Wave Height Measurements Behind Submerged Lens-Shaped Structures

2011 ◽  
Author(s):  
Andrew L. Bloxom ◽  
Karl D. von Ellenrieder ◽  
Matthew R. Anderson ◽  
Ryan S. Mieras ◽  
William S. Weidle
Keyword(s):  
Wave Height ◽  
Focal Point ◽  
Focal Length ◽  
Experimental Tests ◽  
Geometrical Optics ◽  
Width Ratio ◽  
Focal Points ◽  
Wave Amplification ◽  
Strip Theory ◽  
Longitudinal Position

The ability of submerged lens-shaped structures to focus linear surface waves in deep water is explored through a series of experimental tests in a wave making basin. Three lenses were designed using a combination of linear strip theory and a surface wave analogy to geometrical optics. Two of these lenses were designed to focus waves of a single wavelength of 0.482 m (18.97 in.), one with a focal length to lens width ratio (f-number) of 2.0 and the other with an f-number of 0.5. The third lens was designed to function as a compound lens that could focus a range of wavelengths of between 0.39 m (15.37 in.) and 0.694 m (27.32 in.) at an f-number of 2.0. Using resistance wave height gauges, the sensitivity of wave height at the focus to variations in wavelength from between 0.39 m (15.37 in.) to 0.61 m (24.01 in.) was experimentally measured for all three lenses; the sensitivity of wave height at the focus to variations of lens depths of submergence spanning the range of between 0.75 to 1.25 times the design submergence depth was also explored for the two simple lenses. It was found that the linear strip theory and geometrical optics approach predicted the wave amplification to within ten percent at the design wavelengths and depths, but that the longitudinal position of the experimentally observed focal lengths differed substantially from that expected, by as much as a factor of 2.2 for an f-number of 0.5. Additionally, while the theory predicted a single focal point for each lens, multiple focal points were found to exist behind the compound lens.

Electrostatic optics and aberration correction in the 1940s and today

1992 ◽  
Vol 50 (1) ◽  
pp. 6-7
Author(s):  
Gertrude F. Rempfer
Keyword(s):  
Electron Microscope ◽  
Focal Point ◽  
Focal Length ◽  
High Vacuum ◽  
Electron Optics ◽  
Applied Physics ◽  
Electrostatic Lenses ◽  
Commercial Instrument ◽  
The University ◽  
Theory And Experiment

I became involved in electron optics in early 1945, when my husband Robert and I were hired by the Farrand Optical Company. My husband had a mathematics Ph.D.; my degree was in physics. My main responsibilities were connected with the development of an electrostatic electron microscope. Fortunately, my thesis research on thermionic and field emission, in the late 1930s under the direction of Professor Joseph E. Henderson at the University of Washington, provided a foundation for dealing with electron beams, high vacuum, and high voltage.At the Farrand Company my co-workers and I used an electron-optical bench to carry out an extensive series of tests on three-electrode electrostatic lenses, as a function of geometrical and voltage parameters. Our studies enabled us to select optimum designs for the lenses in the electron microscope. We early on discovered that, in general, electron lenses are not “thin” lenses, and that aberrations of focal point and aberrations of focal length are not the same. I found electron optics to be an intriguing blend of theory and experiment. A laboratory version of the electron microscope was built and tested, and a report was given at the December 1947 EMSA meeting. The micrograph in fig. 1 is one of several which were presented at the meeting. This micrograph also appeared on the cover of the January 1949 issue of Journal of Applied Physics. These were exciting times in electron microscopy; it seemed that almost everything that happened was new. Our opportunities to publish were limited to patents because Mr. Farrand envisaged a commercial instrument. Regrettably, a commercial version of our laboratory microscope was not produced.

KNOT POINTS IN TWO-DIMENSIONAL MAPS AND RELATED PROPERTIES

2009 ◽  
Vol 19 (02) ◽  
pp. 545-555 ◽  
Author(s):  
F. TRAMONTANA ◽  
L. GARDINI ◽  
D. FOURNIER-PRUNARET ◽  
P. CHARGE
Keyword(s):  
Focal Point ◽  
Singular Line ◽  
Two Dimensional ◽  
Focal Points ◽  
Singular Set ◽  
One Dimensional ◽  
Attracting Set ◽  
Straight Line ◽  
Special Character ◽  
Stable And Unstable Sets

We consider the class of two-dimensional maps of the plane for which there exists a whole one-dimensional singular set (for example, a straight line) that is mapped into one point, called a "knot point" of the map. The special character of this kind of point has been already observed in maps of this class with at least one of the inverses having a vanishing denominator. In that framework, a knot is the so-called focal point of the inverse map (it is the same point). In this paper, we show that knots may also exist in other families of maps, not related to an inverse having values going to infinity. Some particular properties related to focal points persist, such as the existence of a "point to slope" correspondence between the points of the singular line and the slopes in the knot, lobes issuing from the knot point and loops in infinitely many points of an attracting set or in invariant stable and unstable sets.

