Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
Published Online 11 July 2014
Fast nearfield to farfield conversion algorithm for circular synthetic aperture sonar Daniel S. Plotnick and Philip L. Marston Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814 [email protected], [email protected]
Timothy M. Marston Applied Physics Laboratory, University of Washington, 1013 Northeast 40th Street, Seattle, Washington 98105-6698 [email protected]
Abstract: Monostatic circular synthetic aperture sonar (CSAS) images are formed by processing azimuthal angle dependent backscattering from a target at a fixed distance from a collocated source/receiver. Typical CSAS imaging algorithms [Ferguson and Wyber, J. Acoust. Soc. Am. 117, 2915–2928 (2005)] assume scattering data are taken in the farfield. Experimental constraints may make farfield measurements impractical and thus require objects to be scanned in the nearfield. Left uncorrected this results in distortions of the target image and in the angular dependence of features. A fast approximate Hankel function based algorithm is presented to convert nearfield data to the farfield. Images and spectrograms of an extended target are compared for both cases. C 2014 Acoustical Society of America V
PACS numbers: 43.60.Rw, 43.60.Lq, 43.20.Fn [AL] Date Received: February 3, 2014 Date Accepted: June 12, 2014
1. Introduction Circular synthetic aperture sonar (CSAS, also known as acoustic reflection tomography) is a technique for creating a high resolution two-dimensional image of an object from acoustic scattering data at discrete angles over a full or partial circular aperture.1–3 In the current examination backscattering data collected via a co-located source/receiver pair (hereafter called monostatic CSAS) is considered. Data may be obtained using a turntable with fixed transducer, scanning the transducer about a circular track, or using a vehicle mounted transducer. Time domain data from all captured aspect angles may be mapped to the image domain using a variety of techniques; see Ref. 1 for an overview. Typical CSAS processing methods assume that data are acquired in the farfield of the object, given by4 df ¼
2D2 k
(1)
for an object centered on the aperture. Here df is the farfield distance, D is the total length of the scattering object, and k is the wavelength. For large objects or high frequency sonar systems this can impose an experimentally unrealistic requirement on the radius of the synthetic aperture, forcing data to be acquired in the nearfield. Failure to meet the farfield criteria leads to distortions in the resulting image, angular spreading of narrow glints, and migration in azimuthal angle of elastic features. An algorithm is proposed that allows data to be taken in violation of the farfield condition and then converted to the farfield. The conversion technique presented
J. Acoust. Soc. Am. 136 (2), August 2014
C 2014 Acoustical Society of America V
EL61
Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
Published Online 11 July 2014
in this paper has the less stringent experimental requirement that the aperture radius be larger than the maximum wavelength so as to eliminate evanescent components from the received wavefield. Related methods have been suggested for synthetic aperture radar5 and medical ultrasonic imaging.6 This paper will present the farfield conversion algorithm followed by its application to the results of a small scale laboratory experiment. The resulting changes in time, frequency, and image domains will be examined. 2. Processing methods 2.1 Conversion algorithm Backscattering data W(h, t) are recorded at discrete locations spaced equally in azimuth along a circular aperture of radius R. The resulting time-azimuth data are expanded into a partial wave series (PWS) in cylindrical coordinates with the origin at the center of the aperture.7 In the monochromatic case, Wðh; kÞ ¼
N=2 X
An Hnð1Þ ðkRÞeinh ;
(2)
n¼N=2
where N is the total number of samples, An are the partial wave coefficients, and ð1Þ Hn (kR) are nth order Hankel functions of the first kind corresponding to outgoing ð2Þ waves.8 The ingoing Hn waves have been dropped and the eixt time harmonic term is left as implied. The PWS is truncated at 6N/2 by the finite number of samples. To eliminate spreading ambiguities in converting to 2-D, only the phase component of the Hankel functions is kept. Generalizing to a polychromatic system, the range independent partial wave coefficients are extracted using ð1Þ
A0 n ðxÞ ¼
jHn ðkRÞj ð1Þ
NHn ðkRÞ
=ð2Þ ½Wðh; tÞ;
(3)
where =ð2Þ indicates the 2-D Fourier transform and the azimuthal wavenumber n is the Fourier conjugate variable to the azimuthal angle h. Modification to the wavenumberfrequency relation must be made for monostatic applications. Sound propagation to and from the object must be included and thus the sound speed is effectively halved,9 k ¼ 2x=c:
