Abstract

Building a wide-area, high-efficiency, and accurate detection technology for air targets has become a new challenge for the construction of space situational awareness. Firstly, based on the space-based optical detection requirements for aircraft plume, the method of integrated modeling for sea/cloud background radiation characteristics based on coupling of remote sensing data and physical model is proposed, which can effectively deduce the background radiation field distribution under any environmental conditions. Specifically, combined with meteorological satellite sensor data, such as cloud top temperature, cloud type and cloud top height, three-dimensional atmospheric transmittance and atmospheric path thermal radiation texture are generated for different cloud heights and cloud phase conditions. Then, a coupled sea/cloud bidirectional reflectance model matched to the sampling of space-based detectors is established. Further, the accurate prediction model for multi-spectral imaging features of aircraft plume is built by considering the space-based full imaging chains including the complex coupling of aircraft plume, sea/cloud background, environmental atmosphere, optical system, and imaging detector. Finally, combined with the diffraction effect of the optical system, the multi-spectral imaging features of the aircraft plume are simulated under various spectral bands, flying heights, sea/cloud backgrounds, and detection angles, and the detection performances are analyzed and discussed by using the signal-to-clutter ratio (SCR). Research results show that the detection capability in the narrow band of 2.65–2.90µm and 4.25–4.50µm is better than the wide band of 3–5µm. When the aircraft flying height is greater than 5km, the aircraft plume can be detected in both narrow bands. It is more reliable to use the multispectral joint-band to detect aircraft plume in different backgrounds.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The infrared imaging satellite located in the geostationary orbit has the unique advantage of early detection, good quality observation line of sight, and high coverage efficiency, and is an effective means to improve the ability of reconnaissance and surveillance. When the aircraft plume is detected from space-based platform, the background in the field of view mainly includes Earth’s surface radiation and cloud radiation. The cloud background has a strong upward scattering effect and interferes with satellite detection. Therefore, integrated modeling for sea/cloud background radiation characteristics is of great significance for accurate prediction and analysis of aircraft plume imaging features.

In order to accurately predict the multi-spectral imaging features of the aircraft plume, it is necessary to have a comprehensive understanding of the radiation characteristics of the background and aircraft plume. In the modeling of background radiation characteristics, the influence of the main microphysical characteristics of water and ice clouds, including the effective size, the liquid water content, ice-crystal model, and the concentration of particles, on the optical properties of the cloud was discussed [1,2]. Both single and multiple light-scattering properties of water and ice clouds were presented for radiative transfer calculations and remote sensing of cloud [3,4]. A technique was described that uses a ground-based thermal infrared imager to provide continuous day-night cloud detection and classification according to the cloud optical depth and attenuation [5]. The sea surface reflection characteristics under different wind speed and solar zenith angle were studied [6,7]. Several researchers have made progress in the modeling and measurement of aircraft plume radiation characteristics from the following aspects. In-flight aircraft plume radiance recordings were exploited by Retief [8] to construct a three dimensional radiance model of the plume. A detailed geometrical and spatially distributed radiometric model was used to model the aircraft plume, and the radiation characteristics of the aircraft plume was simulated [9]. In the analysis of the detection performance, Shen X [10] discussed the detection capability of the Low-orbit infrared imaging system for the space target in the long wave infrared range. Caroline Schweitzer [11] analyzed the IR-bands suitable for missile detection by trading off the suppression of background signature against threat signal strength, and discussed the influence on the SCR caused by different observation scenarios and varying spatial resolution. The detectability of the infrared imaging system in the geostationary orbit for aircraft targets based on the coupling of the spatial resolution to point spread function was studied [12]. However, in the current open literature, the coupling modeling of aircraft plume and background was too ideal to accurately predict the multi-spectral imaging features of targets. The study of the target and background radiation characteristics were separated from the detection capability of the space-based system, which failed to form the full imaging chain including aircraft plume, sea/cloud background, atmosphere, optical system, space-based detector. A comprehensive theoretical analysis of the various factors that affect the infrared imaging of aircraft plumes as observed from geostationary orbit was rarely proposed.

In view of the above, a method of integrated modeling for sea/cloud background radiation characteristics coupled with remote sensing data and physical model is proposed, which can effectively deduce the background radiation field distribution under any environmental conditions. The imaging model of sea/cloud background matched with sampling of space-based detectors is established. An accurate prediction platform for the digital full imaging chain is formed. The research results can provide data support for the development of intelligent algorithms for realizing the detection, tracking and identification of air targets in the geostationary orbit, and theoretical basis for system parameter design of geostationary infrared imaging system.

2. Modeling of full imaging chain of sea/cloud background and aircraft plume

2.1 Spectral band analysis for aircraft plume detection

The selection criterion for the detection band is that the contrast between the target and the background is the largest. The target can be captured by the infrared imaging system under certain conditions of SCR which is an important parameter for evaluating the infrared detection system. The formula for calculating the local SCR of the target and background in the scene is as follows:

$$SCR = \frac{{{{\bar{I}}_t} - {{\bar{I}}_b}}}{{{\sigma _b}}}$$
where ${{\bar{I}}_t}$ is mean of target radiation intensity, ${{\bar{I}}_b}$ is mean of background radiation intensity in the range where the target location is 2 times larger than the target, σb is the background variance when the background range is 2 times larger than the target. The temperature of the aircraft plume is about 600K–1000 K, which is much higher than the background temperature. According to the Planck formula, the emitted radiation of the aircraft plume in the mid-wave infrared regions is the largest. Meantime, when the aircraft plume is detected by the infrared imaging system, the atmospheric attenuation at different flight heights is different. Figure 1 shows the atmospheric transmission between the detector in geostationary orbit and the target at different heights.

 

Fig. 1. Atmospheric transmittance.

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As shown in Fig. 1, when the flying height is less than 5 km, ground background clutter is well shielded by the atmosphere in the narrow band of 2.65–2.90µm and 4.25–4.50µm, but the target radiation is basically shielded. When the flight altitude is more than 10 km, the attenuation effect of the atmosphere on the aircraft plume radiation is gradually weakened, but the ground background radiation is completely shielded. The difference between the target and the background radiation is large, and the aircraft plume is easy to detect. Therefore, this paper uses three detection bands of narrow band 2.65–2.90µm, 4.25–4.50µm and wide band 3–5µm to discuss the best detection conditions.

2.2 Modeling of sea/cloud background upward radiation characteristics based on coupling of remote sensing data and physical model

When the aircraft is detected from the space-based platform, the total background radiation is a superposition of the following five sources: self-radiation of the cloud top, the scattering of solar radiation by the cloud top, the radiation of the sea surface through the clouds, the radiation reflected by the sea surface through the clouds, and the atmospheric path radiation. The total background radiation field received by the detector can be expressed as:

$${L^ \uparrow }_{bkg}(\lambda )= {Z_e}{\tau _{c - d}}{L^ \uparrow }_c(\lambda )+ {Z_e}{\tau _{s - c - d}}{L^ \uparrow }_s(\lambda )+ ({1 - {Z_e}} ){\tau _{s - d}}{L^ \uparrow }_s(\lambda )+ {L^ \uparrow }_a(\lambda )$$
where Ze is the proportion of the cloud in the field of view; τc-d is the atmospheric transmittance from the cloud top to the detector in the detection direction; τs-c-d and τs-d are the atmospheric transmittance of the sea surface to the detector in the detection direction when there are clouds and cloudless above the sea surface; Lc is the upward radiation of the cloud; Ls is the upward radiation of the sea surface, and La is the atmospheric path radiation. Figure 2 shows a diagram of an aircraft target being detected by an infrared system in the geostationary orbit.

