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

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References

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    [Crossref]
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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)

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. Atmos. Sci. (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]

J. Geophys. Res. (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]

J. Geophys. Res.: Atmos. (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]

J. Quant. Spectrosc. Radiat. Transfer (1)

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

Opt. Eng. (1)

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]

Opt. Express (2)

Proc. SPIE (3)

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

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

Other (2)

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).

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).

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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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