Analysis and correction of ultrasonic wavefront distortion based on a multilayer phase-screen model

A model is introduced that incorporates the cumulative wavefront distortion effects caused by spatial heterogeneities along the path of propagation, and a corresponding model-based wavefront distortion-correction method is presented. In the proposed model, a distributed heterogeneous medium is lumped into a series of parallel phase screens. The distortion effects can be compensated-without a priori knowledge of the distorting structure-by backpropagation of received wavefronts through hypothetical multiple phase screens located between the imaging system and targets, while each pointwise time shift is adjusted iteratively to maximize a specified image quality factor at the final layer. Theoretical analyses indicate that the mean speckle brightness decreases monotonically with the root-mean-square value of distributed phase distortions; therefore, the speckle brightness can be used as an image quality factor. Experimental one-dimensional (1-D) array data with simulated distortion effects based on a real 2-D abdominal-tissue map were used to evaluate the performance of the proposed method and existing aberration-correction techniques. The simulated characteristics of wavefront distortion and relative performance of existing correction techniques were similar to reports based on abdominal-wall data and breast data. This investigation shows that the proposed method provides better compensation for wavefront distortion.     

Frequency domain compensation for inhomogeneous layers in ultrasound holography

A frequency-domain compensation method is presented that is based on the ultrasound holography B-scan (UHB) imaging principle. In an acoustic imaging system, the wavefront-angle-dependent distortions caused by any kind of known inhomogeneous reason can be compensated by this method. It is applied here in the frequency domain using the so-called rear-ranging operation for the longitudinal distortion and the multiplication of phase factors for the lateral distortion. The method is especially suitable for compensating different velocity layers in acoustic imaging systems. The results of both computer simulations and water-tank experiments are promising.     

Modeling and correction of incoherent wavefront distortion

There are two types of wavefront distortion inside the female breast: incoherent scattering and coherent interference. Adaptive wavefront compensation algorithms developed so far are useful for correction of incoherent distortion caused by scattering. The performances of these algorithms differ according to the extent of wavefront amplitude distortion. It is shown analytically and experimentally in this article that the matched filtering approach, while optimal for detection, is not so for imaging when the wavefront amplitude is distorted in addition to phasefront distortion. Matched filtering algorithms increase wavefront amplitude variance and therefore decrease image contrast. The inverse filtering approach, while ideal for fidelity, is not stable when the signal-to-noise ratio is low. An approach toward inverse filtering, amplitude compression operation in addition to phase deaberration, is introduced in this article. Analysis and experiments show that its performance is superior to matched filtering algorithms and to time-delay type correction algorithms without introducing stability problems. © 1996 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 322–335, 1997     

Aperture size effect on ultrasonic wavefront distortion correction

The influences of aperture size on wavefront distortion correction are investigated both theoretically and numerically. A multilayer, phase-screen model is assumed to be the underlying, distorting medium. Numerical simulations were performed using three wavefront distortion correction methods: time-shift compensation (TSC), backpropagation followed by time-shift compensation (BP+TSC), and the previously proposed, multilayer, phase-screen compensation (MPSC) method. The distorted wavefronts were generated by propagating a planar wavefront through a multilayer, phase-screen model constructed with a two-dimensional (2-D) scanned map of a real abdominal slice. Performances were evaluated by L2 errors between the corrected wavefronts and the undistorted planar wavefront. Point spread functions also were calculated to evaluate the relative image quality. Theoretical analysis shows L2 error will decrease as aperture size grows when exact phase compensation (EPC) is applied, although finite errors will always exist along the edges of the corrected wavefront. Three different aperture sizes, 14.24 mm (64 elements), 28.48 mm (128 elements), and 56.96 mm (256 elements) are considered in this study. Numerical results show that the quality of wavefront with EPC is essentially limited by the aperture size, and the correction methods considered are relatively robust against the aperture size. It also shows that, for low aberration, results with MPSC and EPC are comparable. However, for high aberration, MPSC significantly outperforms EPC in suppression of L2 error and sidelobes. This study suggests that, for most medical ultrasound imaging systems, the exact structure of the distorting medium may not be necessary to be known a priori for optimal distortion correction because of the limitation imposed by finite aperture size.     

