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Physics

1995

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Articles 1 - 30 of 356

Full-Text Articles in Physical Sciences and Mathematics

Novel Switching Phenomena In Ferroelectric Langmuir-Blodgett Films, A. Bune, Stephen Ducharme, V.M. Fridkin, L. Blinov, S. Palto, N. Petukhova, S. Yudin Dec 1995

Novel Switching Phenomena In Ferroelectric Langmuir-Blodgett Films, A. Bune, Stephen Ducharme, V.M. Fridkin, L. Blinov, S. Palto, N. Petukhova, S. Yudin

Stephen Ducharme Publications

We have established ferroelectric switching and observed a novel conductance switching phenomenon in ferroelectric polymer films fabricated by the Langmuir–Blodgett technique. The films consist of 10–30 monolayers (ML) of a copolymer of vinylidene fluoride (70%) and trifluoroethylene (30%), exhibiting a first-order ferroelectric phase transition at 70 °C and nearly rectangular ferroelectric and conductance hysteresis at 24 °C. Ferroelectric switching is accompanied by switching of the conductance by three orders of magnitude. A model describing this switching phenomenon is proposed.


Measured Stark Widths Of A 425,94 Nm Ari Spectral Line, Ljiljana Skuljan, Vladimir Milosavljevic, Aleksandar Sreckovic, Stevan Djenize Dec 1995

Measured Stark Widths Of A 425,94 Nm Ari Spectral Line, Ljiljana Skuljan, Vladimir Milosavljevic, Aleksandar Sreckovic, Stevan Djenize

Articles

No abstract provided.


Locally Optimally Emitting Clouds And The Origin Of Quasar Emission Lines, Jack Baldwin, Gary J. Ferland, Kirk Korista, Dima Verner Dec 1995

Locally Optimally Emitting Clouds And The Origin Of Quasar Emission Lines, Jack Baldwin, Gary J. Ferland, Kirk Korista, Dima Verner

Physics and Astronomy Faculty Publications

The similarity of quasar line spectra has been taken as an indication that the emission line clouds have preferred parameters, suggesting that the environment is subject to a fine-tuning process. We show here that the observed spectrum is a natural consequence of powerful selection effects. We computed a large grid of photoionization models covering the widest possible range of cloud gas density and distance from the central continuum source. For each line only a narrow range of density and distance from the continuum source results in maximum reprocessing efficiency, corresponding to "locally optimally emitting clouds" (LOCs). These parameters depend on …


Singular Vertices And The Triangulation Space Of The D-Sphere, Simon Catterall, G. Thorleifsson, John B. Kogut, R. Renken Dec 1995

Singular Vertices And The Triangulation Space Of The D-Sphere, Simon Catterall, G. Thorleifsson, John B. Kogut, R. Renken

Physics - All Scholarship

By a sequence of numerical experiments we demonstrate that generic triangulations of the D-sphere for D>3 contain one {\it singular} (D-3)-simplex. The mean number of elementary D-simplices sharing this simplex increases with the volume of the triangulation according to a simple power law. The lower dimension subsimplices associated with this (D-3)-simplex also show a singular behaviour. Possible consequences for the DT model of four-dimensional quantum gravity are discussed.


Nanoscale Oxide Patterns On Si (100) Surfaces, T. -C. Shen, C. Wang, J. W. Lyding, J. R. Tucker Dec 1995

Nanoscale Oxide Patterns On Si (100) Surfaces, T. -C. Shen, C. Wang, J. W. Lyding, J. R. Tucker

T. -C. Shen

Ultrathin oxide patterns of a linewidth of 50 Å have been created on Si(100)‐2×1 surfaces by a scanning tunneling microscope operating in ultrahigh vacuum. The oxide thickness is estimated to be 4–10 Å. The morphology and spectroscopy of the oxide region are obtained. Hydrogen passivation is used as an oxidation mask. The defects caused by oxidation in the passivated region before and after the hydrogen desorption are compared and discussed. The multistep silicon processings by an ultrahigh vacuum scanning tunneling micropscope is thus demonstrated.