 

Fig. 2. Infrared system in the geostationary orbit for aircraft target detection.

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In Fig. 2, Esun is the solar irradiance, Lt is the target radiation, Ht is the flying height of the target, Hc-bottom is the cloud bottom height, Hc-thickness is the cloud thickness, da is the distance between the cloud top and the detector, and dc is the cloud thickness in the detection direction.

2.2.1 Modeling of cloud self-radiation

The cloud absorbs solar radiation and radiates energy through its own temperature. The thermal radiation of the cloud can be expressed as:

$$L{ \uparrow _{cloud,self}}(\lambda )={\varepsilon _{cloud}}(\lambda )\frac{{M({{T_{cloud}},\lambda } )}}{\pi }$$
where εcloud is the cloud emissivity; M(Tcloud,λ) is the radiant exitance of blackbody when the cloud top temperature is Tcloud and the wavelength is λ.

According to the physical parameters such as the external shape and internal composition of the cloud, common cloud types are divided into: cirrostratus, stratocumulus, cumulonimbus, altostratus, and cirrus. The cirrostratus and cirrus are ice clouds, and the rest are water clouds. In order to analyze the infrared radiation characteristics of different cloud types, the intrinsic radiation of water cloud and ice cloud are established based on the coupling of cloud top emissivity models and FY-2G cloud classification and temperature data. Figure 3 shows the inversion results of cloud top temperature and cloud classification on December 20, 2017 at local time of 12:00.

 

Fig. 3. (a) Cloud top temperature. (b) Cloud classification.

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If the scattering with respect to the absorption of radiation in a cloud layer can be neglected, the emissivity of a cloud of thickness z at the wavelength λ can be defined as:

$${\varepsilon _{cloud}}(\lambda ) = 1 -\textrm{exp}\left[ { - \int_{{z_1}}^{{z_2}} {{\sigma_a}(z )dz} } \right]$$
where σa is the infrared absorption coefficient, z1 is the cloud-base height, z2 is the cloud-top height. If the particle distribution in the cloud layer is isotropic, Eq. (4) can be simplified as:
$${\varepsilon _{cloud}}(\lambda )= 1 -\textrm{exp}({ - kz} )$$
where k is the absorption coefficient, z is the cloud thickness. For water cloud, the absorption coefficient can be defined as:
$${k_{water - cloud}}(\lambda )=\pi \int_{{r_1}}^{{r_2}} {{r^2}{Q_{abs}}({\lambda ,r} )n(r )dr}$$
where r is a radius of the water droplet, n(r) is a droplet’s size distribution and Qabs is the normalized absorption cross section. For ice cloud, the absorption coefficient can be defined as:
$${k_{ice - cloud}}(\lambda )=({1 - w} )\beta$$
where β is the extinction coefficient, w is the single scattering albedo. Figure 4 shows the spectral emissivity of water clouds and ice clouds.

 

Fig. 4. Spectral emissivity of water clouds and ice clouds. The effective radius of the water cloud (reff,water) is 5µm, and the effective radius of the ice cloud (reff,ice) is 50µm.

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2.2.2 Modeling of cloud reflection radiation

The cloud layer contains a large number of ice-water particles of different scales and shapes, which have a strong scattering effect on the sun and may cause interference to the detection of the aircraft plume. Cloud reflection radiation should be considered with emphasis. Bidirectional reflection distribution function (BRDF) is introduced to measure the reflection ability of the cloud top under different solar incident angles and detection angles. The reflection radiation of water cloud and ice cloud are established based on the coupling of BRDF models and FY-2G cloud classification and solar irradiance data.

$${L^ \uparrow }_{cloud,refl}(\lambda )= {\tau _{S - c}}(\lambda ){E_{sun}}\cos {\theta _i}BRD{F_{cloud}}({\lambda ,{\theta_i},{\varphi_i},{\theta_r},{\varphi_r}} )$$
where τS-c is the atmospheric transmittance from the sun to the cloud top; BRDFcloud is the cloud bidirectional reflectivity; θi(φi) and θr(φr) are the incident zenith (azimuth) angle and the reflection zenith (azimuth) angle. Figure 5 shows the solar incident irradiance at the cloud top.

 

Fig. 5. Solar incident irradiance at the cloud top.

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The validity of the plane-parallel cloud model and the suitability of water droplet and ice polycrystal phase functions for stratocumulus and cirrus clouds were verified [13]. Single scattering in an homogeneous slab admits an analytical solution that can be expressed by [14]:

$$BRDF({{\theta_i},{\varphi_i},{\theta_r},{\varphi_r}} )= \frac{w}{{4\pi }}P(\Theta )\frac{{\textrm{cos}{\theta _i}}}{{\textrm{cos}{\theta _i} + \textrm{cos}{\theta _r}}}$$
where P(Θ) is the effective scattering phase function of the cloud, Θ is the actual scattering angle, which has the following relationship with the incident angle and the reflection angle:
$$\textrm{cos}\Theta = \textrm{cos}{\theta _i}\textrm{cos}{\theta _r} - \textrm{sin}{\theta _i}\textrm{sin}{\theta _r}\textrm{cos}({{\varphi_i} - {\varphi_r}} )$$
P(Θ) can be computed using the normalized size distribution of the given volume,
$$P(\Theta )=\int_{{\lambda _1}}^{{\lambda _2}} {\int_{{r_1}}^{{r_2}} {P({\Theta ,\lambda ,r} )} } n(r )v(\lambda )drd\lambda$$
where v(λ) is the luminous efficiency, n(r) is the normalized size distribution, P(Θ, λ, r) is the scattering phase function of a single particle. To characterize the ice crystal size distribution, the scattering characteristics of ice crystal can be calculated by spherical particles equivalent to a mean effective size using Mie scattering theory [15]. The effective radius of non-spherical ice crystals, reff,ice, can be expressed as [16]:
$${r_{eff}} = {d_v}^3/{d_s}^2$$
where dv is the equivalent volume diameter, and ds is the equivalent area diameter. For non-spherical ice crystal, dv and ds can be expressed as:
$${d_s} = \textrm{exp}\left[ {\sum\limits_{i = 0}^4 {{a_n}{{({\ln D} )}^i}} } \right]$$
$${d_v} = \textrm{exp}\left[ {\sum\limits_{i = 0}^4 {{b_n}{{({\ln D} )}^i}} } \right]$$
where D is the largest size of ice crystals, an and bn are empirical parameters. Figure 6 shows the scattering phase function of clouds in different bands using the Mie scattering theory.

 

Fig. 6. (a) Water cloud scattering phase function. (b) Ice cloud scattering phase function.

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Based on the cloud scattering phase function and Eq. (9), the bidirectional reflectivity distributions of water cloud and ice cloud in different bands are calculated as shown in Fig. 7.

 

Fig. 7. Water cloud bidirectional reflectance distribution (a), (b) and (c). Ice cloud bidirectional reflectance distribution (d), (e), and (f). (The longitude of the area is 105°E, the latitude is 5°N. The solar zenith angle is 28.43°, the azimuth is 0° when the local time is 12:00.)

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Figures 6 and 7 show that the reflection ability of the ice cloud in the three bands is much higher than that of the water cloud. The cloud scattering ability in the 3–5µm band is more significant than in the two narrow bands. In the specular reflection direction, the bidirectional reflectance of the cloud in the 2.65–2.90µm band is larger than in the 4.25–4.50µm band.