Deaberration of incoherent wavefront distortion: An approach towardinverse filtering

Techniques for the correction of ultrasonic wavefront distortion are compared using measured pulse transmission through human breast specimens. The measured data were obtained by recording the pulse signals on each element of a linear array that was moved in elevation to synthesize a two-dimensional aperture. The one-way point spread functions were reconstructed using matched filtering technique, phase conjugation, time-delay compensation, and backpropagation followed by phase conjugation, each with and without amplitude compression. Two measures of performance were compared, the mainlobe diffraction shape and the ratio of the energy outside the mainlobe to the energy inside the mainlobe. Matched filtering, which compensates the phase distortion but also increases the variation in the modulus, performs more poorly than other techniques with respect to both measures. Phase conjugation and time-delay compensation, which leave the magnitude of the wavefront unchanged, have similar beamwidths but phase conjugation is consistently superior with respect to energy ratio. The backpropagation method, which models wavefront distortion using a phase screen at a computed position between the source and aperture, is shown to perform better. The use of a novel amplitude compression that approaches inverse filtering improves the performance of the compensation techniques significantly. This is because inverse filtering optimizes image fidelity, in contrast, for example, to matched filtering, which optimizes SNR. With the amplitude compression method, the results of the one-way experiments show that the mainlobe shape can be recovered down to -30 dB     

Nonrandom quantization errors in timebases

Timebase distortion causes nonlinear distortion of waveforms measured by sampling instruments. When such instruments are used to measure the RMS amplitude of the sampled waveforms, such distortions result in errors in the measured RMS values. This paper looks at the nature of the errors that result from nonrandom quantization errors in an instrument timebase circuit. Simulations and measurements on a sampling voltmeter show that the errors in measured RMS amplitude have a nonnormal probability distribution, such that the probability of large errors is much greater than would be expected from the usual quantization noise model. A novel timebase compensation method is proposed which makes the measured RMS errors normally distributed and reduces their standard deviation by a factor of 25. This compensation method was applied to a sampling voltmeter and the improved accuracy was realized     

Transcranial ultrasound focus reconstruction with phase and amplitude correction

Therapeutic and diagnostic ultrasound procedures performed noninvasively through the skull require a reliable method for maintaining acoustic focus integrity after transmission through layered bone structures. This study used a multiple-element, phased-array transducer to reconstruct ultrasound foci through the human skull by amplitude and phase correction. It was previously demonstrated that adaptive phase correction using a multiple-element, focused transducer array yields a significant correction to an acoustic field that has been distorted by the heterogeneities of the skull bone. The introduction of amplitude correction, in a regime in which acoustic pressures from individual transducer array elements are adjusted to be normalized at the focus, has demonstrated a 6% (-0.27 dB) average decrease in acoustic sidelobe acoustic intensity relative to the focal intensity and a 2% (-0.09 dB) average decrease in the full-width-at-half-maximum (FWHM) of the acoustic intensity profile at the focus. These improvements come at the expense of significant ultrasound intensity loss--as much as 30% lower (-1.55 dB)--at the focus because the amplitude correction method requires that, at constant power, a larger proportion of energy is absorbed or reflected by regions of the skull that transmit less energy. In contrast, a second correction method that distributes pressure amplitudes such that the sections of the skull which transmit more ultrasound energy are exposed with higher ultrasound intensities has demonstrated an average sidelobe intensity decrease of 3% (-0.13 dB) with no change in the FWHM at the focus. On average, there was a 2% (0.09 dB) increase in the acoustic intensity at the focus for this inverse amplitude correction method. These results indicate that amplitude correction according to the transmission properties of various segments of the skull have a clear effect on ultrasound energy throughput into a target site within the brain parenchyma.     

Wavefront amplitude distortion and image sidelobe levels. I. Theory and computer simulations

The quality of an imaging system is degraded by propagation anomalies that distort wavefronts propagating through the medium. Adaptive phase-deaberration algorithms compensate for phase errors in the wavefront. The algorithms suffer, however, when the wavefront is also significantly distorted. A theory which shows that the rise of image background level, which is the average sidelobe floor (ASF), in a single point-like source image is proportional to the amplitude distortion of the wavefront and inversely proportional to the effective number of array elements is derived. From the theory, the tolerance to the amplitude distortion, after the phasefront has been corrected by a deaberration algorithm, can be calculated based on the design requirement of the sidelobe floor for a given array. Computer simulations show good agreement with the theory.     

