in the terrestrial mesosphere and lower thermosphere.

The atmospheric band emission ( $b {}^{1}Σ_{g}^{} \to X {}^{3}Σ_{g}^{}$ ) of O₂ observed in the visible and near infrared region is conventionally selected as a Doppler target for its extended altitude coverage and bright signal [5]. TIDI observes emissions from rotational lines P₁₁ pair in the O₂ (0-1) atmospheric band at 867 nm and P₉ pair in the (0-0) band at 762 nm to determine the Doppler shift and hence the wind from 60 to 85 km and 85 to 120 km respectively, with a statistical uncertainty of about 3-5 m/s [6]. The High Resolution Doppler Imager (HRDI) measure the Doppler shifts of the O₂ emission lines P₁₉Q₁₈ (13052.3228 cm⁻¹) P₁₃P₁₃ (13076.3273 cm⁻¹) and R₅Q₆ (13138.2048 cm⁻¹) in the (0-0) band of the $b {}^{1}Σ_{g}^{} \to X {}^{3}Σ_{g}^{}$ transition to obtain the wind profiles from about 50 to 120 km in the daytime [7]. The WINDII instrument using a Michelson interferometer to look at the small wavelength shifts of the P₇P₇ (13098.8482 cm⁻¹) and P₇Q₆ (13100.8217 cm⁻¹) airglow emission lines in the O₂ (0–0) atmospheric band at 763.2 nm for measurements of neutral winds over the altitude range 75-120 km [4].

The remarkable success of WINDII, HRDI and TIDI stimulates interest in taking measurements of neutral wind at lower altitudes to yield more altitude coverage. However, the atmospheric band emission ( $b {}^{1}Σ_{g}^{} \to X {}^{3}Σ_{g}^{}$ ) of O₂ in the altitude range below 50 km has no enough intensity, instead the infrared atmospheric band emission ( $a {}^{1}Δ_{g}^{} \to X {}^{3}Σ_{g}^{}$ ) at a wavelength of 1.27 μm might like to be considered for use. Differing from the $b {}^{1}Σ_{g}^{} \to X {}^{3}Σ_{g}^{}$ transition of O₂, the $O_{2} (a {}^{1}Δ_{g}^{})$ state is produced primarily by the process of O₃ photolysis in the Hartley band, and therefore provides a strong radiative signal and covers an altitude region between ~20 km and 120 km in the dayglow [8]. Owing to the relationship between the airglow intensity of $O_{2} (a {}^{1}Δ_{g}^{})$ and the O₃ concentration, which can be used to infer the O₃ concentration by measuring the distinct radiative signal of $O_{2} (a {}^{1}Δ_{g}^{})$ emission [9], there have been extensive space-based instruments aboard rockets and satellites, such as the METEORS [10], OSIRIS [11] and SABER [12].

As a matter of fact, the $O_{2} (a {}^{1}Δ_{g}^{})$ emission also provides one of the best spectral features for remote sensing of global atmospheric winds due to its bright signal and extended altitude coverage. The Mesospheric Imaging Michelson Interferometer (MIMI) instrument designed by York University takes advantage of a “strong” emission line pair and a “weak” pair in the (0-0) band of the O₂ $a {}^{1}Δ_{g}^{} \to X {}^{3}Σ_{g}^{}$ transition at 1.27 μm to cover the altitude range from 45 to 85 km for wind observations. The WAves Michelson Interferometer (WAMI), a variant of MIMI, also uses the combination of strong and weak emission lines in the $O_{2} (a {}^{1}Δ_{g}^{})$ infrared atmospheric band for the measurement of wind in the 45-100 km region [13]. Wind measurements on Mars and Venus using 1.27 μm band emission by the electronically excited $O_{2} (a {}^{1}Δ_{g}^{})$ state in the planetary atmosphere are also proposed [14–16]. The observing strategy of using two sets of three emission lines makes MIMI and WAMI ideally suited for simultaneous measurement of horizontal wind, rotational temperature and O₃ concentration with an altitude range of 45 km to 100 km, and therefore provides a perfect approach for probing the dynamics and investigating the odd oxygen chemistry of the lower thermosphere and middle atmosphere. However, for wind-only situations, single emission line with larger spectral separation range may be a more optimum choice due to its low requirement for spectral sampling interval, which would greatly increase the engineering feasibility of wind measuring interferometers.