(4)
Once the partial wave coefficients are obtained the Hankel functions are converted to their asymptotic forms10 rffiffiffiffiffiffiffiffiffi 2 iðkRpn=2p=4Þ ð1Þ e lim Hn ðkRÞ ! : (5) R!1 pkR The leading spreading factor will be suppressed, leaving only the phase component. Farfield data are given by WFF ðh; kÞ ¼
N=2 X
A0 n eiðkRpn=2p=4Þ einh :
(6)
n¼N=2
Suppression of the spreading component in both the exact and asymptotic forms of the Hankel functions allows conversion to the farfield without concern for the limitation to cylindrical spreading. The full conversion process is
EL62 J. Acoust. Soc. Am. 136 (2), August 2014
Plotnick et al.: Nearfield to farfield conversion for sonar
Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
" WFF ðh; tÞ ¼ =ð2Þ
ð1Þ
jHn ðkRÞj ð1Þ
Hn ðkRÞ
Published Online 11 July 2014
# =ð2Þ ½Wðh; tÞn eiðkRpn=2p=4Þ ;
(7)
where =ð2Þ is the 2-D inverse Fourier transform. The above function is cast so that the transform operation is in matrix form in (k, n) space. Additional speed may be gained by applying a second asymptotic expansion. ð1Þ Expanding the Hankel function phase component /n(x) ¼ arg[Hn (x)] gives11 /n ðxÞ x
np p 4n2 1 ð4n2 1Þð4n2 25Þ þ þ þ : 2 4 2ð4xÞ 6ð4xÞ3
(8)
Using this expansion for the initial partial wave series and then canceling the leading terms during conversion to the farfield gives the fast approximation h i ð2Þ ð2Þ iðð4n2 1Þ=2ð4kRÞÞ : (9) = ½Wðh; tÞn e WFF ðh; tÞ = This formulation has the advantage of speed, allowing rapid implementation inside existing imaging algorithms and for application in iterative methods. An aside will be made to examine sampling criteria. For monostatic systems, in order to avoid aliasing effects in either the farfield conversion or imaging processes, the number of samples must meet N int[4kmaxr0 ]. Here, r0 is the minimum radius of a circle enclosing the target and centered on the aperture origin. An object located off of the aperture center will increase the number of samples required. Hankel function azimuthal wavenumbers of |n| > 2kr0 are evanescent and decay exponentially away from the scatterer.7 3. Application to real data 3.1 Experiment design To demonstrate the utility of the algorithm an experiment was performed on a solid 5:1 aluminum cylinder (38.1 190.5 mm or 1.5 in. 7.5 in.) located in the water column of a freshwater tank (c 1486 m/s) in such a way as to minimize boundary effects. The cylinder was hung from two corners so that its axis was horizontal and was rotated through 360 azimuth using a rotating stage. The target was insonified by a fixed wide band (100–700 kHz) transducer placed along the cylinder meridian at a range of R ¼ 0.964 m from the center of rotation. The resulting aperture’s radius was considerably less than the farfield condition of df ¼ 34.2 m but large enough to neglect evanescent effects. A short duration wide band insonifying pulse was used so as to give high spatial resolution. Backscattering data were collected every 0.25 so as to meet sampling requirements. The resulting backscattering spectra were calibrated using backscattering data from a solid sphere of sufficient size that the specular reflection could be isolated.12 3.2 Effect of conversion on image Image reconstruction is performed using the Fourier transform method found in Refs. 1 and 2. Figure 1 shows the process; raw time domain data W(h, t) are Fourier transformed to give W(h,f) and then mapped from polar to Cartesian coordinates in k-space W(kx,ky). Finally, a 2-D inverse Fourier transform places data in the image domain W(x,y). Figure 2 shows the results of image reconstruction on the raw data and on data after farfield conversion using Eq. (9). The original image is heavily distorted; the sides and end caps appear bowed and the corners are not flush. Features associated with elastic effects are also distorted. Conversion to the farfield straightens the sides
J. Acoust. Soc. Am. 136 (2), August 2014
Plotnick et al.: Nearfield to farfield conversion for sonar EL63
Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
Published Online 11 July 2014
Fig. 1. (Color online) Left: Primary stages in image reconstruction. Azimuthal angles 0 , 180 , and 360 correspond to broadside while 90 and 270 correspond to end-on. Clockwise: (a) raw time-azimuth data, (b) Fourier transformed data, (c) polar mapped k-space data, (d) reconstructed image of 5:1 aluminum cylinder taken at Washington State University. Logarithmic color scales were used with dynamic ranges sufficient for displaying the significant scattering processes. See also Figs. 2 and 3. Right: Surface wave features associated with backscattering enhancements on solid elastic cylinders. For aluminum in water the expected coupling angle hl ¼ 30 .
