Abstract

Based on the Physical optics approximation, the scattering field in the far zone by arbitrarily shaped objects with slightly rough surface which obeys Gaussian distribution and its two-frequency mutual coherence function are derived theoretically, and the numerical results for rough spheres and rough cylinders are given and analyzed. The results show that the function has closely relationship with the roughness and the dimension of the rough objects. The roughness and the curvature of the object influence both the amplitude and the profile of the two-frequency mutual coherence function. Also, the smaller the radius of the object, the larger the coherent bandwidth. The two-frequency mutual coherence function can be used to investigate the laser pulse scattering characteristics of arbitrarily shaped rough objects, provide theoretical basis for target recognition.

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  1. S. Abrahamsson, B. Brusmark, H. C. Strifors, and G. C. Gaunaurd, “Extraction of target signature features in the combined time-frequency domain by means of impulse radar,” Proc. SPIE 1700, 102–113 (1992).
    [CrossRef]
  2. H. C. Strifors and G. C. Gaunaurd, “Scattering of electromagnetic pulses by simple-shaped targets with radar cross section modified by a dielectric coating,” IEEE Trans. Antenn. Propag. 46(9), 1252–1262 (1998).
    [CrossRef]
  3. L. Mees, G. Gouesbet, and G. Gréhan, “Scattering of laser pulses (plane wave and focused gaussian beam) by spheres,” Appl. Opt. 40(15), 2546–2550 (2001).
    [CrossRef]
  4. Y. H. Li and Z. S. Wu, “Targets recognition using subnanosecond pulse laser range profiles,” Opt. Express 18(16), 16788–16796 (2010).
    [CrossRef] [PubMed]
  5. Y. H. Li, Z. S. Wu, Y. J. Gong, G. Zhang, and M. J. Wang, “Laser one-dimensional range profile,” Acta Phys. Sin. 59, 6985–6990 (2010).
  6. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).
  7. A. Ishimaru, L. Ailes-sengers, P. Phu, and D. Winebrenner, “Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces,” Waves Random Media 4(2), 139–148 (1994).
    [CrossRef]
  8. C. Hui, W. Zhensenu, and B. Lu, “Infrared laser pulse scattering from randomly rough surfaces,” Int. J. Infrared Millim. Waves 25(8), 1211–1219 (2004).
    [CrossRef]
  9. L. Guo and C. Kim, “Study on the two-frequency scattering cross section and pulse broadening of the one-dimensional fractal sea surface at millimeter wave frequency,” Prog. Electromagn. Res. 37, 221–234 (2002).
    [CrossRef]
  10. E. Bahar and M. A. Fizwater, “Scattering and depolarization by large conducting spheres with rough surface,” Appl. Opt. 24(12), 1820–1825 (1985).
    [CrossRef] [PubMed]
  11. E. Bahar and M. A. Fitzwater, “Scattering and depolarization by conducting cylinders with rough surfaces,” Appl. Opt. 25(11), 1826–1832 (1986).
    [CrossRef] [PubMed]
  12. R. Schiffer, “The Coherent scattering cross-section of a slightly rough sphere,” J. Mod. Opt. 33(8), 959–980 (1986).
  13. M. K. Abdelazeez, “Wave scattering from a large sphere with rough surface,” IEEE Trans. Antenn. Propag. 31(2), 375–377 (1983).
    [CrossRef]
  14. R. G. Berlasso, F. P. Quintián, M. A. Rebollo, N. G. Gaggioli, B. L. Sánchez Brea, and M. E. Bernabeu Martínez, “Speckle size of light scattered from slightly rough cylindrical surfaces,” Appl. Opt. 41(10), 2020–2027 (2002).
    [CrossRef] [PubMed]
  15. R. Berlasso, F. Perez Quintián, M. A. Rebollo, C. A. Raffo, and N. G. Gaggioli, “Study of speckle size of light scattered from cylindrical rough surfaces,” Appl. Opt. 39(31), 5811–5819 (2000).
    [CrossRef]
  16. Z. S. Wu, “IR Laser Backscattering by arbitrarily shaped dielectric object with rough surface,” SPIE's International Symposium on Optical Science and Engineering in San Diego, California, (21–26, July,1991).
  17. W. Zhensen and C. Suomin, “Bistatic scattering by arbitrarily shaped objects with rough surface at optical and infrared frequencies,” Int. J. Infrared Millim. Waves 13(4), 537–549 (1992).
    [CrossRef]
  18. D. J. Schertler and N. George, “Backscattering cross section of a titled, roughened disk,” J. Opt. Soc. Am. A 9(11), 2056–2066 (1992).
    [CrossRef]
  19. D. J. Schertler and N. George, “Backscattering cross section of a roughened sphere,” J. Opt. Soc. Am. A 11(8), 2286–2297 (1994).
    [CrossRef]
  20. S. Zhendong and L. Hongwei, “Model-measurement and reverse evaluation for RCS of stealthy targets,” J. Univ. Electron. Sci. Technol, China 24, 13–17 (1995).