2.2.3 Modeling of sea surface radiation characteristics

Solar radiation is more clearly reflected by the sea surface in short and medium waves. When viewed at a specific angle, there will be a “sparkling” bright band on the sea surface. In order to analyze the influence of the bright band on the detection of aircraft plume, the radiation model of the sea surface must be accurately established.

$$\begin{array}{l} {L_s}(\lambda )= {L^ \uparrow }_{sea,self}(\lambda )+ {L^ \uparrow }_{sea\textrm{,}refl}(\lambda )\\ \quad \quad \;\;\;\, = {\varepsilon _{sea}}\frac{{M({{T_{sea}},\lambda } )}}{\pi } + {\tau _{S - s}}(\lambda ){E_{sun}}\cos {\theta _i}BRD{F_{sea}}({{\theta_i},{\varphi_i},{\theta_r},{\varphi_r}} )\end{array}$$
where Lsea,self is the sea surface self-radiation; Lsea,refl is the sea surface reflection radiation; εsea is the sea surface emissivity; M(Tsea,λ) is the radiant exitance of blackbody when the sea surface temperature (SST) is Tcloud; τS-s is the atmospheric transmittance from the sun to the sea surface; and BRDFcloud is the sea surface bidirectional reflectivity. In order to achieve the spatio-temporal matching of the sea surface and cloud radiation data, the inversion data of the SST using FY-2G remote sensing data is used to establish the sea surface self-radiation model. Combined with Cox–Munk distribution model for slopes, the bidirectional reflection model of the sea surface is established. Figures 8(a)–8(b) show the inversion distribution of the SST field and the bidirectional reflectivity distribution of the sea surface.

 

Fig. 8. (a) Sea surface temperature field. (b) Sea surface bidirectional reflectance distribution. (12:00 local time on December 20, 2017)

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2.2.4 Modeling of sea/cloud background matching space-based detector sampling

Based on the modeling of sea surface and cloud radiation characteristics, a modeling method of background radiation field based on detector spatial sampling is proposed. The radiation field distribution of the sea/cloud background on the focal plane of the detector is generated.

If the field of view of the detector is ωh and ωv in the horizontal and vertical directions, respectively, the number of imaging pixels, n, and the spatial resolution of the detector, rs, according to the projection imaging relationship of beam propagation can be expressed as:

$${n_{h,v}} = f^{\prime}tan {\omega _{h,v}}/d$$
$${r_s} = dR/f^{\prime}$$
Equations (16) and (17) can calculate the coverage length of the background in the horizontal and vertical directions in the object space, lh,v.
$${l_h}_{,v} = {n_{h,v}} \cdot {r_s}$$
Then the number of sea/cloud remote sensing data is cropped in the object space can be expressed in the horizontal and vertical directions as:
$${n_{i,j}} = {l_{h,v}}/r$$
where r is the spatial resolution of remote sensing data. Figure 9 shows the sampling principle of the background radiation field. The reflection zenith angle in the object space corresponding to each sampled pixel of the detector can be expressed as:
$${\theta _r} = \frac{{{n_v}}}{{{n_j}}} \cdot \left\{ {\frac{\pi }{2} - \left[ {\alpha - arctan \left( {\frac{{md}}{{f^{\prime}}}} \right)} \right]} \right\}$$
where α is the detection angle; m is the number of pixels between each pixel and the center pixel; d is the detector size; f’ is the focal length of the optical system. φr can also be obtained according to the above method of calculating the θr. The effective sea/cloud bidirectional reflectivity texture on the focal plane of the detector can be generated.
$$BRD{F_{sea/cloud\_texture}} = \sum\limits_{i = ({h - 1} )({{n_i}/{n_h}} )}^{h({{n_i}/{n_h}} )} {\sum\limits_{j = ({v - 1} )({{n_j}/{n_v}} )}^{v({{n_j}/{n_v}} )} {BRD{F_{sea/cloud}}({{\theta_{ri}},{\varphi_{rj}}} )} }$$

 

Fig. 9. Background radiation field is sampled by the detector.

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Figure 10 shows the modeling flow of the sea/cloud background radiation field in the detector field of view.

 

Fig. 10. Modeling flow of sea/cloud background radiation field in the detector field of view.

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Given the detector parameters of the infrared imaging system, a sea/cloud background temperature texture and a bidirectional reflectance texture are generated based on the imaged area of the background in the object space and bidirectional reflection angle corresponding to each sampling unit. The intrinsic radiation field of the cloud, the reflected radiation field of the cloud and the sea surface radiation field are calculated in the field of view in combination with Eqs. (3), (8) and (12). Based on different cloud top heights and cloud thicknesses, three-dimensional atmospheric transmittance and atmospheric path thermal radiation texture using Modtran 5.2 are generated. The radiation texture of cloud, sea surface, atmosphere and atmospheric attenuation texture are superimposed to generate the radiation field distribution of the sea/cloud background at the focal plane of the detector.

2.3 Modeling of aircraft plume radiation characteristics

Accurate modeling of aircraft plume radiation is a key factor in studying the detection capabilities of the infrared imaging system in the geostationary orbit. According to the relative position of the aircraft and the cloud, the radiation model with the aircraft under the cloud bottom, in the cloud and on the cloud top is established. For the different flying heights, the aircraft plume radiation received by the infrared detector can be expressed as:

$${L_{trg1,2,3}}({\lambda ,\alpha } )= \tau ({\lambda ,\alpha ,{r_{1,2,3}}} ){L^ \uparrow }_{plume}({\lambda ,\alpha } )+ {L_a}^ \uparrow ({\lambda ,\alpha ,{r_{1,2,3}}} )$$
where Ltrg1, Ltrg2, and Ltrg3 represent the aircraft plume radiation received by the detector under the cloud bottom, in the cloud and on the cloud top, respectively; r1, r2, and r3 represent the distance between the aircraft and the detector in the direction of observation, respectively.
$${r_1} = {d_a} + {d_c} + \frac{{{H_{c - bottom}} - {H_t}}}{{\sin \alpha }}$$
$${r_2} = {d_a} + {d_c} - \frac{{{H_t} - {H_{c - bottom}}}}{{\sin \alpha }}$$
$${r_3} = {d_a} - \frac{{{H_t} - ({{H_{c - bottom}} + {H_{c - thickness}}} )}}{{\sin \alpha }}$$
The self-radiation of the aircraft plume can be expressed by:
$${L_{plume}}^ \uparrow ({\lambda ,\alpha } )={\varepsilon _{{\mathop{\rm plume}\nolimits} }}({\lambda ,\alpha } ){M_{bb}}({\lambda ,{T_{plume}}} )/\pi$$
where εplume the plume emissivity. Figure 11 shows the temperature distribution of the plume at different detection angles.

 

Fig. 11. Temperature distribution of the plume at different observation angles.

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Figure 11 shows the temperature profile increases with the increase of the detection angle. The Mach discs start appearing at detection angle of 40°; and become clearly visible at larger angles. The main components in the plume are CO2 and H2O which are selective radiators with large radiation fluctuations at different wavelengths. Figure 12 shows the spectral emissivity of the mixed gas in the plume.

 

Fig. 12. Spectral emissivity of the mixed gas in the plume.

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2.4 Modeling of sub-pixel targets imaging features

For an ideal imagery system, the light beam emitted by sub-pixel target focuses to one point after the modulation of optical system. However, for the practical imagery system, an accurate deduction of infrared imaging features of sub-pixel targets need to be considered [17]. The sub-pixel target is spread over several pixels of the focal plane of the detector due to the diffraction effect of the optical system, which is aliased with the background’s radiation. Figure 13 shows a schematic of sub-pixel target imaging.