and ends as well as makes the corners flush. The corrected image accurately reflects the size and shape of the target. 3.3 Effect of conversion on acoustic color Certain elastic phenomena on the cylinder contribute to enhanced backscatter at intermediate azimuths. These include meridional12 and face crossing13 Rayleigh-like waves, pictured in Fig. 1. The farfield coupling angle for these rays is given by hl ¼ sin1(c/cl), where cl is the phase velocity of the surface wave and c is the fluid sound speed. For
Fig. 2. (Color online) Images of the cylinder. Left: created from raw data. Right: created from data after farfield conversion. The algorithm reduces distortions to the shape of specular and elastic features. Color axis in dB.
EL64 J. Acoust. Soc. Am. 136 (2), August 2014
Plotnick et al.: Nearfield to farfield conversion for sonar
Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
Published Online 11 July 2014
Fig. 3. (Color online) Backscattering spectrum of the cylinder. Left: created from raw data. Right: created from data after farfield conversion. Enhancements due to meridional and face crossing Rayleigh waves are noted. The algorithm moves these loci to expected azimuthal locations. Additionally, the glint at 0 azimuth (broadside) is narrowed. Color axis in dB.
aluminum in water, this is predicted to be approximately14 hl ¼ 30 . Scattering enhancements are thus expected near 30 and 60 azimuth. Such enhancements have been seen in field experiments and can dominate backscattering at these intermediate azimuths.14 Figure 3 shows the effect of farfield conversion on the acoustic color (backscattering spectrum versus azimuthal angle). In the raw nearfield data both meridional and face crossing scattering loci occur at angles differing from those predicted. After farfield conversion both features are observed nearer to the expected value. In addition, the bright feature at 0 azimuth corresponds to specular and elastic broadside scattering. The farfield angular width of the specular broadside main lobe is predicted3 to be hFF ¼ 2 sin1(pc/xL), where L is the length of the cylinder. This feature should be narrow in azimuth and become narrower at higher frequencies. In the nearfield data the broadside feature appears spread in angle and this angular width does not show strong frequency dependence. A simple geometric construction predicts that the nearfield angular width of the main specular lobe is hNF ¼ 2 sin1 ðL=2RÞ 11:3 ;
(10)
which is independent of frequency. The nearfield and farfield data in Fig. 3 are consistent with these estimates of the specular width.