Correlations Between Auditory‐Filter Shape Parameters Measured At Proximal Center Frequencies, Marc A. Fagelson, Craig A. Champlin Dec 1995

Correlations Between Auditory‐Filter Shape Parameters Measured At Proximal Center Frequencies, Marc A. Fagelson, Craig A. Champlin

Marc A. Fagelson

Auditory‐filter shape parameters in 20 normal‐hearing listeners were determined at center frequencies (CFs) of 913, 1095, 3651, and 4382 Hz using the five‐point roex (p,r) method. Slopes of the filters’ skirts were correlated for the CFs in each frequency region at both low and high stimulus levels. In the λ=1000‐Hz region, the auditory filters’ low‐frequency slopes were significantly correlated at the low and high stimulus levels, while the high‐frequency slopes were associated at the high, but not the low level. In the λ=4000‐Hz region the relationships were clearer as the low‐frequency and high‐frequency filter skirts diverged at the low level, …


Broad Ne Viii Λ744 Emission From The Quasar Pg 1148+549, Fred Hamann, Joseph C. Shields, Gary J. Ferland, Kirk T. Korista Dec 1995

Broad Ne Viii Λ744 Emission From The Quasar Pg 1148+549, Fred Hamann, Joseph C. Shields, Gary J. Ferland, Kirk T. Korista

Physics and Astronomy Faculty Publications

We discuss the probable detection of broad Ne VIII λ774 emission from the zɛ = 0.978 quasar PG 1148+549, and we use spectral synthesis calculations to study the physical conditions in the line-forming gas. The theoretical predictions and the measured line wavelength both support Ne VIII λ774 as the most likely identification.

Our calculations show that Ne VIII λ774 forms in hotter and more highly ionized gas than previously recognized in the broad emission line region. If the gas is photoionized by a standard active galactic nucleus continuum, the observed Ne VIII equivalent width, the Ne VIII/O VI flux …


The Anomalous Mössbauer Fraction Of Ferritin And Polysaccharide Iron Complex (Pic), M. E. Y. Mohie-Eldin, Richard B. Frankel, L. Gunther, G. C. Papaefthymiou Dec 1995

The Anomalous Mössbauer Fraction Of Ferritin And Polysaccharide Iron Complex (Pic), M. E. Y. Mohie-Eldin, Richard B. Frankel, L. Gunther, G. C. Papaefthymiou

Physics

Mössbauer studies of the ubiquitous protein molecule ferritin and its synthetic "biomimic" polysaccharide iron complex (PIC) exhibit an anomaly in the Mössbauer spectrum wherein the recoil free fraction f-factor has a sharp drop with respect to temperature as the temperature rises above 30 K for mammalian ferritin and 60 K for PIC. The anomaly coincides with the disappearance of hyperfine splitting, which is due to superparamagnetic relaxation above the blocking temperature. Different absorbers were used to experimentally investigate the effect of absorber thickness on the Mössbauer spectrum. The anomaly persists for thin absorbers. Also, spectra treated with FFT procedures …


Local Magnetic Properties Of Antiferromagnetic Febr2, J. Peloth, R. A. Brand, Takele Seda, M. M. Pereira De Azevedo, W. Kleeman, Ch. Binek, J. Kushauer, D. Bertrand Dec 1995

Local Magnetic Properties Of Antiferromagnetic Febr2, J. Peloth, R. A. Brand, Takele Seda, M. M. Pereira De Azevedo, W. Kleeman, Ch. Binek, J. Kushauer, D. Bertrand

Physics & Astronomy

The antiferromagnet FeBr2 has been studied by Mössbauer spectroscopy in external fields both in the metamagnetic region below the multicritical temperature TMCP and in the second-order transition region above. The local magnetization shows that the metamagnetic transition occurs by spin flips, as in simple models. However, in the second-order transition region, the local magnetization of the sublattice oriented antiparallel to the external field varies continuously but remains parallel to the c axis. This can only be understood if the external magnetic field induces strong transversal spin precession of the moments on the antiparallel sublattice. This shows that the …


Effect Of Disorder On Synchronization In Prototype 2-Dimensional Josephson Arrays, Adam S. Landsberg, Yuri Braiman, Kurt Wiesenfeld Dec 1995

Effect Of Disorder On Synchronization In Prototype 2-Dimensional Josephson Arrays, Adam S. Landsberg, Yuri Braiman, Kurt Wiesenfeld

WM Keck Science Faculty Papers

We study the effects of quenched disorder on the dynamics of two-dimensional arrays of overdamped Josephson junctions. Disorder in both the junction critical currents and resistances is considered. Analytical results for small arrays are used to identify a physical mechanism which promotes frequency locking across each row of the array, and to show that no such locking mechanism exists between rows. The intrarow locking mechanism is surprisingly strong, so that a row can tolerate large amounts of disorder before frequency locking is destroyed.


