Super-Resolution Axial Localization of Ultrasound Scatter Using Multi-Focal Imaging.

OBJECTIVE: This paper aims to develop a method for achieving micrometre axial scatterer localization for medical ultrasound, surpassing the inherent, pulse length dependence limiting ultrasound imaging. METHODS: The method, directly translated from cellular microscopy, is based on multi-focal imaging and the simple, aberration-dependent, image sharpness metric of a single point scatterer. The localization of a point scatterer relies on the generation of multiple overlapping sharpness curves, created by deploying three foci during receive processing, and by assessing the sharpness values after each acquisition as a function of depth. Each derived curve peaks around the receive focus and the unique position of the scatterer is identified by combining the data from all curves using a maximum likelihood algorithm with a calibration standard. RESULTS: Simulated and experimental ultrasound point scatter data show that the sharpness method can provide scatterer axial localization with an average accuracy down to 10.21 m ( 21) and with up to 11.4 times increased precision compared to conventional localization. The improvements depend on the rate of change of sharpness using each focus, and the signal to noise ratio in each image. CONCLUSION: Super-resolution axial imaging from optical microscopy has been successfully translated into ultrasound imaging by using raw ultrasound data and standard beamforming. SIGNIFICANCE: The normalized sharpness method has the potential to be used in scatterer localization applications and contribute in current super-resolution ultrasound imaging techniques.

High resolution depth-resolved imaging from multi-focal images for medical ultrasound.

An ultrasound imaging technique providing sub-diffraction limit axial resolution for point sources is proposed. It is based on simultaneously acquired multi-focal images of the same object, and on the image metric of sharpness. The sharpness is extracted by image data and presents higher values for in-focus images. The technique is derived from biological microscopy and is validated here with simulated ultrasound data. A linear array probe is used to scan a point scatterer phantom that moves in depth with a controlled step. From the beamformed responses of each scatterer position the image sharpness is assessed. Values from all positions plotted together form a curve that peaks at the receive focus, which is set during the beamforming. Selection of three different receive foci for each acquired dataset will result in the generation of three overlapping sharpness curves. A set of three calibration curves combined with the use of a maximum-likelihood algorithm is then able to estimate, with high precision, the depth location of any emitter fron each single image. Estimated values are compared with the ground truth demonstrating that an accuracy of 28.6 µm (0.13λ) is achieved for a 4 mm depth range.

Chromatically-corrected, high-efficiency, multi-colour, multi-plane 3D imaging.

It is shown that grisms, a grating and prism combination, are a simple way to achieve chromatic control in 3D multi-plane imaging. A pair of grisms, whose separation can be varied, provide a collimated beam with a tuneable chromatic shear from a collimated polychromatic input. This simple control permits the correction of chromatic smearing in 3D imaging using off-axis Fresnel zone plates and improved control of the axial profile of a focussed spot in multi-photon experiments.

A new framework for particle detection in low-SNR fluorescence live-cell images and its application for improved particle tracking.

Image denoising and signal enhancement are two common steps to improve particle contrast for detection in low-signal-to-noise ratio (SNR) fluorescence live-cell images. However, denoising may oversmooth features of interest, particularly weak features, leading to false negative detection. Here, we propose a robust framework for particle detection in which image denoising in the grayscale image is not needed, so avoiding image oversmoothing. A key to our approach is the new development of a particle enhancement filter based on the recently proposed particle probability image to obtain significantly enhanced particle features and greatly suppressed background in low-SNR and low-contrast environments. The new detection method is formed by combining foreground and background markers with watershed transform operating in both particle probability and grayscale spaces; dynamical switchings between the two spaces can optimally make use the information in images for accurate determination of particle position, size, and intensity. We further develop the interacting multiple mode filter for particle motion modeling and data association by incorporating the extra information obtained from our particle detector to enhance the efficiency of multiple particle tracking. We find that our methods lead to significant improvements in particle detection and tracking efficiency in fluorescence live-cell applications.

Calculation and correction of subaperture tilt aberration modes in synthesis imaging.

We extend the redundant spacings calibration method for finding piston coefficients affecting the elements of a dilute aperture array so that tilt phase coefficients can also be calculated and corrected without the need for assumptions about the object. The tilt coefficient retrieval method is successfully demonstrated in simulation, and the specifics of correction by image sharpness are discussed, showing that in dilute aperture systems this method does not necessarily produce a unique image.

Nanometric depth resolution from multi-focal images in microscopy.

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.

An adaptive non-local means filter for denoising live-cell images and improving particle detection.