 

Fig. 13. Ideal imagery (a) and practical imagery (b) of sub-pixel target. (c) Diagram of the imaging process.

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In Fig. 13, ADAS is the projected area of the solid angle of the detector size in the object space; Ás1 and Ás2 are the radiant area of aircraft plume in the image space at different sampling units; r is the radius of the diffraction spot, and r = 1.22λF; F is the F number; As is the actual area of the aircraft plume; Ad is the detector area; d is the detector size; p is the center to center spacing. The optical signal is converted to the voltage signal using a signal response model of the point source. Assuming a circular aperture, the output voltage difference of the target and background is:

$$\left\{ \begin{array}{l} \Delta {V_{s1}} = \int\limits_{{\lambda_1}}^{{\lambda_2}} {{R_\lambda }\frac{\pi }{4}\frac{{\Delta {L_1}(\lambda ){A_d}}}{{{F^2}}}\frac{{{A_{s1}}}}{{{A_{DAS}}}}{\tau_o}(\lambda ){\tau_{atm}}(\lambda )d\lambda } \\ \Delta {V_{s2}} = \int\limits_{{\lambda_1}}^{{\lambda_2}} {{R_\lambda }\frac{\pi }{4}\frac{{\Delta {L_2}(\lambda ){A_d}}}{{{F^2}}}\frac{{{A_{s2}}}}{{{A_{DAS}}}}{\tau_o}(\lambda ){\tau_{atm}}(\lambda )d\lambda } \end{array} \right.$$
where Rλ is the band responsivity of the detector; ΔL is the relative radiation difference between the aircraft plume and the background, ΔL(λ)=Lt(λ,TT)-Lb(λ,TT); As1 and As2 are the radiant area of target in the object space at different sampling units; τo is the transmittance of the optical system; τatm is the atmospheric transmittance. Define χ as the ratio of the part in gaps and the total target image area. Thus the effective target area is χ·As, and As1+ As2=χ·As. The ability of the infrared imaging system to detect the plume is directly affected by the area of the diffraction spot. When the diffraction effect is not negligible, the signal voltage generated by the aircraft plume must be corrected.
$$\left\{ \begin{array}{l} \Delta {V_{s1}} = \int\limits_{{\lambda_1}}^{{\lambda_2}} {{R_\lambda }\frac{{\Delta {L_1}(\lambda ){A_{s1}}{A_o}}}{{{R^2}}}TTF{\tau_o}(\lambda ){\tau_{atm}}(\lambda )d\lambda } \\ \Delta {V_{s2}} = \int\limits_{{\lambda_1}}^{{\lambda_2}} {{R_\lambda }\frac{{\Delta {L_2}(\lambda ){A_{s2}}{A_o}}}{{{R^2}}}TTF{\tau_o}(\lambda ){\tau_{atm}}(\lambda )d\lambda } \end{array} \right.$$
where Ao is the entrance area of the optical system; TTF is the target transfer function.

According to the response characteristic of the infrared imaging system, the radiance in each pixel is converted to the voltage value, which is further quantified as gray value. Assume that A/D converter digits of the photoelectric conversion system is α, and the range of the voltage signal is Vmax-Vmin. The gray value of each detector unit output can be calculated by:

$$G({i,j} )= \frac{{{2^\alpha } - 1}}{{{V_{max}} - {V_{mi}}_n}}({\Delta {V_s}({i,j} )- {V_{mi}}_n} )$$

3. Multispectral imaging feature simulation and detection performance analysis

Based on the calculation results of multi-spectral radiation characteristics of cloud, sea background and aircraft plume, the detectability of infrared imaging system is discussed by SCR. According to analysis of the infrared imaging system for aircraft plume detection from geostationary orbit [12] and published article [18], the typical parameters of geostationary infrared imaging system are estimated. The detector size, d, is 15µm, the detector length, b, is 0.016m, the spatial resolution rs, is 600m, the orbital altitude, H, is 35800km, the diameter of the optical system, Do, is 0.55m, the focal length of the optical system, f’, is 1.074m, the transmittance of the optical system, τo, is 0.7, the equivalent noise bandwidth, Δf, is 50Hz, and the normalized detectivity, D*, is 2×1011W−1·m·Hz−1/2. The detection performance under different flight altitudes, cloud backgrounds and detection angles is analyzed, and the imaging features are simulated.

3.1 Different flight heights

Based on the accurate imaging feature prediction model of the full chain including the aircraft plume - the sea surface/ cloud - the environmental atmosphere - the optical system - the imaging detector, 8-bit quantization is used to simulate the multispectral imaging results of the aircraft plume at different heights when the detection angle is 90°, as shown in Figs. 1416.

 

Fig. 14. Imaging features of the target at different heights in 2.65–2.90µm band.

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Fig. 15. Imaging features of the target at different heights in 4.25–4.50µm band.

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Fig. 16. Imaging features of the target at different heights in 3–5µm band.

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Figures 1416 show that as the flight height increases, the atmospheric transmittance from the aircraft to the detector gradually increases, and the ability of the aircraft plume to be detected by the geostationary infrared imaging system is gradually enhanced. In the 2.65–2.90µm and 4.25–4.50µm bands, the aircraft plume is more easily detected when the flight height is greater than 5 km. In the wide-band, the aircraft plume is always submerged by the background and cannot be detected. The main reason is that the 2.65–2.90µm band and the 4.25–4.50µm band are atmospheric shielding bands. The atmospheric transmittance from the background to the detector in the narrow band is much smaller than in the 3–5µm band. Background clutter has a serious impact on detection in the wide band. At the same time, the contribution of background radiation in different bands is different, and the background imaging features are different. Figure 17 shows the variation of the local SCR with the flight height in different bands.

 

Fig. 17. The relationship between the local SCR and the flight height.

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Figure 17 shows that the local SCR at the aircraft plume imaged position in the three bands increases as the flight height increases. In the 4.25–4.50µm band, the local SCR at the aircraft plume imaged position is increased faster than the other two bands; in the 2.65–2.90µm band is the second, and in the 3–5µm band is the slowest. It is generally considered that the detection requirement can be satisfied when the local SCR is greater than 3. When the flight height is 5 km, the local SCR in 2.65–2.90µm and 4.25–4.50µm are 3.697 and 4.192, respectively, and the detection requirements are basically satisfied. Therefore, the aircraft plume can be detected when the flight height is greater than 5 km in two narrow bands. In the wide band, the radiation energy accumulated at the aircraft plume imaged position is much larger than in the narrow band. However, the background radiation through the atmosphere to the detector is also large, and the aircraft plume cannot be detected. It is more reliable to use the multispectral joint-band to detect the aircraft plume.

3.2 Different cloud types

In order to analyze the influence of different backgrounds on the detection capability, Figs. 1820 simulates the multispectral imaging results of the aircraft plume located in ice clouds, water clouds and cloudless backgrounds when the flight height is 15 km. Table 1 shows the variation of the local SCR with the background in different bands.

Tables Icon

Table 1. Local SCR of aircraft plume in different backgrounds

Figures 1820 and Table 1 show that the detection performance of the aircraft plume in the atmospheric shielding band is better than that in the wide band. In two narrow bands, the aircraft plume can be detected in ice cloud, water cloud and cloudless backgrounds. In the 2.65–2.90µm band, the radiation clutter on the ice cloud background is small, and the aircraft plume is most easily detected. In the 4.25–4.50µm band, the aircraft plume is the most easy to detect in the cloudless background. In the 3–5µm band, the aircraft plume cannot be detected. In summary, the selection of reasonable detection bands in different backgrounds is conducive to targets detection.

