Wavefront Profile Research Articles

Topographic- and Wavefront-guided Customized Ablations With the NIDEK-EC5000CXII in LASIK for Myopia

To assess refractive outcomes, changes in the total higher order root mean square (RMS) aberration, and changes in higher order wavefront aberrations after LASIK for myopia and myopic astigmatism with the NIDEK Advanced Vision Excimer Laser platform (NAVEX) using either an aspheric or topography-based or whole eye wavefront ablation algorithm. This was a retrospective study of 1459 eyes that underwent LASIK for myopia and myopic astigmatism. The mean preoperative spherical equivalent refraction was -4.68 diopters (D) (range: -0.50 to -9.63 D) with astigmatism up to -4.50 D. Treatments were classified into three categories depending on the type of ablation algorithm used--optimized aspheric transition zone (OATz) denoted eyes that underwent aspheric treatment zones; customized aspheric treatment zone (CATz) denoted eyes that underwent customized ablations based on corneal topography; and OPDCAT denoted eyes that underwent customized ablation based on the whole eye wavefront profile. Follow-up data are reported at 3 months (69%) and 12 months (17%) postoperatively. Three months after LASIK, the predictability (10.5 D from target refraction) was 80% for OATz, 91% for CATz, and 76% for OPDCAT. Of all eyes, 96% were within +/- 1.0 D of intended refraction 3 months postoperatively and 100% after 12 months (87% +/- 0.5 D). In the aspheric and custom groups, a notable improvement of uncorrected visual acuity was noted between 3 and 12 months after LASIK. No eye lost >1 line of best spectacle-corrected visual acuity. Mean higher order RMS increased in all groups. The data support that the treatment of myopia and myopic astigmatism is safe and effective with NAVEX. Customized ablation based on corneal topography rather than on total wavefront error was more predictable.

Reflectivity of nonideal plasmas

New results on optical reflectance measurements of shock-compressed dense xenon plasma at wavelengths λ = 532 nm and λ = 694 nm are reported. The investigations have been performed for nonideal plasma (Γ = 0.87–2.0) at densities ρ = 0.27–3.84 g cm−3 and pressures P = 1.6–17 GPa. The obtained high optical reflectance values are characteristic of a metallic fluid and are evidence for a conducting state in the shocked xenon. Reflectance measurements at different wavelengths provide information about the density profile of the shock wave front.

Monochromatic Aberrations in Eyes With Different Intraocular Lens Optic Designs

To study the wavefront aberration profile of eyes with three different types of intraocular lenses (IOLs)--the Tecnis Z9000 (modified prolate surface design) (Pfizer, New York, NY), the Acrysof MA60BM (unequal biconvex optic) (Alcon, Ft Worth, Tex), and the Sensar Optiedge AR40e (equibiconvex optic) (AMO, Santa Ana, Calif)--in eyes following cataract surgery. This study was conducted in two parts. The first part was a randomized open study of 32 eyes of 16 patients who underwent bilateral phacoemulsification with a foldable IOL in the capsular bag. A Tecnis Z9000 IOL was implanted in one eye and an Acrysof MA60BM IOL in the fellow eye. The ALLEGRETTO WAVE Analyzer (Wavelight Laser Technologies AG, Erlangen, Germany) was used to measure ocular aberrations 2 weeks after surgery. A paired t test was used to compare each Zernike term from Z3(-3) to Z6(6) between fellow eyes (pupil diameter = 6 mm). In the second part of the study, the wavefront aberrations of 16 eyes that underwent an identical surgical procedure as in the first part of the study but had a Sensar Optiedge AR40e IOL implanted were studied and compared with eyes with the Tecnis Z9000 and Acrysof MA60BM IOLs. The mean spherical aberration (Z4(0)) was statistically significantly lower in eyes with a Tecnis Z9000 IOL (Z4(0) = 0.07 +/- 0.12 microm) compared with eyes with an Acrysof MA60BM IOL (Z4(0) = 0.29 +/- 0.20 microm, P < .001) and with eyes with a Sensar Optiedge AR40e IOL (Z4(0) = 0.20 +/- 0.09 microm, P = .002). No statistically significant differences were noted in any of the Zernike terms between eyes with Acrysof MA60BM and Sensar Optiedge AR40e IOLs, or in the root-mean-square (RMS) of total higher order aberrations among the three IOL groups. The implantation of a Tecnis Z9000 IOL produces a significant reduction in spherical aberration of the eye. No significant differences were noted in the wavefront profile between eyes with Acrysof MA60BM and Sensar Optiedge AR40e IOLs. No significant differences were found in the RMS of total higher order aberrations among the three IOL groups.

