For centuries, flow visualization has been the art of making fluid motion visible in physical and biological systems. Although such flow patterns can be, in principle, described by the Navier-Stokes equations, extracting the velocity and pressure fields directly from the images is challenging. We addressed this problem by developing hidden fluid mechanics (HFM), a physics-informed deep-learning framework capable of encoding the Navier-Stokes equations into the neural networks while being agnostic to the geometry or the initial and boundary conditions. We demonstrate HFM for several physical and biomedical problems by extracting quantitative information for which direct measurements may not be possible. HFM is robust to low resolution and substantial noise in the observation data, which is important for potential applications.

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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations.

The reliable measurement of the 3D3C velocity field in microfluidic devices becomes more and more important for future optimization and developments for lab-on-a-chip applications or point-of-care medical diagnosis systems. In the past years, different particle-based imaging methods, such as confocal scanning microscopy, holography, stereoscopic and tomographic imaging or approaches based on defocused particle images or optical aberrations have been developed and applied successfully to measure velocity fields in microfluidic systems. The benefits and drawbacks of these methods will be discussed in detail as the proper understanding of the measurement principle is essential to select the most appropriate technique for a desired measurement application. Once an imaging method is chosen, the velocity can be estimated by correlation-based methods or tracking approaches. The advantages and disadvantages of both methods and the importance of image preprocessing will also be discussed in detail.

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Particle imaging techniques for volumetric three-component (3D3C) velocity measurements in microfluidics

In this review we discuss the state of the art of the optical whole-field velocity measurement technique micro-scale Particle Image Velocimetry (µPIV). µPIV is a useful tool for fundamental research of microfluidics as well as for the detailed characterization and optimization of microfluidic applications in life science, lab-on-a-chip, biomedical research, micro chemical engineering, analytical chemistry and other related fields of research. An in depth description of the µPIV method is presented and compared to other flow visualization and measurement methods. An overview of the most relevant applications is given on the topics of near-wall flow, electrokinetic flow, biological flow, mixing, two-phase flow, turbulence transition and complex fluid dynamic problems. Current trends and applications are critically reviewed. Guidelines for the implementation and application are also discussed.

Micro-Particle Image Velocimetry (microPIV): recent developments, applications, and guidelines.

Microfluidic devices are becoming increasingly common and are seen in applications ranging from biology to nanotechnology and manufacturing. Flow behavior in these small domains can often be counterintuitive because of the low Reynolds number or the relative importance of surface forces. Micro-particle image velocimetry (μPIV) is a quantitative method that can be used to characterize the performance of such microfluidic systems with spatial resolutions better than one micron. Illustrating the impact of this measurement technique, more than 100 journal articles are published per year that feature μPIV velocity measurements. This article discusses the fundamentals of the technique, its theoretical background, and several applications.

Recent Advances in Micro-Particle Image Velocimetry

A system and method for structured-light dimensioning is disclosed. The method includes combining multiple images using different camera settings to provide all of the information necessary dimensioning. What results is an improved ability to sense a light pattern reflected from an object's surfaces, especially when the lighting and/or object color make imaging all surfaces simultaneously difficult.

System and method for dimensioning

Three-dimensional (3D) quantitative flow visualization by tracking microscale particles has become an invaluable tool in microfluid mechanics. Defocusing digital particle image velocimetry (DDPIV) can recover spatial coordinates by calculating the separation between defocused images generated by an aperture mask with a plurality of pinholes. In this paper, a high-speed 3D micro-DDPIV (μDDPIV) system was devised based on this technique to achieve microscale velocity field measurements. A micro-volume of 400 × 300 μm^2 with a depth of 150 μm has been mapped using an inverted microscope equipped with a 20× objective lens. The proposed technique was successfully applied to 3D tracking of 2-μm fluorescent particles inside an evaporating water droplet.

Microscale 3D flow mapping with μDDPIV

Hardware and software configurations, optionally, for performing profilometry of an object are disclosed. An advantageous imaging device is described. An advantageous approach to determining imager position is also described. Each aspect described may be used independently of the other. Moreover, the teaching may find use in other fields including velocimetry, etc.

Three-dimensional imaging system

A camera has a lens and aperture device for determining 3D information. A projector projects an optical pattern toward a surface. The camera has at least two off-axis apertures thereon, arranged to obtain an image of the projected pattern including defocused information. The camera is movable between different positions to image the surface from said different positions, and the projector is at a specified angle of at least 5° relative to said camera. A processor carries out a first operation using information received through the apertures to determine a pose of said camera, and to determine three dimensional information about the object based on a degree of deformation of said optical pattern on said surface indicative of a three dimensional surface. An embodiment projects a grid of laser dots and uses laser-dot defocusing for approximate Z and thus grid correspondence, which can greatly increase the working depth of the system.

Accurate 3D object reconstruction using a handheld device with a projected light pattern

While quantitative analysis of dynamic biological cell motions in vivo is of great biomedical interest, acquiring 3-D (plus time) information is difficult due to the lack of imaging tools with sufficient spatial and temporal resolution. A novel 3-D high-speed microscopic imaging system is developed to enable 3-D time series data acquisition, based on a defocusing technique (DDPIV). Depth coordinate Z is resolved by the triangular image patterns generated by a mask with three apertures forming an equilateral triangle. Application of this technique to microscale imaging is validated by calibration of targets spread over the image field. 1-µm fluorescent tracer particles are injected into the blood stream of 32 h post-fertilization developing zebrafish embryos to help describe cardiac cell motions. 3-D and velocity fields of cardiovascular blood flow and trajectories of heart-wall motions are obtained.

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Three-dimensional real-time imaging of cardiac cell motions in living embryos

A method and device for high-resolution three-dimensional (3-D) imaging which obtains camera pose using defocusing is disclosed. The device comprises a lens obstructed by a mask having two sets of apertures. The first set of apertures produces a plurality of defocused images of the object, which are used to obtain camera pose. The second set of optical filters produces a plurality of defocused images of a projected pattern of markers on the object. The images produced by the second set of apertures are differentiable from the images used to determine pose, and are used to construct a detailed 3-D image of the object. Using the known change in camera pose between captured images, the 3-D images produced can be overlaid to produce a high-resolution 3-D image of the object.

Jian Lu

Papers

Microscale 3D flow mapping with μDDPIV

Three-dimensional imaging system

Accurate 3D object reconstruction using a handheld device with a projected light pattern

Three-dimensional real-time imaging of cardiac cell motions in living embryos

Method and device for high-resolution three-dimensional imaging which obtains camera pose using defocusing