Polarizationally Non-sensitive Pseudo-holographic Computer Reconstruction of Random Rough Surface

Abstract

The function, describing a profile of a random rough surface (RRS) is expanded in a Fourier series, i.e. the surface is considered as a composition of sinusoidal gratings. The total diffracted optical field from this RRS is a sum of the fields due to all harmonic gratings, since Kirchhoff's condition for ‘locally flat surface’ is realized for each harmonic grating at a given light wavelength and at an appropriate choice of the basic grating period. The registered s and p components of the diffracted (+1 diffraction orders of each harmonic gratings), incident and mixed optic fields are separated with an optical analyser. These fields are experimentally measured and from these values the phase and the amplitude of each grating are determined. The profile of the surface is reconstructed for s and p polarization of the light scattered field, when the electric vector of the incident light concludes an arbitrary angle with the incidence plane. The mean roughness is determined in both cases. It is shown, that both reconstructions of the profile and the determination of the mean roughness are not dependent on the polarization of the incident light. The separation of the s and p components is of great importance at the two-dimensional reconstruction, when independent of incident light polarization (s or p), the scattered optical field is always depolarized. In this case the profile of the two-dimensional surface can be easily reconstructed with s or p component of the mixing and diffracted fields.     

Binary blazed reflection gratings

A reflection grating with a binary surface profile is presented that has high diffraction efficiency. The measured intensity for the + 1st diffracted order was 77%. The binary grating is composed of a minilattice with feature sizes comparable with the wavelength of the incident light. The overall structure is designed in such a way that it imitates a conventional blazed grating. The grating also has interesting polarization properties. The main part of the TE-polarized light is diffracted into the 1st diffracted order, and most of the TM-polarized light remains in the 0th diffracted order. The measurements of the grating are compared with rigorous diffraction theory and found to be in reasonable agreement.     

The surface topography of retrieved femoral heads

Excessive wear of UHMWPE sockets is considered detrimental to the long-term performance of total hip replacement procedures. Although many factors contribute to the wear process, laboratory experiments have indicated that one of the most important factors affecting the wear rate is surface topography and in particular, the arithmetic mean surface roughness, R _a, of the hard counterface. Surface roughness values were therefore obtained from the heads of 37 explanted and five new Charnley prostheses. The surface topography was measured using a Rodenstock RM 600 non-contacting profilometer. Five parameters were used to give a quantitative characterization of the surface texture; arithmetic mean surface roughness, R _a, root mean square (RMS) surface roughness, R _q, peak to valley height, R _t, average single peak to valley height from five adjoining sample lengths, R _z, and the skewness of the height distribution, Sk. Further, qualitative investigations were undertaken using a Joel-JSM-IC848 scanning electron microscope (SEM). The median values of R _a, R _q, R _t and R _z for explanted heads showed statistically significant increases when compared with values from new prostheses. No significant difference was found between any of these parameters measured in the anterior-posterior and the medial-lateral directions. This result may have important implications for the design of joint simulators. No correlation was found between any of the parameters and implant period.     

Influence of roughness parameters on coefficient of friction under lubricated conditions

Surface texture and thus roughness parameters influence coefficient of friction during sliding. In the present investigation, four kinds of surface textures with varying roughness were attained on the steel plate surfaces. The surface textures of the steel plates were characterized in terms of roughness parameter using optical profilometer. Then the pins made of various materials, such as Al-4Mg alloy, Al-8Mg alloy, Cu, Pb, Al, Mg, Zn and Sn were slid against the prepared steel plates using an inclined pin-on-plate sliding tester under lubricated conditions. It was observed that the surface roughness parameter, namely, R _a , for different textured surfaces was comparable to one another although they were prepared by different machining techniques. It was also observed that for a given kind of surface texture the coefficient of friction did not vary with R _a . However, the coefficient of friction changes considerably with surface textures for similar R _a values for all the materials investigated. Thus, attempts were made to study other surface roughness parameters of the steel plates and correlate them with coefficient of friction. It was observed that among the surface roughness parameters, the mean slope of the profile, Del a(Δ _a ), was found to explain the variations best.     

