Sidelobe Amplitude Research Articles

New efficient window function, replacement for the Hamming window

A new simple window function is presented, which for the same window order (M), has a main-lobe width less than or equal to that of the Hamming window, while offering about 2–4.5 dB smaller peak side-lobe amplitude. Furthermore, just like the Hamming window, it is computationally efficient for signal spectrum analysis; this is because of the fact that, the sum of window coefficients with its shifted version by M/2 samples (i.e. 50% overlap) is constant for the overlapped region. The new window is obtained by adding the third harmonic of the cosine function to the Hamming window, and finding the appropriate amplitudes of DC term, cosine function, and its third harmonic to minimise the peak side-lobe amplitude. A comparison with the Kaiser and Dolph–Chebyshev windows is also performed. Finite impulse response filters designed by windowing method show the efficiency of the new window.

Contrast imaging with chirped excitation

Coded excitation has been successfully used in imaging to increase the signal-to-noise ratio (SNR) and penetration depth. With a contrast agent, wideband signals have been hypothesized to increase the contrast-to-tissue ratio (CTR). However, nonlinear properties of contrast agents make decoding difficult when applying coded excitation to contrast imaging. We propose two chirped excitation methods to image contrast agents, with a mechanical index (MI) ranging from 0.05 to 0.34. In the single chirp method, one chirp is transmitted, followed by a clutter filter to reject tissue echoes, then a matched filter is used to recover range resolution. In the chirp sequence method, an increasing and decreasing chirp sequence is transmitted followed by subtraction of the compressed echoes to reject tissue echoes (assuming tissue is a linear scatterer at low MI). Ten independent acoustic experiments were performed to evaluate the CTR for chirp and tone burst insonation, with the same spatial peak temporal averaged intensity (I(SPTA)). A significant increase in CTR, ranging from 4 dB to 8 dB, is observed for chirped excitation as compared with tone burst insonation, at an I(SPTA) of 0.1 and 0.3 mW/cm2 (P < or = 5e-3). To achieve the same CTR of 15 dB, the spatial peak pulse averaged intensity (I(SPPA)) can be decreased by 6 dB for chirp insonation as compared with tone burst insonation (P < 1e-5). Additionally, an increase of more than 10 dB in tissue rejection ratio (TRR) is observed for a chirp sequence insonation compared to tone burst phase inversion for this set of parameters (P < or = 1e-9). Deconvolution of the linear microbubble response from the received echoes is proposed as a method to recover spatial resolution. The difference in the axial resolution resulting from chirp and three-cycle tone burst insonation is approximately 220 microm. The difference in the mainlobe width between experimental and predicted compressed echoes is less than 20%. The side-lobe amplitude is 9 dB to 16 dB below the mainlobe with a transmitted I(SPTA) from 0.1 to 6.6 mW/cm2.

Bezier representations for the multiobjective optimization of conformal array amplitude weights

For conformal phased arrays, generally the excitation amplitude of the array elements must be adjusted in order to maintain low sidelobes as the array is scanned. While the desired phase weights for maximum gain are deterministically set by the array geometry and scan angle, the representation of optimum low sidelobe amplitude weights remains an open problem. Following up on prior work using the efficiency-constrained optimization of a modified Bernstein polynomial for low sidelobe conformal array synthesis, a Bezier surface is shown to provide a good representation of the optimized amplitude weights with a reduced number of parameters, while demonstrating e-constraint multi-objective optimization of conformal aperture efficiency versus sidelobe level. These results are extended to include a Bezier volume representation for the multiobjective optimization of conformal aperture efficiency versus both sidelobe level and scan angle.

ULTRASONIC IMAGING SYSTEM USING A 2D ENVELOPE BEAMFORMING TECHNIQUE: IN-HOMOGENEITIES LOCATION

An algorithm has been developed to implement synthetic aperture focusing technique for B-scan. This is made at a several transmitter/receiver locations to form a map of ultrasonic reflectivity on the insonified region, considering the path travelled by the ultrasonic pulse from the transducer to the target and back again. To reconstruct the image, a time domain beam-former is applied to the envelope of the detected signals. This method minimizes the side-lobe amplitude and the restriction of λ/2 distance between two adjacent transducer positions can be neglected without loosing image resolution. The present work is focused on the location of the in-homogeneities, caused by the presence of a phantom immersed in a water tank. The results are presented when the distance between two adjacent transducer positions are varied from 0.5λ to 2.5λ showing that the longitudinal resolution is not affected but the lateral resolution becomes poorer when the distance is about 2λ. The error in the longitudinal location of in-homogeneities is within the minimum detectable distance of the system, while the lateral location error is increased when the distance between any two adjacent transducer positions is larger than 1.5λ.

