Abstract

The solid angle (Ω) subtended by the hot power-plant surfaces of a typical fighter aircraft, on the detector of an infrared (IR) guided missile, is analytically obtained. The use of the parallel rays projection method simplifies the incorporation of the effect of the optical blocking by engine surfaces, on Ω-subtended. This methodology enables the evaluation of the relative contribution of the IR signature from well-resolved distributed sources, and is important for imaging infrared detection studies. The complex 3D surface of a rear fuselage is projected onto an equivalent planar area normal to the viewing aspect, which would give the same Ω-subtended.

© 2007 Optical Society of America

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  1. C. J. Chen, K. K. Choi, W. H. Chang, and D. C. Tsui, "Two-color corrugated quantum-well infrared photodetector for remote temperature sensing," Appl. Phys. Lett. 72, 7-9 (1998).
    [CrossRef]
  2. K. K. Choi, "Corrugated quantum well infrared photodetectors and arrays," Int. J. High Speed Electronics and Systems 12, 715-759 (2002).
    [CrossRef]
  3. W. A. Bell and B. B. Glasgow, "Impact of advances in imaging infrared detectors on antiaircraft missile performance," in Proc. SPIE, Infrared Imaging Systems: Design, Analysis, Modelling, and Testing, G. C. Holst, ed. 3701, SPIE , Washington, 244-253 (1999).
    [CrossRef]
  4. D. Howe, "Introduction to the basic technology of stealth aircraft. Part 1. Basic considerations and aircraft self-emitted signals (passive considerations)," ASME J. Engineering for Gas Turbines and Power 113, 75-79 (1991).
    [CrossRef]
  5. G. A. Rao and S. P. Mahulikar, "Effect of atmospheric transmission and radiance on aircraft infrared signatures," AIAA J. Aircraft 42, 1046-1054 (2005).
    [CrossRef]
  6. S. P. Mahulikar, G. A. Rao, S. K. Sane, and A. G. Marathe, "Aircraft plume infrared signature in non-afterburning mode," AIAA J. Thermophysics & Heat Transfer 19, 413-415 (2005).
    [CrossRef]
  7. D. R. Hudson, Jr., Infrared System Engineering (Wiley, 1969), pp. 85-87.
  8. W. De Jong, S. P. Van Den Broek, and R. Van Der Nol, "IR seeker simulator to evaluate IR decoy effectiveness," in Proc. SPIE, Targets and Backgrounds VIII: Characterization and Representation, W. R. Watkins, D. Clement, and W. R. Reynolds, eds. 4718, SPIE , Washington, 164-172 (2002).
    [CrossRef]
  9. R. P. Gardner and A. Carnesale, "The solid angle subtended at a point by a circular disk," Nuclear Instruments and Methods 73, 228-230 (1969).
    [CrossRef]
  10. R. P. Gardner and K. Verghese, "On the solid angle subtended by a circular disk," Nucl. Instrum. Methods 93, 163-167 (1971).
    [CrossRef]
  11. K. Verghese, R. P. Gardner, and R. M. Felder, "Solid angle subtended by a circular cylinder," Nucl. Instrum. Methods 101, 391-393 (1972).
    [CrossRef]
  12. S. Tryka, "Angular distribution of the solid angle at a point subtended by a circular disk," Opt. Comm. 137, 317-333 (1997).
    [CrossRef]
  13. E. Galiano and C. Pagnutti, "An analytical solution for the solid angle subtended by a circular detector for a symmetrically positioned linear source," Appl. Radiat. Isot. 64, 603-607 (2006).
    [CrossRef] [PubMed]
  14. M. J. Prata, "Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with orthogonal axes," Radiat. Phys. Chem. 66, 387-395 (2003).
    [CrossRef]
  15. L. M. Milne-Thomson, "Elliptic integrals," in Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, eds. (9th Printing, Dover, 1964), pp. 589-627.
  16. M. J. Prata, "Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals," Radiat. Phys. Chem. 67, 599-603 (2003).
    [CrossRef]
  17. A. V. Paxton, "Solid angle calculation for a circular disk," Rev. Sci. Instrum. 30, 254-258 (1959).
    [CrossRef]
  18. R. Carchon, E. Van Camp, G. Knuyt, R. Van De Vyver, J. Devos, and H. Ferdinande, "A general solid angle calculation by a Monte Carlo method," Nuclear Instrum. Methods 128, 195-199 (1975).
    [CrossRef]
  19. B. Th. Stavroulaki and S. N. Kaplanis, "Monte Carlo solutions of the solid angle integrals for radiation detectors," Comput. Phys. Commun. 18, 7-12 (1979).
    [CrossRef]
  20. L. Wielopolski, "The Monte Carlo calculation of the average solid angle subtended by a right circular cylinder from distributed sources," Nucl. Instrum. Methods 143, 577-581 (1977).
    [CrossRef]
  21. S. P. Mahulikar, P. S. Kolhe, and G. A. Rao, "Skin temperature prediction of aircraft rear fuselage with multi-mode thermal model," AIAA J. Thermophysics and Heat Transfer 19, 114-124 (2005).
    [CrossRef]
  22. S. P. Mahulikar, G. A. Rao, and P. S. Kolhe, "Infrared signatures of low flying aircraft and their rear fuselage skin's emissivity optimization," AIAA J. Aircraft 43, 226-232 (2006).
    [CrossRef]

