scholarly journals Improving Interferometry Instrumentation by Mixing Stereoscopy for 2π Ambiguity Solving

2017 ◽  
Vol 6 (2) ◽  
pp. 43-55
Author(s):  
Avi Karsenty ◽  
Yaron Lichtenstadt ◽  
Sagi Naeim ◽  
Yoel Arieli
Keyword(s):  
New Method ◽  
Phase Measurements ◽  
Wavefront Propagation ◽  
Array Detectors ◽  
Linear And Nonlinear ◽  
High Coherence

Phase measurements obtained by high-coherence interferometry are restricted by the 2π ambiguity to height differences smaller than λ/2. A further restriction considers linear and nonlinear aberrations evolving in most interferometric systems due to the CCD-type array detectors. The authors present a new method to overcome the 2π ambiguity in interferometry when using a stereoscopic approach. In this method, a reconstructed wavefront reflected from an object was propagated into two different angles to obtain two different images of the object. These two different images were subsequently processed by stereo algorithms to resolve the 2π ambiguity. Such a method of wavefront propagation may enable several applications such as focusing and resolving the 2π ambiguity, as described in the article.

scholarly journals Manipulations of Wavefront Propagation: Useful Methods and Applications for Interferometric Measurements and Scanning

Scanning ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Avi Karsenty ◽  
Eitan Novoselski ◽  
Ariel Yifrach ◽  
Emmanuel Lanzmann ◽  
Yoel Arieli
Keyword(s):  
Phase Measurements ◽  
Measured Object ◽  
Wavefront Propagation ◽  
High Coherence

Phase measurements obtained by high-coherence interferometry are restricted by the 2π ambiguity, to height differences smaller than λ/2. A further restriction in most interferometric systems is for focusing the system on the measured object. We present two methods that overcome these restrictions. In the first method, different segments of a measured wavefront are digitally propagated and focused locally after measurement. The divergent distances, by which the diverse segments of the wavefront are propagated in order to achieve a focused image, provide enough information so as to resolve the 2π ambiguity. The second method employs an interferogram obtained by a spectrum constituting a small number of wavelengths. The magnitude of the interferogram’s modulations is utilized to resolve the 2π ambiguity. Such methods of wavefront propagation enable several applications such as focusing and resolving the 2π ambiguity, as described in the article.

Correlation Study between a New Interferometric Asphere Metrology System and Fizeau Interferometer

2007 ◽  
Vol 364-366 ◽  
pp. 1142-1146 ◽  
Author(s):  
Michael F. Kuechel ◽  
Daniel M. Sykora
Keyword(s):  
Classical Problem ◽  
Normal Incidence ◽  
Absolute Measurement ◽  
Correlation Study ◽  
New Method ◽  
Optical Systems ◽  
Production Environment ◽  
Aspheric Surfaces ◽  
Phase Measurements ◽  
Commercial System

Recent developments in next generation disc technology, cameras in mobile phones, zoom-lenses for small digital cameras and camcorders, digital SLRs, and television cameras have amplified the demand for affordable optical systems with outstanding image quality, a combination that can only be achieved using aspheric surfaces. The metrology of aspheric surfaces is a classical problem, but solutions so far have not fulfilled all demands for system cost, TACT (Total Average Cycle Time), minimized tooling, measurement uncertainty, spatial resolution, robustness in a production environment and many more. Zygo Corp. presents here a new method [1,2] for measurement of rotationally symmetrical aspheric surfaces using a new commercial system, which has the potential to fulfill these industry requirements. During measurement, the surface is scanned along its symmetry axis in a Fizeau cavity with a spherical reference surface. The coordinates x,y,z at the (moving) zone of normal incidence are derived from simultaneous phase-measurements at the apex and zone. Phase-shifting Fizeau interferometry and displacement interferometry are combined in the new commercial system to realize this new method. Aspheric departure from a best-fitsphere approaching 800 microns can be measured, and absolute measurement is possible with an absolutely calibrated transmission sphere. A custom parabolic artifact is measured with conventional null Fizeau interferometry and by the new commercial system. Data is reported for each technique along with a difference map achieved by fiducialized data subtract where 32.0 nm peak-to-valley (PV) and 3.6 nm R.M.S. are achieved.

scholarly journals Using Homo-Separation of Variables for Solving Systems of Nonlinear Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Abdolamir Karbalaie ◽  
Hamed Hamid Muhammed ◽  
Bjorn-Erik Erlandsson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Separation Of Variables ◽  
General Purpose ◽  
New Method ◽  
Fractional Partial Differential Equations ◽  
Mathematical Methods ◽  
Partial Differential ◽  
Separation Of Variables Method ◽  
Linear And Nonlinear

A new method proposed and coined by the authors as the homo-separation of variables method is utilized to solve systems of linear and nonlinear fractional partial differential equations (FPDEs). The new method is a combination of two well-established mathematical methods, namely, the homotopy perturbation method (HPM) and the separation of variables method. When compared to existing analytical and numerical methods, the method resulting from our approach shows that it is capable of simplifying the target problem at hand and reducing the computational load that is required to solve it, considerably. The efficiency and usefulness of this new general-purpose method is verified by several examples, where different systems of linear and nonlinear FPDEs are solved.