In this paper, we describe the simulation and application of the emission line O₁₉P₁₈ of O₂(a¹Δ_g) dayglow near 1.27 μm for wind observations from limb-viewing satellites. A new-type interferometer, Doppler Asymmetric Spatial Heterodyne (DASH), is preferred for analysis of the wind precision of the target emission line. This sensor is designed to achieve an enhanced precision in measuring wind profiles from about 40 to 70 km in the daytime with significantly lower cost, risk, and platform requirements. Both multiple scattering radiative transfer and nonlocal thermal equilibrium (non-LTE) models are taken into account for accurate calculation of the absorption and emission line shapes in the O₂ infrared atmospheric band. Simulation results of interferogram images with and without the effect of the interference of the scattered sunlight background are presented. The Influences of four factors, the emitted to scattered radiance, the signal to noise, the limb-view weight and the interferogram contrast, on the wind measurement precision are also studied to assess the flexibility of this instrument concept, which indicates a wind measurement precision of about 2-4 m/s in the target altitude region.

2. The O₂ infrared atmospheric band emission

Remote sensing of airglow emissions has been implemented, and the inferred spectroscopic information and radiation characteristics have contributed significantly to the current understanding of the production and loss mechanisms of the electronically excited $O_{2} (a {}^{1}Δ_{g}^{})$ state in the atmosphere [9, 17, 18]. However, the reliability of the theoretical design of Wind measurement instruments by observing the O₂ infrared atmospheric band, to some extent, still depends on the accuracy of the chemical and radiance models used for calculating the $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0) \to O_{2} (X {}^{3}Σ_{g}^{}, υ^{″} = 0)$ band emission spectra.

2.1 The $O_{2} (a {}^{1}Δ_{g}^{})$ photochemistry and $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0)$ band emission rates

As illustrated in Fig. 1, in the mesosphere and lower thermosphere, there are two predominant mechanisms that produce the lowest-lying electronic state of molecular oxygen, $O_{2} (a {}^{1}Δ_{g}^{})$ , the photolysis of O₃ and the energy transfer from ${O(}^{1} D)$ , although a number of other processes are also important. $O_{2} (a {}^{1}Δ_{g}^{})$ radiates strong emission in the infrared atmospheric band $O_{2} (a {}^{1}Δ_{g}^{}) \to O_{2} (X {}^{3}Σ_{g}^{})$ at 1.27 μm, and is quenched upon collisions with O₂, N₂, and O [19].

Fig. 1 Dayglow production mechanism of the O₂ infrared atmospheric band.

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The $O_{2} (a {}^{1}Δ_{g}^{})$ number density, $n_{O_{2} (a {}^{1}Δ_{g}^{})}$ can be calculated assuming photochemical equilibrium

n_{O_{2} (a {}^{1}Δ_{g}^{})} = \frac{ϕ_{α} R_{1} [O_{3}] + \sum_{i = 1}^{5} K_{i} [Y_{i}] \frac{[O_{2}] {R_{2} + ϕ_{η} R_{3} [O (^{1} D)]}}{A_{O_{2} (b {}^{1}Σ_{g}^{})} + \sum_{i = 1}^{5} K_{i} [Y_{i}]}}{A_{O_{2} (a {}^{1}Δ_{g}^{})} + \sum_{i = 1}^{3} C_{i} [X_{i}]},

where

X = {O_{2}, N_{2},O}

,

Y = {N_{2} {,O}_{2}, C O_{2}, O_{3}, O}

,

0.54 < ϕ_{η} < 1.0

,

R_{1} = 8.1 \times 10^{- 3}

,

R_{2} = 5.35 \times 10^{-9}

,

R_{3} = 3.2 \times 10^{-11} \exp (70 / T)