2006 (2)

E. Galiano and C. Pagnutti, "An analytical solution for the solid angle subtended by a circular detector for a symmetrically positioned linear source," Appl. Radiat. Isot. 64, 603-607 (2006).
[CrossRef] [PubMed]

S. P. Mahulikar, G. A. Rao, and P. S. Kolhe, "Infrared signatures of low flying aircraft and their rear fuselage skin's emissivity optimization," AIAA J. Aircraft 43, 226-232 (2006).
[CrossRef]

2005 (3)

S. P. Mahulikar, P. S. Kolhe, and G. A. Rao, "Skin temperature prediction of aircraft rear fuselage with multi-mode thermal model," AIAA J. Thermophysics and Heat Transfer 19, 114-124 (2005).
[CrossRef]

G. A. Rao and S. P. Mahulikar, "Effect of atmospheric transmission and radiance on aircraft infrared signatures," AIAA J. Aircraft 42, 1046-1054 (2005).
[CrossRef]

S. P. Mahulikar, G. A. Rao, S. K. Sane, and A. G. Marathe, "Aircraft plume infrared signature in non-afterburning mode," AIAA J. Thermophysics & Heat Transfer 19, 413-415 (2005).
[CrossRef]

2003 (2)

M. J. Prata, "Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with orthogonal axes," Radiat. Phys. Chem. 66, 387-395 (2003).
[CrossRef]

M. J. Prata, "Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals," Radiat. Phys. Chem. 67, 599-603 (2003).
[CrossRef]

2002 (2)

K. K. Choi, "Corrugated quantum well infrared photodetectors and arrays," Int. J. High Speed Electronics and Systems 12, 715-759 (2002).
[CrossRef]

W. De Jong, S. P. Van Den Broek, and R. Van Der Nol, "IR seeker simulator to evaluate IR decoy effectiveness," in Proc. SPIE, Targets and Backgrounds VIII: Characterization and Representation, W. R. Watkins, D. Clement, and W. R. Reynolds, eds. 4718, SPIE , Washington, 164-172 (2002).
[CrossRef]

1999 (1)

W. A. Bell and B. B. Glasgow, "Impact of advances in imaging infrared detectors on antiaircraft missile performance," in Proc. SPIE, Infrared Imaging Systems: Design, Analysis, Modelling, and Testing, G. C. Holst, ed. 3701, SPIE , Washington, 244-253 (1999).
[CrossRef]

1998 (1)

C. J. Chen, K. K. Choi, W. H. Chang, and D. C. Tsui, "Two-color corrugated quantum-well infrared photodetector for remote temperature sensing," Appl. Phys. Lett. 72, 7-9 (1998).
[CrossRef]

1997 (1)

S. Tryka, "Angular distribution of the solid angle at a point subtended by a circular disk," Opt. Comm. 137, 317-333 (1997).
[CrossRef]

1991 (1)

D. Howe, "Introduction to the basic technology of stealth aircraft. Part 1. Basic considerations and aircraft self-emitted signals (passive considerations)," ASME J. Engineering for Gas Turbines and Power 113, 75-79 (1991).
[CrossRef]

1979 (1)

B. Th. Stavroulaki and S. N. Kaplanis, "Monte Carlo solutions of the solid angle integrals for radiation detectors," Comput. Phys. Commun. 18, 7-12 (1979).
[CrossRef]

1977 (1)

