Modulation of Point Spread Function for Super-Resolution Imaging.

High image resolution is desired in wave-related areas such as ultrasound, acoustics, optics, and electromagnetics. However, the spatial resolution of an imaging system is limited by the spatial frequency of the point spread function (PSF) of the system due to diffraction. In this article, the PSF is modulated in amplitude, phase, or both to increase the spatial frequency to reconstruct super-resolution images of objects or wave sources/fields, where the modulator can be a focused shear wave produced remotely by, for example, a radiation force from a focused Bessel beam or X-wave, or can be a small particle manipulated remotely by a radiation-force (such as acoustic and optical tweezers) or electrical and magnetic forces. A theory of the PSF-modulation method was developed, and computer simulations and experiments were conducted. The result of an ultrasound experiment shows that a pulse-echo (two-way) image reconstructed has a super-resolution (0.65 mm) as compared to the diffraction limit (2.65 mm) using a 0.5-mm-diameter modulator at 1.483-mm wavelength, and the signal-to-noise ratio (SNR) of the image was about 31 dB. If the minimal SNR of a "visible" image is 3, the resolution can be further increased to about 0.19 mm by decreasing the size of the modulator. Another ultrasound experiment shows that a wave source was imaged (one-way) at about 30-dB SNR using the same modulator size and wavelength above. The image clearly separated two 0.5-mm spaced lines, which gives a 7.26-fold higher resolution than that of the diffraction limit (3.63 mm). Although, in theory, the method has no limit on the highest achievable image resolution, in practice, the resolution is limited by noises. Also, a PSF-weighted super-resolution imaging method based on the PSF-modulation method was developed. This method is easier to implement but may have some limitations. Finally, the methods above can be applied to imaging systems of an arbitrary PSF and can produce 4-D super-resolution images. With a proper choice of a modulator (e.g., a quantum dot) and imaging system, nanoscale (a few nanometers) imaging is possible.

Ultrasound Concave 2-D Ring Array for Retinal Stimulation.

An ultrasound concave 2-D ring array transducer was designed for applications in visual stimulation of the retina with a long-term goal to restore vision in individuals with intact neurons but suffering blindness due to retinopathies. The array was synthesized and has a frequency of 20 MHz (0.075-mm wavelengths in water), 18-mm focal length (the curvature of the concave array), 1004 elements (with a pitch of 4.0 wavelengths), and inner and outer diameters of 9 and 14 mm, respectively. Wave patterns produced with the array at the focal distance were simulated. Results show that the wave patterns obtained can achieve a full-width-at-half-maximum (FWHM) resolution of 0.147 mm that is very close to the FWHM diffraction limit (0.136 mm). In addition, a scaled experiment at a lower frequency of 2.5 MHz was performed. The result is very close to those obtained with the simulations.

Performance Enhanced Ultrasound Probe Tracking With a Hemispherical Marker Rigid Body.

Among tracking techniques applied in the 3-D freehand ultrasound (US), the camera-based tracking method is relatively mature and reliable. However, constrained by manufactured marker rigid bodies, the US probe is usually limited to operate within a narrow rotational range before occlusion issues affect accurate and robust tracking performance. Thus, this study proposed a hemispherical marker rigid body to hold passive noncoplanar markers so that the markers could be identified by the camera, mitigating self-occlusion. The enlarged rotational range provides greater freedom for sonographers while performing examinations. The single-axis rotational and translational tracking performances of the system, equipped with the newly designed marker rigid body, were investigated and evaluated. Tracking with the designed marker rigid body achieved high tracking accuracy with 0.57° for the single-axis rotation and 0.01 mm for the single-axis translation for sensor distance between 1.5 and 2 m. In addition to maintaining high accuracy, the system also possessed an enhanced ability to capture over 99.76% of the motion data in the experiments. The results demonstrated that with the designed marker rigid body, the missing data were remarkably reduced from over 15% to less than 0.5%, which enables interpolation in the data postprocessing. An imaging test was further conducted, and the volume reconstruction of a four-month fetal phantom was demonstrated using the motion data obtained from the tracking system.

Fabrication of an Extremely Cheap Poly(3,4-ethylenedioxythiophene) Modified Pencil Lead Electrode for Effective Hydroquinone Sensing.