Rhesus monkey brain imaging through intact skull with thermoacoustic tomography

Two-dimensional microwave-induced thermoacoustic tomography (TAT) is applied to imaging the Rhesus monkey brain through the intact skull. To reduce the wavefront distortion caused by the skull, only the low-frequency components of the thermoacoustic signals (< 1 MHz) are used to reconstruct the TAT images. The methods of signal processing and image reconstruction are validated by imaging a lamb kidney. The resolution of the system is found to be 4 mm when we image a 1-month-old monkey head containing inserted needles. We also image the coronal and axial sections of a 7-month-old monkey head. Brain features that are 3 cm deep in the head are imaged clearly. Our results demonstrate that TAT has potential for use in portable, cost-effective imagers for pediatric brains.     

Statistical model for fading return signals in coherent lidars

A statistical model for the return signal in a coherent lidar is derived from the fundamental principles of atmospheric scattering and turbulent propagation. The model results in a three-parameter probability distribution for the coherent signal-to-noise ratio in the presence of atmospheric turbulence and affected by target speckle. We consider the effects of amplitude and phase fluctuations, in addition to local oscillator shot noise, for both passive receivers and those employing active modal compensation of wavefront phase distortion. We obtain exact expressions for statistical moments for lidar fading and evaluate the impact of various parameters, including the ratio of receiver aperture diameter to the wavefront coherence diameter, the speckle effective area, and the number of modes compensated.     

Optical compensation of hologram distortion avoiding interpage crosstalk on reconstructed image in angle-multiplexed holograms

We are studying a form of holographic data storage with phase conjugation, and we compensated for hologram distortion due to shrinkage of photopolymer materials in the holographic medium by controlling the wavefront of the reference beam. When a high NA lens and narrow angle interval of angle multiplexing are employed to obtain a high data recording density, some wavefronts cause interpage crosstalk on the reconstructed image. We tried to determine the moving range of actuators in a deformable mirror for controlling the wavefront. As a result, we found that the distortion in the hologram could be compensated while avoiding interpage crosstalk and that the bit error rates of the reproduced data could be decreased. We also found that the optimized wavefront could compensate for distortions in several neighboring data pages. This method can ensure a high data recording density in holographic data storage.     

PWM逆变器死区效应在线补偿

为了减小控制系统中由PWM逆变器死区效应引起的电流波形失真,在分析了死区效应产生的机理及谐波影响基础上,提出了一种死区在线补偿的新方法。该方法结合两相静止坐标系下误差电压的线性特点,估计出误差电压幅值,再在两相同步坐标系下利用误差电压幅值和转子角度的关系对死区效应进行前馈补偿,补偿方法考虑了逆变器的非线性误差,无需额外硬件电路支持或离线测量,避免了电流极性检测,能够摆脱误差电压突变带来补偿不利的缺陷,简单且易于实现。仿真及实验结果表明,该方法能够有效地抑制高次谐波电流分量,改善电流波形质量。     

Fabrication error analysis and experimental demonstration for computer-generated holograms

Aspheric optical surfaces are often tested using computer-generated holograms (CGHs). For precise measurement, the wavefront errors caused by the CGH must be known and characterized. A parametric model relating the wavefront errors to the CGH fabrication errors is introduced. Methods are discussed for measuring the fabrication errors in the CGH substrate, duty cycle, etching depth, and effect of surface roughness. An example analysis of the wavefront errors from fabrication nonuniformities for a phase CGH is given. The calibration of these effects for a CGH null corrector is demonstrated to cause measurement error less than 1 nm.     

Correction of phase distortion in spatial heterodyne spectroscopy

The detailed analysis of measured interferograms generally requires phase correction. Phase-shift correction methods are commonly used and well documented for conventional Fourier-transform spectroscopy. However, measured interferograms can show additional phase errors, depending on the optical path difference and signal frequency, which we call phase distortion. In spatial heterodyne spectroscopy they can be caused, for instance, by optical defects or image distortions, making them a characteristic of the individual spectrometer. They can generally be corrected without significant loss of the signal-to-noise ratio. We present a technique to measure phase distortion by using a measured example interferogram. We also describe a technique to correct for phase distortion and test its performance by using a simulation with a near-UV solar spectrum. We find that for our measured example interferogram the phase distortion is small and nearly frequency independent. Furthermore, we show that the presented phase-correction technique is especially effective for apodized interferograms.     

Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy

The concept of numerical parametric lenses (NPL) is introduced to achieve wavefront reconstruction in digital holography. It is shown that operations usually performed by optical components and described in ray geometrical optics, such as image shifting, magnification, and especially complete aberration compensation (phase aberrations and image distortion), can be mimicked by numerical computation of a NPL. Furthermore, we demonstrate that automatic one-dimensional or two-dimensional fitting procedures allow adjustment of the NPL parameters as expressed in terms of standard or Zernike polynomial coefficients. These coefficients can provide a quantitative evaluation of the aberrations generated by the specimen. Demonstration is given of the reconstruction of the topology of a microlens.     

Experimental demonstrations of the digital correction of complex wave errors caused by arbitrary phase-shift errors in phase-shifting interferometry

In previous papers we proposed a digital method of correcting both amplitude and phase distortions caused by arbitrary phase-shift errors in standard four-frame phase-shifting interferometry (PSI), then extended it to the most generalized PSI, and showed the validity of this technique by computer simulations. Here some new simulations and a series of optical experiments with a plane wave, a spherical wave, and a piece of glass as objects are reported. The experimental results have further proved the correctness of our theoretical analysis and confirmed that our method is able to suppress double-frequency fringes in the retrieved amplitude map and the distortions in the phase map that are introduced by phase-shift errors such as to effectively eliminate the wave ripples and wall-like structures that are present in the unwrapped phase map owing to these errors. In addition, our technique can reduce the density of invalid pixels, which are barriers in phase unwrapping. Therefore the accuracy of both amplitude and phase measurements can be considerably improved.     

Supercritical parametric wave phase conjugation as an instrument for narrowband analysis in ultrasonic harmonic imaging

Supercritical parametric wave phase conjugation (SWPC) is used for selection and phase conjugation of harmonic components of a nonlinear incident wave. The amplitude of the phase conjugate wave in a supercritical mode is high enough for acoustic nonlinearity of the propagation medium to appear. As a result, in particular, doubled and quadrupled frequencies of the incident wave become available for image formation at the same order of the medium nonlinearity. The improvement of the imaging system resolution because of harmonic analysis of the received acoustic signal and compensation of phase distortions caused by wave phase conjugation were observed simultaneously when the propagation medium was inhomogeneous.     

利用正交相位法提取双向性血流的一种补偿方法

正交相位法是超声多普勒技术中提取双向性血流信息的一种重要方法。由于正交信号对之间通常存在幅度和相位的不平衡，从而导致了正、反血流信息的混淆，影响了平均频率，最大的估计和声谱图的正确显示，本文提出的补偿方法，让其中一个正交信号通过按一定要求设计的线性滤波器，从而得到幅度和相位基本平衡的正交信号对，提高了超声多普勒系统提取双向性血流的性能。     

卷曲空间型超表面对声波的调控

声学超表面具有天然材料所不具备的独特属性,为声学器件的设计提供了多样性。以广义斯涅尔定律为理论基础,设计了具有多种声波调控能力的折射型相位梯度超表面。该超表面由8个具有不同结构参数的卷曲空间单元结构组合而成,在中心频率3 500 Hz附近,8个单元结构的相位覆盖π范围且声波透射率较高。通过合理地设计超表面水平方向上的相位梯度变化,能够实现对声波的任意调控,在理论和有限元仿真上依次实现了异常折射、无衍射贝塞尔声束和声聚焦。这种厚度薄、透射率高的声超表面,在声学器件设计方面具有潜在的应用价值。     

Image reconstruction in photoacoustic tomography involving layered acoustic media

Photoacoustic tomography (PAT), also known as thermoacoustic or optoacoustic tomography, is a rapidly emerging biomedical imaging technique that combines optical image contrast with ultrasound detection principles. Most existing reconstruction algorithms for PAT assume the object of interest possesses homogeneous acoustic properties. The images produced by such algorithms can contain significant distortions and artifacts when the object's acoustic properties are spatially variant. In this work, we establish an image reconstruction formula for PAT applications in which a planar detection surface is employed and the to-be-imaged optical absorber is embedded in a known planar layered acoustic medium. The reconstruction formula is exact in a mathematical sense and accounts for multiple acoustic reflections between the layers of the medium. Computer-simulation studies are conducted to demonstrate and investigate the proposed method.