Effect of surface roughness on grain growth and sintering of alumina

The production of ceramic bodies with less surface roughness is industrially important when one considers the aspect of final machining processes. Hence an attempt have been made to study the variation in surface roughness parameters (R _a, R _y, R _z) of alumina having three different kinds of roughness features at different sintering temperatures. Variation in surface roughness properties are also correlated with grain size. R _z shows significant difference between fine and intermediate surfaces, hence predicts small difference in their microstructural features. As a general trend, average grain size increases with increase in sintering temperature, but wide distribution of grains with enhanced non-uniform grain growth is observed when the surface is coarse. Hence, creation of fine surface in the green body is necessary for homogeneously distributed grains with controlled uniform grain growth. The final roughness and grain size of the sintered alumina depend on the initial surface roughness of the green body.     

Cylinder and metal grating polarization beam splitter

We propose a novel and compact metal grating polarization beam splitter (PBS) based on its different reflected and transmitted orders. The metal grating exhibits a broadband high reflectivity and polarization dependence. The rigorous coupled wave analysis is used to calculate the reflectivity and the transmitting spectra and optimize the structure parameters to realize the broadband PBS. The finite-element method is used to calculate the field distribution. The characteristics of the broadband high reflectivity, transmitting and the polarization dependence are investigated including wavelength, period, refractive index and the radius of circle grating. When grating period d = 400 nm, incident wavelength λ = 441 nm, incident angle θ = 60° and radius of circle d/5, then the zeroth reflection order R₀ = 0.35 and the transmission zeroth order T₀ = 0.08 for TE polarization, however, T₀ = 0.34 and R₀ = 0.01 for TM mode. The simple fabrication method involves only single etch step and good compatibility with complementary metal oxide semiconductor technology. PBS designed here is particularly suited for optical communication and optical information processing.     

Nonparaxial scalar treatment of sinusoidal phase gratings

Scalar diffraction theory is frequently considered inadequate for predicting diffraction efficiencies for grating applications where lambda/d>0.1. It has also been stated that scalar theory imposes energy upon the evanescent diffracted orders. These notions, as well as several other common misconceptions, are driven more by an unnecessary paraxial approximation in the traditional Fourier treatment of scalar diffraction theory than by the scalar limitation. By scaling the spatial variables by the wavelength, we have previously shown that diffracted radiance is shift invariant in direction cosine space. Thus simple Fourier techniques can now be used to predict a variety of wide-angle (nonparaxial) diffraction grating effects. These include (1) the redistribution of energy from the evanescent orders to the propagating ones, (2) the angular broadening (and apparent shifting) of wide-angle diffracted orders, and (3) nonparaxial diffraction efficiencies predicted with an accuracy usually thought to require rigorous electromagnetic theory.     

Investigation on performance of abrasive water jet in machining hybrid composites

For machining of composites, abrasive water jet machining is widely employed. For assembly of the machine tool structure, production of slots is essential. In this paper, abrasive water jet machining of composite laminates was experimentally investigated for various cutting parameters in terms of average surface roughness (R_a) and kerf taper (K_t). By generating a response surface model, the experimental values obtained for quality characteristics (R_a and K_t) were empirically related to cutting parameters. The effects of cutting parameters on quality characteristics were analyzed by utilizing empirical models and also optimized within the tested range based on desirability approach. The optimum parameter levels were also validated by confirmation test. From this investigation, it is evident that for obtaining a minimum kerf taper, traverse speed, water pressure, and abrasive mass flow rate are significant parameters and for obtaining less surface roughness traverse speed is the significant parameter.     