Neutron Damage In Distributed Bragg Reflectors And Microcavity Lasers, Mark A. Suriano Dec 1995

Neutron Damage In Distributed Bragg Reflectors And Microcavity Lasers, Mark A. Suriano

Theses and Dissertations

Distributed Bragg Reflectors (DBRs) grown on a gallium-arsenide substrate for a solid state mirror and a vertical cavity surface emitting laser (VCSEL) were subjected to a neutron fluence to determine the sensitivity of the DBRs. The samples were irradiated at Ohio State University's 500 kW research reactor. Relative and absolute reflectance measurements were taken before and after each irradiation over a spectral band of 530 880 µm. Relative reflectance measurements showed that the irradiation did not cause any spectral shift over seven decades of neutron fluences. The reflectivity of the DBRs decreased from their initial measurements after being irradiated. The …


Methods For Generating Quasi-Exactly Solvable Potentials, Asim Gangopadhyaya, Avinash Khare, Uday P. Sukhatme Dec 1995

Methods For Generating Quasi-Exactly Solvable Potentials, Asim Gangopadhyaya, Avinash Khare, Uday P. Sukhatme

Physics: Faculty Publications and Other Works

We describe three different methods for generating quasi-exactly solvable potentials, for which a finite number of eigenstates are analytically known. The three methods are respectively based on (i) a polynomial ansatz for wave functions; (ii) point canonical transformations; (iii) supersymmetric quantum mechanics. The methods are rather general and give considerably richer results than those available in the current literature.


Band Structure For Acoustic Waves Propagating In A Periodic Elastic Media And Impurity Modes Arising From Slab Substitutions, Abdur Rahman Dec 1995

Band Structure For Acoustic Waves Propagating In A Periodic Elastic Media And Impurity Modes Arising From Slab Substitutions, Abdur Rahman

Masters Theses

In this thesis I study the band structure for acoustic waves propagating in a one-dimensional elastic array which forms a periodic elastic system in which band gaps are opened in the frequency spectrum. Specifically, I study the single impurity problem in this system. An impurity is introduced in the system by replacing one of the acoustic slabs with a new slab of different acoustic medium or by changing the thickness of impurity slab. I study the very narrow (in frequency) impurity modes in the band gaps which are localized about the impurity sites. Then I study the frequency of impurity …


Local Magnetic Properties Of Antiferromagnetic Febr2, J. Pelloth, R.A. Brand, S. Takele, M.M. Pereira De Azevedo, Wolfman Kleemann, Christian Binek, J. Kushauer, D. Bertrand Dec 1995

Local Magnetic Properties Of Antiferromagnetic Febr2, J. Pelloth, R.A. Brand, S. Takele, M.M. Pereira De Azevedo, Wolfman Kleemann, Christian Binek, J. Kushauer, D. Bertrand

Christian Binek Publications

The antiferromagnet FeBr2 has been studied by Mössbauer spectroscopy in external fields both in the metamagnetic region below the multicritical temperature TMCP and in the second-order transition region above. The local magnetization shows that the metamagnetic transition occurs by spin flips, as in simple models. However, in the second-order transition region, the local magnetization of the sublattice oriented antiparallel to the external field varies continuously but remains parallel to the c axis. This can only be understood if the external magnetic field induces strong transversal spin precession of the moments on the antiparallel sublattice. This shows that the …


Failure Of The Optical Theorem For Gaussian-Beam Scattering By A Spherical Particle, James A. Lock, Joseph T. Hodges, Gérard Gouesbet Dec 1995

Failure Of The Optical Theorem For Gaussian-Beam Scattering By A Spherical Particle, James A. Lock, Joseph T. Hodges, Gérard Gouesbet

Physics Faculty Publications

It is shown that when an electromagnetic wave with some degree of amplitude rolloff in the transverse direction is scattered by a spherical particle, the optical theorem is not valid. For such shaped beams the extinction cross section may be written as an infinite series in powers of the reciprocal of the beam width. The imaginary part of the forward-scattering amplitude is shown to be the first term in this series. Two approximations to based on the dominance of diffraction in the forward direction for w(0) greater than or similar to a, where w(0) is the beam half-width and a …