,

K_{1} =2 .1 \times 10^{-15}

,

K_{2} =4 .2 \times 10^{-13}

,

K_{3} =2 .2 \times 10^{-11}

,

K_{4} =8 .0 \times 10^{-14}

,

K_{5} =3 .9 \times 10^{-17}

,

C_{1} =3 .6 \times 10^{-18} e^{- 220 / T}

,

C_{2} =1 .0 \times 10^{-20}

and

C_{3} =1 .3 \times 10^{-16}

.

The $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'})$ molecules can be vibrationally removed, electronically quenched, and radiatively lost to the $O_{2} (X {}^{3}Σ_{g}^{}, ν^{″})$ ground state. However, the excited vibrational states $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} \geq 1)$ are quenched into the $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)$ state much more rapidly than the electronic transition takes place. The modelled number density profiles of the excited vibrational states $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} \geq 0)$ is shown in Fig. 2. As illustrated, the vibrational distribution of the excited vibrational states $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} \geq 1)$ are negligible and the contribution from emission in the $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)$ state dominates the $O_{2} (a {}^{1}Δ_{g}^{})$ infrared atmospheric band

Fig. 2 Modelled number density profiles of the excited vibrational states. $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} \geq 0)$ .

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n_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)} \approx n_{O_{2} (a {}^{1}Δ_{g}^{})}

The local emission rate of the infrared atmospheric band $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0) \to O_{2} (X {}^{3}Σ_{g}^{}, υ^{″} = 0)$ , $η_{1.27 μm}$ depends on its vibrational distribution $n_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}$ and the Einstein transition probability $A_{1.27 μm}$ [12]

η_{_{1.27 μm}} = A_{1.27 μm} n_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)} .

2.2 Non-LTE population

The $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)$ state distribution is in chemical and collisional balance. Below 50 km, the production rate of the $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)$ state increases, however, thermal collisions are frequent enough, so that the loss rate of the $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)$ state through collisional quenching also increases and thus the distribution is strongly connected to the kinetic energy pool and can be given by the Boltzmann distribution. While, for altitude range more than 50 km, the distribution of $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)$ state is no longer a function of a single parameter, the kinetic temperature, because the thermal collisions are no frequent enough to dominate the level populations, and this condition is referred to as non-LTE.

The behavior of non-LTE population of a vibrational state can be described in the form of vibrational temperature, which defines the excitation degree of the excited vibrational state relative to the ground state. For the infrared atmospheric band $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0) \to O_{2} (X {}^{3}Σ_{g}^{}, υ^{″} = 0)$ , the vibrational temperature of the $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0)$ state can be expressed as [20]

T_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)} = \frac{E_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}}{k \ln (\frac{n_{O_{2} (X {}^{3}Σ_{g}^{}, ν^{″} = 0)}}{n_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}} \frac{g_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}}{g_{O_{2} (X {}^{3}Σ_{g}^{}, ν^{″} = 0)}})},

where

E_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}

is the vibrational energy of the

O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0)

state,

k

is the Boltzmann constant, and

g_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}

and

g_{O_{2} (X {}^{3}Σ_{g}^{}, ν^{″} = 0)}

refer to the statistical weight of the upper and lower state.

Fig. 3 The vibrational temperature of the $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0)$ state, as well as the kinetic temperature varies with the altitude.

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2.3 The Non-LTE absorption coefficient and source function

Under conditions of LTE, the distribution between two energy levels is determined by the kinetic temperature alone and thus the absorption coefficient for a two-level transition can be expressed as

\bar{α} (ν) = S (T_{K}) P ϕ (ν - ν_{0}, P, T_{K}, γ_{a i r}, γ_{s e l f}, n, δ) .