Shift and shape of grating diffracted beams

Abstract

The grating diffraction of beams is theoretically investigated by applying an electromagnetic method (the Integral Equation System Method with Parametrization of the grating profile = IESMP) to their plane wave components. For the first time, explicit values for the displacement of grating diffracted Gaussian beams are calculated with this method. For total reflection this displacement of beams is known as the Goos-Hänchen shift. A maximum shift of 36 μm has been found for the investigated sinusoidal grating near an anomaly which is much greater than the known Goos–Hänchen shift of about 1 μm for the total reflection case. The replacement of the angular spectrum of plane waves with constant wavelength by a wavelength spectrum of plane waves of constant direction allows an analogous treatment of short-time pulses. Surprisingly, the above anomaly causes a maximum temporal shift of 80 fs for the pulse diffraction. These temporal shifts and additional effects like pulse deformations can influence ultra short-time pulse experiments. Furthermore, the behaviour of temporally and spatially Gaussian shaped light pulses (TSG pulses) by grating diffraction are studied considering the diffraction of an angular and wavelength dependent spectrum of plane waves. The diffraction of a short TSG pulse at the above grating deforms the pulse and creates an additional smaller satellite pulse. All described effects occur only at positions of the space–time complex filtering function in the angular-wavelength frequency space with high gradient of the phase.     

Measuring the focal length of optical systems by grating shearing interferometry

Using grating shearing interferometry, a new and simple technique to measure the effective focal length of optical systems is described. The diffraction pattern of a phase grating positioned at the focal point of the lens under test is evaluated for this purpose. The relative lateral shift between the undiffracted zero order and the diffracted first orders caused by the grating is measured. By utilizing knowledge of the wavelength of light, the grating period, and the diameter of an aperture stop placed in front of the test lens, we can determine the effective focal length of the test lens. Results of measurements are presented and compared with calculated values. The dependence of the focal length on the wavelength of the light is shown by using two laser sources of different wavelengths. An analysis of the measurement accuracy is given.     

Methods to characterize the surface roughness of metallic implants

The surface roughness of surgical implants has a significant influence on the tissue reaction at the interface. The purpese of the present study is to describa methods which allow a detailed characterization of the surface roughness. Pure titanium plates with different surface treatments and electropolished stainless steel plates, were analysed. For the surface roughness measurement, a profilometer with a 4 m tip was used to determine the following roughness parameters: R _a = arithmetic mean of the roughness height, S _m = arithmetic mean of the groove distance, R _tm = average of the roughness height. Furthermore the surface was observed under a scanning electron microscope (SEM) at a magnification of 1000x and 2000x so that even small pores which cannot be measured using the profilometer are detectable. Standard reflected light microscopy and interference contrast microscopy was used to optically measure the height of depressions and elevations, and to study in particular the surface colour, which is related to the thickness of the oxide film of anodized implants. It is concluded that, for the characterization of the surface roughness of metallic implants, the measurements using the profilometer and SEM are recommended. For anodized surface treatments, interference contrast microscopy seems to be a valuable aid to judgement of the homogeneity and, via colour, the thickness of the oxide layer.     

Sidewall roughness characterization and comparison between silicon and SU-8 microcomponents

Surface characterization of microcomponents provides key information to help understand and predict the performance of microdevices. For example, in a microgear transmission, the surface roughness has a strong effect on the friction, running life and power consumption. In a static fluid microdevice, the liquid distribution is influenced by the surface tension and capillary force, which are primarily determined by the surface roughness. In a flowing microchannel case, surface roughness results in unsteady secondary flows. In this paper, a study is presented to characterize the surface roughness of silicon and SU-8 microcomponents. The silicon components studied are fabricated using an ICP plasma etching system manufactured by Surface Technology Systems. The sidewall roughness of the component is measured using atomic force microscopy. Repeated measurements have been conducted at different sidewall depths of the microstructure. The AFM images of the measurements are present. The measurement results show that the sidewall is smoother at the lower level than that at the upper level in a Si microstructure, and the average roughness R_a obtained throughout the depth is 151.11 nm. The UltraThick SU-8 Process (UTSP) provides another way to fabricate microstructures as thick as 1 mm with a very vertical sidewall. The roughness contour of the sidewall shows that the surface topography is similar throughout the depth. The average roughness R_a is 46.46 nm. Other surface parameters, such as R_q, R_p − p, R_pk and R_sk, are also obtained and analysed. The implication of the smooth surface roughness of SU-8 structures to their applications is discussed in terms of transmission efficiency, the changes in friction to flowing liquid in a microchannel and the changes in the surface tension and capillary effect.     

