Null-screen testing of fast convex aspheric surfaces

A method for null-testing fast convex aspheric optical surfaces is presented. The method consists of using a cylindrical screen with a set of lines drawn on it in such a way that its image, which is formed by reflection on a perfect surface, yields a perfect square grid. Departures from this geometry are due to imperfections of the surface, allowing one to know if the surface is close to the design shape. Tests conducted with a full hemisphere and with the parabolic surface of a lens show the feasibility of the method. Numerical simulations show that it is possible to detect surface departures as small as 5 mum.     

Point shifting in the optical testing of fast aspheric concave surfaces by a cylindrical screen

A method for increasing the precision and sensitivity of the quantitative evaluation of fast aspheric surfaces through the null screen method is presented. This consists of applying small displacements to the cylindrical null screen along the optical axis. These movements allow a scan of the image spots over zones that with the analysis of a single image are more difficult to evaluate. The precision of the test is increased due to a greater density of sampling reducing the numerical errors during the integration. Results of the evaluation of an elliptical concave mirror on axis show that the numerical integration errors can be reduced from 20% for short paths to 80% for larger integration paths.     

Improving fast aspheric convex surface tests with dynamic null screens using LCDs

A method for testing fast aspheric convex surfaces with dynamic null screens using LCDs is shown. A flat null screen is designed and displayed on an LCD monitor with drop-shaped spots in such a way that the image, which is formed by reflection on the test surface, becomes an exactly square array of circular spots if the surface is perfect. Any departure from this geometry is indicative of defects on the surface. Here the whole surface is tested at once. The position of the spots on the LCD can be changed in a dynamic way, to perform point-shifting of the image spots. The proposed procedure improves the dynamic point-shifting method. As has been shown previously, this process reduces the numerical error during the integration procedure, thereby improving the sensitivity of the test. The positioning accuracy for the screen spots is related to the LCD's spatial resolution. Results of the evaluation of a parabolic convex surface with f/#=0.22 are shown.     

Smoothing of nanoscale roughness based on the Kelvin effect

A novel method of smoothing surfaces with nanoscale roughness is described, based on the Kelvin effect. The problem of vapor redistribution in cylindrical channels and over rough planar walls with nanoscale texture is posed and solved analytically. Vapor deposition (condensation) on the walls initially produces a deposit emulating the surface landscape. After a saturated state at the deposit surface is reached, the Kelvin effect should result in higher vapor pressure/ concentration near the convex sections of the wall and in lower vapor pressure/ concentration near the concave sections. As a result, local vapor fluxes should arise directed from the locally convex to the locally concave regions. Accordingly, the deposited layer at the wall should vaporize (or sublimate) at the convex sections due to depletion and vapor should condense at the concave sections, thus causing smoothing of physical surface unevenness. This mechanism of smoothing of nanoscale roughness has not been considered in detail or used before, even though the basic physics of the Kelvin effect is well known. In the present work, the smoothing kinetics is predicted and the characteristic timescales are calculated in the general case of axisymmetric and non-axisymmetric perturbations of the cylindrical channel walls, as well as for planar surfaces. In addition, experimental data are presented to show that the theoretically motivated approach is also practically realizable.     

Medium-precision null-screen testing of off-axis parabolic mirrors for segmented primary telescope optics: the large millimeter telescope

The feasibility of using null screens for testing the segments of a parabolic segmented telescope mirror for the Large Millimeter Telescope (LMT) is analyzed. An algorithm for designing the null screen for testing the off-axis segments of conic surfaces is described. Actual screen designs for the different classes of segments of the LMT are presented. The sensitivity of the test and the required accuracies for the fabrication and positioning of the screen are analyzed. A measuring accuracy of approximately 12 microm in surface sagitta is within the reach of the technique.     

Performance Analysis and Evaluation of Geometric Parameters in Stereo Deflectometry

This paper presents a novel geometric parameters analysis to improve the measurement accuracy of stereo deflectometry. Stereo deflectometry can be used to obtain form information for freeform specular surfaces. A measurement system based on stereo deflectometry typically consists of a fringe-displaying screen, a main camera, and a reference camera. The arrangement of the components of a stereo deflectometry system is important for achieving high-accuracy measurements. In this paper, four geometric parameters of a stereo deflectometry system are analyzed and evaluated: the distance between the main camera and the measured object surface, the angle between the main camera ray and the surface normal, the distance between the fringe-displaying screen and the object, and the angle between the main camera and the reference camera. The influence of the geometric parameters on the measurement accuracy is evaluated. Experiments are performed using simulated and experimental data. The experimental results confirm the impact of these parameters on the measurement accuracy. A measurement system based on the proposed analysis has been set up to measure a stock concave mirror. Through a comparison of the given surface parameters of the concave mirror, a global measurement accuracy of 154.2 nm was achieved.     