And the source function of a radiating system in the LTE case can be given by the Planck's law

B (ν, T_{K}) = 2 h c^{2} ν^{3} {[\exp (\frac{h c ν}{k T_{K}}) - 1]}^{- 1},

where

T_{K}

is the kinetic temperature, h is Planck’s constant, c is the speed of light and k is Boltzmann’s constant.

In the non-LTE case, the absorption coefficient and the source function can then be written as [21]

α (ν) = \bar{α} (ν) \frac{{\bar{n}}_{1}}{n_{1}} \frac{(1 - \frac{n_{2} g_{2}}{n_{1} g_{1}})}{(1 - \frac{{\bar{n}}_{2} g_{2}}{{\bar{n}}_{1} g_{1}})}

J (ν) = B (ν, T_{K}) \frac{n_{2}}{{\bar{n}}_{2}} \frac{α (ν)}{\bar{α} (ν)} .

For the infrared atmospheric band $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0) \to O_{2} (X {}^{3}Σ_{g}^{}, υ^{″} = 0)$ , $\frac{{\bar{n}}_{O_{2} (X {}^{3}Σ_{g}^{}, ν^{″} = 0)}}{n_{O_{2} (X {}^{3}Σ_{g}^{}, ν^{″} = 0)}} \approx 1$ , $\frac{n_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}}{{\bar{n}}_{O_{2} (X {}^{3}Σ_{g}^{}, ν^{″} = 0)}} \approx 0$ , $\frac{{\bar{n}}_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}}{{\bar{n}}_{O_{2} (X {}^{3}Σ_{g}^{}, ν^{″} = 0)}} \approx 0$ and $\frac{n_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}}{{\bar{n}}_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}} = \exp (- \frac{E_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}}{k} (\frac{1}{T_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}} - \frac{1}{T_{K}}))$ . Therefore, the absorption coefficient and the source function of the $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0) \to O_{2} (X {}^{3}Σ_{g}^{}, υ^{″} = 0)$ band become

α (ν) \approx \bar{α} (ν)

J (ν) \approx B (ν, T_{K}) \exp (- \frac{h c}{k} (\frac{1}{T_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}} - \frac{1}{T_{K}}) E_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}),

where

E_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)} = 7882.42 c m^{- 1}

is the vibrational energy of

O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0)

. The quantity hc/k has a numerical value of 1.438 cm K.

The radiance profile is a strong function of atmospheric state, such as temperature, pressure, gas abundance and solar zenith angle (SZA). Figure 4 shows the source functions of the $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0) \to O_{2} (X {}^{3}Σ_{g}^{}, υ^{″} = 0)$ band varying with altitude in both LTE and non-LTE cases under day-time condition (SZA = 30) for the summer illuminated atmosphere (January) at low latitude (10°S). As can be seen, the source function is determined by the kinetic temperature in the LTE case, but dominated by the difference between $T_{O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)}$ and $T_{K}$ under non-LTE condition.

Fig. 4 The source functions of the infrared atmospheric band vary with the altitude in both LTE and non-LTE cases.

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3. The spectral radiance and line-shape

In the case of limb-viewing simulation, the spectral radiance is typically a straightforward Abel-type integration of the source function profile along the line-of-sight path. However, for the infrared atmospheric band $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0) \to O_{2} (X {}^{3}Σ_{g}^{}, υ^{″} = 0)$ , the spectral radiance is modified by the attenuation due to the self-absorption of O₂ molecules in the ground state. In addition, solar radiation elastically scattered by aerosols (Mie) and molecules (Rayleigh) will contribute to the limb-measured spectral radiance, especially at low tangent heights. Therefore, the airglow emission and the scattered sunlight, as well as the self-absorption for both emitted and scattered radiance, should be taken into account for accurate simulation of the observed infrared atmospheric band spectral radiance.