 

Fig. 18. Imaging features of the target at different backgrounds in 2.65–2.90µm band.

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Fig. 19. Imaging features of the target at different backgrounds in 4.25–4.50µm band.

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Fig. 20. Imaging features of the target at different backgrounds in 3–5µm band.

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3.3 Different detection angles

In order to analyze the influence of different detection angles on the target detection capability, Fig. 21 shows that 11×11 pixels are extracted with the aircraft plume as the center, and the 11-bit quantization is used to simulate the difference between the target and the local background in the 2.65–2.90µm band.

 

Fig. 21. The grayscale difference between the aircraft plume and the local background at the different angles.

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Figure 21 shows that the grayscale difference between the aircraft plume and the local background is the largest, and the aircraft plume is the most easy to detect when the detection angle is 90°. When the detection angle is 60°, the fluctuation of the aircraft plume and the local background is the smallest, and the aircraft plume is the least likely to be detected. The main reason is that the cloud background has a strong scattering effect on the sun, which has a strong interference to the geostationary infrared imaging system when the solar incident zenith angle is 28.43° and the reflection zenith angle is about 30°. In order to better detect weak targets, the detection angle of the background with strong reflection should be avoided as much as possible.

4. Conclusion

In view of the optical detection requirements for wide area continuous surveillance of air targets, the detectability of geostationary infrared imaging system to aircraft plume in sea/cloud background is discussed. In this paper, a method for constructing a sea/cloud background spectral radiation model using FY-2G remote sensing data is proposed. This method is convenient for modeling any complex background with high reliability. Combining the inversion of the plume radiation characteristics at different detection angles, the optical radiation imaging feature of the full chain including aircraft plume, sea surface, environmental atmosphere, optical system, imaging detector is established. The detectability of the aircraft plume under different detection conditions is analyzed. Research shows that it is feasible to detect the aircraft plume by the geostationary infrared imaging system, and the detection performance in the narrow band is better than in the wide band. It is more reliable to use the multispectral joint-band to detect the aircraft plume in different backgrounds. The results of this paper provide a new method for modeling sea/cloud backgrounds, and provide data support for the development of intelligent algorithms for realizing the detection, tracking and identification of air targets in the geostationary orbit.

Funding

National Natural Science Foundation of China (61377007, 61575152, 61775174); National Defense Basic Scientific Research Program of China (JCKY2016208B001).

References

1. P. Yang, L. Bi, B. A. Baum, K. N. Liou, and B. Cole, “Spectrally consistent scattering, absorption, and polarization properties of atmospheric ice crystals at wavelengths from 0.2 to 100µm,” J. Atmos. Sci. 70(1), 330–347 (2013). [CrossRef]  

2. A. Kokhanovsky, “Optical properties of terrestrial clouds,” Earth-Sci. Rev. 64(3-4), 189–241 (2004). [CrossRef]  

3. W. H. Knap, L. C. Labonnote, G. Brogniez, and P. Stammes, “Modeling total and polarized reflectances of ice clouds: evaluation by means of polder and atsr-2 measurements,” Appl. Opt. 44(19), 4060–4073 (2005). [CrossRef]  

4. L. C. Labonnote, G. Brogniez, M. Doutriaux-Boucher, J. C. Buriez, J. F. Gayet, and H. Chepfer, “Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. Comparison with in-situ and ADEOS-POLDER measurements,” Geophys. Res. Lett. 27(1), 113–116 (2000). [CrossRef]  

5. P. W. Nugent, J. A. Shaw, and S. Piazzolla, “Infrared cloud imaging in support of Earth-space optical communication,” Opt. Express 17(10), 7862–7872 (2009). [CrossRef]  

6. X. Zhang, S. He, A. Shabani, P. W. Zhai, and K. Du, “Spectral sea surface reflectance of skylight,” Opt. Express 25(4), A1–A13 (2017). [CrossRef]  

7. F. Schwenger and R. Endre, “Simulation of oceanic whitecaps and their reflectance characteristics in the short wavelength infrared,” Appl. Opt. 56(6), 1662–1673 (2017). [CrossRef]  

8. S. J. P. Retief, “Aircraft plume infrared radiance inversion and subsequent simulation model,” Proc. SPIE 8543, 85430P (2012). [CrossRef]  

9. C. J. Cornelius, M. S. Willers, and A. D. Waal, “Aircraft vulnerability analysis by modeling and simulation,” Proc. SPIE 9251, 92510M (2014). [CrossRef]  

10. F. Huang, X. Shen, G. Li, G. Wang, and Z. Zhao, “Influence of background radiation on space target detection in the long wave infrared range,” Opt. Eng. 51(8), 086402 (2012). [CrossRef]  

11. C. Schweitzer, K. Stein, and N. Wendelstein, “Evaluation of appropriate sensor specifications for space based ballistic missile detection,” Proc. SPIE 8541, 85410M (2012). [CrossRef]  

12. H. Yuan, X. R. Wang, B. T. Guo, D. Ren, W. G. Zhang, and K. Li, “Performance analysis of the infrared imaging system for aircraft plume detection from geostationary orbit,” Appl. Opt. 58(7), 1691–1698 (2019). [CrossRef]  

13. J. Descloitres, J. C. Buriez, F. Parol, and Y. Fouquart, “Polder observations of cloud bidirectional reflectances compared to a plane-parallel model using the international satellite cloud climatology project cloud phase functions,” J. Geophys. Res.: Atmos. 103(D10), 11411–11418 (1998). [CrossRef]  

14. A. Bouthors and F. Neyret, “Realistic rendering of clouds in real-time / rendu réaliste de nuages en temps-réel,” Ph.D. thesis, Université Joseph Fourier (2011).

15. F. Zhang and J. Li, “A note on double Henyey-Greenstein phase function,” J. Quant. Spectrosc. Radiat. Transfer 184, 40–43 (2016). [CrossRef]  

16. M. D. Chou, “Parameterization of shortwave cloud optical properties for a mixture of ice particle habits for use in atmospheric models,” J. Geophys. Res. 107(D21), 4600 (2002). [CrossRef]  

17. K. Li, X. R. Wang, B. T. Guo, W. G. Zhang, H. Yuan, X. X. Wu, and C. Zhao, “Accurate deduction of infrared imaging features of subpixel targets based on the conversion of radiation fields of measured area targets,” Appl. Opt. 57(31), 9499–9507 (2018). [CrossRef]  