L. Wielopolski, "The Monte Carlo calculation of the average solid angle subtended by a right circular cylinder from distributed sources," Nucl. Instrum. Methods 143, 577-581 (1977).
[CrossRef]

1975 (1)

R. Carchon, E. Van Camp, G. Knuyt, R. Van De Vyver, J. Devos, and H. Ferdinande, "A general solid angle calculation by a Monte Carlo method," Nuclear Instrum. Methods 128, 195-199 (1975).
[CrossRef]

1972 (1)

K. Verghese, R. P. Gardner, and R. M. Felder, "Solid angle subtended by a circular cylinder," Nucl. Instrum. Methods 101, 391-393 (1972).
[CrossRef]

1971 (1)

R. P. Gardner and K. Verghese, "On the solid angle subtended by a circular disk," Nucl. Instrum. Methods 93, 163-167 (1971).
[CrossRef]

1969 (2)

R. P. Gardner and A. Carnesale, "The solid angle subtended at a point by a circular disk," Nuclear Instruments and Methods 73, 228-230 (1969).
[CrossRef]

D. R. Hudson, Jr., Infrared System Engineering (Wiley, 1969), pp. 85-87.

1964 (1)

L. M. Milne-Thomson, "Elliptic integrals," in Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, eds. (9th Printing, Dover, 1964), pp. 589-627.

1959 (1)

A. V. Paxton, "Solid angle calculation for a circular disk," Rev. Sci. Instrum. 30, 254-258 (1959).
[CrossRef]

Bell, W. A.

W. A. Bell and B. B. Glasgow, "Impact of advances in imaging infrared detectors on antiaircraft missile performance," in Proc. SPIE, Infrared Imaging Systems: Design, Analysis, Modelling, and Testing, G. C. Holst, ed. 3701, SPIE , Washington, 244-253 (1999).
[CrossRef]

Carchon, R.

R. Carchon, E. Van Camp, G. Knuyt, R. Van De Vyver, J. Devos, and H. Ferdinande, "A general solid angle calculation by a Monte Carlo method," Nuclear Instrum. Methods 128, 195-199 (1975).
[CrossRef]

Carnesale, A.

R. P. Gardner and A. Carnesale, "The solid angle subtended at a point by a circular disk," Nuclear Instruments and Methods 73, 228-230 (1969).
[CrossRef]

Chang, W. H.

C. J. Chen, K. K. Choi, W. H. Chang, and D. C. Tsui, "Two-color corrugated quantum-well infrared photodetector for remote temperature sensing," Appl. Phys. Lett. 72, 7-9 (1998).
[CrossRef]

Chen, C. J.

C. J. Chen, K. K. Choi, W. H. Chang, and D. C. Tsui, "Two-color corrugated quantum-well infrared photodetector for remote temperature sensing," Appl. Phys. Lett. 72, 7-9 (1998).
[CrossRef]

Choi, K. K.

K. K. Choi, "Corrugated quantum well infrared photodetectors and arrays," Int. J. High Speed Electronics and Systems 12, 715-759 (2002).
[CrossRef]

C. J. Chen, K. K. Choi, W. H. Chang, and D. C. Tsui, "Two-color corrugated quantum-well infrared photodetector for remote temperature sensing," Appl. Phys. Lett. 72, 7-9 (1998).
[CrossRef]

De Jong, W.

W. De Jong, S. P. Van Den Broek, and R. Van Der Nol, "IR seeker simulator to evaluate IR decoy effectiveness," in Proc. SPIE, Targets and Backgrounds VIII: Characterization and Representation, W. R. Watkins, D. Clement, and W. R. Reynolds, eds. 4718, SPIE , Washington, 164-172 (2002).
[CrossRef]

Devos, J.

R. Carchon, E. Van Camp, G. Knuyt, R. Van De Vyver, J. Devos, and H. Ferdinande, "A general solid angle calculation by a Monte Carlo method," Nuclear Instrum. Methods 128, 195-199 (1975).
[CrossRef]

Felder, R. M.

K. Verghese, R. P. Gardner, and R. M. Felder, "Solid angle subtended by a circular cylinder," Nucl. Instrum. Methods 101, 391-393 (1972).
[CrossRef]

Ferdinande, H.

R. Carchon, E. Van Camp, G. Knuyt, R. Van De Vyver, J. Devos, and H. Ferdinande, "A general solid angle calculation by a Monte Carlo method," Nuclear Instrum. Methods 128, 195-199 (1975).
[CrossRef]

Galiano, E.