3.1 The airglow emission spectral radiance

The monochromatic radiance $I (ν, z_{o b s})$ at wavenumber $ν$ can be calculated according to [21]

I (ν, z_{o b s}) = \int_{z_{s}}^{z_{o b s}} [J (ν, z) α (ν, z) n (z)] τ (ν, z, z_{o b s}) d z,

where z is a certain position along the limb line of sight between the point z_s at the furthest extent of the limb and the observation point z_obs, and

n (z)

is the number density of O₂ molecules.

The transmittance between z and z_obs, can be defined as

τ (ν, z, z_{o b s}) = e x p (- \int_{z_{s}}^{z_{o b s}} α (ν, z^{'}) n (z^{'}) d z^{'}) .

For the multilayer atmospheres, each viewing direction defines a ray path. The path segments allocated for the target absorbing specie are defined by the intersection of each of these ray paths with the profile levels. In the case of limb-viewing, the tangent point also serves to delimit path segments. Figure 5 illustrates the construction of the path model. The inhomogeneous atmospheric layer within each path segment is assumed to have the same absorption and emission characteristics and represented by an equivalent homogeneous path.

Fig. 5 Construction of path segments for the limb-viewing geometry.

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For a line-by-line code, the integral over z can be divided into a sum over discrete thin layers l, for in order to treat each layer as approximately homogeneous and characterized it by an appropriate mean temperature and pressure. Therefore, the radiative transfer equation evaluated on the layer-by-layer basis can be expressed as

I {(ν)}_{l} = I {(ν)}_{l - 1} \exp (- α {(ν)}_{l} u_{l}) + J {(ν)}_{l} α {(ν)}_{l} n_{l} \int_{z_{L}}^{z_{U}} τ (ν, z, z_{U}) d z,

where

z_{U}

and

z_{L}

are the upper and lower boundaries of layer l, and

u_{l} = n_{l} (z_{U} - z_{L})

is the layer O₂ molecules amount.

An important mathematical expression playing a fundamental role in radiative transfer is the transmittance contained in the integrand of Eq. (12), i.e.,

\int_{z_{L}}^{z_{U}} τ (ν, z, z_{U}) d z = \frac{1}{α {(ν)}_{l} n_{l}} [1 - e x p (- α {(ν)}_{l} u_{l})] .

Then the radiative transfer equation for a line-by-line calculation involving many lines i becomes

I {(ν)}_{l} = I {(ν)}_{l - 1} \exp (- \sum_{i} α {(ν)}_{l, i} u_{l}) + \frac{\sum_{i} J {(ν)}_{l, i} α {(ν)}_{l, i} u_{l}}{\sum_{i} α {(ν)}_{l, i} u_{l}} [1 - e x p (- \sum_{i} α {(ν)}_{l, i} u_{l})] .

Figure 6 shows the calculated spectral radiance of the infrared atmospheric band at tangent heights of 30, 50, 70, 90 km, respectively, assuming there is no velocity induced shift between atmospheric wind and the limb-viewing satellite. The spectral line brightness neglecting the self-absorption is also shown for comparison. As illustrated, even at relatively high tangent heights (up to ~70 km), the self-absorption is still significant. The absorber $O_{2} (X {}^{3}Σ_{g}^{}, υ^{″} = 0)$ in the atmosphere along the line of sight can be optically thick for a large portion of the infrared atmospheric band, making utilization of this portion of the band difficult and impractical for many applications at low tangent heights. For tangent heights between 35 and 70 km, the atmospheric temperature is relatively high, and therefore, the Boltzmann distribution forces a more dispersed population, increasing the relative strength of radiative transitions associated with high lower-state energies. This makes the lines in the red far wing (between 7750 cm⁻¹ and 7820 cm⁻¹) candidate for wind detection, because their emission spectra suffer little from self-absorption. The emission line O₁₉P₁₈ (7772.030 cm⁻¹) in this attractive wavelength region is the optimum detection among the main group of candidate lines for its relatively larger spectral separation range, which leads to significantly lower cost, risk, and platform requirements.

Fig. 6 The emission spectra of the O₂ infrared atmospheric band at tangent heights of 30 km, 50 km, 70 km and 90 km (with and without the effect of self-absorption).

