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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 8 — Apr. 11, 2011
  • pp: 7007–7019
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Two-frequency mutual coherence function of scattering from arbitrarily shaped rough objects

Geng Zhang and Zhensen Wu  »View Author Affiliations


Optics Express, Vol. 19, Issue 8, pp. 7007-7019 (2011)
http://dx.doi.org/10.1364/OE.19.007007


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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.

© 2011 OSA

1. Introduction

In this paper, the two-frequency mutual coherent function is obtained to investigate the scattering from arbitrarily shaped rough objects, providing some theoretical basis for the further study on the laser pulse scattering from 3-D rough objects. From scalar Helmholtz integral relation, the scattering formula in the far field from an arbitrarily shaped object is derived detailed, and then the two-frequency mutual coherence function is obtained. At last, some brief numerical results and analysis are given taking rough spheres and cylinders for examples.

2. Two frequency mutual coherence function of the scattering from arbitrarily shaped rough objects

A plane waveEi(r)=exp(ikk^r)illuminates a roughened convex object, the scattering geometry is as illustrated in Fig. 1
Fig. 1 scattering geometry for a roughened object.
. The surface S is the unperturbed surface, n^ is the corresponding external normal, rcis its vector distance and θiis the local incident angle at rc while Sis the roughened surface which is the surface S plus a random fluctuationξ(rc), N^is its corresponding normal, andris the vector distance, θi is the incident angle at r.k^ andk^sare the incident unit vector and the scattering unit vector, respectively. k=2π/λ=ω/cis the wavenumber, λ is the wavelength and ω is its angular frequency. The time harmonic factor exp(iωt) is omitted for convenience.

According to the scalar Helmholtz integral relation, the scattered field from a rough object at a receiver point P in the far field can be expressed as [6

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

]
Es(rs)=S[E(r)G(rs,r)N^G(rs,r)E(r)N^]dS
(1)
wherersis the vector distance between the observation point P and the origin of coordinate, E(r)andE(r)/N^ are the total electric field and its normal derivative on the scattering surfaceS,G(rs,r)and G(rs,r)/N^are Green’s function and its normal derivative, respectively. The Green’s functionG(rs,r)is given by
G(rs,r)=exp[ik|rsr|]4π|rsr|
(2)
The total electric field E(r) is a sum of the incident field Ei(r)and the scattered E(r)on the surfaceS, that is
E(r)=Ei(r)+E(r)
(3)
Since the incident fieldEi(r)satisfies
S[Ei(r)G(rs,r)N^G(rs,r)Ei(r)N^]dS=0
(4)
The scattered fieldEs(rs)at point P can be obtained
Es(rs)=S[E(r)G(rs,r)N^G(rs,r)E(r)N^]dS
(5)
The radius of principal curvature at any point of the surface is assumed to be much larger than the incident wavelength, and then the tangent-plane approximation can be applied. The scattered field and its normal derivative atron the rough surface are written as following, respectively
E(r)=(1+Ri)Ei(r)
(6)
E(r)N^=i(1Ri)kk^N^Ei(r)
(7)
whereRiis the Fresnel reflection coefficient.

Because the point P is in the far field, the following approximation can be used
G(rs,r)N^=ikk^sN^G(rs,r)
(8)
Inserting Eqs. (6), (7) and (8) into Eq. (5), we can get
Es(rs)=ik4πS(RiVW)N^exp[ik(|rsr|+k^r)]|rsr|dS
(9)
wherek^=(sinθicosφi,sinθisinφi,cosθi),k^s=(sinθscosφs,sinθssinφs,cosθs), (θi,φi) is the incident direction, and (θs,φs)is the scattering direction, andV=k^k^s,W=k^+k^s.

As illustrated in Fig. 1, the vector distance of the point on the rough surface S can be approximated as the vector distance of the point on the unperturbed surface S plus its fluctuation along the normal direction, i.e.
r=rc+n^(rc)ξ(rc)
(10)
Also we have
|rsr||rsrc|ξ(rc)n^(rc)k^s
(11)
Since
dS=n^N^dS
(12)
Assuming the mean square slope is much smaller than unit,
n^N^1(RiVW)N^(RiVW)n^
(13)
Using Eqs. (10) to (13) in Eq. (9) yields
Es(rs)=ik4πS(RiVW)n^exp(ikVn^ξ)exp[ik(|rsrc|+k^rc)]/|rsrc|dS
(14)
Assuming the object is to be conducting, Eq. (14) can be further approximated as following
Es(rs)=ik2πSk^n^exp(ikVn^ξ)exp[ik(|rsrc|+k^rc)]|rsrc|dS
(15)
Making use of the far-zone approximation, the exponential term above can be rewritten as
|rsrc|Rrck^s
(16)
and the denominator in Eq. (15) can be approximated as R which is the distance between the point P and the surface S. Then the far-field scattered field from a rough object can be given by
Es=ikexp(ikR)2πRSk^n^exp(ikVn^ξ)exp(ikVrc)dS
(17)
Equation (17) is the tangent-plane approximation solution of the scattered field in the far field by an arbitrarily shaped rough object. From the equation we can see that comparing with the scattering from a rough surface [8

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]

], the scattering from a rough object has a factor exp(ikVrc) which is introduced by the curvature of the object.