E. Galiano and C. Pagnutti, "An analytical solution for the solid angle subtended by a circular detector for a symmetrically positioned linear source," Appl. Radiat. Isot. 64, 603-607 (2006).
[CrossRef] [PubMed]

Gardner, R. P.

K. Verghese, R. P. Gardner, and R. M. Felder, "Solid angle subtended by a circular cylinder," Nucl. Instrum. Methods 101, 391-393 (1972).
[CrossRef]

R. P. Gardner and K. Verghese, "On the solid angle subtended by a circular disk," Nucl. Instrum. Methods 93, 163-167 (1971).
[CrossRef]

R. P. Gardner and A. Carnesale, "The solid angle subtended at a point by a circular disk," Nuclear Instruments and Methods 73, 228-230 (1969).
[CrossRef]

Glasgow, B. B.

W. A. Bell and B. B. Glasgow, "Impact of advances in imaging infrared detectors on antiaircraft missile performance," in Proc. SPIE, Infrared Imaging Systems: Design, Analysis, Modelling, and Testing, G. C. Holst, ed. 3701, SPIE , Washington, 244-253 (1999).
[CrossRef]

Howe, D.

D. Howe, "Introduction to the basic technology of stealth aircraft. Part 1. Basic considerations and aircraft self-emitted signals (passive considerations)," ASME J. Engineering for Gas Turbines and Power 113, 75-79 (1991).
[CrossRef]

Hudson, D. R.

D. R. Hudson, Jr., Infrared System Engineering (Wiley, 1969), pp. 85-87.

Kaplanis, S. N.

B. Th. Stavroulaki and S. N. Kaplanis, "Monte Carlo solutions of the solid angle integrals for radiation detectors," Comput. Phys. Commun. 18, 7-12 (1979).
[CrossRef]

Knuyt, G.

R. Carchon, E. Van Camp, G. Knuyt, R. Van De Vyver, J. Devos, and H. Ferdinande, "A general solid angle calculation by a Monte Carlo method," Nuclear Instrum. Methods 128, 195-199 (1975).
[CrossRef]

Kolhe, P. S.

S. P. Mahulikar, G. A. Rao, and P. S. Kolhe, "Infrared signatures of low flying aircraft and their rear fuselage skin's emissivity optimization," AIAA J. Aircraft 43, 226-232 (2006).
[CrossRef]

S. P. Mahulikar, P. S. Kolhe, and G. A. Rao, "Skin temperature prediction of aircraft rear fuselage with multi-mode thermal model," AIAA J. Thermophysics and Heat Transfer 19, 114-124 (2005).
[CrossRef]

Mahulikar, S. P.

S. P. Mahulikar, G. A. Rao, and P. S. Kolhe, "Infrared signatures of low flying aircraft and their rear fuselage skin's emissivity optimization," AIAA J. Aircraft 43, 226-232 (2006).
[CrossRef]

S. P. Mahulikar, P. S. Kolhe, and G. A. Rao, "Skin temperature prediction of aircraft rear fuselage with multi-mode thermal model," AIAA J. Thermophysics and Heat Transfer 19, 114-124 (2005).
[CrossRef]

G. A. Rao and S. P. Mahulikar, "Effect of atmospheric transmission and radiance on aircraft infrared signatures," AIAA J. Aircraft 42, 1046-1054 (2005).
[CrossRef]

S. P. Mahulikar, G. A. Rao, S. K. Sane, and A. G. Marathe, "Aircraft plume infrared signature in non-afterburning mode," AIAA J. Thermophysics & Heat Transfer 19, 413-415 (2005).
[CrossRef]

Marathe, A. G.

S. P. Mahulikar, G. A. Rao, S. K. Sane, and A. G. Marathe, "Aircraft plume infrared signature in non-afterburning mode," AIAA J. Thermophysics & Heat Transfer 19, 413-415 (2005).
[CrossRef]

Milne-Thomson, L. M.

L. M. Milne-Thomson, "Elliptic integrals," in Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, eds. (9th Printing, Dover, 1964), pp. 589-627.

Pagnutti, C.

E. Galiano and C. Pagnutti, "An analytical solution for the solid angle subtended by a circular detector for a symmetrically positioned linear source," Appl. Radiat. Isot. 64, 603-607 (2006).
[CrossRef] [PubMed]

Paxton, A. V.