Stationary and Quasi-Stationary Waves in Even-Order Dissipative Systems

A new equation was recently suggested by Rudenko and Robsman [1] for describing the nonlinear wave propagation in scattering media that are characterized by weak sound signal attenuation proportional to the fourth power of frequency. General self-similar properties of the solutions to this equation were studied. It was shown that stationary solutions to this equation in the form of a shock wave exhibit unusual oscillations around the shock front, as distinct from the classical Burgers equation. Here, similar solutions are studied in detail for nonlinear waves in even-order dissipative media; namely, the solutions are compared for the media with absorption proportional to the second, fourth, and sixth powers of frequency. Based on the numerical results and the self-similar properties of the solutions, the fine structure of the shock front of stationary waves is studied for different absorption laws and magnitudes. It is shown that the amplitude and number of oscillations appearing in the stationary wave profile increase with increasing power of the frequency-dependent absorption term. For initial disturbances in the form of a harmonic wave and a pulse, quasi-stationary solutions are obtained at the stage of fully developed discontinuities and the evolution of the profile and width of the shock wave front is studied. It is shown that the smoothening of the shock front in the course of wave propagation is more pronounced when the absorption law is quadratic in frequency.

Bounded solutions and wavefronts for discrete dynamics

This paper deals with the second-order nonlinear difference equation δ(r kMδu k)+q kg(u k+1)=0, where { ifr k } and { q k } are positive real sequences defined on N U {0}, and the nonlinearity g: R → R is nonnegative and nontrivial. Sufficient and necessary conditions are given, for the existence of bounded solutions starting from a fixed initial condition u o . The same dynamic, with f instead of g such that uf( u) > 0 for u ≠ 0, was recently extensively investigated. On the contrary, our nonlinearity g is of a small appearance in the discrete case. Its introduction is motivated by the analysis of wavefront profiles in biological and chemical models. The paper emphasizes the many different dynamical behaviors caused by such a g with respect to the equation involving function f. Some applications in the study of wavefronts complete this work.

Frequency-dependent reflectivity of shock-compressed xenon plasmas.

Results for the reflection coefficient of shock-compressed dense xenon plasmas at pressures of 1.6-20 GPa and temperatures around 30 000 K using laser beams of wavelengths 1.06 micro m and 0.694 micro m are presented, which indicate metallic behavior at high densities. For the theoretical description of the experiments, a quantum statistical approach to the dielectric function is used. The comparison with molecular dynamics simulations is discussed. We conclude that reflectivity measurements at different wavelengths can provide information about the density profile of the shock wave front.

On the design of a tunnel-entrance hood with multiple windows

An analysis is made to determine the optimal distribution of ‘windows’ in the wall of a long tunnel-entrance hood used to suppress the micro-pressure wave produced when the compression wave generated by an entering high-speed train reaches the far end of the tunnel. An ideally designed hood causes the pressure to rise linearly across a compression wavefront of thickness equal approximately to the ratio of the hood length to the train Mach number. At moderate train Mach numbers the hood length can be assumed to be ‘acoustically compact’, and the initial form of the compression wave can then be expressed in terms of an equivalent source distribution representing the train and the compact Green's function for sources in the hood. The requirement that the wavefront profile be linear imposes certain conditions on the Green's function that permits the determination of the hood window dimensions. Our calculations take no account of the influence on compression wave formation of separated air flow over the train, from the hood portal and from the peripheries of the windows. The explicit predictions of the optimum window sizes given in this paper may therefore be too small, and should be refined by using model scale tests that allow window dimensions to be varied from their predicted optimal values to incorporate the effects of flow separation.

Oscillatory wave fronts in chains of coupled nonlinear oscillators.

Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress F: for |F|<F(cd) (dynamic Peierls stress), wave fronts fail to propagate, for F(cd)<|F|<F(cs) stable static and moving wave fronts coexist, and for |F|>F(cs) (static Peierls stress) there are only stable moving wave fronts. For piecewise linear models, extending an exact method of Atkinson and Cabrera's to chains with damped dynamics corroborates this description. For smooth nonlinearities, an approximate analytical description is found by means of the active point theory. Generically for small or zero damping, stable wave front profiles are nonmonotone and become wavy (oscillatory) in one of their tails.

Acoustic pulse in a wall-less waveguiding

The reflection of an acoustic wave from a concave cone-shaped surface leads to the formation of an intense wave propagating along the symmetry axis, with a flat front and a radial profile described by a zero-order (n=0) Bessel function of the first kind. The wave front profile retains the shape over an extended path, as if the wave would be propagating in an acoustic waveguide; the role of the waveguide walls is performed by the side energy supply. In the case of a cone-shaped reflecting surface with a spiral directrix, the radial profile of the reflected wave field corresponds to the first-kind Bessel function with n>0 and the wave propagates as if in a hollow waveguide.

6061-T6アルミニウム中を伝播する塑性衝撃波面の立ち上がり形状計測

The present paper reports observation of rising particle velocity profile of shock wave front in 6061-T6 aluminum. The elastic and plastic shock waves are generated in the present material by planer impact experiments using the single stage light gas gun that has 40mm muzzle diameter. The impact angle is also checked on using 4-pin-sensor system, and the fluctuation of particle velocity at the rear surface of target material is measured by the velocity interferometer system (VISAR). High-resolution measurements on the plastic shock wave front are carried out, and detailed experimental data that are needed for evaluating the estimating simulation of the shock wave profile are obtained.

Prolongation of the rise time of the compression wave generated by a high-speed train entering a tunnel

An analysis is made of the large–amplitude compression wave formed when a high speed train enters a tunnel whose entrance is ‘vented’ by perforations in the tunnel walls. The vents are designed to increase the rise time of the wave in order to alleviate shock formation in a long tunnel by progressive nonlinear steepening of the wavefront. The wave emerges from the far end as an impulsive ‘micro–pressure wave’, and the presence of shocks increases its propensity to cause significant structural damage and environmental annoyance. Detailed predictions are given for a ‘tunnel’ consisting of a thin–walled circular cylinder, of the type frequently used in model–scale experiments. A finite length of the cylinder entrance is perforated with an axisymmetric distribution of circular apertures. The apertures are equivalent to a distribution of sources, and it is shown that the profile of the compression wavefront can be greatly extended, so that the wave amplitude increases smoothly and linearly, by ‘shading’ the aperture distribution to make the effective source strengths approximately uniform along the perforated zone. The maximum compression wave rise time that can be obtained by this means is equal to the time of passage of the front of the train through the perforated section.

Propagation failure of traveling waves in a discrete bistable medium

Propagation failure (pinning) of traveling waves is studied in a discrete scalar reaction-diffusion equation with a piecewise linear, bistable reaction function. The critical points of the pinning transition, and the wavefront profile at the onset of propagation are calculated exactly. The scaling of the wave speed near the transition, and the leading corrections to the front shape are also determined. We find that the speed vanishes logarithmically close to the critical point, thus the model belongs to a different universality class than the standard Nagumo model, defined with a smooth, polynomial reaction function.

Application of the Hartmann method in the investigation of the profile of wavefronts of high-power pulsed lasers

The Hartmann method was used in an investigation of the wavefront profile of the infrared radiation emitted by high-power pulsed lasers. The wavefront profiles were studied for the iodine lasers used in the ISKRA-4 and ISKRA-5 facilities.