According to the reference [7

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]

], the two-frequency mutual coherence function of the scattering from an arbitrarily shaped object with rough surface can be easily written as
Esf1Esf2*=KdS1dS2(k^n^1)(k^n^2)exp[iV(k1rc1k2rc2)](χtχ1χ2)
(18)
whereEsf1is the incoherent part of the scattering field, K=k1k2exp(iωdR/c)/(2πR)2, and χ1,2=<exp(±ik1,2Vn^1,2ξ1,2>, χt=<exp[iV(k1ξ1n^1k2ξ2n^2)]> are the first- and second-order characteristic function of the random variables, respectively.Since the mean curvature radius of the object is much larger than the incident wavelength and the correlation length of the rough surface, the tangent-plane approximation can be applied to simplify the Eq. (18)
Esf1Esf2*=KdSdR(k^n^)2exp(iωdVrc/c)exp(ik2VR)(χtχ1χ2)
(19)
whereRis the tangent plane at rc.The fluctuationξ(rc)obeys Gaussian distribution with rms δ and correlation length lc
χ1,2=exp(k1,22Vz2δ2/2)
χt=exp{[(k12+k22)Vz2δ2/2k1k2Vz2δ2<ξ1ξ2>]}
whereVz=Vn^. Letωc=(ω1+ω2)/2, ωd=ω1ω2, and for a narrow incident pulse wave, ω|ωc|>>ωd, the two-frequency mutual coherence function can be simplified as

Esf1Esf2*=KdS(k^n^)2exp(iωdVrc/c)exp(δ2Vz2ωd2/2c2)×dRexp(ikqR)(χtχ2)
(20)
whereχt=exp[k2δ2Vz2(1<ξ1ξ2>)],χ=exp(k2δ2Vz2/2).

According to the definition of the scattering cross section per unit area when a plane wave illuminates a rough surface [9

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]

]
σp0=Vz24πdRexp(ikVR)(χtχ2)
Then the Eq. (20) can be rewritten as
Esf1Esf2*=4πKγ12
(21)
and
γ12=dSσp0exp(iωdVrc/c)exp(δ2Vz2ωd2/2c2)
(22)
which is the main factor in the two-frequency mutual coherence function.

So far, we get the two-frequency mutual coherence function by arbitrarily shaped objects with Gaussian fluctuating rough surface.

3. Numerical results and analysis

For simplicity, we define γ12 to be the two frequency scattering function, and in the following, the numerical results and analysis are forγ12. As an example, the functions γ12of rough conducting spheres and cylinders with Gaussian slightly rough surface will be computed and analyzed in detail. The incident wavelength is 1.06μm, the roughness of the rough surface is characterized by rms δ and correlation lengthlc. In the following we will give the numerical results to illustrate the effect of the roughness and the dimension of the object on the two-frequency mutual coherence function. The correlation length lcin all the numerical results keeps invariable.

3.1 Rough spheres

As illustrated in Fig. 2
Fig. 2 scattering geometry for rough spheres.
, the center of the sphere is located at the origin of coordinate, its radius is a, the incident wave illuminates the sphere along the directionZ^, the observation plane is in the plane ofXOZ, therefore, the anglesθi=φi=φs=0°, the function γ12changes with the scattering angleθs.

According to Eq. (22), the variations of the functionγ12with the scattering angle and the frequency difference under different conditions are illustrated in Figs. 3
Fig. 3 Function γ12of spheres with δ=0.03μm,lc=5δ,a=5cm.
5
Fig. 5 Function γ12of spheres with δ=0.03μm,lc=5δ,a=2cm.
.

From the figures above, we can see that the functionγ12decrease rapidly with the increases of the scattering angle and the frequency difference. From Fig. 3 and Fig. 4
Fig. 4 Function γ12of spheres with δ=0.05μm,lc=5δ,a=5cm.
, it illustrates the effect of the roughness on the functionγ12. With the increase of the roughness, the peak value ofγ12increases, and the decrease ofγ12with the frequency difference becomes smoother. From Fig. 4 and Fig. 5, we can see the effect of the radius a on the functionγ12. With same roughness, the smaller the radius, the smaller the peak value ofγ12, the slower the decrease of γ12with the frequency difference.

In order to demonstrate the effect of the roughness and the radius of the sphere on the functionγ12more concretely, in the following we give the normalized numerical results ofγ12in the backscattering direction under different conditions.

From Fig. 6
Fig. 6 Normalized γ12of spheres with different roughness.
below, we can see that with the increase of the roughness, the backscattering γ12 becomes smoother, but its fluctuation is very obvious. If we define that the coherent bandwidth is the frequency differenceωd whenγ12reaches its first minimize, the coherent bandwidth ofγ12is approximately invariant with different roughness.

