Grzegorz Świrniak

Inverse analysis of the rainbow for the case of low-coherent incident light to determine the diameter of a glass fiber

The aim of this paper is to discuss the possibility of a noninvasive, optical characterization of a transparent (glass) fiber on the basis of scattered light in the vicinity of a primary rainbow. Computational studies show that with the use of a spectrally adjusted incident beam of light, it is possible to form a rainbow with no strong nonlinearities typical for coherent light and that may be interpreted in terms of Airys theory of rainbow. An inverse analysis is applied to obtain the fiber diameter with the help of a straightforward mathematical formula based on the Airy integral, corrected by comparison with the solution according to the complex angular momentum method.

Inverse analysis of light scattered at a small angle for characterization of a transparent dielectric fiber

The objective of this paper is to discuss the possibility of noninvasive optical characterization of a transparent (glass) fiber by means of low-coherent light scattering. It will be shown that, by adjusting the temporal coherence of incident light, it is possible to select these specific orders of scattering, which are related to diffraction. Discussion will be devoted to the direct scattering and the inverse problem, where an inference about the diameter of a multilayered and transparent fiber is accomplished.

Approximate solution for optical measurements of the diameter and refractive index of a small and transparent fiber.

When a plane electromagnetic wave is scattered by an optically transparent object, whose size is much larger than the wavelength, a series of bright and dark fringes forms the primary rainbow, which is one of the most splendid phenomena in nature. In this work, an optical technique is discussed for simultaneous measurement of the diameter and refractive index of an axisymmetric and dielectric fiber by studying some rainbow features. This noncontact optical technique uses a beam of light exhibiting low temporal coherence, which enabled us to reduce the detrimental sensitivity of the rainbow features to variations of the fiber properties, thus allowing for high-precision estimates. Approximate mathematical formulas for the diameter and refractive index measurements were derived from the lowest-order complex angular momentum correction to Airy theory of rainbow. Furthermore, sensitivity of the measurement data to small deformation of the fibers cross section into an ellipse was discussed. Preliminary empirical results provide a qualitative verification.

An optical flow-based method for velocity field of fluid flow estimation

The aim of this paper is to present a method for estimating flow-velocity vector fields using the Lucas-Kanade algorithm. The optical flow measurements are based on the Particle Image Velocimetry (PIV) technique, which is commonly used in fluid mechanics laboratories in both research institutes and industry. Common approaches for an optical characterization of velocity fields base on computation of partial derivatives of the image intensity using finite differences. Nevertheless, the accuracy of velocity field computations is low due to the fact that an exact estimation of spatial derivatives is very difficult in presence of rapid intensity changes in the PIV images, caused by particles having small diameters. The method discussed in this paper solves this problem by interpolating the PIV images using Gaussian radial basis functions. This provides a significant improvement in the accuracy of the velocity estimation but, more importantly, allows for the evaluation of the derivatives in intermediate points between pixels. Numerical analysis proves that the method is able to estimate even a separate vector for each particle with a 5× 5 px2 window, whereas a classical correlation-based method needs at least 4 particle images. With the use of a specialized multi-step hybrid approach to data analysis the method improves the estimation of the particle displacement far above 1 px.

Particle image models for optical flow-based velocity field estimation in image velocimetry

This paper examines two models for image representation used for optical flow estimation in Particle Image Velocimetry (PIV). The common approach for flow estimation bases on a cross-correlation between PIV images. An alternative solution bases on an optical flow, which has the advantage of calculating vector fields with much better spatial resolution. The optical flow-based estimation requires calculations of temporal and spatial derivatives of the image intensity, which is usually achieved by using finite differences. Due to rapid intensity changes in the PIV images caused by particles having small diameters, an exact estimation of spatial derivatives using finite differences may lead to numerical errors that render data interpretation limited or even impractical. The present study aims at solving this problem by introducing two algorithms for PIV image processing, which differs in terms of a digital image representation. Both algorithms rely on a PIV image model, wherein the particle image complies with an Airy disc, which is well approximated by using a Gaussian function. Numerical analysis of sample PIV images (uniform and turbulent fields) show that both methods allow for high precision flow-velocity fields estimates in conjunction with the Lucas-Kanade algorithm.

Fluid flow measurements using optical flow velocity field estimation and LED-based light sheet illumination

The aim of this work is to present a technique for non-intrusive velocity vector measurements of micron-sized tracer particles following a fluid flow. The technique is based on Particle Image Velocimetry (PIV). In contrast to conventional PIV, which analyzes light scattering for incident high-energy laser pulses, the technique uses a light sheet produced by a prototype LED-based illuminator. A sequence of exposures from the flow taken by a high-speed camera is analyzed by means of a multi-scale optical flow-based algorithm developed by the authors. The LED illuminator offers the possibility to deliver high-power light pulses at microsecond levels and high-repetition rates. An integrated optics produce a lightsheet with adjustable thickness and width, enabling the user to measure velocity components either in a plane or in a volume. Compared to pulse lasers used in PIV systems, the illuminator has the advantages of low cost, safe operation, and much simpler construction. For the purposes of experimental verification, velocity vector measurements in a crosssection of a rotary water flow seeded with micron sized tracer particles have been performed. The velocity vectors have been computed using a multi-scale estimation algorithm based on optical flow and four-level pyramidal decomposition of PIV images. In order to validate our optical flow-based approach, the experimental results have been finally analyzed by means of a commercial PIV software that uses image cross-correlation for velocity field estimation.

Step-index optical fiber sizing with a rainbow technique

This paper reports an application of a rainbow technique to characterize both the core and cladding diameter of a single, silica-based, step-index optical fiber. Both quantities are inversely calculated using a correlation formula from the farfield scattering pattern where multiple primary rainbows occur. A set of observations of scattering allows one to retrieve the parameters of interest. Numerical studies assume variable core (10–50 μm) as well as cladding diameter (120– 130 μm). A part of analysis shows how the temporal coherence of the incident beam of light affects the solutions.

Capillary-scale interferometry at high angles of scattering for refractive index measurements of small volumes

This paper focuses on the problem of elastic scattering of a collimated beam of light on an unmodified glass capillary to perform a non-destructive small volume refractive index characterization. An interaction between the beam of light and the capillary causes that a series of dark and bright fringes is formed in the far field observed at high angles of scattering. By analyzing the spatial profile of the scattered light, the absolute value of the refractive index of a small volume may be measured unambiguously.

Optical sensing of rainbow for non-contact gauging of diameter and refractive index of an axisymmetric transparent fiber

In the present paper an optical technique is described to measure non-invasively the diameter and refractive index of a transparent (glass or polymer) fiber that possess a circular cross-section. The method is based on an inverse analysis of the rainbow, which is formed by light scattering of low temporal coherency. This enables to achieve unambiguous mathematical relationships between fringe structure of the rainbow and the fiber.

High-angle light scattering to determine the optical fiber core

The aim of the paper is to discuss the possibility of non-invasive sizing of a step-index optical fiber with the use of a beam of light of low temporal coherence. For this purpose we examine the angular profile of light scattered from the fiber at a high angle. The scattered pattern comprises chiefly two coupled, twin rainbows and depends on the fiber physical characteristics, i.e. its dimensions, shape, and refractive index profile. In order to find a causal link between the scattering pattern and the fiber morphology, a spectral analysis (Fast Fourier Transform, FFT) is performed over the scattering intensity. From the spectral data, the core diameter of a step-index optical fiber is extracted inversely.