A new approach to vector scattering: The 3S boundary source method

© 2019 OSA - The Optical Society. All rights reserved. This paper describes a novel Boundary Source Method (BSM) applied to the vector calculation of electromagnetic fields from a surface defined by the interface between homogenous, isotropic media. In this way, the reflected and transmitted fields are represented as an expansion of the electric fields generated by a basis of orthogonal electric and magnetic dipole sources that are tangential to, and evenly distributed over the surface of interest. The dipole moments required to generate these fields are then calculated according to the extinction theorem of Ewald and Oseen applied at control points situated at either side of the boundary. It is shown that the sources are essentially vector-equivalent Huygens’ wavelets applied at discrete points at the boundary and special attention is given to their placement and the corresponding placement of control points according to the Nyquist sampling criteria. The central result of this paper is that the extinction theorem should be applied at control points situated at a distance d = 3s (where s is the separation of the sources) and consequently we refer to the method as 3sBSM. The method is applied to reflection at a plane dielectric surface and a spherical dielectric sphere and good agreement is demonstrated in comparison with the Fresnel equations and Mie series expansion respectively (even at resonance). We conclude that 3sBSM provides an accurate solution to electromagnetic scattering from a bandlimited surface and efficiently avoids the singular surface integrals and special basis functions proposed by others

Focus variation microscope: linear theory and surface tilt sensitivity

In a recent publication [3rd International Conference on Surface Metrology, Annecy, France, 2012, p. 1] it was shown that surface roughness measurements made using a focus variation microscope (FVM) are influenced by surface tilt. The effect appears to be most significant when the surface has microscale roughness (Ra ≈ 50 nm) that is sufficient to provide a diffusely scattered signal that is comparable in magnitude to the specular component. This paper explores, from first principles, image formation using the focus variation method. With the assumption of incoherent scattering, it is shown that the process is linear and the 3D point spread characteristics and transfer characteristics of the instrument are well defined. It is argued that, for the case of micro-scale roughness and through the objective illumination, the assumption of incoherence cannot be justified and more rigorous analysis is required. Using a foil model of surface scattering the images that are recorded by a FVM have been calculated. It is shown that for the case of through the objective illumination at small tilt angles, the signal quality is degraded in a systematic manner. This is attributed to the mixing of specular and diffusely reflected components and leads to an asymmetry in the k-space representation of the output signals. It is shown that by using extra-aperture illumination or at tilt angles greater than the acceptance angle of aperture (such that the specular component is lost), the incoherent assumption can be justified once again. The work highlights the importance of using ring-light illumination and/or polarizing optics, which are often available as options on commercial instruments, as a means to mitigate or prevent these effects

Developments in laser Doppler accelerometry (LDAc) and comparison with laser Doppler velocimetry

This paper outlines the principles and early development of an interferometric technique for remote measurement of vibration acceleration — laser Doppler accelerometry (LDAc). One of the key advantages of LDAc over laser Doppler velocimetry (LDV) is its ability to measure extremely high vibration accelerations and shocks, effectively without limit, and this point is expanded upon in the paper. Early LDAc development showed how unwanted, velocity-dependent optical beats could occur on the photodetector but novel use of a frequency shifting device, whose primary purpose was for direction discrimination, was successful in isolating the required acceleration-dependent beat. A problem remained in the rate at which the velocity-dependent and acceleration-dependent beats broadened during target motion. In a further development, it was possible to 'select’ a back reflection to produce a velocity-dependent beat that was NOT modulated in the presence of target motion. The acceleration-dependent beat could then be demodulated and preliminary results are given to demonstrate this outcome

Optical measurements of cavitation in tribological contacts

The paper describes the use of a white light interformeter to measure the cavitation bubble and oil film thickness in a tribological contact and compares the results to theory. It is found that oil film thickness is best predicted by the theory proposed by Coyne and Elrod.