Fabrication of switchable liquid crystal devices using surface relief gratings in photopolymer

Holographically recorded surface relief gratings in dry, self-developing acrylamide based photopolymer were used to fabricate two types of switchable liquid crystal (LC) device. One is an electrically switchable LC diffraction grating and the other is an electrically switchable polarization rotator. The electrically switchable diffraction grating was characterized by measuring the dependence of the intensity in the first diffracted order on the applied electric field. The polarization rotator was characterized by studying the influence of the applied electric field on the twist angle and the variation of intensity in the zero and the first orders of diffraction.     

Experimental Investigation and Optimization of Process Parameters of Al/SiC MMCs Finished by Abrasive Flow Machining

In the era of nontraditional finishing processes, it is of upmost importance that these processes can be applied to composite materials as these have replaced traditional materials in many applications. Abrasive Flow Machining (AFM) is an advanced finishing process. Composite materials have replaced traditional materials as their properties such as light weight, high strength, and good economy are of great benefit. In the literature, work has been reported on AFM of materials such as aluminum, brass, and EN8. In the present work, composite materials with a high percentage of SiC (e.g., 20–60% SiC in Al/SiC composites) were machined using abrasive flow finishing. The Taguchi method was applied to find the effect of input parameters on material removal rate (MRR), change in surface roughness (ΔR_a), and surface topography, and L27 array was designed for experimentation. It was observed that extrusion pressure is the most significant factor in regard to MRR and ΔR_a. Optimization of response parameters (MRR and ΔR_a) was determined using the Taguchi method. Microstructure analysis was also done for workpiece materials using SEM and XRD.     

Modeling and Optimization of Surface Roughness of Epoxy/Nanoparticles Composite Coating

In power plants, flue gases can cause severe corrosion damage in metallic parts such as flue ducts, heat exchangers, and boilers. Coating is an effective technique to prevent this damage. A robust fuzzy model of the surface roughness (R_a and R_z) of flue gas ducts coated by protective composite coating from epoxy and nanoparticles was constructed based on the experimental dataset. The proposed model consists of four nanoparticles (ZnO, ZrO₂, SiO₂, and NiO) with 2%, 4%, 6%, and 8%, respectively. Response surface methodology (RSM) was used to optimize the process parameters and identify the optimal conditions for minimum surface roughness of this coated duct. To prove the superiority of the proposed fuzzy model, the model results were compared with those obtained by ANOVA, with the coefficient of determination and the root-mean-square error (RMSE) used as metrics. For R_a, for the first output response, using ANOVA, the coefficient-of-determination values were 0.9137 and 0.4037, respectively, for training and prediction. Similarly, for R_z, the second output response, the coefficient-of-determination results were 0.9695 and 0.4037, respectively, for training and prediction. In the fuzzy modeling of R_a, for the first output response, the RMSE values were 0.0 and 0.1455, respectively, for training and testing. The values for the coefficient of determination were 1.00 and 0.9807, respectively, for training and testing. The results prove the superiority of fuzzy modeling. For modeling the second output response R_z, the RMSE values were 0.0 and 0.0421, respectively, for training and testing, and the coefficient-of-determination values were 1.00 and 0.9959, respectively, for training and testing.     