4. Conclusion The Hankel function based nearfield to farfield algorithm allows data to be gathered using smaller apertures and then converted into their farfield form. The algorithm preserves amplitudes by suppressing spreading. Due to the form of the algorithm, computation time required for conversion and imaging is short compared to alternative methods of recovering the farfield image such as back-propagation. Many scattering theories for elastic targets utilize a farfield assumption. If an object is instead scanned in the nearfield, scattering loci may occur at azimuthal locations differing from predicted. Converting to the farfield removes this ambiguity and shifts backscattering loci closer to expected values, aiding manual analysis or use in automatic classifiers. In addition, current CSAS methods assume that data have been taken in the farfield. This process removes nearfield distortions from the resulting image. This may be important for automatic classification and iterative image based techniques such as autofocusing. Some processing procedures also rely on masking out portions of data in either the angle or image domains, both of which may be more easily understood in the farfield. Work of future interest includes cases where the
J. Acoust. Soc. Am. 136 (2), August 2014
Plotnick et al.: Nearfield to farfield conversion for sonar EL65
Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
Published Online 11 July 2014
transducer is outside the target’s plane of rotation and in understanding how phase noise in the raw data affects the conversion. Acknowledgments Work supported by ONR. References and links 1
B. G. Ferguson and R. J. Wyber, “Application of acoustic reflection tomography to sonar imaging,” J. Acoust. Soc. Am. 117, 2915–2928 (2005). 2 T. M. Marston, J. L. Kennedy, and P. L. Marston, “Coherent and semi-coherent processing of limitedaperture circular synthetic aperture (CSAS) data,” in Proceedings of the 2011 IEEE Oceans Conference (2011), pp. 1–6. 3 A. D. Friedman, S. K. Mitchell, T. L. Kooij, and K. N. Scarbrough, “Circular synthetic aperture sonar design,” in Proceedings of the 2005 IEEE Oceans Conference (2005), Vol. 2, pp. 1038–1045. 4 J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 57–61. 5 L. Nanjing, H. Chufeng, L. Ying, and Z. Linxi, “A new algorithm about transforming from near-field to far-field of radar target scattering,” in ISAPE 2008, IEEE Antennas, Propagation and EM Theory Symposium (2008), pp. 661–663. 6 R. C. Waag, F. Lin, T. K. Varslot, and J. P. Astheimer, “An eigenfunction method for reconstruction of large-scale and high-contrast objects,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 1316–1332 (2007). 7 F. Simonetti, L. Huang, and N. Duric, “On the spatial sampling of wave fields with circular ring apertures,” J. Appl. Phys. 101, 083103 (2007). 8 E. G. Williams, Fourier Acoustics (Academic Press, London, 1999), pp. 115–121. 9 D. J. Zartman, D. S. Plotnick, T. M. Marston, and P. L. Marston, “Quasi-holographic processing as an alternative to synthetic aperture sonar imaging,” Proc. Meetings Acoust. 19, 055011 (2013). 10 G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier, Burlington, 2005), pp. 707–723. 11 M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1972), pp. 364–365. 12 K. Gipson and P. L. Marston, “Backscattering enhancements due to reflection of meridional leaky Rayleigh waves at the blunt truncation of a tilted solid cylinder in water: Observations and theory,” J. Acoust. Soc. Am. 106, 1673–1680 (1999). 13 K. Gipson and P. L. Marston, “Backscattering enhancements from Rayleigh waves on the flat face of a tilted solid cylinder in water,” J. Acoust. Soc. Am. 107, 112–117 (2000). 14 K. L. Williams, S. G. Kargl, E. I. Thorsos, D. S. Burnett, J. L. Lopes, M. Zampolli, and P. L. Marston, “Acoustic scattering from a solid aluminum cylinder in contact with a sand sediment: Measurements, modeling, and interpretation,” J. Acoust. Soc. Am. 127, 3356–3371 (2010).