2010

Y. H. Li, Z. S. Wu, Y. J. Gong, G. Zhang, and M. J. Wang, “Laser one-dimensional range profile,” Acta Phys. Sin. 59, 6985–6990 (2010).

Y. H. Li and Z. S. Wu, “Targets recognition using subnanosecond pulse laser range profiles,” Opt. Express 18(16), 16788–16796 (2010).
[CrossRef] [PubMed]

2004

C. Hui, W. Zhensenu, and B. Lu, “Infrared laser pulse scattering from randomly rough surfaces,” Int. J. Infrared Millim. Waves 25(8), 1211–1219 (2004).
[CrossRef]

2002

L. Guo and C. Kim, “Study on the two-frequency scattering cross section and pulse broadening of the one-dimensional fractal sea surface at millimeter wave frequency,” Prog. Electromagn. Res. 37, 221–234 (2002).
[CrossRef]

R. G. Berlasso, F. P. Quintián, M. A. Rebollo, N. G. Gaggioli, B. L. Sánchez Brea, and M. E. Bernabeu Martínez, “Speckle size of light scattered from slightly rough cylindrical surfaces,” Appl. Opt. 41(10), 2020–2027 (2002).
[CrossRef] [PubMed]

2001

2000

1998

H. C. Strifors and G. C. Gaunaurd, “Scattering of electromagnetic pulses by simple-shaped targets with radar cross section modified by a dielectric coating,” IEEE Trans. Antenn. Propag. 46(9), 1252–1262 (1998).
[CrossRef]

1995

S. Zhendong and L. Hongwei, “Model-measurement and reverse evaluation for RCS of stealthy targets,” J. Univ. Electron. Sci. Technol, China 24, 13–17 (1995).

1994

D. J. Schertler and N. George, “Backscattering cross section of a roughened sphere,” J. Opt. Soc. Am. A 11(8), 2286–2297 (1994).
[CrossRef]

A. Ishimaru, L. Ailes-sengers, P. Phu, and D. Winebrenner, “Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces,” Waves Random Media 4(2), 139–148 (1994).
[CrossRef]

1992

S. Abrahamsson, B. Brusmark, H. C. Strifors, and G. C. Gaunaurd, “Extraction of target signature features in the combined time-frequency domain by means of impulse radar,” Proc. SPIE 1700, 102–113 (1992).
[CrossRef]

W. Zhensen and C. Suomin, “Bistatic scattering by arbitrarily shaped objects with rough surface at optical and infrared frequencies,” Int. J. Infrared Millim. Waves 13(4), 537–549 (1992).
[CrossRef]

D. J. Schertler and N. George, “Backscattering cross section of a titled, roughened disk,” J. Opt. Soc. Am. A 9(11), 2056–2066 (1992).
[CrossRef]

1986

E. Bahar and M. A. Fitzwater, “Scattering and depolarization by conducting cylinders with rough surfaces,” Appl. Opt. 25(11), 1826–1832 (1986).
[CrossRef] [PubMed]

R. Schiffer, “The Coherent scattering cross-section of a slightly rough sphere,” J. Mod. Opt. 33(8), 959–980 (1986).

1985

1983

M. K. Abdelazeez, “Wave scattering from a large sphere with rough surface,” IEEE Trans. Antenn. Propag. 31(2), 375–377 (1983).
[CrossRef]

Abdelazeez, M. K.

M. K. Abdelazeez, “Wave scattering from a large sphere with rough surface,” IEEE Trans. Antenn. Propag. 31(2), 375–377 (1983).
[CrossRef]

Abrahamsson, S.

S. Abrahamsson, B. Brusmark, H. C. Strifors, and G. C. Gaunaurd, “Extraction of target signature features in the combined time-frequency domain by means of impulse radar,” Proc. SPIE 1700, 102–113 (1992).
[CrossRef]

Ailes-sengers, L.

A. Ishimaru, L. Ailes-sengers, P. Phu, and D. Winebrenner, “Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces,” Waves Random Media 4(2), 139–148 (1994).
[CrossRef]

Bahar, E.