Transitions Between Convective Patterns In Chemical Fronts, Y. Wu, D. A. Vasquez, Boyd F. Edwards, J. W. Wilder Dec 1995

Transitions Between Convective Patterns In Chemical Fronts, Y. Wu, D. A. Vasquez, Boyd F. Edwards, J. W. Wilder

All Physics Faculty Publications

We present a theory for the transition from nonaxisymmetric to axisymmetric convection in iodate-arsenous acid reaction fronts propagating in a vertical slab. The transition takes place away from the onset of convection, where a convectionless flat front becomes unstable to a nonaxisymmetric convective front. The transition is studied by numerically solving a reaction-diffusion equation coupled with nonlinear hydrodynamics in a two-dimensional slab.


Study Of The Long-Term Desorption Of Trichloroethylene From Clay Soils Using Infrared Spectroscopy, Mary P. Stager Dec 1995

Study Of The Long-Term Desorption Of Trichloroethylene From Clay Soils Using Infrared Spectroscopy, Mary P. Stager

Theses and Dissertations

Slow desorption of contaminants from soil presents one of the greatest challenges to modeling contaminant fate and transport and implementing effective remediation technologies. The kinetics of long-term desorption of trichloroethylene (TCE) from powdered clay soils were studied to determine the desorption rates and mechanism. Infrared absorption spectroscopy was used to monitor the concentration of TCE desorbed from contaminated flint clay for 71 hours. Observed gas phase TCE concentrations as a function of time were compared to that predicted by a one-site Langmuir desorption mechanism. The Langmuir model, with a single type of bonding site, did not account for the release …


Single Molecule Emission Characteristics In Near-Field Microscopy, Randy X. Bian, Robert C. Dunn, X. Sunney Xie, P.T. Leung Dec 1995

Single Molecule Emission Characteristics In Near-Field Microscopy, Randy X. Bian, Robert C. Dunn, X. Sunney Xie, P.T. Leung

Physics Faculty Publications and Presentations

In near-field scanning optical microscopy (NSOM), the measured fluorescence lifetime of a single dye molecule can be shortened or lengthened, sensitively dependent on the relative position between the molecule and aluminum coated fiber tip. The modified lifetimes and other emission characteristics are simulated by solving Maxwell equations with the finite-difference time-domain (FDTD) method. The 2D computation reveals insight into the lifetime behaviors and provides guidance for nonperturbative spectroscopic measurements with NSOM. This new methodology is capable of predicting molecular emission properties in front of a metal/dielectric interface of arbitrary geometry.


Design, Fabrication And Characterization Of Micro Opto-Electro-Mechanical Systems, Darren E. Sene Dec 1995

Design, Fabrication And Characterization Of Micro Opto-Electro-Mechanical Systems, Darren E. Sene

Theses and Dissertations

Several micro-opto-electro-mechanical structures were designed using the Multi-User MEMS Process (MUMPS). Specific design techniques were investigated for improving the capabilities of elevating flip up structures. The integration of several flip up microoptical structures into a microoptical system was explored with emphasis on the development of a microinterferometer. The thermal effects on the Modulus of Elasticity were determined by detecting the resonant frequency for a square Flexure Beam Micromirror Device. The resonance of the device was found to match theory to within 0.1 % and the Modulus of Elasticity was found to decrease by 0.041 GPa/K from 290 to 450 K. …


Two-Wavelength Neodymium Based Lasers, Scott H. Mccracken Dec 1995

Two-Wavelength Neodymium Based Lasers, Scott H. Mccracken

Theses and Dissertations

A dual wavelength Q switched laser cavity has been successfully designed and assembled to evaluate the new neodymium (Nd) based materials. Initial characterization has been achieved for Nd:YAG and Nd:YLF. The results indicate that for a fixed pulse repetition frequency, the delay time can be used to adjust the relative energy between the 1.06 and 1.32 micrometer pulses. Any deficiency in the performance of one transition can be made up by performance in the other simply by changing the relative amount of time the population inversion is allowed to build up for each pulse. The best performance was obtained using …


