Conventional optical components rely on gradual phase shifts accumulated during light propagation to shape light beams. New degrees of freedom are attained by introducing abrupt phase changes over the scale of the wavelength. A two-dimensional array of optical resonators with spatially varying phase response and subwavelength separation can imprint such phase discontinuities on propagating light as it traverses the interface between two media. Anomalous reflection and refraction phenomena are observed in this regime in optically thin arrays of metallic antennas on silicon with a linear phase variation along the interface, which are in excellent agreement with generalized laws derived from Fermat’s principle. Phase discontinuities provide great flexibility in the design of light beams, as illustrated by the generation of optical vortices through use of planar designer metallic interfaces.

http://www.zenogaburro.it/papers/LightPropagation.pdf

Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

As a practical and effective tool for quantitative in-plane deformation measurement of a planar object surface, two-dimensional digital image correlation (2D DIC) is now widely accepted and commonly used in the field of experimental mechanics. It directly provides full-field displacements to sub-pixel accuracy and full-field strains by comparing the digital images of a test object surface acquired before and after deformation. In this review, methodologies of the 2D DIC technique for displacement field measurement and strain field estimation are systematically reviewed and discussed. Detailed analyses of the measurement accuracy considering the influences of both experimental conditions and algorithm details are provided. Measures for achieving high accuracy deformation measurement using the 2D DIC technique are also recommended. Since microscale and nanoscale deformation measurement can easily be realized by combining the 2D DIC technique with high-spatial-resolution microscopes, the 2D DIC technique should find more applications in broad areas.

https://iopscience.iop.org/article/10.1088/0957-0233/20/6/062001/pdf

Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

The QRS complex is the most striking waveform within the electrocardiogram (ECG). Since it reflects the electrical activity within the heart during the ventricular contraction, the time of its occurrence as well as its shape provide much information about the current state of the heart. Due to its characteristic shape it serves as the basis for the automated determination of the heart rate, as an entry point for classification schemes of the cardiac cycle, and often it is also used in ECG data compression algorithms. In that sense, QRS detection provides the fundamentals for almost all automated ECG analysis algorithms. Software QRS detection has been a research topic for more than 30 years. The evolution of these algorithms clearly reflects the great advances in computer technology. Within the last decade many new approaches to QRS detection have been proposed; for example, algorithms from the field of artificial neural networks genetic algorithms wavelet transforms, filter banks as well as heuristic methods mostly based on nonlinear transforms. The authors provide an overview of these recent developments as well as of formerly proposed algorithms.

/pdf/the-principles-of-software-qrs-detection-1vgts9f7g6.pdf

The principles of software QRS detection

The imaging resolution in turbid media is severely degraded by light scattering. Resolution can be improved if the unscattered or weakly scattered light is extracted. Here the state of polarization of the emerging light is used to discriminate photon path length, with the more weakly scattered photons maintaining their original polarization state. It is experimentally demonstrated that over a wide range of scatterer concentrations there exist three distinct imaging regimes. It is also shown that within the intermediate regime one of two distinct imaging techniques is appropriate, depending on the particle size.

Effects of polarization state and scatterer concentration on optical imaging through scattering media

Wavelet transform as a potential tool for ECG analysis and compression

Surface plasmons (SP's) are electromagnetic surface waves that propagate along the interface between conductors and dielectrics. The k vector of these waves is larger than the free-space wave vector. The importance of SP's lies in the fact that they are extremely sensitive to small changes in the dielectric properties of substances that are in contact with the conductors. This property means that SP's have many sensor applications; however, when they are used in microscopic applications the lateral resolution is limited to several micrometers. We discuss how this limit can be overcome by use of defocused high-numerical-aperture liquid-immersion objectives. We also present SP images that demonstrate a resolution comparable with that expected from high-numerical-aperture optical microscopes. Finally, we discuss how ultrahigh-numerical-aperture objectives with numerical apertures greater than 1.5 can be expected to have considerable influence on biological imaging.

High-resolution scanning surface-plasmon microscopy

This paper discusses theoretical aspects of the V ( z ) response of the scanning acoustic microscope (s. a. m.) when used to examine specimens with lateral discontinuities. The problem is introduced in terms of a simple ray model to establish a physical picture of the processes involved. An approximate Green function is then developed which enables use of a modified form of the Fourier optical formulations to calculate V ( z ) for a cylindrical lens. These calculations explain two different types of contrast observed when imaging specimens in the reflection s. a. m., such as (i) the ability to image fine discontinuities and display them with enhanced contrast and an apparent width determined by the acoustic wavelength; and (ii) to give a quantitative account of the amplitude of periodic ripple often observed running parallel to cracks on acoustic micrographs. Both these types of contrast may be predicted by using the same model and arise naturally from variation of the reflection and transmission properties of the discontinuity, the relative value of these parameters determines which type of contrast predominates. At an interface between media with different elastic properties, the contrast is affected not only by the scattering properties of the boundary but also by the very fact that surface waves must propagate in media with different elastic properties. This effect alone can provide a powerful contrast mechanism which enables one to understand the light to dark contrast reversals often observed at grain boundaries in polycrystalline specimens at different values of defocus.

A Two-Dimensional Imaging Theory of Surface Discontinuities with the Scanning Acoustic Microscope

We describe a scanning optical interferometer that can simultaneously perform ellipsometry measurements and thus provides a true surface profile. This is accomplished by projecting the back focal plane of the objective lens onto a CCD array. The measured phase differences between the p- and s-polarization components are converted, by using a specially developed algorithm, to optical phase changes caused by material variations. The compensation process is then applied to extract the true profile of the object surface. Experimental results obtained with the system are shown.

Michael Geoffrey Somekh

Papers

Effects of polarization state and scatterer concentration on optical imaging through scattering media

Wavelet transform as a potential tool for ECG analysis and compression

High-resolution scanning surface-plasmon microscopy

A Two-Dimensional Imaging Theory of Surface Discontinuities with the Scanning Acoustic Microscope

Scanning optical microellipsometer for pure surface profiling