Optimal amplitude shading for arrays of irregularly spaced or non-coplanar elements

Abstract

The majority of optimal amplitude shading methods for arrays of irregularly spaced or non-coplanar elements rely on numerical optimizations and iterative techniques to compute the desired weighting function because analytic solutions generally do not exist. Optimality is meant here in the Dolph–Chebyshev sense to provide the narrowest mainlobe width for a given sidelobe level. A simpler and more efficient technique to compute the shading weights for arbitrary line array shapes or element spacings is presented and it is shown that it is sufficient to sample the optimal Dolph–Chebyshev window, computed for a uniform line array of equivalent aperture length, at the element position of the nonuniform array. Examples are given for narrow-band plane-wave beamforming with curved arrays in which phase compensation is achieved by projecting the elements on a line tangent to the array. For the same mainlobe width, the resulting peak sidelobe levels are within 3 dB of a 30-dB Dolph–Chebyshev weighted uniform line array of equal aperture length and number of elements. Results are presented for computer simulations and for data collected at sea with the Toroidal Volume Search Sonar by the Coastal Systems Station, Panama City, Florida. [Work sponsored by ONR-NRL (Contract No. N00014-96-1-G913).]

Multibeam volume acoustic backscatter imagery and reverberation measurements in the northeastern Gulf of Mexico

“…The processing scheme that we have developed for the TVSS acoustic data is designed for conformal arrays and includes quadrature sampling, resampled amplitude shading, element-pattern compensation, and broadside beamforming on phase-compensated, overlapping subarrays with asymmetric projected element spacings. 23 This procedure permits split aperture processing of the beamformed output, which is performed because the processed data also were used to study acoustic backscatter from the ocean boundaries, and the phase zero-crossing of the output phasor is the most accurate means to detect the arrival time of boundary reflections on the maximum response axis of the beam. 24,25 For each ping, the split aperture process is used to form a phasor P(,t) for a given beam direction and time sample t every 3 degrees for directions spanning the 360 degrees around the TVSS axis.…”

“…We used these response patterns because they successfully removed pointing errors which were observed in previous beamforming efforts with the TVSS. 23 Computer simulations, which used the TVSS transmit pattern and towfish attitude data for each run, indicated that the TVSS array beampatterns produced a maximum bias error of Ϫ7 dB and a maximum random error of Ϯ3.3 dB in the TVSS data. After echo-integrating and averaging over successive pings, these values were reduced to approximately Ϫ5 dB for the bias error and Ϯ1 dB for the random error.…”

“…24 This sidelobe interference is somewhat enhanced by our choice of a resampled Dolph-Chebyshev amplitude shading window designed to produce a nearly uniform sidelobe level between Ϫ28 and Ϫ30 dB for all the receive beampatterns. 23 Lower sidelobe levels are achievable, but the corresponding increase in mainlobe beam width would degrade the spatial resolution in the images. Due to the strong boundary echo sidelobe returns in the TVSS data, sidelobe cancellation methods are necessary to use data in the upward looking beams beyond slant ranges equal to the towfish's depth ͑ϳ78 m͒, and in the downward looking beams beyond slant ranges equal to the towfish's altitude ͑ϳ115 m͒.…”