Nonlinear Response of a Weakly Damaged Metal Sample: A Dissipative Modulation Mechanism of Vibro-Acoustic Interaction

The nonlinear vibro-acoustic response of solid samples containing quite a small amount of defects can be anomalously high in magnitude compared to the case of undamaged intact solids. Functional de pendencies of the nonlinear effects exhibit rather interesting behavior. In this paper, experimental results on nonlinearity-induced cross-modulation of a high-frequency (HF) f = 15 — 30 kHz signal by a low-frequency (LF) F = 20 - 60 Hz vibration in an aluminum plate with a small single crack are reported. Comparison with a reference sample (the identical plate without a crack) has proven that the presence of such a small defect can be easily detected due to its nonlinear manifestations. It is demonstrated that under proper choice of the sounding signal parameters, the effect level can be so pronounced that the amplitude of the modulation side-lobes originated due to the nonlinearity exceeds the amplitude of the fundamental harmonic of the HF signal. Main functional features of the observed phenomena are analyzed, and a new physical explana tion is suggested based on a dissipative mechanism of vibro-acoustic interaction. Results of the numerical simulation of the effect are also presented.

Broadband source imaging in a shallow water wedge by an array of receivers

The combination of time domain source imaging techniques and arrays to consider the localization of an impulsive source in a wedge waveguide, with a free surface and rigid bottom, is investigated. An impulsive signal is transmitted from an unknown location, received by an array of hydrophones, and stored. The signals are time reversed and transmitted into the model wedge by a transducer at each receiver location. Model transmission functions are used to compute the pressures at a set of locations. The field calculations use an image construction from D. Chu’s exact solution for a density contrast wedge [J. Acoust. Soc. Am. 86, 1883–1896 (1989)]. A map of the peak pressures gives an image of the source location. Particular attention is given to the peak amplitudes, sidelobe amplitudes, and spatial resolution as a function of the number and placement of receivers. Source localization is enhanced by the range dependency of the environment, which eliminates ‘‘range’’ sidelobes, even for a single hydrophone. Adding receivers along an arc eliminates ‘‘angle’’ sidelobes; but adding receivers along an arc or radial gives little reduction in overall background level. Adding receivers parallel to the wedge axis gives sharp, unambiguous azimuthal imaging.

High Resolution Imaging at mm-Wavelengths with the Hat Creek Array

The Hat Creek mm-wavelength array, operated by the Berkeley-Illinois-Maryland Association (BIMA), is undergoing an expansion to nine telescopes. The first six of these telescopes will be operational in January, 1993. The telescopes are relatively small, 6 m in diameter, and are moved on rubber-tired dollies so it will be possible to transport them on roads in the vicinity of the main array. Initially, we plan to place two of the telescopes at outrigger sites located 0.5 and 1.0 km from the main array. Use of these outrigger telescopes will yield angular resolutions of 0.45 arc-sec at 2.7 mm wavelength and 0.21 arc-sec at 1.2 mm wavelength. When all nine telescopes are operational, reasonable image quality will be obtained with a single 12-hour observation. The maximum sidelobe amplitude depends upon source declination, but is about 16%. Figures 1, 2, and 3 show the uv coverage and beamshapes which will be achieved at various declinations.

Acoustic source localization in a wedge waveguide using time-domain techniques.

