Angular Tolerance Research Articles

An investigation of the robustness of the nonlinear least-squares sphere fitting method to small segment angle surfaces

This paper presents an investigation of the nonlinear least-squares sphere fitting algorithm (TLSA). The work concentrates on investigating the reliability of the TLSA algorithm when applied to a small segment angle of a sphere. The definition of small segment angle is discussed in the paper and taken to be below 1° (in both x and y directions) of the spherical surface. This application of the TLSA method is important when it is used on data from optical scanning systems where the measurements are limited by the gauge range and the angular tolerance of the sensor. The TLSA algorithm has been first compared with the TLSD algorithm suggested by Forbes for this application. The results show that the TLSA algorithm can be used in small surface segment angles. The main study is focused on testing the algorithm on a sphere superimposed with surface irregularities (sensor/measurement noise or roughness). Two properties of the TLSA algorithm are covered: the bias and the uncertainty of the estimated radius. Both simulation and theoretical approaches have been attempted. A new algorithm to estimate the bias of the TLSA algorithm has been derived in this paper based on Box's method. Together with uncertainty estimation, which can be produced by using either a conventional method or Zhang's error propagation function (EPF), a comprehensive understanding of the TLSA algorithm in this application is thus achieved, and used to develop a number of recommendations for the precision metrology of spherical and near spherical surfaces.

Authentication labels based on guided-mode resonant filters

A guided-mode resonance (GMR) filter with wide angular tolerances is experimentally demonstrated as an authentication label illuminated with unpolarized white light. The proposed filter, based on a free-standing silicon nitride membrane suspended on a silicon substrate, is fabricated by using anisotropic wet etching to remove the substrate beneath the silicon nitride layer. Both grating and waveguide structures without a lower cladding layer, i.e., a substrate, are fabricated simultaneously on a silicon nitride membrane. Since the silicon nitride is transparent within the spectra of visible and infrared light, such suspended-membrane-type GMR filters are well suited for applications within the visible spectrum. Moreover, the high refractive index of silicon nitride allows the proposed filters to have strongly modulated gratings and an immunity to high angular deviation. The measured reflection resonance has an angular tolerance up to +/-5 degrees under normal incidence for the wavelength of 629.5 nm.

Angular tolerance of Shack-Hartmann wavefront sensors with microaxicons

Wavefront sensing under nonparaxial conditions was studied with Shack-Hartmann setups based on arrays of microaxicons. The robustness of the generated pseudonondiffracting subbeams against tilt and axial displacement was demonstrated for ultraflat Gaussian- and inverse-Gaussian-shaped elements in transmission and reflection. To characterize slight aberrations and to identify optimum parameter fields, spatial moments of intensity profiles were analyzed with high sensitivity. Reflective design enables for wavefront sensing at oblique incidence as necessary for low-feedback detection and phase diagnostics of ultrashort pulses.

Source misalignment in multimode polymer tapered waveguides for optical backplanes

Polymer tapered multimode waveguides were modeled using the finite difference wide-angle beam propagation method to investigate whether tapered input waveguide couplers decreasing in width away from the waveguide entrance give improved tolerance to lateral misalign- ments of an optical source compared to straight waveguides and whether there is any effect on angular misalignment tolerance for use in optical backplane interconnections. Input tapered couplers having a larger entrance and tapering down in width do indeed improve the lateral misalignment tolerance compared to straight waveguides but do so at the expense of an increased loss. Tapers have no effect on angular tolerance for strongly driven vertical cavity surface-emitting laser VCSEL sources although they cause a loss of angular tolerance for single-mode fiber sources and VCSELs at low drive currents. © 2007 So-

Narrow-band filtering with whispering modes in gratings made of fibers

We present a numerical study of whispering modes in gratings made of fibers. Due to the strong localization of the modes inside each fiber, it is possible to obtain narrow-band filters with very broad angular tolerance.

A rational extension of Piegl’s method for filling [formula omitted]-sided holes

N -sided hole filling plays an important role in vertex blending. To deal with the case that the corner is surrounded by rational surfaces (i.e. NURBS surfaces), an algorithm to fill n -sided holes with ε - G 1 continuous NURBS patches that interpolate the given boundary curves and approximate the given cross-boundary derivatives is presented based on Piegl’s method. The NURBS surfaces joining along inner or boundary curves have normal vectors that do not deviate more than the user-specified angular tolerance ε . The boundaries as well as cross-boundary derivatives can all be NURBS curves. No restrictions are imposed on the number of boundary curves, and the cross-boundary derivatives can be specified independently.

CCATA - A Computer-Aided Angular Tolerance Charting System

This paper introduces a computer-aided angular tolerance charting (CAATC) system, which can deal with products with both angular features and square-shouldered features. The information needed to construct an angular tolerance chart electronically is described and the data structures used in the system are explained. The principle of angular tolerance charting is concisely depicted through analysing the overall structure of the system. The major functional modules of the system are also presented. Finally, an example is adopted to illustrate how to use the CAATC system.