A. V. Paxton, "Solid angle calculation for a circular disk," Rev. Sci. Instrum. 30, 254-258 (1959).
[CrossRef]

Prata, M. J.

M. J. Prata, "Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with orthogonal axes," Radiat. Phys. Chem. 66, 387-395 (2003).
[CrossRef]

M. J. Prata, "Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals," Radiat. Phys. Chem. 67, 599-603 (2003).
[CrossRef]

Rao, G. A.

S. P. Mahulikar, G. A. Rao, and P. S. Kolhe, "Infrared signatures of low flying aircraft and their rear fuselage skin's emissivity optimization," AIAA J. Aircraft 43, 226-232 (2006).
[CrossRef]

S. P. Mahulikar, P. S. Kolhe, and G. A. Rao, "Skin temperature prediction of aircraft rear fuselage with multi-mode thermal model," AIAA J. Thermophysics and Heat Transfer 19, 114-124 (2005).
[CrossRef]

G. A. Rao and S. P. Mahulikar, "Effect of atmospheric transmission and radiance on aircraft infrared signatures," AIAA J. Aircraft 42, 1046-1054 (2005).
[CrossRef]

S. P. Mahulikar, G. A. Rao, S. K. Sane, and A. G. Marathe, "Aircraft plume infrared signature in non-afterburning mode," AIAA J. Thermophysics & Heat Transfer 19, 413-415 (2005).
[CrossRef]

Sane, S. K.

S. P. Mahulikar, G. A. Rao, S. K. Sane, and A. G. Marathe, "Aircraft plume infrared signature in non-afterburning mode," AIAA J. Thermophysics & Heat Transfer 19, 413-415 (2005).
[CrossRef]

Stavroulaki, B. Th.

B. Th. Stavroulaki and S. N. Kaplanis, "Monte Carlo solutions of the solid angle integrals for radiation detectors," Comput. Phys. Commun. 18, 7-12 (1979).
[CrossRef]

Tryka, S.

S. Tryka, "Angular distribution of the solid angle at a point subtended by a circular disk," Opt. Comm. 137, 317-333 (1997).
[CrossRef]

Tsui, D. C.

C. J. Chen, K. K. Choi, W. H. Chang, and D. C. Tsui, "Two-color corrugated quantum-well infrared photodetector for remote temperature sensing," Appl. Phys. Lett. 72, 7-9 (1998).
[CrossRef]

Van Camp, E.

R. Carchon, E. Van Camp, G. Knuyt, R. Van De Vyver, J. Devos, and H. Ferdinande, "A general solid angle calculation by a Monte Carlo method," Nuclear Instrum. Methods 128, 195-199 (1975).
[CrossRef]

Van De Vyver, R.

R. Carchon, E. Van Camp, G. Knuyt, R. Van De Vyver, J. Devos, and H. Ferdinande, "A general solid angle calculation by a Monte Carlo method," Nuclear Instrum. Methods 128, 195-199 (1975).
[CrossRef]

Van Den Broek, S. P.

W. De Jong, S. P. Van Den Broek, and R. Van Der Nol, "IR seeker simulator to evaluate IR decoy effectiveness," in Proc. SPIE, Targets and Backgrounds VIII: Characterization and Representation, W. R. Watkins, D. Clement, and W. R. Reynolds, eds. 4718, SPIE , Washington, 164-172 (2002).
[CrossRef]

Van Der Nol, R.

W. De Jong, S. P. Van Den Broek, and R. Van Der Nol, "IR seeker simulator to evaluate IR decoy effectiveness," in Proc. SPIE, Targets and Backgrounds VIII: Characterization and Representation, W. R. Watkins, D. Clement, and W. R. Reynolds, eds. 4718, SPIE , Washington, 164-172 (2002).
[CrossRef]

Verghese, K.

K. Verghese, R. P. Gardner, and R. M. Felder, "Solid angle subtended by a circular cylinder," Nucl. Instrum. Methods 101, 391-393 (1972).
[CrossRef]

R. P. Gardner and K. Verghese, "On the solid angle subtended by a circular disk," Nucl. Instrum. Methods 93, 163-167 (1971).
[CrossRef]

Wielopolski, L.