In previous work [C. Feuillade and C. S. Clay, J. Acoust. Soc. Am. Suppl. 1 88, S26 (1990)], the results of an investigation into time domain source imaging techniques in a range-independent, shallow-water waveguide were reported. The research reported here extends this method to consider the case of an impulsive source in a density penetrable wedge waveguide. Single-channel source location information is used by means of time domain transmissions to multiple receivers. The signals from the receivers are time reversed and transmitted through sources at the receiver locations. The field is mapped to locate the source. Particular attention is given to the peak amplitudes, sidelobe amplitudes, and spatial resolution as a function of receiver channels. The field calculations are performed by using an image approximation that is based on D. Chu’s exact solution for a wedge [J. Acoust. Soc. Am. 86, 1883–1896 (1989)]. S. Li and C. S. Clay have also given a discussion of single channel theory and experiment [J. Acoust. Soc. Am. 82, 1409–1417 (1987)]. The results show that source localization in a wedge is significantly promoted by the range dependency of the environment, which eliminates ‘‘range’’ sidelobes, even for a single hydrophone. The signal peak is more effectively resolved by locating the receivers as far from the wedge apex as possible. ‘‘Angle’’ sidelobes may be effectively eliminated by introducing additional receivers in an arc at constant range from the apex. [This work was supported by the Naval Res. Lab. and by the Office of Naval Res. under Contract No. N00014-89-J-1515 (CSC).]

An approximation technique for determining optimal Combisweep parameters

The autocorrelation of a linear FM (frequency modulated) signal consists of a main peak, a primary side lobe, and far side lobes (Figure 1), the side lobes often being referred to as correlation noise (Werner and Krey, 1979; Edelmann and Werner, 1982). One of the aims of Vibroseis signal design is to find and input sweep signal whose autocorrelation has a narrow main peak (high temporal resolution) and low correlation noise as defined by the main peak to primary side lobe amplitude ratio [Formula: see text] (Figure 1) (Werner and Krey, 1979). A simple and easily implemented method of reducing correlation noise is amplitude tapering (Edelmann, 1966), but unfortunately tapering induces an increase in main peak width (Berkhout, 1984), an undesirable effect. A technique of linearly combining individual autocorrelations, called Combisweep, was shown to increase [Formula: see text] (Werner and Krey, 1979). However, Werner and Krey made no attempt to optimize parameter selection.

Peak sidelobe estimator for randomized arrays

A randomized line array is formed by randomly perturbing an equally spaced, deterministic array. For small perturbations, it has been shown that the variance of the sidelobe amplitude is less, over a significant portion of the beam pattern, than for larger perturbations. The present paper quantifies the effect of this variance dependency on the magnitude of the peak sidelobe. The analysis follows that presented by Steinberg [Principles of Aperture and Array System Design (Wiley, New York, 1976), pp. 147–166], in which for a given confidence level the upper bound on the peak sidelobe is derived. Steinberg's work is based on a totally random array, and makes use of the fact that all the sidelobes are statistically the same to obtain a closed‐form expression for the peak sidelobe level as a function of confidence level. In the present work the mean and variance associated with each independent sidelobe position are computed and combined to give results that depend on the original array configuration and on the size of the perturbation. It is shown that a randomized array with a moderately small perturbation may have a significantly lower peak sidelobe than the corresponding totally random array.

Methods for seismic exploration

First Page

Pattern synthesis by use of an augmented Lagrangian algorithm

The augmented Lagrangian algorithm is applied to the optimisation of an array antenna. As examples, the optimal directivities of a broadside array with constraints on sidelobe and excitation amplitudes are computed. The following technique is feasible for use in wide application on pattern synthesis.

Boresight-gain loss and gore-related sidelobes of an umbrella reflector

It is shown that energy in the gore-related sidelobes of an umbrella reflector comes from energy lost from the main beam. Both boresight gore-loss and sidelobe level correlate directly with cyclic aperture phase error caused by the geometry. The gore-sidelobe peak is located near \theta_{p} , where \sin \theta_{p} = 1.2N_{G} (\pi/D\lambda) where N_{G} is the number of gores and D is the reflector diameter. An expression is also derived for the amplitude of the gore-related sidelobe.

Delay Quantization Error in Phased Array Images

Time quantization errors in phased array systems can cause increased sidelobe amplitude, thereby limiting the dynamic range of the ultrasound system. A simulation program predicting the position and amplitude of these anomalous quantization error grating lobes has been developed to study the effects of transmitted pulse length on the ampli- tude of these anomalous lobes. Three parallel processing techniques for decreasing these sidelobe amplitudes while smoothing the speckle pat- tern are investigated.