Optimized sequential design of two-dimensional tolerances

Tolerancing has great impact on the cost and quality of a product. Previous research essentially focussed on one-dimensional tolerancing where sized tolerances accumulate only in one direction. When sized and angular tolerances are considered simultaneously, tolerances accumulate, however, in two different directions in the given view plane. We utilize related tolerance zones to illustrate the accumulation processes of sized and angular tolerances. The orientational tolerances are converted into the equivalent sized or angular tolerances in terms of their engineering semantics. We establish the sequential linear optimization models to maximize the 2D sized, angular, and orientational working tolerances of a 3D machined part based on the process capabilities. At any completion stage of operations, we measure the processed sized dimensions and then substitute them into the dimensional chains to dynamically re-calculate the mean working dimensions for remaining operations. We also re-evaluate the working tolerances for remaining operations using sequential optimization models. This approach can release the working tolerances, reduce manufacturing costs, and enhance the acceptance rate of machined parts when we manufacture the complex, low-volume, and high-value-added parts. The approach is finally illustrated with a practical example.

Microelectromechanical etalon modulator designs with wide angular tolerance for free-space optical links

Optical retrocommunication links have been demonstrated using microelectromechanical system (MEMS) etalon modulators. Here, designs for high data rate membrane MEMS modulators are shown with angular coverage up to 170/spl deg/.

Mie plasmon enhanced diffraction of light from nanoporous metal surfaces

The diffractive properties of gold films with a periodic lattice of sub-micron voids beneath the surface are investigated. It has been shown that nanoporous metal surfaces exhibit frequency-selective non-dispersive diffraction enhanced by Mie plasmons in nanovoids, which leads to absolute angular tolerance of the diffracted beam intensity that can be useful for a variety of applications covering angle-tolerant optical filters, deflectors, absorbers, and beam splitters. Diffraction spectra are measured and calculated to support these conclusions, showing good qualitative agreement.

Tolerance charting for components with both angular and square shoulder features

This paper deals with tolerance charting for a component with both angular and square shoulder features. First of all, a unified surface model is proposed for a component with both angular and square-shoulder-featured surfaces. Then, a two-dimensional tolerance chart is constructed and parameterized for the machining of the component. Also, two general formulae are derived to calculate the surface changes due to machining cuts. The recording of the surface changes during all machining cuts means that the reverse dimensional chains and the “solid” stock removals can be identified automatically. Finally, the forward dimensional chains are obtained by inverting the reverse dimensional chains. Both the reverse and forward dimensional chains developed in this paper are two-dimensional, with both axial and radial dimensions. The approach presented in this paper is very useful in the development of a computer-aided angular tolerance charting system.

Broadband polarizing beam splitter with an embedded metal-wire nanograting

An embedded metal-wire nanograting is designed and fabricated for the first time to our knowledge. This artificial material could be used as a broadband polarizing beam splitter to reflect s-polarized light and transmit p-polarized light. An upper-cladding layer of the same material as the gratings is deposited on the ridge of the gratings, whereas the metal wire is deposited in the grating trenches. This embedded structure makes the grating more firm in its applications. High polarization efficiency and low insertion loss with a broad wavelength range (900-1700 nm) and a wide angular tolerance are obtained by optimization of the designed structure.

Angular tolerant resonant grating filters under oblique incidence

Resonant grating filters have been proposed as a promising alternative to multilayer stacks for narrowband free-space filtering. The efficiency of such filters under normal incidence has been demonstrated. Unfortunately, under oblique incidence, the limited angular tolerance of the resonance forbids any filtering applications with use of standard collimated incident beams. Using a multimode planar waveguide and a bi-atom grating, we show how to increase the angular tolerance up to the divergence of standard beams (0.2 deg) without modifying the spectral bandwidth (0.1 nm), under any oblique angle of incidence.

Process tolerance allocation in angular tolerance charting

The paper deals with the process tolerance allocation problem for manufacturing a product with angular features in two-dimensional angular tolerance charting. First, a discrete interval cost–tolerance model is investigated to represent the relationship between manufacturing cost and tolerance. Then a multichoice knapsack model is formulated to allocate systematically the best tolerance to each individual machining dimension in both radial and axial directions with the objective of minimizing the total manufacturing cost. Furthermore, a genetic algorithm is developed to obtain the optimal solution to the multichoice knapsack model. Finally, a numerical example is presented to illustrate the model and the approach developed.