scholarly journals Implementation and Optimization of a Dual-confocal Autofocusing System

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3479
Author(s):  
Chia-Ming Jan ◽  
Chien-Sheng Liu ◽  
Jyun-Yi Yang
Keyword(s):  
Focal Point ◽  
Focal Length ◽  
Characteristic Curve ◽  
Polynomial Equation ◽  
Systematic Design ◽  
Focal Position ◽  
Exact Position ◽  
Time Position ◽  
Major Factors ◽  
Auto Focusing

This paper describes the implementation and optimization of a dual-confocal autofocusing system that can easily describe a real-time position by measuring the response signal (i.e., intensity) of the front and the rear focal points of the system. This is a new and systematic design strategy that would make it possible to use this system for other applications while retrieving their characteristic curves experimentally; there is even a good chance of this technique becoming the gold standard for optimizing these dual-confocal configurations. We adopt two indexes to predict our system performance and discover that the rear focal position and its physical design are major factors. A laboratory-built prototype was constructed and demonstrated to ensure that its optimization was valid. The experimental results showed that a total optical difference from 150 to 400 mm significantly affected the effective volume of our designed autofocusing system. The results also showed that the sensitivity of the dual-confocal autofocusing system is affected more by the position of the rear focal point than the position of the front focal point. The final optimizing setup indicated that the rear focal length and the front focal length should be set at 200 and 100 mm, respectively. In addition, the characteristic curve between the focus error signal and its position could successfully define the exact position by a polynomial equation of the sixth order, meaning that the system can be straightforwardly applied to an accurate micro-optical auto-focusing system.

Determination of Geometric Distortions in Automotive Lamps Using Non-Linear Parametric Estimations

2002 ◽  
Author(s):  
Asad A. Usman ◽  
Mohammad Usman
Keyword(s):  
Motor Vehicle ◽  
Focal Point ◽  
Focal Length ◽  
Parametric Estimation ◽  
Geometric Distortions ◽  
Reflected Light ◽  
Non Linear ◽  
Gauss Method ◽  
Reflector Geometry

In automotive lamps, an ideal paraboloid is the reflector shape of choice when lens optics is utilized. However, geometric distortions occur among manufactured automotive lamps. This paper discusses the effects of geometric distortions on spread, packing, and gradient of reflected light from automotive lamps. Relevant legal requirements set by Federal Motor Vehicle Safety Standard on the performance of automotive lamps are also discussed. A new parametric mathematical model is developed to represent the geometry of an ideal lamp reflector. A non-linear parametric estimation problem is formulated using the Box-Kanemasu modification of the Gauss method. An application of methodology is also presented in this paper. The results show significant distortions of paraboloidal reflector with respect to the ideal design-intent reflector geometry. The numerically calculated deviations of focal point, focal length and paraboloidal axis from the ideally designed reflector necessitate improvements in the tooling and the manufacturing process for better dimensional control.

scholarly journals Investigation of tribo-mechanical properties and structure of specimens obtained by selective laser melting of stainless steel powders

2018 ◽  
Vol 207 ◽  
pp. 03015
Author(s):  
Leonid Belyaev ◽  
Aleksey Zhdanov ◽  
Valentin Morozov
Keyword(s):  
Stainless Steel ◽  
Focal Point ◽  
Radiation Power ◽  
Focal Length ◽  
Selective Laser Sintering ◽  
Three Dimensional ◽  
Steel Powder ◽  
Hardness Measurement ◽  
Quality Parameters ◽  
Length Range

The article presents experimental data about the quality parameters of the stainless steel three-dimensional parts obtained by the selective laser sintering procedure. The results of the porosity, tribological properties, tensile test, hardness measurement and density for different values of the focal point position during the engineering process of the three-dimensional parts sintering were given. For parts made from steel powder CL20ES at a laser radiation power of 200 W in a different focal length range, it is demonstrate that the specimens with the highest density and microhardness values are obtained during the synthesis by using a converging laser beam.