Hydroquinone (HQ) is one of the major deleterious metabolites of benzene in the human body, which has been implicated to cause various human diseases. In order to fabricate a feasible sensor for the accurate detection of HQ, we attempted to electrochemically modify a piece of common 2B pencil lead (PL) with the conductive poly(3,4-ethylenedioxythiophene) or PEDOT film to construct a PEDOT/PL electrode. We then examined the performance of PEDOT/PL in the detection of hydroquinone with different voltammetry methods. Our results have demonstrated that PEDOT film was able to dramatically enhance the electrochemical response of pencil lead electrode to hydroquinone and exhibited a good linear correlation between anodic peak current and the concentration of hydroquinone by either cyclic voltammetry or linear sweep voltammetry. The influences of PEDOT film thickness, sample pH, voltammetry scan rate, and possible chemical interferences on the measurement of hydroquinone have been discussed. The PEDOT film was further characterized by SEM with EDS and FTIR spectrum, as well as for stability with multiple measurements. Our results have demonstrated that the PEDOT modified PL electrode could be an attractive option to easily fabricate an economical sensor and provide an accurate and stable approach to monitoring various chemicals and biomolecules.

Synthesis of MOF525/PEDOT Composites as Microelectrodes for Electrochemical Sensing of Dopamine.

Dopamine (DA) is an important neurotransmitter responsible for the functions and activities of multiple systems in human. Electrochemical detection of DA has the advantages of fast analysis and cost-effectiveness, while a regular electrode probe is restricted to laboratory use because the probe size is too large to be suitable for an in vivo or in vitro analysis. In this study, we have developed porphyrin-based metal organic framework (MOF525) and poly(3,4-ethylenedioxythiophene) (PEDOT)-based composites to modify microelectrode for DA detection. Two types of PEDOT monomers with different functional groups were investigated in this study. By varying the monomer ratios, electrolyte concentrations, and electropolymerization temperature, it was found that the PEDOT monomer containing carboxylic group facilitated the formation of regular morphology during the electropolymerization process. The uniform morphology of the PEDOT promoted the electron transmission efficiency in the same direction, while the MOF525 provided a large reactive surface area for electrocatalysis of DA. Thus, the MOF525/PEDOT composite improved the sensitivity-to-noise ratio of DA signaling, where the sensitivity reached 11 nA/µM in a good linear range of 4-100 µM. In addition, porphyrin-based MOF could also increase the selectivity to DA against other common clinical interferences, such as ascorbic acid and uric acid. The as-synthesized microelectrode modified with MOF525/PEDOT in this study exhibited great potential in real time analysis.

Point Spread Function Formation in Plane-Wave Imaging: A Theoretical Approximation in Fourier Migration.

The point spread function (PSF) is often analyzed to determine the image quality of an ultrasound system. The formation of PSF is determined by practical factors, such as transducer aperture, element directivity, apodization, pitch, imaging position, and steering angle. Conventional numerical simulations provide an iterative approach to examine those factors' effects but cannot explain the inherent mechanism of PSF formation. This article presents a theoretical approximation of PSF formation for plane-wave imaging throughout the Fourier-based reconstruction process. Aforementioned factors are incorporated in the theory. The proposed theory is used to analyze the effects of those factors and presents a high degree of consistency with numerical simulations and experiments.

Quantitative assessment of effects of phase aberration and noise on high-frame-rate imaging.

The goal of this paper is to quantitatively study effects of phase aberration and noise on high-frame-rate (HFR) imaging using a set of traditional and new parameters. These parameters include the traditional -6-dB lateral resolution, and new parameters called the energy ratio (ER) and the sidelobe ratio (SR). ER is the ratio between the total energy of sidelobe and the total energy of mainlobe of a point spread function (PSF) of an imaging system. SR is the ratio between the peak value of the sidelobe and the peak value of the mainlobe of the PSF. In the paper, both simulation and experiment are conducted for a quantitative assessment and comparison of the effects of phase aberration and noise on the HFR and the conventional delay-and-sum (D&S) imaging methods with the set of parameters. In the HFR imaging method, steered plane waves (SPWs) and limited-diffraction beams (LDBs) are used in transmission, and received signals are processed with the Fast Fourier Transform to reconstruct images. In the D&S imaging method, beams focused at a fixed depth are used in transmission and dynamically focused beams are used in reception for image reconstruction. The simulation results show that the average differences between the -6-dB lateral beam widths of the HFR imaging and the D&S imaging methods are -0.1337mm for SPW and -0.1481mm for LDB, which means that the HFR imaging method has a higher lateral image resolution than the D&S imaging method since the values are negative. In experiments, the average differences are also negative, i.e., -0.2804mm for SPW and -0.3365mm for LDB. The results for the changes of ER and SR between the HFR and the D&S imaging methods have negative values, too. After introducing phase aberration and noise, both simulations and experiments show that the HFR imaging method has also less change in the -6-dB lateral resolution, ER, and SR as compared to the conventional D&S imaging method. This means that the HFR imaging method is less sensitive to the phase aberration and noise. Based on the study of the new parameters on the HFR and the D&S imaging methods, it is expected that the new parameters can also be applied to assess quality of other imaging methods.