Vibration measurement with a micromachined mirror in a very-short external cavity laser

We have fabricated, modeled and tested a displacement sensor based on an external cavity laser with a micro-mirror integrated with a positioning actuator. We have developed an improved model for simulating the intensity change in the external cavity laser when the feedback from the external mirror exceed 20% of the feedback from the laser facet. A special surface-micromachined mirror has been developed to obtain a very short external cavity laser ( ≈10 μ m) that allow removing all coupling optical elements in the external cavity. During testing, we could verify the theoretical prediction and achieve a large relative feedback providing a strong intensity modulation. We observed a good angular tolerance suggesting a good manufacturability of the device. The tested device has a noise floor at 5 pm/ Hz above 500 Hz. This sensor could be used as a high sensitivity acceleration sensor.

Wave Localization of Doubly Periodic Guided-mode Resonant Grating Filters

It is known that a doubly periodic guided-mode resonant grating (GMRG) filter has a broad angular selectivity with a narrow spectral bandwidth. This means that the doubly periodic GMRG filter operates for small beam diameter and grating area. This report describes the wave localization in the doubly periodic GMRG filter. We investigated the spread area of light waves in the waveguide layer and the accumulation of field energy by numerical simulation using the finite differential time domain (FDTD) method. Simulation results showed that, in the case of a doubly periodic GMRG filter with a Q factor of 600, the field energy is spread over an area 5 um in width, which corresponds to the expected value from the angular tolerance. And the magnitude of the field energy in the waveguide layer was Q factor times greater than the incident energy. On the other hand, a singly periodic GMRG filter with the same Q factor spread the field energy over an area 72 urn in width. This filter does not work for a small size structure or a small diameter light beam.

First clinical experiences with a new cervical fixation device - technical report.

In a first clinical series of ten patients the new cervical fixation device StarLock trade mark (Synthes, Umkirch, Germany) was implanted.[nl]Characteristics of the device are deep threaded screws with higher pullout resistance and a high angular tolerance while inserting the rods thus simplifying the implantation.[nl]62 lateral mass screws in ten patients were inserted. In 2 cases placement of screws was insufficient (3.2 %) because of surgical difficulties not attributable to the system technique.[nl]In all other cases a radiologically proven stabilization was created. [nl]Due to the high angular tolerance of the screw clamps bending of rods is simplified, especially in cases of longer constructs, and shortens the operation time.[nl]The design of the StarLock trade mark system allows an easy application of computer-navigated placing of transpedicular screws.[nl]This new cervical fixation device is easy to handle and simplifies rod application especially in longer constructs.

A General Expression for Bimolecular Association Rates with Orientational Constraints

We present a general expression for the association rate for partially diffusion-controlled reactions between spherical molecules with an asymmetric reactive patch on each surface. Reaction can occur only if the two patches are in contact and properly aligned to within specified angular tolerances. This extends and generalizes previous approaches that considered only axially symmetric patches; the earlier solutions are shown to be limiting cases of our general expression. Previous numerical results on the rate of protein -protein association with high steric specificity are in very good agreement with the value computed from our analytic expression. Using the new expression, we investigate the influence of orientational constraints on the rate constant. We find that for angular constraints of 5°-15°, a typical range for example in the case of protein-protein interactions, the reaction rate is about 2 to 3 orders of magnitude higher than expected from a naive geometric model.

Wavelength selectivity of on-axis surface plasmon laser filters

Excitation of surface plasmons on a metal substrate, via the attenuated total reflection method can theoretically offer preferential absorption of light at one particular wavelength, whilst reflecting the nearby spectrum. Normally this `filtering' action is limited to removal of p-polarized light, and the acceptance angle of such a filtering device is very narrow, which limits practical applications, such as separation of fundamental and laser harmonics. The possibility of avoiding this angular precision is explored by considering the complex permittivity of metal composites. By using a two or more layer structure, as opposed to a single metal substrate, the acceptance angle of the device can be broadened, by a factor of about 15 times. An example is discussed for separation of the fundamental and harmonics from a Nd : YAG laser. Variants of the structure allow the design of an in-line transmission filter for the various wavelengths with sufficient angular tolerance to include focusing lenses. Avoidance of laser ablation of the metal is discussed.

Extending the algebraic method to identify dimensional chains for angular tolerance charting

Tolerance charting, as a practical tool to determine nominal working dimensions and their tolerances for the process operations of a product, has been used in manufacturing industry for many decades. In the past years, many researchers have made great efforts on the tolerance charts for products with square-shouldered features (that is, 1D tolerance charting) and a few researchers have discussed tolerance charts for products with angular features, which are more complicated than the former. A few researchers have even presented an approach to identifying dimensional chains for angular tolerance charting. This paper proposes an algebraic method to establish dimensional chains for angular tolerance charting, which is the extension of the previous algebraic approach for 1D tolerance charting. The problems and characteristics of angular tolerance charting and the new algebraic approach are discussed. Both the forward and the reverse dimensional chains can be obtained from the algebraic method, so the nominal values and tolerances of the working dimensions can be determined. An example is presented to illustrate the method.