Experimental Investigation And Computer Modeling Of Optical Switching In Distributed Bragg Reflector And Vertical Cavity Surface Emitting Laser Structures, Richard J. Bagnell Dec 1995

Experimental Investigation And Computer Modeling Of Optical Switching In Distributed Bragg Reflector And Vertical Cavity Surface Emitting Laser Structures, Richard J. Bagnell

Theses and Dissertations

The optical switching capabilities of Distributed Bragg Reflector (DBR) structures, including Vertical Cavity Surface Emitting Lasers (VCSELs) are examined. Reflectivity switching is demonstrated using both thermal and carrier generated effects to alter the DBR/VCSEL layers' refractive indices. Optical bistability is demonstrated at room temperature, under CW photopumped excitation. The optical bistability hysteresis is controllable by spectral location of the pump on the stop band edge. In the VCSEL, reflective bistability is also evidenced; additionally, this bistability is accompanied by a bistability in the VCSEL lasing output intensity, spot size, and wavelength. Modeling of the DBR/VCSEL thermally induced bistability was accomplished …


A Monte Carlo Analysis Of Computerized Tomography, Karyl J. Davis Dec 1995

A Monte Carlo Analysis Of Computerized Tomography, Karyl J. Davis

Theses and Dissertations

The purpose of this thesis was to model a computerized tomography device (CT) using Monte Carlo methods to determine the scattered radiation spectrum inside and the dose outside the suite at Wright-Patterson Medical Center and at a generic suite to non-occupational personnel. This was driven by the recent inclusion of the most recent NCRP recommended dose limits into 10CFR20 of 50 mSv, occupational; 1 mSv; non-occupational continuous exposure; and 5 mSv, infrequent exposure. The rotating fan beam of the CT was modeled for MCNP, a general-purpose Monte Carlo n-particle transport modeL The CT target was a standard human phantom defined …


Micromirror Array Control Of A Phase-Locked Laser Diode Array, Carl J. Christensen Dec 1995

Micromirror Array Control Of A Phase-Locked Laser Diode Array, Carl J. Christensen

Theses and Dissertations

A ten element micromirror array has been designed, fabricated, and employed to control the far field irradiance pattern of a phase locked laser diode array. The laser array used in this experiment was a ten element, gain guided array lasing at a nominal wavelength of 828 nm and operating in the it out of phase supermode. The laser's near field irradiance was imaged onto a micromirror array, where the it phase differences between adjacent laser elements were corrected. This was accomplished by moving the micromirrors with individually applied voltages. The result was the desirable single lobed far field pattern, placing …


Computer-Aided Diagnosis Of Mammographic Masses, William E. Polakowski Dec 1995

Computer-Aided Diagnosis Of Mammographic Masses, William E. Polakowski

Theses and Dissertations

A new Model-Based Vision algorithm was developed to find possibly cancerous regions of interest (ROIs) in digitized mammograms and to correctly identify the malignant masses. This work has shown a sensitivity of 92 percent for locating malignant ROIs. The database contained 272 images (12 bit, 1OO microns) with 36 malignant and 53 benign mass images. Of the 53 biopsied benign cases, 74 percent were correctly classified. The Focus of Attention (segmentation) Module algorithm used a physiologically motivated Difference of Gaussians (DoG) filter to highlight mass-like regions in the mammogram. The Index Module labeled the regions by their hypothesized class: large …


Effects Of Neutron Radiation On Resonant Cavity Light-Emitting Diodes, Daniel S. Hinkel Dec 1995

Effects Of Neutron Radiation On Resonant Cavity Light-Emitting Diodes, Daniel S. Hinkel

Theses and Dissertations

Resonant Cavity Light Emitting Diodes (RCLEDs) were irradiated in Ohio State University's nuclear reactor to determine the effects of Neutron displacement damage. The RCLEDs were characterized both before and after irradiation by their current versus voltage curves (I-V curves) and external light power versus current curves (L-I curves). The I-V curves showed an increase in the "knee voltage" at a neutron fluence of 1.45x1017 neutrons/cm2. Logarithmic decreases in external light power and differential quantum efficiency were observed. Significant decreases in external light power were observed at neutron fluences greater than 5.1x1013 neutrons/cm2. Equations were developed to …


A Comparison Of Methods For Estimating Rms Error: A `Brute Force" Approach Versus A Mathematically-Elegant Approach, As Applied To The Calculation Of A Specific Retrieval Error For A Limb-Scanning Microwave Radiometer-Spectrometer, Larry L. Johnson Dec 1995