However, in Fig. 7
Fig. 7 Normalized γ12of spheres with different radius.
, we can see that with a smaller radius, the coherent bandwidth increases andγ12becomes smoother. In Fig. 8
Fig. 8 Normalized γ12 of rough spheres versus scattering angle under different condition.
, ωd=0,θsθi, the normalized function γ12changes into the normalized bistatic scattering cross section. The figure illustrates that the bistatic scattering cross section of the sphere is depend on the roughness not the radius which is consistent with the reduced scale theory proposed in reference [20

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).

].

3.2 rough cylinders

As illustrated in Fig. 9
Fig. 9 scattering geometry for rough cylinders.
, the center of the cylinder is located at the origin of coordinate, its radius and length are a and L, respectively. The incident wave illuminates the cylinders along the directionX^, the observation plane is in the plane ofXOY, the incident direction (θi,φi)=(90°,180°) and the scattering angle θsis90°, the functionγ12changes with the scattering azimuth angleφs.

The variations of the functionγ12with the scattering angle and the frequency difference under different conditions are illustrated in Figs. 10
Fig. 10 Function γ12 with δ=0.03μm,lc=5δ,a=L=5cm.
12
Fig. 12 Function γ12of cylinders with δ=0.03μm,lc=5δ,a=2cm,L=5cm.
.

Fig. 11 Function γ12of cylinders with δ=0.05μm,lc=5δ,a=L=5cm.

From Figs. 1012 above, we can see that the functionγ12 of rough cylinders decreases rapidly with the increases of the scattering azimuth angle and the frequency difference. With the increase of the roughness, the peak value ofγ12increases, the decrease ofγ12with the frequency difference becomes smoother; With same roughness, the smaller the radius, the smaller the peak value ofγ12, the slower the decrease of the functionγ12against the frequency difference.

Also, in order to demonstrate the effect of the roughness and the dimension of the cylinder on the functionγ12more concretely, we give the normalized numerical results ofγ12in the backscattering direction under different conditions.

From Fig. 13
Fig. 13 Normalized γ12of cylinders with various roughness.
below, we can see that the decrease of the backscatteringγ12against the frequency difference is also fluctuating, with the increase of the roughness, this fluctuation becomes weakened, the profile becomes smoother, and the decrease of the function γ12 becomes slower.

In Fig. 14
Fig. 14 Normalized γ12of cylinders with various sizes.
, we only can see the effect of the radius not the length of the cylinders on the functionγ12. Combing with Fig. 14 and Fig. 15
Fig. 15 Backscattering γ12of rough cylinders with different dimensions.
, we can see that the smaller the radius of the cylinder, the larger the coherent bandwidth, the slower the decrease of the normalized functionγ12 while the larger the length of the cylinder, the bigger the value of the functionγ12. That is, the radius mainly influents the profile of the function γ12 while the length only influents the value ofγ12. The coherent bandwidth is closely dependent on the radius of the object, but has no relationship with the length and the roughness.

In Fig. 16
Fig. 16 Normalized γ12 versus scattering angle with different roughness and different dimensions.
, ωd=0, the normalized two-frequency scattering function changes into the normalized bistatic scattering cross section. The figure illustrates that the bistatic scattering cross section of the cylinder only depend on the roughness not the dimension.

4. Conclusion

Based on the Physical optics approximation, the narrow pulse plane wave scattering from slightly rough conducting object was investigated by its two-frequency mutual coherence function. The scattering field in the far zone by arbitrarily shaped objects with Gaussian rough surface and its two-frequency mutual coherence function were derived theoretically. And for simplification, the numerical results for a rough sphere and a rough cylinder were given and analyzed. The results showed that the two-frequency scattering functionγ12had closely relationship with the roughness and the radii of the objects, and when the light was vertical incident on a cylinder, the length of the cylinder only influenced the amplitude not the profile of γ12. The function γ12decreased rapidly with the increase of the scattering angle and the frequency difference. The rougher the object, the bigger the peak value ofγ12, the slower the decrease ofγ12; the coherent bandwidth ofγ12had no obvious relationship with the roughness but was closely dependent on the curvature radius of the object, the smaller the radius, the bigger the coherent bandwidth. The work in this paper will be further applied to investigate the time domain scattering and the statistical properties of speckle from complicated rough objects and the range-Doppler imaging, then it can provide some theoretical basis for the radar system design, target detection and reorganization, tracking and positioning and feature extraction.

Acknowledgments

The authors gratefully acknowledge support from the National Natural Science Foundation of China under Grant No. 60771038.

References and links

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).

OCIS Codes
(260.0260) Physical optics : Physical optics
(290.1350) Scattering : Backscattering
(140.3538) Lasers and laser optics : Lasers, pulsed

ToC Category:
Scattering

History
Original Manuscript: September 13, 2010
Revised Manuscript: October 17, 2010
Manuscript Accepted: October 18, 2010
Published: March 29, 2011

Citation
Geng Zhang and Zhensen Wu, "Two-frequency mutual coherence function of scattering from arbitrarily shaped rough objects," Opt. Express 19, 7007-7019 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7007


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References

  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).

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