Berlasso, R.

Berlasso, R. G.

Bernabeu Martínez, M. E.

Brusmark, B.

S. Abrahamsson, B. Brusmark, H. C. Strifors, and G. C. Gaunaurd, “Extraction of target signature features in the combined time-frequency domain by means of impulse radar,” Proc. SPIE 1700, 102–113 (1992).
[CrossRef]

Fitzwater, M. A.

Fizwater, M. A.

Gaggioli, N. G.

Gaunaurd, G. C.

H. C. Strifors and G. C. Gaunaurd, “Scattering of electromagnetic pulses by simple-shaped targets with radar cross section modified by a dielectric coating,” IEEE Trans. Antenn. Propag. 46(9), 1252–1262 (1998).
[CrossRef]

S. Abrahamsson, B. Brusmark, H. C. Strifors, and G. C. Gaunaurd, “Extraction of target signature features in the combined time-frequency domain by means of impulse radar,” Proc. SPIE 1700, 102–113 (1992).
[CrossRef]

George, N.

Gong, Y. J.

Y. H. Li, Z. S. Wu, Y. J. Gong, G. Zhang, and M. J. Wang, “Laser one-dimensional range profile,” Acta Phys. Sin. 59, 6985–6990 (2010).

Gouesbet, G.

Gréhan, G.

Guo, L.

L. Guo and C. Kim, “Study on the two-frequency scattering cross section and pulse broadening of the one-dimensional fractal sea surface at millimeter wave frequency,” Prog. Electromagn. Res. 37, 221–234 (2002).
[CrossRef]

Hongwei, L.

S. Zhendong and L. Hongwei, “Model-measurement and reverse evaluation for RCS of stealthy targets,” J. Univ. Electron. Sci. Technol, China 24, 13–17 (1995).

Hui, C.

C. Hui, W. Zhensenu, and B. Lu, “Infrared laser pulse scattering from randomly rough surfaces,” Int. J. Infrared Millim. Waves 25(8), 1211–1219 (2004).
[CrossRef]

Ishimaru, A.

A. Ishimaru, L. Ailes-sengers, P. Phu, and D. Winebrenner, “Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces,” Waves Random Media 4(2), 139–148 (1994).
[CrossRef]

Kim, C.

L. Guo and C. Kim, “Study on the two-frequency scattering cross section and pulse broadening of the one-dimensional fractal sea surface at millimeter wave frequency,” Prog. Electromagn. Res. 37, 221–234 (2002).
[CrossRef]

Li, Y. H.

Y. H. Li, Z. S. Wu, Y. J. Gong, G. Zhang, and M. J. Wang, “Laser one-dimensional range profile,” Acta Phys. Sin. 59, 6985–6990 (2010).

Y. H. Li and Z. S. Wu, “Targets recognition using subnanosecond pulse laser range profiles,” Opt. Express 18(16), 16788–16796 (2010).
[CrossRef] [PubMed]

Lu, B.

C. Hui, W. Zhensenu, and B. Lu, “Infrared laser pulse scattering from randomly rough surfaces,” Int. J. Infrared Millim. Waves 25(8), 1211–1219 (2004).
[CrossRef]

Mees, L.

Perez Quintián, F.

Phu, P.

A. Ishimaru, L. Ailes-sengers, P. Phu, and D. Winebrenner, “Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces,” Waves Random Media 4(2), 139–148 (1994).
[CrossRef]

Quintián, F. P.

Raffo, C. A.

Rebollo, M. A.

Sánchez Brea, B. L.

Schertler, D. J.

Schiffer, R.

R. Schiffer, “The Coherent scattering cross-section of a slightly rough sphere,” J. Mod. Opt. 33(8), 959–980 (1986).

Strifors, H. C.

H. C. Strifors and G. C. Gaunaurd, “Scattering of electromagnetic pulses by simple-shaped targets with radar cross section modified by a dielectric coating,” IEEE Trans. Antenn. Propag. 46(9), 1252–1262 (1998).
[CrossRef]

S. Abrahamsson, B. Brusmark, H. C. Strifors, and G. C. Gaunaurd, “Extraction of target signature features in the combined time-frequency domain by means of impulse radar,” Proc. SPIE 1700, 102–113 (1992).
[CrossRef]

Suomin, C.

W. Zhensen and C. Suomin, “Bistatic scattering by arbitrarily shaped objects with rough surface at optical and infrared frequencies,” Int. J. Infrared Millim. Waves 13(4), 537–549 (1992).
[CrossRef]

Wang, M. J.