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3.2 The scattered sunlight background

The scattered sunlight background plays a key role in spectral interference for the dayglow observations from limb-viewing satellites. This absorption features can be observed when solar radiation is elastically scattered by aerosols (Mie) and molecules (Rayleigh) into the field of view of the observer.

A variety of techniques have been developed for computing the intensity of scattered light. In order to carry out theoretical simulations of the line shapes to be measured by HRDI. Abreu et al. developed a line-by-line multiple scattering radiative transfer code to calculate the scattering spectrum in the A, B, and γ bands of the atmospheric system ( $b {}^{1}Σ_{g}^{} \to X {}^{3}Σ_{g}^{}$ ) [7]. This technique is quite accurate and computationally intensive, and therefore attracts us to use this multiple scattering model to simulate the scattered sunlight background in the infrared atmospheric band.

The development of this model is based on the complex assumption that light scattered by the atmosphere not only comes directly from the Sun or the light reflected by the surface below, but also contains multiple scattering contributions. In computing the scattered sunlight background, incorporating the effects of multiple scattering is a major difficulty. Doubling and adding techniques were used to solve the radiative transfer equations. Details of technique and model concept are presented in [7]. Figure 7 shows the calculated spectral radiance of the scattered sunlight background in the red far wing of the fundamental band at tangent heights of 20, 30, 40, 50 km, respectively. As illustrated, the scattered sunlight gets stronger as the tangent height decreases and the scattering spectrum is strongly marked by rotational lines of the infrared atmospheric band of molecular oxygen.

Fig. 7 The scattered sunlight radiance in the red far wing of the O₂ infrared atmospheric band at tangent heights of 20 km, 30 km, 40 km and 50 km.

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3.3 The total spectral radiance

Depending on the atmospheric region, the infrared atmospheric band can be observed both in emission and absorption. The airglow emission spectral radiance is calculated separately assuming attenuation by self-absorption and single scattering, and the spectral radiance of the scattered sunlight background is also calculated using the radiative transfer model described above. The two components are then combined to give the total radiance in both emission and absorption, which is shown in Fig. 8. As illustrated, the rotational lines are relatively broad at low altitudes, but dominated by emission features at higher altitudes, and become narrower and sharper as the tangent heights increase.

Fig. 8 The total spectral radiance in the red far wing of the O₂ infrared atmospheric band as a function of tangent height.

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It is also interesting to compare the line center intensity and asymptotic radiance changing over the tangent height altitude, which is shown in Fig. 9. The line center intensity changes as a function of tangent height due to the combined effects of emission, absorption, and scattering, while the asymptotic radiance relates only to scattering. The asymptotic radiance approximately shows an exponentially decline trend with the tangent height, due to the variation of scattering radiance with altitude coincides with power function. However, the effect of altitude was not so equally obvious for the line center intensity. Because the distribution of $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)$ state is subject to non-LTE population (as shown in Fig. 3), although the atmospheric density decreases exponentially with altitude.

Fig. 9 The line center and asymptotic intensities vary with tangent height.

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4. Simulations of science measurements

The recent technical availability of new-type interferometer, Doppler Asymmetric Spatial Heterodyne (DASH), offers the possibility of applying a high-stability and high-resolution spectroscopy measurement method on Doppler-shift measurements of atmospheric emission lines [22–26]. Therefore, we use the DASH interferometer to assess the measurement precision of the emission line O₁₉P₁₈ of O₂(a¹Δ_g) dayglow for wind observations from limb-viewing satellites.

A single row of the interferogram recorded by the DASH array detector can generally be written as [27]

S (x) = \frac{1}{2} \int_{0}^{\infty} I (ν) [1 + \cos {2 π [4 (ν - ν_{L}) \tan θ_{L}] \times [x + \frac{Δ d}{2 \tan θ_{L}}]}] d ν,

where

θ_{L}

is the Littrow angle of the gratings, x is the location on the detector array related to optical path difference OPD (x = 0 is the center of the array),

Δ d

is the offset of an arm in the interferometer, and

ν_{L}

is the Littrow wavenumber.