A Comparison Of Methods For Estimating Rms Error: A `Brute Force" Approach Versus A Mathematically-Elegant Approach, As Applied To The Calculation Of A Specific Retrieval Error For A Limb-Scanning Microwave Radiometer-Spectrometer, Larry L. Johnson

Theses and Dissertations

The Millimeter-wave Atmospheric Sounder (MAS) is a high resolution limb- scanning microwave radiometer-spectrometer which has been flown aboard the Space Shuttle. The instrument was designed to sense the microwave emission from several upper atmospheric constituents, including water vapor and ozone. The resonant frequencies of water vapor and ozone are extremely close (183 and 184 GHz, respectively), so that the high-frequency wing of the water vapor spectrum overlaps the low frequency wing of the ozone spectrum. Consequently, the measured ozone spectrum incorporates a slight water vapor contribution; therefore, the retrieved ozone profile is dependent on the true water vapor profile. The …


A Portable Compton Gamma-Ray Camera Design, Brian L. Evans Dec 1995

A Portable Compton Gamma-Ray Camera Design, Brian L. Evans

Theses and Dissertations

The purpose of this research is to investigate the angular resolution, efficiency, and energy resolution possible from a portable Compton camera gamma ray imaging system for possible use in the field of nuclear nonproliferation. The proposed device uses room temperature semiconductor and position sensitive scintillation detectors. The position and energy resolution (and their energy dependence) of a room temperature lithium drifted silicon (Si(Li)) detector and a position sensitive thallium -doped sodium iodide (NaI(Tl)) scintillation detector are investigated. The position and energy resolution of the position sensitive scintillation detector is also modeled computationally, and the results compared to measured data. An …


Determining The Effects Of Waste Coal Ash On Landfill Radon Levels, Richard S. Krysiak Jr. Dec 1995

Determining The Effects Of Waste Coal Ash On Landfill Radon Levels, Richard S. Krysiak Jr.

Theses and Dissertations

Coal contains trace amounts of the primary radionuclides 40K, and elements of the 4n (232Th), 4n+2 (238U), and 4n+3 (235U) series including 220Rn and 222Rn. Combustion of coal by electric power and heat plants result in concentration of noncombustible mineral matter, including most of the radionuclides, in the coal ash. The increased radiation due to the concentration of radionuclides is known as technologically enhanced natural radiation. The purpose of this research was to determine the effects of landfilled coal ash on one specific aspect of technologically enhanced natural radiation, radon levels. …


Maximum Likelihood Estimation Of Wave Front Slopes Using A Hartmann-Type Sensor, Scott A. Sallberg Dec 1995

Maximum Likelihood Estimation Of Wave Front Slopes Using A Hartmann-Type Sensor, Scott A. Sallberg

Theses and Dissertations

Current methods for estimating the wave front slope at the pupil of a telescope equipped with a Hartmann-type wave front sensor (H-WFS) are based on a simple centroid calculation of the intensity distributions (spots) recorded in each subaperture of the H-WFS. The centroid method does not include any knowledge concerning correlation properties of the slopes over the subapertures or the amount of light collected by the telescope and diverted to the H-WFS for wave front reconstruction purposes. This thesis devises a maximum likelihood (ML) estimation of the spot centroids by incorporating statistical knowledge of the spot shifts. The light level …


Characterization Of Atmospheric Turbulence Over Long Horizontal Paths Using Optical Slope Measurements, Eric E. Silbaugh Dec 1995

Characterization Of Atmospheric Turbulence Over Long Horizontal Paths Using Optical Slope Measurements, Eric E. Silbaugh

Theses and Dissertations

Atmospheric turbulence has long been recognized as one of the fundamental factors affecting optical systems operating through the atmosphere. Turbulence over vertical paths has been well characterized, both theoretically and experimentally. Much less is known about turbulence over long, horizontal paths. Perturbations of the wave front phase can be measured using a Hartmann wave front sensor (H-WFS). Theoretical expressions for the tilt removed structure function of the H-WFS slope measurements were derived and evaluated using quadrature. These slope structure functions are functions of the phase structure function. The Kolmogorov turbulence model was assumed. Simulated H-WFS slope measurements were generated using …