EL66 J. Acoust. Soc. Am. 136 (2), August 2014
Plotnick et al.: Nearfield to farfield conversion for sonar
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[http://dx.doi.org/10.1121/1.4885486]
Published Online 11 July 2014
Fast nearfield to farfield conversion algorithm for circular synthetic aperture sonar Daniel S. Plotnick and Philip L. Marston Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814 [email protected], [email protected]
Timothy M. Marston Applied Physics Laboratory, University of Washington, 1013 Northeast 40th Street, Seattle, Washington 98105-6698 [email protected]
Abstract: Monostatic circular synthetic aperture sonar (CSAS) images are formed by processing azimuthal angle dependent backscattering from a target at a fixed distance from a collocated source/receiver. Typical CSAS imaging algorithms [Ferguson and Wyber, J. Acoust. Soc. Am. 117, 2915–2928 (2005)] assume scattering data are taken in the farfield. Experimental constraints may make farfield measurements impractical and thus require objects to be scanned in the nearfield. Left uncorrected this results in distortions of the target image and in the angular dependence of features. A fast approximate Hankel function based algorithm is presented to convert nearfield data to the farfield. Images and spectrograms of an extended target are compared for both cases. C 2014 Acoustical Society of America V
PACS numbers: 43.60.Rw, 43.60.Lq, 43.20.Fn [AL] Date Received: February 3, 2014 Date Accepted: June 12, 2014
1. Introduction Circular synthetic aperture sonar (CSAS, also known as acoustic reflection tomography) is a technique for creating a high resolution two-dimensional image of an object from acoustic scattering data at discrete angles over a full or partial circular aperture.1–3 In the current examination backscattering data collected via a co-located source/receiver pair (hereafter called monostatic CSAS) is considered. Data may be obtained using a turntable with fixed transducer, scanning the transducer about a circular track, or using a vehicle mounted transducer. Time domain data from all captured aspect angles may be mapped to the image domain using a variety of techniques; see Ref. 1 for an overview. Typical CSAS processing methods assume that data are acquired in the farfield of the object, given by4 df ¼
2D2 k
(1)
for an object centered on the aperture. Here df is the farfield distance, D is the total length of the scattering object, and k is the wavelength. For large objects or high frequency sonar systems this can impose an experimentally unrealistic requirement on the radius of the synthetic aperture, forcing data to be acquired in the nearfield. Failure to meet the farfield criteria leads to distortions in the resulting image, angular spreading of narrow glints, and migration in azimuthal angle of elastic features. An algorithm is proposed that allows data to be taken in violation of the farfield condition and then converted to the farfield. The conversion technique presented
J. Acoust. Soc. Am. 136 (2), August 2014
C 2014 Acoustical Society of America V
EL61
Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
Published Online 11 July 2014
in this paper has the less stringent experimental requirement that the aperture radius be larger than the maximum wavelength so as to eliminate evanescent components from the received wavefield. Related methods have been suggested for synthetic aperture radar5 and medical ultrasonic imaging.6 This paper will present the farfield conversion algorithm followed by its application to the results of a small scale laboratory experiment. The resulting changes in time, frequency, and image domains will be examined. 2. Processing methods 2.1 Conversion algorithm Backscattering data W(h, t) are recorded at discrete locations spaced equally in azimuth along a circular aperture of radius R. The resulting time-azimuth data are expanded into a partial wave series (PWS) in cylindrical coordinates with the origin at the center of the aperture.7 In the monochromatic case, Wðh; kÞ ¼
N=2 X
An Hnð1Þ ðkRÞeinh ;
(2)
n¼N=2
where N is the total number of samples, An are the partial wave coefficients, and ð1Þ Hn (kR) are nth order Hankel functions of the first kind corresponding to outgoing ð2Þ waves.8 The ingoing Hn waves have been dropped and the eixt time harmonic term is left as implied. The PWS is truncated at 6N/2 by the finite number of samples. To eliminate spreading ambiguities in converting to 2-D, only the phase component of the Hankel functions is kept. Generalizing to a polychromatic system, the range independent partial wave coefficients are extracted using ð1Þ
A0 n ðxÞ ¼
jHn ðkRÞj ð1Þ
NHn ðkRÞ
=ð2Þ ½Wðh; tÞ;
(3)
where =ð2Þ indicates the 2-D Fourier transform and the azimuthal wavenumber n is the Fourier conjugate variable to the azimuthal angle h. Modification to the wavenumberfrequency relation must be made for monostatic applications. Sound propagation to and from the object must be included and thus the sound speed is effectively halved,9 k ¼ 2x=c:
(4)
Once the partial wave coefficients are obtained the Hankel functions are converted to their asymptotic forms10 rffiffiffiffiffiffiffiffiffi 2 iðkRpn=2p=4Þ ð1Þ e lim Hn ðkRÞ ! : (5) R!1 pkR The leading spreading factor will be suppressed, leaving only the phase component. Farfield data are given by WFF ðh; kÞ ¼
N=2 X
A0 n eiðkRpn=2p=4Þ einh :
(6)
n¼N=2
Suppression of the spreading component in both the exact and asymptotic forms of the Hankel functions allows conversion to the farfield without concern for the limitation to cylindrical spreading. The full conversion process is
EL62 J. Acoust. Soc. Am. 136 (2), August 2014
Plotnick et al.: Nearfield to farfield conversion for sonar
Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
" WFF ðh; tÞ ¼ =ð2Þ
ð1Þ
jHn ðkRÞj ð1Þ
Hn ðkRÞ
Published Online 11 July 2014
# =ð2Þ ½Wðh; tÞn eiðkRpn=2p=4Þ ;
(7)
where =ð2Þ is the 2-D inverse Fourier transform. The above function is cast so that the transform operation is in matrix form in (k, n) space. Additional speed may be gained by applying a second asymptotic expansion. ð1Þ Expanding the Hankel function phase component /n(x) ¼ arg[Hn (x)] gives11 /n ðxÞ x
np p 4n2 1 ð4n2 1Þð4n2 25Þ þ þ þ : 2 4 2ð4xÞ 6ð4xÞ3
(8)
Using this expansion for the initial partial wave series and then canceling the leading terms during conversion to the farfield gives the fast approximation h i ð2Þ ð2Þ iðð4n2 1Þ=2ð4kRÞÞ : (9) = ½Wðh; tÞn e WFF ðh; tÞ = This formulation has the advantage of speed, allowing rapid implementation inside existing imaging algorithms and for application in iterative methods. An aside will be made to examine sampling criteria. For monostatic systems, in order to avoid aliasing effects in either the farfield conversion or imaging processes, the number of samples must meet N int[4kmaxr0 ]. Here, r0 is the minimum radius of a circle enclosing the target and centered on the aperture origin. An object located off of the aperture center will increase the number of samples required. Hankel function azimuthal wavenumbers of |n| > 2kr0 are evanescent and decay exponentially away from the scatterer.7 3. Application to real data 3.1 Experiment design To demonstrate the utility of the algorithm an experiment was performed on a solid 5:1 aluminum cylinder (38.1 190.5 mm or 1.5 in. 7.5 in.) located in the water column of a freshwater tank (c 1486 m/s) in such a way as to minimize boundary effects. The cylinder was hung from two corners so that its axis was horizontal and was rotated through 360 azimuth using a rotating stage. The target was insonified by a fixed wide band (100–700 kHz) transducer placed along the cylinder meridian at a range of R ¼ 0.964 m from the center of rotation. The resulting aperture’s radius was considerably less than the farfield condition of df ¼ 34.2 m but large enough to neglect evanescent effects. A short duration wide band insonifying pulse was used so as to give high spatial resolution. Backscattering data were collected every 0.25 so as to meet sampling requirements. The resulting backscattering spectra were calibrated using backscattering data from a solid sphere of sufficient size that the specular reflection could be isolated.12 3.2 Effect of conversion on image Image reconstruction is performed using the Fourier transform method found in Refs. 1 and 2. Figure 1 shows the process; raw time domain data W(h, t) are Fourier transformed to give W(h,f) and then mapped from polar to Cartesian coordinates in k-space W(kx,ky). Finally, a 2-D inverse Fourier transform places data in the image domain W(x,y). Figure 2 shows the results of image reconstruction on the raw data and on data after farfield conversion using Eq. (9). The original image is heavily distorted; the sides and end caps appear bowed and the corners are not flush. Features associated with elastic effects are also distorted. Conversion to the farfield straightens the sides
J. Acoust. Soc. Am. 136 (2), August 2014
Plotnick et al.: Nearfield to farfield conversion for sonar EL63
Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
Published Online 11 July 2014
Fig. 1. (Color online) Left: Primary stages in image reconstruction. Azimuthal angles 0 , 180 , and 360 correspond to broadside while 90 and 270 correspond to end-on. Clockwise: (a) raw time-azimuth data, (b) Fourier transformed data, (c) polar mapped k-space data, (d) reconstructed image of 5:1 aluminum cylinder taken at Washington State University. Logarithmic color scales were used with dynamic ranges sufficient for displaying the significant scattering processes. See also Figs. 2 and 3. Right: Surface wave features associated with backscattering enhancements on solid elastic cylinders. For aluminum in water the expected coupling angle hl ¼ 30 .