18. G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

References

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  1. P. Yang, L. Bi, B. A. Baum, K. N. Liou, and B. Cole, “Spectrally consistent scattering, absorption, and polarization properties of atmospheric ice crystals at wavelengths from 0.2 to 100µm,” J. Atmos. Sci. 70(1), 330–347 (2013).
    [Crossref]
  2. A. Kokhanovsky, “Optical properties of terrestrial clouds,” Earth-Sci. Rev. 64(3-4), 189–241 (2004).
    [Crossref]
  3. W. H. Knap, L. C. Labonnote, G. Brogniez, and P. Stammes, “Modeling total and polarized reflectances of ice clouds: evaluation by means of polder and atsr-2 measurements,” Appl. Opt. 44(19), 4060–4073 (2005).
    [Crossref]
  4. L. C. Labonnote, G. Brogniez, M. Doutriaux-Boucher, J. C. Buriez, J. F. Gayet, and H. Chepfer, “Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. Comparison with in-situ and ADEOS-POLDER measurements,” Geophys. Res. Lett. 27(1), 113–116 (2000).
    [Crossref]
  5. P. W. Nugent, J. A. Shaw, and S. Piazzolla, “Infrared cloud imaging in support of Earth-space optical communication,” Opt. Express 17(10), 7862–7872 (2009).
    [Crossref]
  6. X. Zhang, S. He, A. Shabani, P. W. Zhai, and K. Du, “Spectral sea surface reflectance of skylight,” Opt. Express 25(4), A1–A13 (2017).
    [Crossref]
  7. F. Schwenger and R. Endre, “Simulation of oceanic whitecaps and their reflectance characteristics in the short wavelength infrared,” Appl. Opt. 56(6), 1662–1673 (2017).
    [Crossref]
  8. S. J. P. Retief, “Aircraft plume infrared radiance inversion and subsequent simulation model,” Proc. SPIE 8543, 85430P (2012).
    [Crossref]
  9. C. J. Cornelius, M. S. Willers, and A. D. Waal, “Aircraft vulnerability analysis by modeling and simulation,” Proc. SPIE 9251, 92510M (2014).
    [Crossref]
  10. F. Huang, X. Shen, G. Li, G. Wang, and Z. Zhao, “Influence of background radiation on space target detection in the long wave infrared range,” Opt. Eng. 51(8), 086402 (2012).
    [Crossref]
  11. C. Schweitzer, K. Stein, and N. Wendelstein, “Evaluation of appropriate sensor specifications for space based ballistic missile detection,” Proc. SPIE 8541, 85410M (2012).
    [Crossref]
  12. H. Yuan, X. R. Wang, B. T. Guo, D. Ren, W. G. Zhang, and K. Li, “Performance analysis of the infrared imaging system for aircraft plume detection from geostationary orbit,” Appl. Opt. 58(7), 1691–1698 (2019).
    [Crossref]
  13. J. Descloitres, J. C. Buriez, F. Parol, and Y. Fouquart, “Polder observations of cloud bidirectional reflectances compared to a plane-parallel model using the international satellite cloud climatology project cloud phase functions,” J. Geophys. Res.: Atmos. 103(D10), 11411–11418 (1998).
    [Crossref]
  14. A. Bouthors and F. Neyret, “Realistic rendering of clouds in real-time / rendu réaliste de nuages en temps-réel,” Ph.D. thesis, Université Joseph Fourier (2011).
  15. F. Zhang and J. Li, “A note on double Henyey-Greenstein phase function,” J. Quant. Spectrosc. Radiat. Transfer 184, 40–43 (2016).
    [Crossref]
  16. M. D. Chou, “Parameterization of shortwave cloud optical properties for a mixture of ice particle habits for use in atmospheric models,” J. Geophys. Res. 107(D21), 4600 (2002).
    [Crossref]
  17. K. Li, X. R. Wang, B. T. Guo, W. G. Zhang, H. Yuan, X. X. Wu, and C. Zhao, “Accurate deduction of infrared imaging features of subpixel targets based on the conversion of radiation fields of measured area targets,” Appl. Opt. 57(31), 9499–9507 (2018).
    [Crossref]
  18. G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

2019 (1)

2018 (1)

2017 (2)

2016 (1)

F. Zhang and J. Li, “A note on double Henyey-Greenstein phase function,” J. Quant. Spectrosc. Radiat. Transfer 184, 40–43 (2016).
[Crossref]

2014 (1)

C. J. Cornelius, M. S. Willers, and A. D. Waal, “Aircraft vulnerability analysis by modeling and simulation,” Proc. SPIE 9251, 92510M (2014).
[Crossref]

2013 (1)

P. Yang, L. Bi, B. A. Baum, K. N. Liou, and B. Cole, “Spectrally consistent scattering, absorption, and polarization properties of atmospheric ice crystals at wavelengths from 0.2 to 100µm,” J. Atmos. Sci. 70(1), 330–347 (2013).
[Crossref]

2012 (3)

F. Huang, X. Shen, G. Li, G. Wang, and Z. Zhao, “Influence of background radiation on space target detection in the long wave infrared range,” Opt. Eng. 51(8), 086402 (2012).
[Crossref]

C. Schweitzer, K. Stein, and N. Wendelstein, “Evaluation of appropriate sensor specifications for space based ballistic missile detection,” Proc. SPIE 8541, 85410M (2012).
[Crossref]

S. J. P. Retief, “Aircraft plume infrared radiance inversion and subsequent simulation model,” Proc. SPIE 8543, 85430P (2012).
[Crossref]

2009 (1)

2005 (1)

2004 (1)

A. Kokhanovsky, “Optical properties of terrestrial clouds,” Earth-Sci. Rev. 64(3-4), 189–241 (2004).
[Crossref]

2002 (1)

M. D. Chou, “Parameterization of shortwave cloud optical properties for a mixture of ice particle habits for use in atmospheric models,” J. Geophys. Res. 107(D21), 4600 (2002).
[Crossref]

2000 (1)

L. C. Labonnote, G. Brogniez, M. Doutriaux-Boucher, J. C. Buriez, J. F. Gayet, and H. Chepfer, “Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. Comparison with in-situ and ADEOS-POLDER measurements,” Geophys. Res. Lett. 27(1), 113–116 (2000).
[Crossref]

1998 (1)

J. Descloitres, J. C. Buriez, F. Parol, and Y. Fouquart, “Polder observations of cloud bidirectional reflectances compared to a plane-parallel model using the international satellite cloud climatology project cloud phase functions,” J. Geophys. Res.: Atmos. 103(D10), 11411–11418 (1998).
[Crossref]

Abell, G.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Baum, B. A.

P. Yang, L. Bi, B. A. Baum, K. N. Liou, and B. Cole, “Spectrally consistent scattering, absorption, and polarization properties of atmospheric ice crystals at wavelengths from 0.2 to 100µm,” J. Atmos. Sci. 70(1), 330–347 (2013).
[Crossref]

Bi, L.

P. Yang, L. Bi, B. A. Baum, K. N. Liou, and B. Cole, “Spectrally consistent scattering, absorption, and polarization properties of atmospheric ice crystals at wavelengths from 0.2 to 100µm,” J. Atmos. Sci. 70(1), 330–347 (2013).
[Crossref]

Bouthors, A.

A. Bouthors and F. Neyret, “Realistic rendering of clouds in real-time / rendu réaliste de nuages en temps-réel,” Ph.D. thesis, Université Joseph Fourier (2011).

Brogniez, G.

W. H. Knap, L. C. Labonnote, G. Brogniez, and P. Stammes, “Modeling total and polarized reflectances of ice clouds: evaluation by means of polder and atsr-2 measurements,” Appl. Opt. 44(19), 4060–4073 (2005).
[Crossref]

L. C. Labonnote, G. Brogniez, M. Doutriaux-Boucher, J. C. Buriez, J. F. Gayet, and H. Chepfer, “Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. Comparison with in-situ and ADEOS-POLDER measurements,” Geophys. Res. Lett. 27(1), 113–116 (2000).
[Crossref]

Buriez, J. C.

