Determination of Ratio of Complex Eigenvalues of Optical Systems with Known Eigenpolarizations by Ellipsometry

1974 ◽  
Vol 21 (6) ◽  
pp. 497-507 ◽  
Author(s):  
R.M.A. Azzam ◽  
N.M. Bashara
Keyword(s):  
Optical Systems ◽  
Complex Eigenvalues

Locating complex eigenvalues for analytical eddy-current models used to detect flaws

2019 ◽  
Vol 38 (6) ◽  
pp. 1800-1809
Author(s):  
Grzegorz Tytko ◽  
Łukasz Dawidowski
Keyword(s):  
Eddy Current ◽  
Design Methodology ◽  
Complex Function ◽  
Precise Determination ◽  
Argument Principle ◽  
Content Type ◽  
Conductive Material ◽  
Complex Roots ◽  
Complex Eigenvalues

Purpose Discrete eigenvalues occur in eddy current problems in which the solution domain was truncated on its edge. In case of conductive material with a hole, the eigenvalues are complex numbers. Their computation consists of finding complex roots of a complex function that satisfies the electromagnetic interface conditions. The purpose of this paper is to present a method of computing complex eigenvalues that are roots of such a function. Design/methodology/approach The proposed approach involves precise determination of regions in which the roots are found and applying sets of initial points, as well as the Cauchy argument principle to calculate them. Findings The elaborated algorithm was implemented in Matlab and the obtained results were verified using Newton’s method and the fsolve procedure. Both in the case of magnetic and nonmagnetic materials, such a solution was the only one that did not skip any of the eigenvalues, obtaining the results in the shortest time. Originality/value The paper presents a new effective method of locating complex eigenvalues for analytical solutions of eddy current problems containing a conductive material with a hole.

Weyl’s theory applied to predissociation by rotation. II. Determination of resonances and complex eigenvalues: Application to HgH

1976 ◽  
Vol 65 (11) ◽  
pp. 4571-4574 ◽  
Author(s):  
Michael Hehenberger ◽  
Piotr Froelich ◽  
Erkki Brändas
Keyword(s):  
Complex Eigenvalues

Increased Productivity for Redundant Laser Scanners Using an Optimal Trajectory Separation Method

2016 ◽  
Vol 10 (6) ◽  
pp. 941-949
Author(s):  
Titus Haas ◽  
◽  
Maximilian Warhanek ◽  
Michael Dietlicher ◽  
Konrad Wegener ◽  
...  
Keyword(s):  
Optimal Trajectory ◽  
Laser Scanning ◽  
Optical Systems ◽  
Scanning System ◽  
Machining Time ◽  
Dynamic Movement ◽  
Laser Scanners ◽  
Windowing Technique ◽  
Laser Scanning System

Combining an optical laser scanning system with mechanical axes in a redundant configuration and synchronised control allows the separation of scanning motions according to the strengths of the two systems. Assigning the highly dynamic movement part to the agile optical axes reduces the acceleration and jerk of the mechanical axes. The mechanical axes enable precise motion over the whole workspace, that cannot be achieved by optical systems. The determination of the ideal trajectory separation among the two redundant systems poses an optimisation problem. This study proposes a method for the calculation of the optimal trajectory separation and for productivity increases. Furthermore, a windowing technique is introduced to limit the required computational power. The operation of the optimisation algorithm is demonstrated based on example geometries. It is shown that the machining time is decreased, and the jerk of the solution is minimised. The method is verified using a laser scanning system.

scholarly journals AN IMPROVED AIR-DRIVEN TYPE OF ULTRACENTRIFUGE FOR MOLECULAR SEDIMENTATION

1937 ◽  
Vol 65 (4) ◽  
pp. 565-586 ◽  
Author(s):  
Johannes H. Bauer ◽  
Edward G. Pickels
Keyword(s):  
High Speed ◽  
Optical Systems ◽  
Centrifugal Field ◽  
Braking System ◽  
Axis Of Rotation ◽  
Protein Molecules ◽  
Transparent Cell ◽  
Definition Of ◽  
Operation Characteristics

1. A description is given of the construction details and operation characteristics of an improved type of air-driven ultracentrifuge operating in vacuum and suitable for the determination of sedimentation constants of protein molecules. 2. The rotor of the centrifuge is made of a forged aluminum alloy; it is oval in shape, measures 185 mm. at its greatest diameter, and weighs 3,430 gm. It carries a transparent cell located at a distance of 65 mm. from the axis of rotation and designed to accommodate a fluid column 15 mm. high. 3. The rotor has been run repeatedly over long periods at a speed of 60,000 R.P.M., which corresponds to a centrifugal force of 260,000 times gravity in the center of the cell. At this speed no deformation of the rotor nor leakage of the cell has been observed. 4. The sharp definition of sedimentation photographs taken at high speed serves to indicate the absence of detectable vibrations in the centrifuge. 5. When a vacuum of less than 1 micron of mercury is maintained in the centrifuge chamber, the rise in the rotor temperature amounts to only 1 or 2°C. after several hours' run at high speed. 6. There has been no evidence of convection currents interfering with normal sedimentation of protein molecules in the centrifugal field. 7. A driving air pressure of about 18 pounds per square inch is sufficient to maintain the centrifuge at a steady speed of 60,000 R.P.M. With a driving pressure of 80 pounds per square inch, it can be accelerated to this speed in less than 20 minutes, and also brought to rest in about the same length of time by the application of the braking system. 8. The adaptation of Svedberg's optical systems to this centrifuge for photographically recording the movement of sedimentation boundaries is described.

Acquisition of 3-D Optical Information

1989 ◽  
Vol 1 (4) ◽  
pp. 255-255
Author(s):  
Masanori Idesawa
Keyword(s):  
Optical Method ◽  
High Speed ◽  
Distance Measurement ◽  
Optical Systems ◽  
Target Point ◽  
Optical Information ◽  
Universal Method ◽  
Distance Information ◽  
Speed Measurement

In order for a machine to have the capacity to operate flexibly in a 3-D environment, it is indispensable for it to be equipped with space information acquisition capability, and tools for distance measurement are in turn indispensable for obtaining space information. Indeed distance measurement is basic and important not only for a robot, but also for science and technology in general. Many methods have been proposed for obtaining distance information, ranging from the mechanical contact type through optical and acoustic to electric and magnetic methods, and many are in practical use. Among them the optical method permits measurement of distance without contact and from a remote position, advantages which have led to it being widely applied. One of the most important principles for measuring distance is the triangulation principle. This permits determination of the position of an object from the distance between two observation points together with the angles in the triangle formed by these two points and a target point on the object. Based on this principle, the detection of one specific point in each of the two images obtained from two sets of image input equipment installed at two observation points permits determination of coordinate values in 3-D space. However, this extraction of the point in the second image corresponding to a specified point in the first image is a very difficult subject of study, and no universal method has been developed. To cope with this, active methods, which evade the problem by applying projection of laser light on the surface of an object to identify a bright point or bright line, are widely used. The special feature articles on obtaining 3-D optical information in this issue present some principles and new trial applications of distance acquisition methods for 3-D information, the optical method in particular. There are three reports on active method optical systems developed for robots. These include (1) a high speed measurement method applying space encoding which employs a liquid crystal lattice to project light in changing lattice patterns onto an object dynamically; (2) realization of high speed measurement through projecting and processing multiple light spots; (3) development of a visual sensor for disaster prevention use which can detect objects in flames and smoke utilizing projection of a CO2 gas laser. These are nearly at the level of operational use and are expected to become visual sensors for robots.

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