Some considerations regarding finishing by abrasive flap wheels

The diminishing of the surface roughness of a metallic part can be performed by using various finishing methods, polishing by means of abrasive flap wheels being one of them. There are several factors that influence the roughness of surfaces finished by means of abrasive flap wheels. When polishing external cylindrical surfaces by means of abrasive flap wheels, the surface roughness can be changed more easily if the following elements are modified: the peripheral speed of the workpiece and of the abrasive flap wheel, the speed of the longitudinal feed, and the grit size of the abrasive material. Experimental research has allowed for the establishment of power-type functions which highlight the influence exerted by the above-mentioned factors on the size of the surface roughness parameters R _a , RS, RSm, Rku. Analyses of the experimental results have shown that, in the case of the R _a roughness parameter, from among the range of interactions of orders 2 and 3, only the interaction between the rotation speed of the abrasive flap wheel and the speed of the longitudinal feed seems to be significant.     

Three-dimensional Computer Reconstruction of Random Rough Surface

Abstract

The two-dimensional function f(x y) with slow variation in the y direction and describing a random rough surface in the x direction is expanded in a Fourier series i.e. considered as a sum of sinusoidal harmonic grating in the x direction. The scattered optical field by each line of this surface in the x direction is considered as a sum of the diffracted optical fields from the sinusoidal gratings. The diffracted fields are registered by consecutive scanning of the surface in the y direction, and the surface profile of each line is reconstructed using the theory developed in [1,2]. The studied surface is visualized by the reconstructed profiles in ten lines using a program visualizing a function depending on two variables. The calculated mean roughness Ra is averaged along all lines and is found to be in satisfactory agreement with that averaged by the Hobson type profilometer within the laser spot.     

Spectrograph based on a single diffractive element for real-time measurement of circular dichroism

In this study, a novel and simple diffractive spectrographic method for real-time measurements of circular dichroism (CD) is considered from a theoretical and experimental approach. A demonstrator prototype of the CD spectrograph has been developed and its performance has been compared with a commercial phase-modulation CD spectrometer. The main element of the device is a polarization holographic grating, recorded in a thin photosensitive organic film, by two interfering opposite circularly polarized beams. A peculiarity of this grating is that the amplitude of the +1 (-1) order of diffraction is proportional to the right (left) circular polarization component of the incoming beam. Here we demonstrate that the CD spectrum of a specimen can be easily evaluated from the intensities of the diffracted beams. A white light beam passing through the specimen is diffracted from the grating and the intensities of the +/-1 orders of diffraction are measured. Due to the spectral selectivity of the grating, the CD at each wavelength can be evaluated at the same time using two linear array detectors.     

Magnetorheological nanofinishing of BK7 glass for lens manufacturing

BK7 is a high-quality crown glass which is used where additional benefits such as temperature sensitive applications of fused silica glass are not required. Due to very low inclusion content with extremely low bubbles, BK7 glass can find its application in lens manufacturing. The present work focuses on nanofinishing of the BK7 glass specimen for ratifying its utility in practical application. A programmable logic controlled 3-axis motions are fed to the magnetorheological (MR) rotating tool for finishing the glass specimen. MR polishing fluid used for nanofinishing consists of deionized water, magnetic iron particles, and cerium oxide powder. Under the influence of magnetic field, the stiffened MR polishing fluid is assisted in reducing the surface roughness of glass up to nanolevel range. Optical properties such as transmittance, absorbance, and reflectance of finished BK7 glass are analyzed and found suitable for lens manufacturing. Results of higher surface quality with excellent finishing are obtained by the present MR finishing process. After 90?min of finishing, the surface roughness values R_a and R_q are reduced to 17 and 27?nm from the initial values of 41 and 57?nm, respectively. To study the surface morphology, scanning electron microscopy is performed on BK7 glass.     

Parameter range extension in reflectometric roughness measurement

Light scattering is considered in relation to roughness of machine surfaces with actual autocorrelation functions. Numerical characteristics are given as functions of the ratio between R_a and the wavelength, and practical recommendations are made.Translated from Izmeritel'naya Tekhnika, No. 2, pp. 24–26, February, 1995.