On the use of the I&amp;lt;inf&amp;gt;0&amp;lt;/inf&amp;gt;-sinh window for spectrum analysis

Closed form expressions for main-lobe width, modified main-lobe width, and relative sidelobe amplitude are given for the I_{0}- \sinh window function. These formulas facilitate exploring the tradeoff between record length, spectral resolution, and leakage in digital spectrum analysis. An especially simple empirical approximation relating main-lobe width and relative sidelobe amplitude is given.

Approximations to Dolph-Cbebyshev data windows

A family of optimum data windows was presented recently [J. C. Burgess, J. Acoust. Soc. Am. 62, S51(A) (1977)]. These windows are optimum in the sense that their spectral representations have the narrowest main lobes possible for a specified ratio of maximum side lobe amplitude to main lobe amplitude subject to the condition that the windows are described by Fourier series having very few nonzero coefficients. The process by which the Fourier coefficients are determined is equivalent to fixing the amplitude of one lobe in the spectral representation for each nonzero coefficient. A Fourier series having M + 1 coefficients thus controls the amplitudes of M side lobes. The Dolph-Chebyshev windows have the narrowest main lobes possible, and all side lobes for each window have the same level. The windows described by Burgess can thus be thought of as approximations to Dolph-Chebyshev windows. For M + 1 = 4 (i.e., four nonzero Fourier coefficients), the approximations have main lobe widths less than 5% wider than the corresponding Dolph-Chebyshev windows.

Contrast and imaging performance in the scanning acoustic microscope

Several articles have been written on the subject of scanning acoustic microscopy. Nevertheless, apart from some specific papers dealing with reflection microscopy, little has been said about the various contrast mechanisms involved in the process of image formation, and the effects of parameters such as acoustic antireflection coatings on the lens surface and absorption in the water on the quality of the recorded image. This paper is devoted to an analysis of these problems. It is shown that in the amplitude mode of operation, the acoustic microscope acts as a phase contrast microscope and is sensitive to the local phase gradients in the object. Furthermore, it is shown that the effect of an acoustic antireflection coating on the lens surface is to substantially reduce the side lobe amplitude of the focal distribution at the expense of a slight increase in the width of the main lobe. Experimental observations agree with theory.

Real-time Fourier transformation via acousto-optics

An implementation of the chirp transform algorithm for performing a real-time Fourier transform is described. The implementation is based upon an acousto-optic convolver with a large time-bandwidth product An instantaneous bandwidth of about 75 MHz was achieved for the Fourier transformer with a dynamic range in excess of 60 dB for a cw time-gated waveform. By using an almost-uniform light-beam intensity across the device, the measured sidelobe amplitudes were within 0.5 dB of the theoretical values. The corresponding measured phase errors were less than 5°. The adaptability of this acousto-optic implementation is demonstrated by the ease with which one can vary both the sidelobe weighting function and the time rate of the transform.

Simple optimum data windows for digital signal processing

The spectral representation of a finite–length sample from a sinusoidal signal can be regarded as a convolution of the spectral representation of the infinite-length signal and a finite-length “window.” The spectral representation of the window consists of a main lobe and a sequence of side lobes. By changing the shape of the window, maximum side lobe amplitude can be decreased. The cost is that main lobe amplitude is increased. Window design consists in finding an acceptable trade-off between these two effects. A useful and practical criterion for design is that the main lobe be the narrowest possible for a specified ratio of maximum side lobe amplitude to main lobe amplitude subject to the condition that the window is described by a Fourier series having very few non-zero coefficients (e.g., for a ratio of −60.00 dB, B0=1, B1=0.534 373, B2=0.051 800, B3=−0.000 051, B−ν=Bν. The resulting family of data windows have the narrowest main lobes of any known to the author.

Sidelobe Height and Placement of Quasi-Complementary Sequences

The rules given in this correspondence enable the positions and amplitudes of the nonzero sidelobes of quasi-complementary sequences to be determined without use of a computer and without knowing the autocorrelation functions of the individual codes beforehand. They enable the system designer to synthesize a set of codes directly from system specifications. They also shed light on the code structure itself. Examples are given.