A new algorithm for spatial impulse response of rectangular planar transducers.

Previous solutions for spatial impulse responses of rectangular planar transducers require either approximations or complex geometrical considerations. This paper describes a new, simplified and exact solution using only trigonometric functions and simple set operations. This solution, which can be numerically implemented with a straightforward algorithm, is an exact implementation of the Rayleigh integral without any far field or paraxial approximation. Additionally, a nonlinear relationship was also established for spatial impulse responses from two field points which share the same projection point on the transducer surface plane. By incorporating this relationship in the algorithm, the computational efficiency of spatial impulse responses and continuous fields is improved about 20-folds and 14-folds, respectively. This algorithm has practical applications in designing l-D linear/phased arrays, 1.5-D arrays and 2-D arrays, as demonstrated through numerical simulations with array transducers. Experiments were also conducted to verify the new solution and results show that the algorithm is both accurate and efficient. The application of this method may include development of ultrasound imaging system for hard and soft tissue nondestructive assessment.

Motion artifacts of extended high frame rate imaging.

Based on the high frame rate (HFR) imaging method developed in our lab, an extended high frame rate imaging method with various transmission schemes was developed recently. In this method, multiple, limited-diffraction array beams or steered plane wave transmissions are used to increase image resolution and field of view as well as to reduce sidelobes. Furthermore, the multiple, limited-diffraction array beam transmissions can be approximated with square-wave aperture weightings, allowing one or two transmitters to be used with a multielement array transducer to simplify imaging systems. By varying the number of transmissions, the extended HFR imaging method allows a continuous trade-off between image quality and frame rate. Because multiple transmissions are needed to obtain one frame of image for the method, motion could cause phase misalignment and thus produce artifacts, reducing image contrast and resolution and leading to an inaccurate clinical interpretation of images. Therefore, it is important to study how motion affects the method and provide a useful guidance of using the method properly in various applications. In this paper, computer simulations, in vitro and in vivo experiments were performed to study the effects of motion on the method in different conditions. Results show that a number of factors may affect the motion effects. However, it was found that the extended HFR imaging method is not sensitive to the motions commonly encountered in the clinical applications, as is demonstrated by an in vivo heart experiment, unless the number of transmissions is large and objects are moving at a high velocity near the surface of a transducer.

Effects of phase aberration and noise on extended high frame rate imaging.

Based on the high frame rate (HFR) imaging theories, an extended HFR imaging method has been developed recently in our lab where multiple limited-diffraction array beams or steered plane waves are used in transmissions to reconstruct a high quality image of an equivalent dynamic focusing in both transmissions and receptions. The method has the potential to simplify imaging systems because the fast Fourier transform and square-wave aperture weightings can be used. The method is also flexible in using different numbers of transmissions for a continuous trade-off between image quality and frame rate. In this paper, we study the effects of phase aberration and noise on the extended HFR imaging method with in vitro experiments and compare the results with those obtained with a conventional delay-and-sum (D&S) method of a fixed-transmission focus and a dynamically-focused reception. In the experiments, an ATS539 tissue-mimicking phantom and an Acuson V2 phase array transducer (128 elements, 2.5 MHz, and 0.15-mm pitch) were used. The transducer was driven by a homemade general-purpose HFR imaging system that was capable of producing both the limited-diffraction array beams and steeredplane waves and echo data were acquired with the same system and then transferred to a personal computer via a universal serial bus (USB) 2.0 link for image reconstructions. The phase aberration was introduced by adding random phase shifts to both transmission and reception beams. The random noise was added to the received radiofrequency echo data. Results show that the phase aberration and noise degrade both the extended HFR and the conventional delay-and-sum (D&S) imaging method. However, images reconstructed with the extended HFR imaging method have an overall higher quality than those with the D&S method given the phase aberration and noise models studied.

High frame rate imaging system for limited diffraction array beam imaging with square-wave aperture weightings.