L. C. Labonnote, G. Brogniez, M. Doutriaux-Boucher, J. C. Buriez, J. F. Gayet, and H. Chepfer, “Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. Comparison with in-situ and ADEOS-POLDER measurements,” Geophys. Res. Lett. 27(1), 113–116 (2000).
[Crossref]

J. Descloitres, J. C. Buriez, F. Parol, and Y. Fouquart, “Polder observations of cloud bidirectional reflectances compared to a plane-parallel model using the international satellite cloud climatology project cloud phase functions,” J. Geophys. Res.: Atmos. 103(D10), 11411–11418 (1998).
[Crossref]

Chepfer, H.

L. C. Labonnote, G. Brogniez, M. Doutriaux-Boucher, J. C. Buriez, J. F. Gayet, and H. Chepfer, “Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. Comparison with in-situ and ADEOS-POLDER measurements,” Geophys. Res. Lett. 27(1), 113–116 (2000).
[Crossref]

Chou, M. D.

M. D. Chou, “Parameterization of shortwave cloud optical properties for a mixture of ice particle habits for use in atmospheric models,” J. Geophys. Res. 107(D21), 4600 (2002).
[Crossref]

Cole, B.

P. Yang, L. Bi, B. A. Baum, K. N. Liou, and B. Cole, “Spectrally consistent scattering, absorption, and polarization properties of atmospheric ice crystals at wavelengths from 0.2 to 100µm,” J. Atmos. Sci. 70(1), 330–347 (2013).
[Crossref]

Cornelius, C. J.

C. J. Cornelius, M. S. Willers, and A. D. Waal, “Aircraft vulnerability analysis by modeling and simulation,” Proc. SPIE 9251, 92510M (2014).
[Crossref]

Descloitres, J.

J. Descloitres, J. C. Buriez, F. Parol, and Y. Fouquart, “Polder observations of cloud bidirectional reflectances compared to a plane-parallel model using the international satellite cloud climatology project cloud phase functions,” J. Geophys. Res.: Atmos. 103(D10), 11411–11418 (1998).
[Crossref]

Doutriaux-Boucher, M.

L. C. Labonnote, G. Brogniez, M. Doutriaux-Boucher, J. C. Buriez, J. F. Gayet, and H. Chepfer, “Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. Comparison with in-situ and ADEOS-POLDER measurements,” Geophys. Res. Lett. 27(1), 113–116 (2000).
[Crossref]

Du, K.

Endre, R.

Fouquart, Y.

J. Descloitres, J. C. Buriez, F. Parol, and Y. Fouquart, “Polder observations of cloud bidirectional reflectances compared to a plane-parallel model using the international satellite cloud climatology project cloud phase functions,” J. Geophys. Res.: Atmos. 103(D10), 11411–11418 (1998).
[Crossref]

Gayet, J. F.

L. C. Labonnote, G. Brogniez, M. Doutriaux-Boucher, J. C. Buriez, J. F. Gayet, and H. Chepfer, “Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. Comparison with in-situ and ADEOS-POLDER measurements,” Geophys. Res. Lett. 27(1), 113–116 (2000).
[Crossref]

Guo, B. T.

He, S.

Huang, F.

F. Huang, X. Shen, G. Li, G. Wang, and Z. Zhao, “Influence of background radiation on space target detection in the long wave infrared range,” Opt. Eng. 51(8), 086402 (2012).
[Crossref]

Jansen, J.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Kerwin, F.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Knap, W. H.

Kokhanovsky, A.

A. Kokhanovsky, “Optical properties of terrestrial clouds,” Earth-Sci. Rev. 64(3-4), 189–241 (2004).
[Crossref]

Kriek, J.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Krylo, R.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Labonnote, L. C.

W. H. Knap, L. C. Labonnote, G. Brogniez, and P. Stammes, “Modeling total and polarized reflectances of ice clouds: evaluation by means of polder and atsr-2 measurements,” Appl. Opt. 44(19), 4060–4073 (2005).
[Crossref]

L. C. Labonnote, G. Brogniez, M. Doutriaux-Boucher, J. C. Buriez, J. F. Gayet, and H. Chepfer, “Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. Comparison with in-situ and ADEOS-POLDER measurements,” Geophys. Res. Lett. 27(1), 113–116 (2000).
[Crossref]

Lafferty, R.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Li, G.

F. Huang, X. Shen, G. Li, G. Wang, and Z. Zhao, “Influence of background radiation on space target detection in the long wave infrared range,” Opt. Eng. 51(8), 086402 (2012).
[Crossref]

Li, J.

F. Zhang and J. Li, “A note on double Henyey-Greenstein phase function,” J. Quant. Spectrosc. Radiat. Transfer 184, 40–43 (2016).
[Crossref]

Li, K.

Liou, K. N.

P. Yang, L. Bi, B. A. Baum, K. N. Liou, and B. Cole, “Spectrally consistent scattering, absorption, and polarization properties of atmospheric ice crystals at wavelengths from 0.2 to 100µm,” J. Atmos. Sci. 70(1), 330–347 (2013).
[Crossref]

Mellwain, M.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Neyret, F.

A. Bouthors and F. Neyret, “Realistic rendering of clouds in real-time / rendu réaliste de nuages en temps-réel,” Ph.D. thesis, Université Joseph Fourier (2011).

Nugent, P. W.

Orlando, H.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Parol, F.

J. Descloitres, J. C. Buriez, F. Parol, and Y. Fouquart, “Polder observations of cloud bidirectional reflectances compared to a plane-parallel model using the international satellite cloud climatology project cloud phase functions,” J. Geophys. Res.: Atmos. 103(D10), 11411–11418 (1998).
[Crossref]

Piazzolla, S.

Platt, R.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Price, G.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Rehberger, D.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Ren, D.

Retief, S. J. P.

S. J. P. Retief, “Aircraft plume infrared radiance inversion and subsequent simulation model,” Proc. SPIE 8543, 85430P (2012).
[Crossref]

Rysanek, J.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Schweitzer, C.

C. Schweitzer, K. Stein, and N. Wendelstein, “Evaluation of appropriate sensor specifications for space based ballistic missile detection,” Proc. SPIE 8541, 85410M (2012).
[Crossref]

Schwenger, F.

Shabani, A.

Shaw, J. A.

Shen, X.

F. Huang, X. Shen, G. Li, G. Wang, and Z. Zhao, “Influence of background radiation on space target detection in the long wave infrared range,” Opt. Eng. 51(8), 086402 (2012).
[Crossref]

Stammes, P.

Stein, K.

C. Schweitzer, K. Stein, and N. Wendelstein, “Evaluation of appropriate sensor specifications for space based ballistic missile detection,” Proc. SPIE 8541, 85410M (2012).
[Crossref]

Waal, A. D.

C. J. Cornelius, M. S. Willers, and A. D. Waal, “Aircraft vulnerability analysis by modeling and simulation,” Proc. SPIE 9251, 92510M (2014).
[Crossref]

Wang, G.

F. Huang, X. Shen, G. Li, G. Wang, and Z. Zhao, “Influence of background radiation on space target detection in the long wave infrared range,” Opt. Eng. 51(8), 086402 (2012).
[Crossref]

Wang, X. R.

Wendelstein, N.

C. Schweitzer, K. Stein, and N. Wendelstein, “Evaluation of appropriate sensor specifications for space based ballistic missile detection,” Proc. SPIE 8541, 85410M (2012).
[Crossref]

Willers, M. S.

C. J. Cornelius, M. S. Willers, and A. D. Waal, “Aircraft vulnerability analysis by modeling and simulation,” Proc. SPIE 9251, 92510M (2014).
[Crossref]

Williams, R.