The measurement of rough surface topography using coherence scanning interferometry

This guide describes good practice for the measurement and characterisation of rough surface topography using coherence scanning interferometry (commonly referred to as vertical scanning white light interferometry). It is aimed at users of coherence scanning interferometry for the optical measurement of surface texture within production and research environments. The general guidelines described herein can be applied to the measurement of rough surfaces exhibiting different types of surface topography. For the purpose of this guide, the definition of a rough surface is one that has features with heights ranging from approximately 10 nm to less than 100 µ

Depth-resolved imaging and displacement measurement techniques viewed as linear filtering operations

The last 5 years have seen the emergence of a family of optical interferometric techniques that provide deformation measurements throughout three-dimensional (3-D) weakly scattering materials. They include wavelength scanning interferometry (WSI), tilt scanning interferometry (TSI), phase contrast spectral optical coherence tomography (PC SOCT) and hyperspectral interferometry (HSI) and can be thought of as a marriage between the phase sensing capabilities of Phase Shifting Interferometry and the depth-sensing capabilities of Optical Coherence Tomography. It was recently shown that some closely related 3-D optical imaging techniques can be treated as shift-invariant linear filtering operations. In this paper, we extend that work to include WSI, TSI, PC SOCT and HSI as spatial filtering operations and also relate the properties of their transfer functions in the spatial frequency domain to their spatial resolution and phase sensitivity, for depth-resolved displacement measurements

Microstructural and mechanical characterisation of laser-welded high-carbon and stainless steel

Laser welding is becoming an important joining technique for welding of stainless steel to carbon steel and is extensively used across various sectors, including aerospace, transportation, power plants, electronics and other industries. However, welding of stainless steel to high-carbon steel is still at its early stage, predominantly due to the formation of hard brittle phases, which undermine the mechanical strength of the joint. This study reports a scientific investigation on controlling the brittle phase formation during laser dissimilar welding of high-carbon steel to stainless steel. Attempts have been made to tailor the microstructure and phase composition of the fusion zone through influencing the alloying composition and the cooling rate. Results show that the heat-affected zone (HAZ) within the high-carbon steel has significantly higher hardness than the weld area, which severely undermines the weld quality. To reduce the hardness of the HAZ, a new heat treatment strategy was proposed and evaluated using a finite element analysis-based numerical simulation model. A series of experiments has been performed to verify the developed thermo-metallurgical finite element analysis (FEA) model, and a qualitative agreement of predicted martensitic phase distribution is shown to exist

Numerical simulation of alloy composition in dissimilar laser welding

A three-dimensional multiphase computational fluid dynamic model was developed to investigate the meltpool fluid dynamics, dilution and alloy composition in laser welding of low carbon steel and stainless steel. Using the developed model, independent predictions on weld properties are made for a range of laser parameters, and in all cases the results of the numerical model were found to be in close agreement with experimental observations. The investigation revealed that above certain specific point energy the materials within the melt pool are predominantly homogenous. A minimum meltpool convention is required in dissimilar laser welding to obtain weld bead properties suitable for industrial applications. The present model provides a simple yet effective method to predicting the weld bead alloying concentration and homogeneity encompassing wide range of materials

Cavitation bubble measurement in tribological contacts using digital holographic microscopy

The use of advanced measurement techniques such as the digital holography method described in this paper improves the understanding of the cavitation phenomenon in tribological contacts such as the sliding contact of the piston ring–cylinder liner conjunction. The paper describes the use of digital holography measurement technique to measure cavitation bubble formation and thickness. The position of observed lubricant film rupture preceding the cavitation region is compared with some commonly predicted boundary often used with Reynolds equation. The experimental results indicate that the Reynolds and Elrod boundary conditions are the most suitable for the investigated sliding contact conditions

Cavitation bubble measurement in tribological contacts using digital holographic microscopy

The use of advanced measurement techniques such as the digital holography method described in this paper improves the understanding of the cavitation phenomenon in tribological contacts such as the sliding contact of the piston ring–cylinder liner conjunction. The paper describes the use of digital holography measurement technique to measure cavitation bubble formation and thickness. The position of observed lubricant film rupture preceding the cavitation region is compared with some commonly predicted boundary often used with Reynolds equation. The experimental results indicate that the Reynolds and Elrod boundary conditions are the most suitable for the investigated sliding contact conditions