Y. H. Li, Z. S. Wu, Y. J. Gong, G. Zhang, and M. J. Wang, “Laser one-dimensional range profile,” Acta Phys. Sin. 59, 6985–6990 (2010).

Winebrenner, D.

A. Ishimaru, L. Ailes-sengers, P. Phu, and D. Winebrenner, “Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces,” Waves Random Media 4(2), 139–148 (1994).
[CrossRef]

Wu, Z. S.

Y. H. Li, Z. S. Wu, Y. J. Gong, G. Zhang, and M. J. Wang, “Laser one-dimensional range profile,” Acta Phys. Sin. 59, 6985–6990 (2010).

Y. H. Li and Z. S. Wu, “Targets recognition using subnanosecond pulse laser range profiles,” Opt. Express 18(16), 16788–16796 (2010).
[CrossRef] [PubMed]

Zhang, G.

Y. H. Li, Z. S. Wu, Y. J. Gong, G. Zhang, and M. J. Wang, “Laser one-dimensional range profile,” Acta Phys. Sin. 59, 6985–6990 (2010).

Zhendong, S.

S. Zhendong and L. Hongwei, “Model-measurement and reverse evaluation for RCS of stealthy targets,” J. Univ. Electron. Sci. Technol, China 24, 13–17 (1995).

Zhensen, W.

W. Zhensen and C. Suomin, “Bistatic scattering by arbitrarily shaped objects with rough surface at optical and infrared frequencies,” Int. J. Infrared Millim. Waves 13(4), 537–549 (1992).
[CrossRef]

Zhensenu, W.

C. Hui, W. Zhensenu, and B. Lu, “Infrared laser pulse scattering from randomly rough surfaces,” Int. J. Infrared Millim. Waves 25(8), 1211–1219 (2004).
[CrossRef]

Acta Phys. Sin.

Y. H. Li, Z. S. Wu, Y. J. Gong, G. Zhang, and M. J. Wang, “Laser one-dimensional range profile,” Acta Phys. Sin. 59, 6985–6990 (2010).

Appl. Opt.

IEEE Trans. Antenn. Propag.

M. K. Abdelazeez, “Wave scattering from a large sphere with rough surface,” IEEE Trans. Antenn. Propag. 31(2), 375–377 (1983).
[CrossRef]

H. C. Strifors and G. C. Gaunaurd, “Scattering of electromagnetic pulses by simple-shaped targets with radar cross section modified by a dielectric coating,” IEEE Trans. Antenn. Propag. 46(9), 1252–1262 (1998).
[CrossRef]

Int. J. Infrared Millim. Waves

C. Hui, W. Zhensenu, and B. Lu, “Infrared laser pulse scattering from randomly rough surfaces,” Int. J. Infrared Millim. Waves 25(8), 1211–1219 (2004).
[CrossRef]

W. Zhensen and C. Suomin, “Bistatic scattering by arbitrarily shaped objects with rough surface at optical and infrared frequencies,” Int. J. Infrared Millim. Waves 13(4), 537–549 (1992).
[CrossRef]

J. Mod. Opt.

R. Schiffer, “The Coherent scattering cross-section of a slightly rough sphere,” J. Mod. Opt. 33(8), 959–980 (1986).

J. Opt. Soc. Am. A

J. Univ. Electron. Sci. Technol, China

S. Zhendong and L. Hongwei, “Model-measurement and reverse evaluation for RCS of stealthy targets,” J. Univ. Electron. Sci. Technol, China 24, 13–17 (1995).

Opt. Express

Proc. SPIE

S. Abrahamsson, B. Brusmark, H. C. Strifors, and G. C. Gaunaurd, “Extraction of target signature features in the combined time-frequency domain by means of impulse radar,” Proc. SPIE 1700, 102–113 (1992).
[CrossRef]

Prog. Electromagn. Res.

L. Guo and C. Kim, “Study on the two-frequency scattering cross section and pulse broadening of the one-dimensional fractal sea surface at millimeter wave frequency,” Prog. Electromagn. Res. 37, 221–234 (2002).
[CrossRef]

Waves Random Media

A. Ishimaru, L. Ailes-sengers, P. Phu, and D. Winebrenner, “Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces,” Waves Random Media 4(2), 139–148 (1994).
[CrossRef]

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).

Z. S. Wu, “IR Laser Backscattering by arbitrarily shaped dielectric object with rough surface,” SPIE's International Symposium on Optical Science and Engineering in San Diego, California, (21–26, July,1991).