Simultaneous characterization of the quality and orientation of cylindrical lens surfaces

A diffractive grazing-incidence interferometer for the test of cylindrical lenses is described. Besides surface aberrations from the ideal shape, the interferometer allows for the simultaneous determination of the relative position and orientation of surfaces to another. The measurement principle as well as a classification of deviation types is given. Measurement results for planar concave lenses are presented.     

Three-Dimensional Interaction of a Supersonic Gas-Droplet Jet and Obstacles with Regard for Phase Transitions

The inleakage of a non-single-phase non-single-component jet consisting of a passive gas, evaporating droplets, and vapor on solid surfaces is investigated. In the physical model of the jet, the diffusion mechanism of interphase mass transfer is assumed, along with the presence of the velocity and thermal nonequilibrium between droplets and the carrier binary mixture of gases. This relaxing two-phase medium is treated as locally monodispersed, with the droplet integrity being defined by the Weber number. The droplets colliding with the surface break down into small fragments which vaporize instantaneously to produce the injection of the vapor mass equal to the mass of incident droplets into the flux. The numerical investigations are performed in the region of determined parameters corresponding to the steady-state regime of inleakage of a jet with a dispersed annular screen onto flat and concave cylindrical obstacles at different angles.     

Testing a fast off-axis parabolic mirror by using tilted null screens

We propose the design of tilted null screens for testing off-axis segments of conic surfaces. The tilt allows us to control the size of the screen and the sensitivity of the test. For positive tilt angles the sensitivity is increased while the size of the screen is reduced in the sagittal caustic region and vice versa in the tangential caustic region. Further analysis and preliminary experimental results are presented for a fast off-axis concave parabolic mirror with an elliptical aperture. An offset distance of X(C) = 25.4 mm yields radius of curvature at the vertex R = 20.4 mm; major axis of the mirror D(M) = 49.4 mm; and minor axis D(m) = 29.5 mm.     

Point force excitation of a thick-walled elastic infinite pipe with an embedded inhomogeneity

The propagation of elastic waves in thick-walled pipe with an embedded inhomogeneity is considered. The pipe is excited by a point force applied on its surface and the time harmonic problem is solved using the null field approach, a method whose main characteristics are surface integral representations and expansions in spherical and cylindrical vector wave functions. Entering in the expression for the scattered field are the transition matrix for the cavity, the reflection matrices for the inner and outer surfaces of the pipe, the transformation functions between the spherical and cylindrical vector wave functions and also the translation for the cylindrical waves. Numerical examples, both in the frequency and time domain, are presented for a spherical cavity and an open circular crack.     

Effect of tool geometry and process condition on static strength of a magnesium friction stir lap linear weld

Friction stir lap linear welding is conducted on overlapped AZ31 magnesium plates with different welding tools. Welds are made mainly with the orientation such that the weld retreating side on the upper plate is to be placed under load. Welding tools consist of a concave shoulder and a pin having a cylindrical, or triangular, or pie shape. This work addresses the effects of tool geometry and process condition on lap shear strength of welds. The shape of the hook formed due to upward bending of the plate interface on the retreating side and the strength of friction stir processed material are quantitatively characterized. Compared to the cylindrical tool, the triangular tool effectively suppresses the hook on the retreating side due to enhanced horizontal material flow. This primarily leads to a 78% increase in optimized weld strength. A ‘pure’ shear surface present on the tool pin significantly reduces weld strength.     

Optimization of plasmon excitation at structured apertures

Surface plasmon excitation that is due to a single or a structured circular aperture in a flat metallic screen is investigated theoretically and numerically with a view to enhancing the electric field close to the metallic surface. A systematic study of the homogeneous solution of the electromagnetic scattering problem is made with cylindrical coordinates, expanding Maxwell equations on a Fourier-Bessel basis. A perturbation analysis devoted to simple physical analyses of different types of cylindrical nanostructure is developed for the optimization of plasmon excitation by a normally incident linearly polarized monochromatic plane wave. The conclusions drawn from this analysis agree well with the results of rigorous electromagnetic calculations obtained with the differential theory of diffraction in cylindrical coordinates.     

Parameterized Finite Element Modeling and Buckling Analysis of Six Typical Composite Grid Cylindrical Shells

Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.     

Influence of circumferential curve shapes and surface options on curve length and volume of axisymmetric components in modelling for reverse engineering applications

In this work axisymmetric components are scanned using Coordinate Measuring Machine (CMM) and modeled using circular section/boundary curves. Surface options such as Surfaces of revolution, lofted surface and coons surface are considered in modelling. The curve length and volume are numerically evaluated for various surface options. The error percentage is obtained for curve length and volume by taking the values measured from the components as reference values. Result are presented for six different circumferential curves shapes viz., parallel (cylindrical), inclined upwards (inverted frustum), inclined downwards (frustum), convex (barrel), concave (sand-clock shape) and combined convex-concave shape. The results show that percentage error is negligible only for Surfaces of revolution and lofted surface in modelling convex, concave and combined convex-concave shapes. In modelling parallel and inclined shapes all three surface options fit well. In modelling convex, concave and combined convex-concave shapes, coons surface does not fit well. The suggestion to designers is to use surfaces of revolution and lofted surface rather than using coons surface. Otherwise the shapes of components will be different from the designed shape. Also the volume of components will be different from the designed volume. In such cases the designed components fail to meet the shape and volume requirements.     