A general-purpose high frame rate (HFR) medical imaging system has been developed. This system has 128 independent linear transmitters, each of which is capable of producing an arbitrary broadband (about 0.05-10 MHz) waveform of up to +/- 144 V peak voltage on a 75-ohm resistive load using a 12-bit/40-MHz digital-to-analog converter. The system also has 128 independent, broadband (about 0.25-10 MHz), and time-variable-gain receiver channels, each of which has a 12-bit/40-MHz analog-to-digital converter and up to 512 MB of memory. The system is controlled by a personal computer (PC), and radio frequency echo data of each channel are transferred to the same PC via a standard USB 2.0 port for image reconstructions. Using the HFR imaging system, we have developed a new limited-diffraction array beam imaging method with square-wave aperture voltage weightings. With this method, in principle, only one or two transmitters are required to excite a fully populated two-dimensional (2-D) array transducer to achieve an equivalent dynamic focusing in both transmission and reception to reconstruct a high-quality three-dimensional image without the need of the time delays of traditional beam focusing and steering, potentially simplifying the transmitter subsystem of an imager. To validate the method, for simplicity, 2-D imaging experiments were performed using the system. In the in vitro experiment, a custom-made, 128-element, 0.32-mm pitch, 3.5-MHz center frequency linear array transducer with about 50% fractional bandwidth was used to reconstruct images of an ATS 539 tissue-mimicking phantom at an axial distance of 130 mm with a field of view of more than 90 degrees. In the in vivo experiment of a human heart, images with a field of view of more than 90 degrees at 120-mm axial distance were obtained with a 128-element, 2.5-MHz center frequency, 0.15-mm pitch Acuson V2 phased array. To ensure that the system was operated under the limits set by the U.S. Food and Drug Administration, the mechanical index, thermal index, and acoustic output were measured. Results show that higher-quality images can be reconstructed with the square-wave aperture weighting method due to an increased penetration depth as compared to the exact weighting method developed previously, and a frame rate of 486 per second was achieved at a pulse repetition frequency of about 5348 Hz for the human heart.

Extended high-frame rate imaging method with limited-diffraction beams.

Fast three-dimensional (3-D) ultrasound imaging is a technical challenge. Previously, a high-frame rate (HFR) imaging theory was developed in which a pulsed plane wave was used in transmission, and limited-diffraction array beam weightings were applied to received echo signals to produce a spatial Fourier transform of object function for 3-D image reconstruction. In this paper, the theory is extended to include explicitly various transmission schemes such as multiple limited-diffraction array beams and steered plane waves. A relationship between the limited-diffraction array beam weighting of received echo signals and a 2-D Fourier transform of the same signals over a transducer aperture is established. To verify the extended theory, computer simulations, in vitro experiments on phantoms, and in vivo experiments on the human kidney and heart were performed. Results show that image resolution and contrast are increased over a large field of view as more and more limited-diffraction array beams with different parameters or plane waves steered at different angles are used in transmissions. Thus, the method provides a continuous compromise between image quality and image frame rate that is inversely proportional to the number of transmissions used to obtain a single frame of image. From both simulations and experiments, the extended theory holds a great promise for future HFR 3-D imaging.

Field computation for two-dimensional array transducers with limited diffraction array beams.

A method is developed for calculating fields produced with a two-dimensional (2D) array transducer. This method decomposes an arbitrary 2D aperture weighting function into a set of limited diffraction array beams. Using the analytical expressions of limited diffraction beams, arbitrary continuous wave (cw) or pulse wave (pw) fields of 2D arrays can be obtained with a simple superposition of these beams. In addition, this method can be simplified and applied to a 1D array transducer of a finite or infinite elevation height. For beams produced with axially symmetric aperture weighting functions, this method can be reduced to the Fourier-Bessel method studied previously where an annular array transducer can be used. The advantage of the method is that it is accurate and computationally efficient, especially in regions that are not far from the surface of the transducer (near field), where it is important for medical imaging. Both computer simulations and a synthetic array experiment are carried out to verify the method. Results (Bessel beam, focused Gaussian beam, X wave and asymmetric array beams) show that the method is accurate as compared to that using the Rayleigh-Sommerfeld diffraction formula and agrees well with the experiment.

Fourier-Bessel field calculation and tuning of a CW annular array.

A 1-D Fourier-Bessel series method for computing and tuning the linear lossless field of flat continuous wave (CW) annular arrays is given and discussed with both numerical simulation and experimental verification. The technique provides a new method for modelling and manipulating the propagated field by linking the quantized surface pressure profile to a set of limited diffraction Bessel beams propagating into the medium. In the limit, these become a known set of nondiffracting Bessel beams satisfying the lossless linear wave equation, which allow us to derive a linear matrix formulation for the field in terms of the ring pressures on the transducer surface. Tuning (beamforming) of the field then follows by formulating a least squares design with respect to the transducer ring pressures. Results are presented in the context of a 10-ring annular array operating at 2.5 MHz in water.