G. Abell, R. Lafferty, R. Williams, G. Price, R. Krylo, J. Jansen, F. Kerwin, J. Rysanek, R. Platt, H. Orlando, D. Rehberger, J. Kriek, and M. Mellwain, “SBIRS high IR sensor on-orbit bakeout testing,” in 35th Aiaa Thermophysics Conference (2013).

Wu, X. X.

Yang, P.

P. Yang, L. Bi, B. A. Baum, K. N. Liou, and B. Cole, “Spectrally consistent scattering, absorption, and polarization properties of atmospheric ice crystals at wavelengths from 0.2 to 100µm,” J. Atmos. Sci. 70(1), 330–347 (2013).
[Crossref]

Yuan, H.

Zhai, P. W.

Zhang, F.

F. Zhang and J. Li, “A note on double Henyey-Greenstein phase function,” J. Quant. Spectrosc. Radiat. Transfer 184, 40–43 (2016).
[Crossref]

Zhang, W. G.

Zhang, X.

Zhao, C.

Zhao, Z.

F. Huang, X. Shen, G. Li, G. Wang, and Z. Zhao, “Influence of background radiation on space target detection in the long wave infrared range,” Opt. Eng. 51(8), 086402 (2012).
[Crossref]

Appl. Opt. (4)

Earth-Sci. Rev. (1)

A. Kokhanovsky, “Optical properties of terrestrial clouds,” Earth-Sci. Rev. 64(3-4), 189–241 (2004).
[Crossref]

Geophys. Res. Lett. (1)

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Figures (21)

Fig. 1.
Fig. 1. Atmospheric transmittance.
Fig. 2.
Fig. 2. Infrared system in the geostationary orbit for aircraft target detection.
Fig. 3.
Fig. 3. (a) Cloud top temperature. (b) Cloud classification.
Fig. 4.
Fig. 4. Spectral emissivity of water clouds and ice clouds. The effective radius of the water cloud (reff,water) is 5µm, and the effective radius of the ice cloud (reff,ice) is 50µm.
Fig. 5.
Fig. 5. Solar incident irradiance at the cloud top.
Fig. 6.
Fig. 6. (a) Water cloud scattering phase function. (b) Ice cloud scattering phase function.
Fig. 7.
Fig. 7. Water cloud bidirectional reflectance distribution (a), (b) and (c). Ice cloud bidirectional reflectance distribution (d), (e), and (f). (The longitude of the area is 105°E, the latitude is 5°N. The solar zenith angle is 28.43°, the azimuth is 0° when the local time is 12:00.)
Fig. 8.
Fig. 8. (a) Sea surface temperature field. (b) Sea surface bidirectional reflectance distribution. (12:00 local time on December 20, 2017)
Fig. 9.
Fig. 9. Background radiation field is sampled by the detector.
Fig. 10.
Fig. 10. Modeling flow of sea/cloud background radiation field in the detector field of view.
Fig. 11.
Fig. 11. Temperature distribution of the plume at different observation angles.
Fig. 12.
Fig. 12. Spectral emissivity of the mixed gas in the plume.
Fig. 13.
Fig. 13. Ideal imagery (a) and practical imagery (b) of sub-pixel target. (c) Diagram of the imaging process.
Fig. 14.
Fig. 14. Imaging features of the target at different heights in 2.65–2.90µm band.
Fig. 15.
Fig. 15. Imaging features of the target at different heights in 4.25–4.50µm band.
Fig. 16.
Fig. 16. Imaging features of the target at different heights in 3–5µm band.
Fig. 17.
Fig. 17. The relationship between the local SCR and the flight height.
Fig. 18.
Fig. 18. Imaging features of the target at different backgrounds in 2.65–2.90µm band.
Fig. 19.
Fig. 19. Imaging features of the target at different backgrounds in 4.25–4.50µm band.
Fig. 20.
Fig. 20. Imaging features of the target at different backgrounds in 3–5µm band.
Fig. 21.
Fig. 21. The grayscale difference between the aircraft plume and the local background at the different angles.

Tables (1)

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Table 1. Local SCR of aircraft plume in different backgrounds

Equations (29)

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S C R = I ¯ t I ¯ b σ b
L b k g ( λ ) = Z e τ c d L c ( λ ) + Z e τ s c d L s ( λ ) + ( 1 Z e ) τ s d L s ( λ ) + L a ( λ )
L c l o u d , s e l f ( λ ) = ε c l o u d ( λ ) M ( T c l o u d , λ ) π
ε c l o u d ( λ ) = 1 exp [ z 1 z 2 σ a ( z ) d z ]
ε c l o u d ( λ ) = 1 exp ( k z )
k w a t e r c l o u d ( λ ) = π r 1 r 2 r 2 Q a b s ( λ , r ) n ( r ) d r
k i c e c l o u d ( λ ) = ( 1 w ) β
L c l o u d , r e f l ( λ ) = τ S c ( λ ) E s u n cos θ i B R D F c l o u d ( λ , θ i , φ i , θ r , φ r )
B R D F ( θ i , φ i , θ r , φ r ) = w 4 π P ( Θ ) cos θ i cos θ i + cos θ r
cos Θ = cos θ i cos θ r sin θ i sin θ r cos ( φ i φ r )
P ( Θ ) = λ 1 λ 2 r 1 r 2 P ( Θ , λ , r ) n ( r ) v ( λ ) d r d λ
r e f f = d v 3 / d s 2
d s = exp [ i = 0 4 a n ( ln D ) i ]
d v = exp [ i = 0 4 b n ( ln D ) i ]
L s ( λ ) = L s e a , s e l f ( λ ) + L s e a , r e f l ( λ ) = ε s e a M ( T s e a , λ ) π + τ S s ( λ ) E s u n cos θ i B R D F s e a ( θ i , φ i , θ r , φ r )
n h , v = f t a n ω h , v / d
r s = d R / f
l h , v = n h , v r s
n i , j = l h , v / r
θ r = n v n j { π 2 [ α a r c t a n ( m d f ) ] }
B R D F s e a / c l o u d _ t e x t u r e = i = ( h 1 ) ( n i / n h ) h ( n i / n h ) j = ( v 1 ) ( n j / n v ) v ( n j / n v ) B R D F s e a / c l o u d ( θ r i , φ r j )
L t r g 1 , 2 , 3 ( λ , α ) = τ ( λ , α , r 1 , 2 , 3 ) L p l u m e ( λ , α ) + L a ( λ , α , r 1 , 2 , 3 )
r 1 = d a + d c + H c b o t t o m H t sin α
r 2 = d a + d c H t H c b o t t o m sin α
r 3 = d a H t ( H c b o t t o m + H c t h i c k n e s s ) sin α
L p l u m e ( λ , α ) = ε plume ( λ , α ) M b b ( λ , T p l u m e ) / π
{ Δ V s 1 = λ 1 λ 2 R λ π 4 Δ L 1 ( λ ) A d F 2 A s 1 A D A S τ o ( λ ) τ a t m ( λ ) d λ Δ V s 2 = λ 1 λ 2 R λ π 4 Δ L 2 ( λ ) A d F 2 A s 2 A D A S τ o ( λ ) τ a t m ( λ ) d λ
{ Δ V s 1 = λ 1 λ 2 R λ Δ L 1 ( λ ) A s 1 A o R 2 T T F τ o ( λ ) τ a t m ( λ ) d λ Δ V s 2 = λ 1 λ 2 R λ Δ L 2 ( λ ) A s 2 A o R 2 T T F τ o ( λ ) τ a t m ( λ ) d λ
G ( i , j ) = 2 α 1 V m a x V m i n ( Δ V s ( i , j ) V m i n )

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