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

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

Transport of intensity equation: a tutorial

We present a method to generate complete arbitrary spatially variant polarization modulation of a light beam by means of a parallel aligned nematic liquid crystal spatial light modulator (SLM). We first analyze the polarization modulation properties in a transmission mode. We encode diffraction gratings onto the SLM and show how to achieve partial polarization control of the zero order transmitted light. We then extend the technique to a double modulation scheme, which is implemented using a single SLM divided in two areas in a reflective configuration. The polarization states of the transmitted beam from the first pass through the first area are rotated using two passes through a quarter wave plate. The beam then passes through the second area of the SLM where additional polarization information can be encoded. By combining previously reported techniques, we can achieve complete amplitude, phase and polarization control for the diffracted light that allows the creation of arbitrary diffractive optical elements including polarization control. Theoretical analysis based on the Jones matrix formalism, as well as excellent experimental results are presented.

http://tecnopto.edu.umh.es/wp-content/uploads/sites/605/2014/05/Opt.Exp_.2012-Complete-polarization-control-of-light-from-a-liquid-crystal-spatial-light-modulator.pdf

Complete polarization control of light from a liquid crystal spatial light modulator

The availability of free space optics (FSO) systems in dependence on weather conditions and on FSO link parameters, such as transmitted optical power, beam divergence, receiver sensitivity or link path distance, is discussed. A number of phenomena in the atmosphere, such as absorption, scattering, and turbulence, can affect beam attenuation, but in the case of wavelengths typical of FSO systems operation, only scattering and turbulence are appropriate to be taken into consideration. We model the power loss caused by turbulence by using the Rytov scintillation theory. Attenuation due to scattering, which can be expressed as a function of the link distance, wavelength, and meteorological visibility, is calculated from visibility data collected at several airports in Europe. Statistical evaluation of the attenuation caused by scattering and the power link margin calculated from FSO link parameters are used for calculating the link availability.

https://www.spiedigitallibrary.org/journals/optical-engineering/volume-48/issue-6/066001/Atmospheric-effects-on-availability-of-free-space-optics-systems/10.1117/1.3155431.pdf

Atmospheric effects on availability of free space optics systems

Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes

In this study the Moire deflectometry technique is applied to the investigation of diffusion dynamics in transparent liquid mixtures. We describe the experimental details and present theoretical analysis for obtaining the magnitude of diffusion coefficient using the Moire fringe patterns. The theoretical aspects of the method are presented and the relationship between the Moire fringes shift and the diffusion coefficient is derived. Our method is applied for measuring the diffusion coefficient of sugar in pure water at room temperature. The value of D = 0.66 (±0.05) × 10−5 cm2 s−1 is obtained for diffusion of sugar molecules in pure water and it is in excellent agreement with the reported value in literatures.In diffusion of high concentration sugar solutions we observed the formation of a dense layer above the initial boundary of two liquids that may be related to so-called baro-diffusion effect—influence of the gravity on diffusant molecules—that forms where the upward motion of sugar molecules are balanced by gravity. This layer becomes denser and denser and goes down as time advances.

https://iopscience.iop.org/article/10.1088/0022-3727/37/14/016/pdf

Diffusion coefficient measurements of transparent liquid solutions using Moiré deflectometry

When a thin film that is prepared in a step form on a substrate and coated uniformly with a reflective material is illuminated by a parallel coherent beam of monochromatic light, the Fresnel diffraction fringes are formed on a screen perpendicular to the reflected beam. The visibility of the fringes depends on film thickness, angle of incidence, and light wavelength. Measuring visibility versus incident angle provides the film thickness with an accuracy of a few nanometers. The technique is easily applicable and it covers a wide range of thicknesses with highly reliable results.

Application of Fresnel diffraction from a phase step to the measurement of film thickness

Spectral modification by line singularity in Fresnel diffraction from 1D phase step

We introduce a relatively simple and efficient optical technique to measure nanoscale displacement based on visibility variations of the Fresnel diffraction fringes from a two-dimensional phase step. In this paper we use our technique to measure electromechanical expansions by a thin piezoelectric ceramic and also thermal changes in the diameter of a tungsten wire. Early results provide convincing evidence that sensitivity up to a few nanometers can be achieved, and our technique has the potential to be used as a nanodisplacement probe.

Mohammad Taghi Tavassoly

Papers

Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes

Diffusion coefficient measurements of transparent liquid solutions using Moiré deflectometry

Application of Fresnel diffraction from a phase step to the measurement of film thickness

Spectral modification by line singularity in Fresnel diffraction from 1D phase step

Nanometer displacement measurement using Fresnel diffraction