L. Wielopolski, "The Monte Carlo calculation of the average solid angle subtended by a right circular cylinder from distributed sources," Nucl. Instrum. Methods 143, 577-581 (1977).
[CrossRef]

AIAA J. Aircraft (2)

G. A. Rao and S. P. Mahulikar, "Effect of atmospheric transmission and radiance on aircraft infrared signatures," AIAA J. Aircraft 42, 1046-1054 (2005).
[CrossRef]

S. P. Mahulikar, G. A. Rao, and P. S. Kolhe, "Infrared signatures of low flying aircraft and their rear fuselage skin's emissivity optimization," AIAA J. Aircraft 43, 226-232 (2006).
[CrossRef]

AIAA J. Thermophysics & Heat Transfer (1)

S. P. Mahulikar, G. A. Rao, S. K. Sane, and A. G. Marathe, "Aircraft plume infrared signature in non-afterburning mode," AIAA J. Thermophysics & Heat Transfer 19, 413-415 (2005).
[CrossRef]

AIAA J. Thermophysics and Heat Transfer (1)

S. P. Mahulikar, P. S. Kolhe, and G. A. Rao, "Skin temperature prediction of aircraft rear fuselage with multi-mode thermal model," AIAA J. Thermophysics and Heat Transfer 19, 114-124 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

C. J. Chen, K. K. Choi, W. H. Chang, and D. C. Tsui, "Two-color corrugated quantum-well infrared photodetector for remote temperature sensing," Appl. Phys. Lett. 72, 7-9 (1998).
[CrossRef]

Appl. Radiat. Isot. (1)

E. Galiano and C. Pagnutti, "An analytical solution for the solid angle subtended by a circular detector for a symmetrically positioned linear source," Appl. Radiat. Isot. 64, 603-607 (2006).
[CrossRef] [PubMed]

ASME J. Engineering for Gas Turbines and Power (1)

D. Howe, "Introduction to the basic technology of stealth aircraft. Part 1. Basic considerations and aircraft self-emitted signals (passive considerations)," ASME J. Engineering for Gas Turbines and Power 113, 75-79 (1991).
[CrossRef]

Comput. Phys. Commun. (1)

B. Th. Stavroulaki and S. N. Kaplanis, "Monte Carlo solutions of the solid angle integrals for radiation detectors," Comput. Phys. Commun. 18, 7-12 (1979).
[CrossRef]

Int. J. High Speed Electronics and Systems (1)

K. K. Choi, "Corrugated quantum well infrared photodetectors and arrays," Int. J. High Speed Electronics and Systems 12, 715-759 (2002).
[CrossRef]

Nucl. Instrum. Methods (3)

R. P. Gardner and K. Verghese, "On the solid angle subtended by a circular disk," Nucl. Instrum. Methods 93, 163-167 (1971).
[CrossRef]

K. Verghese, R. P. Gardner, and R. M. Felder, "Solid angle subtended by a circular cylinder," Nucl. Instrum. Methods 101, 391-393 (1972).
[CrossRef]

L. Wielopolski, "The Monte Carlo calculation of the average solid angle subtended by a right circular cylinder from distributed sources," Nucl. Instrum. Methods 143, 577-581 (1977).
[CrossRef]

Nuclear Instrum. Methods (1)

R. Carchon, E. Van Camp, G. Knuyt, R. Van De Vyver, J. Devos, and H. Ferdinande, "A general solid angle calculation by a Monte Carlo method," Nuclear Instrum. Methods 128, 195-199 (1975).
[CrossRef]

Nuclear Instruments and Methods (1)

R. P. Gardner and A. Carnesale, "The solid angle subtended at a point by a circular disk," Nuclear Instruments and Methods 73, 228-230 (1969).
[CrossRef]

Opt. Comm. (1)

S. Tryka, "Angular distribution of the solid angle at a point subtended by a circular disk," Opt. Comm. 137, 317-333 (1997).
[CrossRef]

Radiat. Phys. Chem. (2)

M. J. Prata, "Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with orthogonal axes," Radiat. Phys. Chem. 66, 387-395 (2003).
[CrossRef]

M. J. Prata, "Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals," Radiat. Phys. Chem. 67, 599-603 (2003).
[CrossRef]

Rev. Sci. Instrum. (1)

A. V. Paxton, "Solid angle calculation for a circular disk," Rev. Sci. Instrum. 30, 254-258 (1959).
[CrossRef]

SPIE (2)

W. De Jong, S. P. Van Den Broek, and R. Van Der Nol, "IR seeker simulator to evaluate IR decoy effectiveness," in Proc. SPIE, Targets and Backgrounds VIII: Characterization and Representation, W. R. Watkins, D. Clement, and W. R. Reynolds, eds. 4718, SPIE , Washington, 164-172 (2002).
[CrossRef]