Analysis of the resonant scattering of light by cylinders at oblique incidence

We study the resonant scattering of light at oblique incidence by dielectric uncoated and coated cylinders. We develop a stable algorithm that permits us to calculate the resonances of a single dielectric cylinder as the tilting angle varies. This algorithm is based on semiclassical formulas for the distance between resonances. Results show that the resonances and the resonant electromagnetic energy flux near and internal to the cylindrical surface are highly sensitive to variations in the tilting angle. In addition, the coating effects are studied for scattering of light at oblique incidence by an infinite, perfect cylindrical conductor coated by a dielectric layer. In this case the resonance calculations show a peculiar similarity between this light scattering and atomic-molecular scattering. A physical interpretation for these effects is given, based on an analogy of optics and quantum mechanics.     

Enhanced transmission of light through a circularly structured aperture

Using the differential theory of light diffraction by finite cylindrical objects, we study light transmission through a small circular aperture in a metallic screen with concentric corrugation around the nanohole. Poynting vector maps in the region below the screen show that the field enhancement compared with an unstructured aperture is obtained with corrugation lying on the entrance face of the screen. Corrugation on the exit face leads to a more directional radiation close to the normal to the screen. The spectral dependence of the transmission shows a sharp maximum linked with surface plasmon excitation.     

Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. IV. Frequency-domain analysis

Part IV examines frequency-domain photon diffusion in a homogeneous medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator, both geometries being infinite in the longitudinal dimension. The aim is to assess by analogical and finite-element methods the changes of AC amplitude, modulation depth, and phase with respect to the line-of-sight source-detector distance for a source and a detector located along the azimuthal or longitudinal direction on the concave or convex medium-applicator interface. By comparing to their counterparts along a straight line on a semi-infinite medium-applicator interface, for the same line-of-sight source-detector distance, it is found that: (1) the decay-rate of AC photon fluence is smaller along the azimuthal direction and greater along the longitudinal direction on the concave interface, (2) the decay-rate of AC photon fluence is greater along the azimuthal direction and smaller along the longitudinal direction on the convex interface, (3) the modulation depth along both azimuthal and longitudinal directions decays more slowly on the concave interface and faster on the convex interface, and (4) the phase along both azimuthal and longitudinal directions increases more slowly on the concave interface and faster on the convex interface.     

Three‐dimensional Displacement and Shape Measurement with a Diffraction‐assisted Grid Method

The grid method is a full‐field optical technique for computing surface displacements and strains of a material by analyzing the phase of grid lines patterned on the specimen. To date, most experiments using the grid method have measured only two‐dimensional in‐plane deformations. Here, the grid method is extended to three dimensions by using a crossed grid pattern and a diffraction grating which enables acquiring images from multiple viewing angles on a single camera. In‐plane displacements and strains are computed using the conventional grid method, and the corresponding three‐dimensional (3D) displacements—including out‐of‐plane displacements or shapes—are computed by analyzing the images collected at different viewing angles. The technique is demonstrated by measuring 3D rigid body motion, the 3D displacements of a membrane in a pressure‐bulge experiment, and the out‐of‐plane curvature of a cylindrical specimen.     

An axisymmetric external crack problem for an infinite medium with a cylindrical inclusion

Summary This paper deals with the determination of stresses in an infinite medium containing an external crack surrounding a cylindrical inclusion. The two media are assumed to be homogeneous, isotropic and elastic but with different elastic constants. The continuity of stresses and displacements is assumed at the common cylindrical surface due to perfect bonding. The problem is reduced to the solution of a Fredholm integral equation of the second kind. A closed-form expression is obtained for the stress-intensity factor. The integral equation is solved numerically and the results are used to obtain the numerical values of the stress-intensity factor which are displayed graphically.The authors thank the National Research Council of Canada for supporting this research through NRC Grant No. A-4177.     

Flexible null test for form measurement of highly astigmatic surfaces

We report the application of interferometry to the form measurement of a family of highly astigmatic optical surfaces. These measurements are based on a null test that employs a double-pass off-axis test arrangement with a tilted test surface and a reference sphere. This arrangement provides a perfect null test for an ellipsoid of revolution, or prolate spheroid. Its application is illustrated in detail in the presentation of results for the measurement of a specific family of eight differing surfaces that are incorporated into the K-Band Multi-Object Spectrometer Integral Field Unit. All surfaces measured here are sufficiently close to a prolate spheroid to justify its practical application. We discuss the application of the technique as a flexible low-cost approach for the generation of null interferograms in the measurement of a variety of complex surfaces.