Comparative Study of Some Fiber-Optic Remote Raman Probe Designs. Part II: Tests of Single-Fiber, Lensed, and Flat- and Bevel-Tip Multi-Fiber Probes

1996 ◽  
Vol 50 (7) ◽  
pp. 849-860 ◽  
Author(s):  
Thomas F. Cooney ◽  
H. Trey Skinner ◽  
S. M. Angel
Keyword(s):  
Fiber Optic ◽  
Focal Point ◽  
Focal Length ◽  
Numerical Aperture ◽  
Optical Filters ◽  
Organic Liquids ◽  
Raman Signal ◽  
Immersion Medium ◽  
Lens Focal Length ◽  
Overlap Model

We compare relative performances of flat-tipped, beveled (two-fiber and six-around-one), and single-lensed focused fiber-optic Raman probes and, where feasible, evaluate the utility of optical filters for reducing fiber background. The sensitivity profile of each probe is determined by measuring the relative intensity of light backscattered off a flat surface as a function of distance from the probe tip. The experimental results are compared with a simple light-cone-overlap model incorporating fiber numerical aperture, fiber and immersion medium refractive indices, separation between excitation and collection fibers, number of fibers, and fiber bevel angle and/or lens focal length. The model and sensitivity profiles are used to interpret the sampling regions for Raman spectra obtained by using each of the probes with a clear, transparent sample (single-crystal sparry calcite), a white, partially transparent sample (acetaminophen tablet), and a set of organic liquids of varying refractive index. The sensitivity of the tested commercial lensed probe drops off symmetrically about the focal point. For both solid samples, the intensity of fiber background follows a profile determined primarily by laser backscattering off the surface, whereas the sample Raman signal follows a profile dependent upon sampling depth.

Numerical Simulation of Tsunami Run-Up and Inundation for the 2011 Tōhuku-Oki Tsunami: A Parametric Analysis for Tsunami Run-Up and Wave Height

2014 ◽  
Author(s):  
Debashis Basu ◽  
Robert Sewell ◽  
Kaushik Das ◽  
Ron Janetzke ◽  
Biswajit Dasgupta ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Wave Height ◽  
Seismic Waves ◽  
Source Model ◽  
Tsunami Source ◽  
Computational Framework ◽  
Wave Amplification ◽  
Source Models ◽  
Run Up ◽  
Tsunami Run Up

This paper presents computational results for predicting earthquake-generated tsunami from a developed integrated computational framework. The computational framework encompasses the entire spectrum of modeling the earthquake-generated tsunami source, open-sea wave propagation, and wave run-up including inundation and on-shore effects. The present work develops a simplified source model based on pertinent local geologic and tectonic processes, observed seismic data (i.e., data obtained by inversion of seismic waves from seismographic measurements), and geodetic data (i.e., directly measured seafloor and land deformations). These source models estimated configurations of seafloor deformation used as initial waveforms in tsunami simulations. Together with sufficiently accurate and resolved bathymetric and topographic data, they provided the inputs needed to numerically simulate tsunami wave propagation, inundation and coastal impact. The present work systematically analyzes the effect of the tsunami source model on predicted tsunami behavior and the associated variability for the 2011 Tōhuku-Oki tsunami. Simulations were carried out for the 2011 Tōhuku -Oki Tsunami that took place on March 11, 2011, from an MW 9.1 earthquake. The numerical simulations were performed using the fully nonlinear Boussinesq hydrodynamics code, FUNWAVE-TVD (distributed by the University of Delaware). In addition, a sensitivity analysis was also carried out to study the effect of earthquake magnitude on the predicted wave height. The effect of coastal structure on the wave amplification at the shore is also studied. Simulated tsunami results for wave heights are compared to the available observational data from GPS (Global Positioning System) at the central Miyagi location.

Price Ceilings as Focal Points for Tacit Collusion: Evidence from Credit Cards

2003 ◽  
Vol 93 (5) ◽  
pp. 1703-1729 ◽  
Author(s):  
Christopher R Knittel ◽  
Victor Stango
Keyword(s):  
Credit Card ◽  
Focal Point ◽  
Credit Cards ◽  
State Level ◽  
Tacit Collusion ◽  
Focal Points ◽  
National Integration ◽  
Credit Card Market ◽  
Using Data ◽  
Perverse Effect

We test whether a nonbinding price ceiling may serve as a focal point for tacit collusion, using data from the credit card market during the 1980’s. Our empirical model can distinguish instances when firms match a binding ceiling from instances when firms tacitly collude at a nonbinding ceiling. The results suggest that tacit collusion at nonbinding state-level ceilings was prevalent during the early 1980’s, but that national integration of the market reduced the sustainability of tacit collusion by the end of the decade. The results highlight a perverse effect of price regulation.

scholarly journals On Some Properties of Focal Points

2009 ◽  
Vol 2009 ◽  
pp. 1-11
Author(s):  
M. R. Ferchichi ◽  
I. Djellit
Keyword(s):  
Fixed Point ◽  
Focal Point ◽  
Two Dimensional ◽  
Focal Points ◽  
Dynamical Properties

We consider some dynamical properties of two-dimensional maps having an inverse with vanishing denominator. We put in evidence a link between a fixed point of a map with fractional inverse and a focal point of this inverse.

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