A new method to analyze and understand molecular linear and nonlinear optical responses via field-induced functions: a straightforward alternative to sum-over-states (SOS) analysis

2019 ◽  
Vol 21 (11) ◽  
pp. 6274-6286 ◽  
Author(s):  
Nicolás Otero ◽  
Panaghiotis Karamanis ◽  
Marcos Mandado
Keyword(s):  
Excited State ◽  
Nonlinear Optical ◽  
New Method ◽  
Optical Responses ◽  
Linear And Nonlinear ◽  
Orbital Analysis

Using coupled-perturbed theory the same excited state/orbital analysis as the sum-over-states method may be performed.

scholarly journals A New Approximate Analytical Method for ODEs

2014 ◽  
Vol 10 (1) ◽  
pp. 19-30
Author(s):  
Hossein Aminikhah
Keyword(s):  
Exact Solution ◽  
Nonlinear System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Analytical Method ◽  
New Method ◽  
Good Stability ◽  
Linear And Nonlinear ◽  
Stability And Accuracy ◽  
Theoretical Considerations

Abstract In this paper, we propose a new algorithm for solving ordinary differential equations. We show the superiority of this algorithm by applying the new method for some famous ODEs. Theoretical considerations are discussed. The first He's polynomials have used to reach the exact solution of these problems. This method which has good stability and accuracy properties is useful in deal with linear and nonlinear system of ordinary differential equations.

Demonstration of a New, Fast Probability Integration Method for Reliability Analysis

1987 ◽  
Vol 109 (1) ◽  
pp. 24-28 ◽  
Author(s):  
Yih-Tsuen Wu
Keyword(s):  
Reliability Analysis ◽  
Integration Method ◽  
Limit State ◽  
Probability Of Failure ◽  
New Method ◽  
Limit States ◽  
Linear And Nonlinear ◽  
Accurate Probability

The performance of a new, fast probability integration method which combines an improved equivalent normal concept and a scheme for linearizing a quadratic limit state is carefully examined. The examples tested include various combinations of linear and nonlinear limit states with normal and non-normal variables; some examples are considered the worst possible cases. It is demonstrated that the new method is able to provide accurate probability-of-failure estimates for most cases and performs reasonably well when the Rackwitz-Fiessler method produces severe errors.

Bulk Modulus in Polycrystalline Inert Gas Solids at 0 K

1972 ◽  
Vol 50 (17) ◽  
pp. 2027-2032 ◽  
Author(s):  
R. A. Aziz ◽  
D. H. Bowman ◽  
C. C. Lim
Keyword(s):  
Experimental Data ◽  
Liquid Phase ◽  
Bulk Modulus ◽  
Solid Phase ◽  
New Method ◽  
Inert Gas ◽  
Saturated Liquid ◽  
Empirical Observation ◽  
Phase Measurements ◽  
Solid Density

Bulk modulus values in the inert gas solids at 0 K are of interest because they may be compared with theoretical estimates based on assumed models of the solid. Various methods have been used to estimate the 0 K bulk modulus B(0) from experimental data. In this paper we propose a new method for estimating B(0) which is based on the empirical observation that saturated liquid phase sound velocities, when extrapolated linearly in density to 0 K solid density, give results agreeing with the best solid phase measurements.

scholarly journals A new approach for solving systems of fractional differential equations via natural transform

2016 ◽  
Vol 12 (1) ◽  
pp. 5797-5804 ◽  
Author(s):  
A. S Abedl Rady ◽  
S. Z Rida ◽  
A. A. M Arafa ◽  
H. R Abedl Rahim
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Variational Iteration Method ◽  
New Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

In this paper, A new method proposed and coined by the authors as the natural variational iteration  transform method(NVITM) is utilized to solve linear and nonlinear systems of fractional differential equations. The new method is a combination of natural transform method and variational iteration method. The solutions of our modeled systems are calculated in the form of convergent power series with easily computable components. The numerical results shows that the approach is easy to implement and accurate when applied to various linear and nonlinear systems of fractional differential equations.

ADAPTIVE GENERALIZED SYNCHRONIZATION OF HYPERCHAOS SYSTEMS

2011 ◽  
Vol 25 (32) ◽  
pp. 4563-4571 ◽  
Author(s):  
XINGYUAN WANG ◽  
YAQIN WANG
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
New Method ◽  
Generalized Synchronization ◽  
Chen System ◽  
Response Systems ◽  
Hyperchaotic Lorenz System ◽  
Linear And Nonlinear ◽  
Simulation Results

This paper studies the generalized synchronization of hyperchaos systems, and a new method, by which adaptive generalized synchronization of chaotic systems with a kind of linear and nonlinear relationship between the drive and response systems can be achieved, is proposed. This new method has more extensive application scope. Based on the Lyapunov stability theory, the correctness of the proposed scheme is strictly demonstrated. It is also illustrated by applications to hyperchaotic Chen system and hyperchaotic Lorenz system and the simulation results show the effectiveness of the proposed scheme.

Sign in / Sign up

Export Citation Format

Share Document