The simulated interferogram images of the rotational emission line O₁₉P₁₈ in the red far wing of the O₂ infrared atmospheric band is shown in Fig. 10. A narrow bandpass filter with a full width at half maximum (FWHM) of 1 nm is used to isolate the target emission line. In order to analyze the influence of the scattered sunlight background, we take the airglow emission spectral radiance into account in Fig. 10(a), and for comparison, the total spectral radiance with the influence of sunlight radiance scattered by the atmosphere is considered in Fig. 10(b). The vertical axis represents the tangent altitude, and the horizontal axis contains spectral information. The increasing optical path difference along the horizontal axis of the CCD array produces fringe pattern. Three major noise sources, including shot noise, readout noise and detector dark noise, are taken into account in the simulation of the interferogram images, with specifications listed in Table 1. The phase of the fringe pattern is affected by the line-of-sight wind and the average intensity is related to the spectral density of the incident radiation. The Doppler shift of each line resulting from the variation of wind in the vertical direction could cause slight changes in the phase of the interferogram. However, the spectral interference of the scattered radiance will increase the difficulty in the extraction of the phase change. As illustrated in Fig. 10, the scattered sunlight background, an interfering and meaningless signal, decreases the contrast of the interferogram obviously due to the broad band nature of the scattered signal, especially at low tangent heights.

Fig. 10 The simulated interferogram images of the emission line O₁₉P₁₈ of the O₂(a¹Δ_g) dayglow (with and without the effect of the spectral interference of the scattered sunlight background).

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Table 1. The basic parameters of the DASH interferometer

View Table

The basic parameters of the DASH interferometer involved in the simulation is shown in Table 1.

Four ratio values, the emitted to scattered radiance, the signal to noise, the limb-view weight and the interferogram contrast, work together to affect the precision of wind measurement. The first factor, emitted and scattered radiances, is illustrated in Fig. 9 and the other three factors varying with the tangent altitude are shown in Fig. 11. The growing scattered sunlight background at low tangent heights leads to an increase of signal to noise ratio, but a decrease of interferogram contrast. In addition, the limb-view weight also decreases with the tangent height reduction, resulting from the attenuation of the $O_{2} (a {}^{1}Δ_{g}^{}, ν^{'} = 0)$ state density at low tangent height.

Fig. 11 The signal to noise ratio, the limb-view weight and the interferogram contrast vary with tangent altitude.

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The limb-view weight and interferogram contrast increase with the rising of the tangent height, which leads to an increase of measurement precision in wind observations. While the decrease of signal to noise ratio at higher tangent altitude reduces the precision of wind measurement. The wind precision varying with the tangent altitude is shown in Fig. 12. The wind precision without the scattered sunlight background remains approximately constant with a value of 1-2 m/s for the altitude range of 40-70 km, increasing from 3 to 5 m/s as the altitude increases from 70 to 80 km or from 40 to 30 km. The presence of the spectral interference of the scattered radiance decreases the wind measurement precision at all altitudes with the largest impact, especially for altitudes below 40 km.

Fig. 12 Calculated wind precision profiles along the line of sight (with and without the effect of the spectral interference of the scattered sunlight background).

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In order to show the flexibility of this instrument which uses the emission line O₁₉P₁₈ of O₂(a¹Δ_g) dayglow for wind observations, the signal to noise ratio and the wind precision varying with tangent height under day-time condition at four seasons is simulated by taking the mid-latitude (45°N) for example. As can be seen from Fig. 13, there are only minor differences between different seasons both for the signal to noise ratio and the wind precision profiles. The signal to noise ratio for the summer illuminated atmosphere (July) is slightly larger at high tangent altitude compared with the other three seasons. This is a consequence of larger solar illumination at north latitude in summertime, because the daytime airglow near 1.27 μm originates mainly from the production of the O₂(a¹Δ_g) state through photolysis of ozone. However, the wind precision at low tangent altitude is not satisfactory, especially for summer time conditions. This results from the fact that large scattered sunlight background leads to well signal to noise ratio, but poor interferogram contrast, shown as Fig. 11(b).