and ends as well as makes the corners flush. The corrected image accurately reflects the size and shape of the target. 3.3 Effect of conversion on acoustic color Certain elastic phenomena on the cylinder contribute to enhanced backscatter at intermediate azimuths. These include meridional12 and face crossing13 Rayleigh-like waves, pictured in Fig. 1. The farfield coupling angle for these rays is given by hl ¼ sin1(c/cl), where cl is the phase velocity of the surface wave and c is the fluid sound speed. For
Fig. 2. (Color online) Images of the cylinder. Left: created from raw data. Right: created from data after farfield conversion. The algorithm reduces distortions to the shape of specular and elastic features. Color axis in dB.
EL64 J. Acoust. Soc. Am. 136 (2), August 2014
Plotnick et al.: Nearfield to farfield conversion for sonar
Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
Published Online 11 July 2014
Fig. 3. (Color online) Backscattering spectrum of the cylinder. Left: created from raw data. Right: created from data after farfield conversion. Enhancements due to meridional and face crossing Rayleigh waves are noted. The algorithm moves these loci to expected azimuthal locations. Additionally, the glint at 0 azimuth (broadside) is narrowed. Color axis in dB.
aluminum in water, this is predicted to be approximately14 hl ¼ 30 . Scattering enhancements are thus expected near 30 and 60 azimuth. Such enhancements have been seen in field experiments and can dominate backscattering at these intermediate azimuths.14 Figure 3 shows the effect of farfield conversion on the acoustic color (backscattering spectrum versus azimuthal angle). In the raw nearfield data both meridional and face crossing scattering loci occur at angles differing from those predicted. After farfield conversion both features are observed nearer to the expected value. In addition, the bright feature at 0 azimuth corresponds to specular and elastic broadside scattering. The farfield angular width of the specular broadside main lobe is predicted3 to be hFF ¼ 2 sin1(pc/xL), where L is the length of the cylinder. This feature should be narrow in azimuth and become narrower at higher frequencies. In the nearfield data the broadside feature appears spread in angle and this angular width does not show strong frequency dependence. A simple geometric construction predicts that the nearfield angular width of the main specular lobe is hNF ¼ 2 sin1 ðL=2RÞ 11:3 ;
(10)
which is independent of frequency. The nearfield and farfield data in Fig. 3 are consistent with these estimates of the specular width.
4. Conclusion The Hankel function based nearfield to farfield algorithm allows data to be gathered using smaller apertures and then converted into their farfield form. The algorithm preserves amplitudes by suppressing spreading. Due to the form of the algorithm, computation time required for conversion and imaging is short compared to alternative methods of recovering the farfield image such as back-propagation. Many scattering theories for elastic targets utilize a farfield assumption. If an object is instead scanned in the nearfield, scattering loci may occur at azimuthal locations differing from predicted. Converting to the farfield removes this ambiguity and shifts backscattering loci closer to expected values, aiding manual analysis or use in automatic classifiers. In addition, current CSAS methods assume that data have been taken in the farfield. This process removes nearfield distortions from the resulting image. This may be important for automatic classification and iterative image based techniques such as autofocusing. Some processing procedures also rely on masking out portions of data in either the angle or image domains, both of which may be more easily understood in the farfield. Work of future interest includes cases where the
J. Acoust. Soc. Am. 136 (2), August 2014
Plotnick et al.: Nearfield to farfield conversion for sonar EL65
Plotnick et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4885486]
Published Online 11 July 2014
transducer is outside the target’s plane of rotation and in understanding how phase noise in the raw data affects the conversion. Acknowledgments Work supported by ONR. References and links 1
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EL66 J. Acoust. Soc. Am. 136 (2), August 2014
Plotnick et al.: Nearfield to farfield conversion for sonar
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