There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

This paper describes the principles of a novel 3D PIV system based on the illumination, recording and reconstruction of tracer particles within a 3D measurement volume The technique makes use of several simultaneous views of the illuminated particles and their 3D reconstruction as a light intensity distribution by means of optical tomography The technique is therefore referred to as tomographic particle image velocimetry (tomographic-PIV) The reconstruction is performed with the MART algorithm, yielding a 3D array of light intensity discretized over voxels The reconstructed tomogram pair is then analyzed by means of 3D cross-correlation with an iterative multigrid volume deformation technique, returning the three-component velocity vector distribution over the measurement volume The principles and details of the tomographic algorithm are discussed and a parametric study is carried out by means of a computer-simulated tomographic-PIV procedure The study focuses on the accuracy of the light intensity field reconstruction process The simulation also identifies the most important parameters governing the experimental method and the tomographic algorithm parameters, showing their effect on the reconstruction accuracy A computer simulated experiment of a 3D particle motion field describing a vortex ring demonstrates the capability and potential of the proposed system with four cameras The capability of the technique in real experimental conditions is assessed with the measurement of the turbulent flow in the near wake of a circular cylinder at Reynolds 2,700

Tomographic particle image velocimetry

Digital holography is an emerging field of new paradigm in general imaging applications. We present a review of a subset of the research and development activities in digital holography, with emphasis on microscopy techniques and applications. First, the basic results from the general theory of holography, based on the scalar diffraction theory, are summarized, and a general description of the digital holographic microscopy process is given, including quantitative phase microscopy. Several numerical diffraction methods are described and compared, and a number of representative configurations used in digital holography are described, including off-axis Fresnel, Fourier, image plane, in-line, Gabor, and phase-shifting digital holographies. Then we survey numerical techniques that give rise to unique capabilities of digital holography, including suppression of dc and twin image terms, pixel resolution control, optical phase unwrapping, aberration compensation, and others. A survey is also given of representative application areas, including biomedical microscopy, particle field holography, micrometrology, and holographic tomography, as well as some of the special techniques, such as holography of total internal reflection, optical scanning holography, digital interference holography, and heterodyne holography. The review is intended for students and new researchers interested in developing new techniques and exploring new applications of digital holography.

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Principles and techniques of digital holographic microscopy

Physiology of Behavior

Application of wavelet transform to hologram analysis: three-dimensional location of particles

We have used a digital in-line holography system with numerical reconstruction for 3D particle field extraction. In this system the diffraction patterns (holograms) are directly recorded on a charge-coupled device (CCD) camera. The numerical reconstruction is based on the wavelet transformation method. A sample volume is reconstructed by computing the wavelet components for different scale parameters. These parameters are related to the axial distance between a particle and the CCD camera. The particle images are identified and localized by analyzing the maximum of the wavelet transform modulus and the equivalent diameter of the particle image. The general process for the 3D particle location and data processing method are presented. As in classical holography we found that the signal to noise ratio depends only on the shadow density. Nevertheless, we show that both the volume depth and the shadow density affect the percentage of extracted particles.

Digital in-line holography: influence of the shadow density on particle field extraction.

Recent developments have shown the potential of digital in-line holography for diagnostics in fluids. This new method provides a low-cost and easy access method for measuring both size and velocity of small particles in a volume. Here it is shown that by applying traditional image processing tools on the particle images digitally reconstructed, statistically reliable results on particles size and location are provided. The method is experimentally illustrated by glass microspheres that are moving in a turbulent flow generated by an annular jet. A comparison with the histogram diameters provided by a common diffraction particle sizer are presented.

Particle field characterization by digital in-line holography: 3D location and sizing

Digital holography is applied to the reconstruction of small particles in a plane whose orientation is arbitrary as specified by the user The diffraction pattern produced by the particles is directly recorded by a conventional CCD camera The digital recorded image enables the recovery of particle-images in several parallel planes of the probe volume Afterwards, an interrogation slice corresponding to a thin layer around a theoretical arbitrary tilted plane is fixed The pixels whose 3D coordinates belong to this slice are selected and juxtaposed to rebuild the particle images The feasibility is demonstrated on a fiber tilted with respect to the camera plane A second example is given on an experimental particle field These results let us predict future applications such as the characterization of particle fields in planes other than those parallel with the camera plane

Particle field digital holographic reconstruction in arbitrary tilted planes

We present the preliminary results of a digital holographic system that can determine the two-dimensional velocity vector fields in several slices of a sample volume. A CCD camera directly records the diffraction patterns of small particles illuminated by a double-pulse laser diode. In fact, the diffraction can be interpreted as a convolution with a wavelet family of functions. The scale parameter a is related to the distance z between a particle and the CCD camera. Then, the intensity distributions in a plane located at a distance z are reconstructed by computing the wavelet components for the corresponding scale parameter a. Afterwards, a particle image velocimetry algorithm is applied to the numerically reconstructed pair of images. The feasibility of this technique is demonstrated for two simulated displacements.

http://iopscience.iop.org/article/10.1088/0957-0233/12/9/303/pdf

Denis Lebrun

Papers

Application of wavelet transform to hologram analysis: three-dimensional location of particles

Digital in-line holography: influence of the shadow density on particle field extraction.

Particle field characterization by digital in-line holography: 3D location and sizing

Particle field digital holographic reconstruction in arbitrary tilted planes

Application of in-line digital holography to multiple plane velocimetry