Fig. 13 The signal to noise ratio and the wind precision vary with tangent height under day-time condition at mid-latitude (45°N) for the four seasons (January, April, June, and October).

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5. Conclusions

We have simulated the spectral features of O₂ dayglow at 1.27 μm, proved the emission line O₁₉P₁₈ (7772.030 cm⁻¹) to be suitable for wind detection from limb-viewing satellites and analyzed the wind precision of this target emission line. We first developed a radiative transfer model by taking the effects of non-LTE and multiple scattering into account to simulate the emission spectral radiances of O₂ dayglow in the case of limb-viewing. The $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0)$ band emission rates was calculated by a photochemical model incorporating the most recent spectroscopic parameters, solar fluxes and rate constants. The vibrational temperature profile of the $O_{2} (a {}^{1}Δ_{g}^{}, υ^{'} = 0)$ state was then obtained to describe the behavior of non-LTE population of this vibrational state. Formulas for the absorption coefficient and source function calculation under conditions of the non-LTE case were carried out in detail. It was shown that the source function of the infrared atmospheric band in non-LTE differed greatly from the Planck's law, while the absorption coefficient changed little. The emission line O₁₉P₁₈ in the red far wing of the O₂ infrared atmospheric band was proved to be suitable for wind detection for limb-viewing satellites, because of its weak self-absorption and bright radiation intensity, as well as large spectral separation range. We also modeled the scattered sunlight background to analyze its spectral interference for the dayglow observations. It was apparent from the simulations that the rotational lines in the O₂ infrared atmospheric band can be observed both in absorption and emission, the latter dominating over about 40 km. A DASH-type interferometer was adopted to analyze the wind precision of emission line O₁₉P₁₈ due to its advantages of state-of-the-art optical techniques while avoiding some of their limitations. Interferogram images with and without the effect of the spectral interference from the scattered sunlight background were presented. The simulated results indicated that the wind precision with ignoring the presence of the scattered sunlight background was about 1 to 2 m/s for the altitude range of 40-70 km, increasing from 2 to 5 m/s as the altitude increased from 70 to 80 km or decreased from 40 to 30 km. The presence of the spectral interference of the scattered radiance lowered the wind precision, especially for altitudes below 40 km. The signal to noise ratio and the wind precision was also simulated at different seasons, which indicated the good flexibility of interferometer instruments by using the emission line O₁₉P₁₈ of O₂(a¹Δ_g) dayglow for wind observations.

Funding

National Natural Science Foundation of China (NSFC) (61705253, 41005019); Open Research Fund of Key Laboratory of Spectral Imaging Technology, Chinese Academy of Sciences (LSIT201701D); The West Young Scholar of CAS (No.XAB 2016A07).

Acknowledgments

The authors gratefully acknowledge informative and helpful discussions with Wang Dingyi on theoretical details of this work.

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Parameters	Value
Satellite Orbital Altitude	645 km
Exposure Time	27 s
Pixel Pitch	30 μm
Vertical Pixel Number	1024
Horizontal Pixel Number	240
Vertical Pixel Binning	8 pixels
Horizontal Pixel Binning	N/A
Vertical Resolution	2 km
Horizontal Resolution	200 km
Interferometer Optical Path	5.0 cm
Spectral Sampling Interval	0.11 nm
Total Etendue	0.0482 cm² sr
Optical Efficiency	0.45
Grating Efficiency	0.6
Readout Noise	20 electron
Detector dark noise	10 electron
Quantum efficiency (QE)	0.6 electron photon⁻¹

Simulation and application of the emission line O₁₉P₁₈ of O₂(a¹Δ_g) dayglow near 1.27 μm for wind observations from limb-viewing satellites

Abstract

1. Introduction