Fluorescence imaging of dynamical processes in live cells often results in a low signal-to-noise ratio. We present a novel feature-preserving non-local means approach to denoise such images to improve feature recovery and particle detection. The commonly used non-local means filter is not optimal for noisy biological images containing small features of interest because image noise prevents accurate determination of the correct coefficients for averaging, leading to over-smoothing and other artifacts. Our adaptive method addresses this problem by constructing a particle feature probability image, which is based on Haar-like feature extraction. The particle probability image is then used to improve the estimation of the correct coefficients for averaging. We show that this filter achieves higher peak signal-to-noise ratio in denoised images and has a greater capability in identifying weak particles when applied to synthetic data. We have applied this approach to live-cell images resulting in enhanced detection of end-binding-protein 1 foci on dynamically extending microtubules in photo-sensitive Drosophila tissues. We show that our feature-preserving non-local means filter can reduce the threshold of imaging conditions required to obtain meaningful data.

Multiplane imaging and three dimensional nanoscale particle tracking in biological microscopy.

A conventional microscope produces a sharp image from just a single object-plane. This is often a limitation, notably in cell biology. We present a microscope attachment which records sharp images from several object-planes simultaneously. The key concept is to introduce a distorted diffraction grating into the optical system, establishing an order-dependent focussing power in order to generate several images, each arising from a different object-plane. We exploit this multiplane imaging not just for bio-imaging but also for nano-particle tracking, achieving approximately 10 nm z position resolution by parameterising the images with an image sharpness metric.

Calculation and correction of piston phase aberration in synthesis imaging.

The principle of redundant spacings calibration has previously been described for the purpose of calibrating piston phase aberration affecting elements of a dilute aperture array using a system of linear equations in terms of the aperture phases as well as object phase information. Here we develop matrices for the correction of piston phase aberration by use of image sharpness and also by phase retrieval. These are both presented in wavefront sensor formulation in order to draw analogy between the approaches. We then discuss solution ambiguity affecting both methods and describe array design criteria to prevent such ambiguity. The problem of increased image aliasing under image sharpness correction is also highlighted.

Three-dimensional particle imaging by defocusing method with an annular aperture.

We propose an annular-aperture-based defocusing technique for three-dimensional (3D) particle metrology from a single camera view. This simple configuration has high optical efficiency and the ability to deal with overlapped defocused images. Initial results show that an uncertainty in depth of 23 microm can be achieved over a range of 10 mm for macroscopic systems. This method can also be applied in microscopy for the measurement of fluorescently doped microparticles, thus providing a promising solution for 3D flow metrology at both macroscales and microscales.

Three-dimensional particle imaging by wavefront sensing.

We present two methods for three-dimensional particle metrology from a single two-dimensional view. The techniques are based on wavefront sensing where the three-dimensional location of a particle is encoded into a single image plane. The first technique is based on multiplanar imaging, and the second produces three-dimensional location information via anamorphic distortion of the recorded images. Preliminary results show that an uncertainty of 8 microm in depth can be obtained for low-particle density over a thin plane, and an uncertainty of 30 microm for higher particle density over a 10 mm deep volume.

High-speed, 3-dimensional, telecentric imaging.

The design, testing and operation of a system for telecentric 3-dimensional imaging of dynamic objects is presented. The simple system is capable of rapid electronic scanning of a single focal plane within a specimen or of simultaneous focusing on multiple planes whose depth and relative spacing within the specimen can be changed electronically. Application to studies of dynamic processes in microscopy is considered.

Generalized phase diversity for wave-front sensing.

Phase diversity is a phase-retrieval algorithm that uses a pair of intensity images taken symmetrically about the wave front to be determined. If these images are taken about the system input pupil this is equivalent to a curvature-sensing algorithm. Traditionally a defocus aberration kernel is used to produce the phase-diverse data. We present a generalization of this method to allow the use of other functions as the diversity kernel. We discuss the necessary and sufficient conditions that such a function must satisfy for use in a null wave-front sensor. Computer simulations were used to validate these results.

Compact optical system for pulse-to-pulse laser beam quality measurement and applications in laser machining.

Fluctuations in beam quality (M2) have been observed on a pulse-to-pulse basis from an industrial Nd:YAG laser. This was achieved with a compact multiplane imaging method incorporating quadratically distorted diffraction gratings, which enabled simultaneous imaging of nine planes on a single CCD array. With this system, we measured across a range of beam qualities with an associated error (in M2 variation) of the order of 0.7%. Application of the system to fiber-optic beam delivery and laser drilling is demonstrated.

Wave-front sensing by use of a Green's function solution to the intensity transport equation.

A method for reconstructing an unknown wave front from measurements of its intensity distribution on two planes along the direction of propagation is described. The method solves the intensity transport equation by use of Neumann boundary conditions, leading to a solution that requires only matrix multiplication. The method provides real-time wave-front reconstruction with high accuracy and is easily reposed to permit reconstruction of the wave front in any orthonormal basis set.