W. A. Bell and B. B. Glasgow, "Impact of advances in imaging infrared detectors on antiaircraft missile performance," in Proc. SPIE, Infrared Imaging Systems: Design, Analysis, Modelling, and Testing, G. C. Holst, ed. 3701, SPIE , Washington, 244-253 (1999).
[CrossRef]

Other (2)

D. R. Hudson, Jr., Infrared System Engineering (Wiley, 1969), pp. 85-87.

L. M. Milne-Thomson, "Elliptic integrals," in Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, eds. (9th Printing, Dover, 1964), pp. 589-627.

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Figures (11)

Fig. 1
Fig. 1

Schematic of typical aircraft engine layout for estimation of Ω-subtended.

Fig. 2
Fig. 2

(Color online) Planar area ( A pl ) of a surface element in discretized aircraft engine layout.

Fig. 3
Fig. 3

(Color online) Classification of axially discretized elements in jet-pipe and C-D nozzle (a) ϕ = 0 ° , (b) 0 ° < ϕ < 90 ° .

Fig. 4
Fig. 4

Visible portion of bounding disc in type 1 visible elements (a) 0 ° ϕ α d , (b) α d < ϕ < ϕ 1 .

Fig. 5
Fig. 5

(Color online) Visible area of bounding disc in jet-pipe and convergent section, for different ϕ (a) ϕ = 0 ° , (b) 0 ° < ϕ ϕ 2 , (c) ϕ 2 < ϕ ϕ 3 , (d) ϕ 3 < ϕ ϕ 4 .

Fig. 6
Fig. 6

(Color online) Visible area of bounding disc of element in invisible elements of type 2.

Fig. 7
Fig. 7

(Color online) The A pl variation for axially discretised rear fuselage skin element, for different ϕ (a) ϕ = 0 ° (axial viewing aspect), (b) 0 ° < ϕ < α , (c) ϕ = α , (d) α < ϕ < 90 ° , (e) ϕ = 90 ° .

Fig. 8
Fig. 8

(Color online) Polar plot of Ω-subtended by inner surfaces of jet-pipe and C-D nozzle, and inlet disc.

Fig. 9
Fig. 9

(Color online) Distribution of ( Ω / l ) for jet-pipe and C-D nozzle inner surfaces.

Fig. 10
Fig. 10

Polar plot of Ω-subtended by all inner surfaces, rear fuselage skin, and entire engine layout.

Fig. 11
Fig. 11

(Color online) Distribution of ( Ω / l ) for rear fuselage skin elements.

Tables (1)

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Table 1 View Angle and Axial Range of Visibility, and Planar Area of Inner Surface Elements

Equations (11)

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Ω = S ρ ^ · d S ρ 2 ;
Ω = ( A pl / ρ 2 ) .
A p l = ( m a g n i t u d e o f d i f f e r e n c e i n v i s i b l e a r e a s o f t w o b o u n d i n g d i s c s o f e l e m e n t ) cos ( ϕ ) .
A R r = Sum   of   areas   of   two   sectors—area   of   quadrilateral = r 2 cos 1 ( d 2 + r 2 R 2 2 d · r ) + R 2 cos 1 ( d 2 r 2 + R 2 2 d · R ) ½ [ ( d + r R ) ( d r + R ) ( d + r + R ) × ( r + R d ) ] 0.5 ;
Case   ( a ) , ϕ = 0 ° :    A vis,bd = ( π / 4 ) D t 2 ;
Case   ( b ) , 0 ° < ϕ ϕ 2 :    A vis,bd = A R r [ Eq .   ( 4 ) ] ,
Case   ( c ) , ϕ 2 < ϕ ϕ 3 :    A vis,bd = [ ( A R r ) a + ( A R r ) b ( π / 4 ) D t 2 ] ,
Case ( d ) , ϕ 3 < ϕ ϕ 4 :    A vis,bd = A R r [ Eq . ( 4 ) ] ,
ϕ 3 = tan 1 [ ( 1 l ed bd l d ) · ( D ed 2 D t 2 4 l d D ed 2 D bd 2 4 l ed bd ) ] ,
A pl = ( π / 4 ) ( D i 2 D i + 1 2 ) cos   ϕ .
A pl = max ( A P , A Q ) ,

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