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Figures (16)

Fig. 1
Fig. 1

scattering geometry for a roughened object.

Fig. 2
Fig. 2

scattering geometry for rough spheres.

Fig. 3
Fig. 3

Function γ 12 of spheres with δ = 0.03 μ m , l c = 5 δ , a = 5 c m .

Fig. 5
Fig. 5

Function γ 12 of spheres with δ = 0.03 μ m , l c = 5 δ , a = 2 c m .

Fig. 4
Fig. 4

Function γ 12 of spheres with δ = 0.05 μ m , l c = 5 δ , a = 5 c m .

Fig. 6
Fig. 6

Normalized γ 12 of spheres with different roughness.

Fig. 7
Fig. 7

Normalized γ 12 of spheres with different radius.

Fig. 8
Fig. 8

Normalized γ 12 of rough spheres versus scattering angle under different condition.

Fig. 9
Fig. 9

scattering geometry for rough cylinders.

Fig. 10
Fig. 10

Function γ 12 with δ = 0.03 μ m , l c = 5 δ , a = L = 5 c m .

Fig. 12
Fig. 12

Function γ 12 of cylinders with δ = 0.03 μ m , l c = 5 δ , a = 2 c m , L = 5 c m .

Fig. 11
Fig. 11

Function γ 12 of cylinders with δ = 0.05 μ m , l c = 5 δ , a = L = 5 c m .

Fig. 13
Fig. 13

Normalized γ 12 of cylinders with various roughness.

Fig. 14
Fig. 14

Normalized γ 12 of cylinders with various sizes.

Fig. 15
Fig. 15

Backscattering γ 12 of rough cylinders with different dimensions.

Fig. 16
Fig. 16

Normalized γ 12 versus scattering angle with different roughness and different dimensions.

Equations (19)

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G ( r s , r ) = exp [ i k | r s r | ] 4 π | r s r |
E ( r ) N ^ = i ( 1 R i ) k k ^ N ^ E i ( r )
E s ( r s ) = i k 4 π S ( R i V W ) N ^ exp [ i k ( | r s r | + k ^ r ) ] | r s r | d S
r = r c + n ^ ( r c ) ξ ( r c )
| r s r | | r s r c | ξ ( r c ) n ^ ( r c ) k ^ s
n ^ N ^ 1 ( R i V W ) N ^ ( R i V W ) n ^
E s ( r s ) = i k 4 π S ( R i V W ) n ^ exp ( i k V n ^ ξ ) exp [ i k ( | r s r c | + k ^ r c ) ] / | r s r c | d S
E s ( r s ) = i k 2 π S k ^ n ^ exp ( i k V n ^ ξ ) exp [ i k ( | r s r c | + k ^ r c ) ] | r s r c | d S
| r s r c | R r c k ^ s
E s = i k exp ( i k R ) 2 π R S k ^ n ^ exp ( i k V n ^ ξ ) exp ( i k V r c ) d S
E s f 1 E s f 2 * = K d S 1 d S 2 ( k ^ n ^ 1 ) ( k ^ n ^ 2 ) exp [ i V ( k 1 r c 1 k 2 r c 2 ) ] ( χ t χ 1 χ 2 )
E s f 1 E s f 2 * = K d S d R ( k ^ n ^ ) 2 exp ( i ω d V r c / c ) exp ( i k 2 V R ) ( χ t χ 1 χ 2 )
χ 1 , 2 = exp ( k 1 , 2 2 V z 2 δ 2 / 2 )
χ t = exp { [ ( k 1 2 + k 2 2 ) V z 2 δ 2 / 2 k 1 k 2 V z 2 δ 2 < ξ 1 ξ 2 > ] }
E s f 1 E s f 2 * = K d S ( k ^ n ^ ) 2 exp ( i ω d V r c / c ) exp ( δ 2 V z 2 ω d 2 / 2 c 2 ) × d R exp ( i k q R ) ( χ t χ 2 )
χ t = exp [ k 2 δ 2 V z 2 ( 1 < ξ 1 ξ 2 > ) ] , χ = exp ( k 2 δ 2 V z 2 / 2 )
σ p 0 = V z 2 4 π d R exp ( i k V R ) ( χ t χ 2 )
E s f 1 E s f 2 * = 4 π K γ 12
γ 12 = d S σ p 0 exp ( i ω d V r c / c ) exp ( δ 2 V z 2 ω d 2 / 2 c 2 )

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