Coherent homodyne optical communication receivers with photorefractive optical beam combiners

The principles of operation and the results of performance measurements are reported of a new type of coherent optical receiver that used a dynamic volume index of refraction grating formed inside a photorefractive material to coherently combine signal and local oscillator light prior to photodetection. Because the refractive index grating is formed by the interference pattern generated where mutually coherent optical beams overlap, the receiver can automatically adjust to changes in angle of arrival or optical wavefront profiles which occur on time scales longer than the grating formation time. The grating appears stationary to high-speed phase modulation imposed on the signal beam and coherently diffracts local oscillator light into the signal beam direction. Performance measurements are reported for a prototype system that used two independent Nd:YAG lasers at 1.064 /spl mu/m, an iron-doped indium phosphide photorefractive crystal, and a four-slot phase modulation signal format. A receiver BER of 10/sup -6/ was obtained at received signal powers that corresponded to an average of 70 detected signal photons per bit at a source data rate of 50 Mb/s, 130 detected signal photons/bit at 220 Mb/s, and about 400 detected signal photons/bit at a 325 Mb/s source data rate. Quantum-limited operation corresponds to an average of six detected signal photons per transmitted information bit for this signal format.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Study of Wave Formation in Shot Sleeve of a Die Casting Machine

The objective of this study was to find the optimum process variables for minimizing the amount of air entrapped within the shot sleeve during the slow shot phase of the injection process. To achieve this objective, the relations between process variables (e.g., plunger speed/acceleration, initial filling percentage, sleeve diameter, etc.) and the wave formation within the shot sleeve of a die casting machine have to be determined. For this purpose, a mathematical model has been developed to study the transient wave formation in shot sleeve. The model based on the theory of waves of finite amplitude can predict the critical plunger speed and the profile of wave front, which in turn affect the degree of air entrapment. The optimum plunger speeds for minimum air entrapment are thus determined based on the predicted profile of wave front. Good agreement with the results from water analogue experiments is found.

A study of residual stress and the stress-optic effect in mixed crystals of K(DxH1−x)2PO4

In electro-optic applications of the mixed crystal K(DxH1−x)2PO4 (KDP-KD*P), strain-induced refractive index variations result in beam depolarization and transmitted wave-front distortion. Here the combined linear stress-optic and electro-optic effects in crystals of KDP-KD*P oriented perpendicular to the c axis are analyzed and it is shown that while the depolarization is caused by the induced birefringence, the wave-front distortion is due to average index shifts. Furthermore, the birefringence is determined by the shear stress in the xy plane of the crystal while the average index shift depends only on the normal stresses. For depolarization losses of 0.1%–1% and wave-front distortion of 0.1–1λ, the critical range of stress is 105–106 Pa. Measured depolarization loss and wave-front distortion profiles of 5, 16, and 27 cm K(DxH1−x)2PO4 crystals for 0≤x≤0.98 are also presented. Using the analysis described above it is shows that the maximum internal stresses in these crystals are within the critical range, but that the area-averaged stresses are substantially lower. It is found that crystals from different locations along the length of a boule can have similar strain birefringence and wave-front distortion profiles indicating that the growth conditions which generate the internal strain persist throughout a significant portion of the growth history of the boule. It is also observed that the most highly strained crystals come from near the seed cap. Finally, potential sources of strain in KD*P are discussed and thermodynamic and structural arguments are given which suggest that inhomogeneities in the H/D ratio are a potential source of the strain in KD*P.

Tilt sensor based on the angular dispersion of the transmission coefficient of an interface between two media

An analysis was made of the feasibility of constructing a sensor for measuring the tilt of a wavefront based on the dispersion dependence of the transmission of an interface between two transparent media on the angle of incidence. A study was made of the main characteristics of such a sensor and it was found that the threshold sensitivity in respect to the angle was determined by the power of a probe light beam and by the noise of a photodetector. Expressions were obtained for the range of the angles of incidence and for the transmission of a multibeam interferometer based on the angular dispersion of the reflection coefficient of an interface between insulators with different refractive indices. It was found that an interferometer of this type could ensure a higher sharpness of the fringes than a transverse wavefront-shearing interferometer and could be used to determine the wavefront profile.

Propagation of a Gaussian-profile laser beam in nematic liquid crystals and the structure of its nonlinear diffraction rings

We present experimental results on and a theoretical explanation of the laser- and electric-field-induced diffraction effect in both homeotropic and homogeneous nematic liquid-crystal (NLC) films. The diffraction effect is due to the Gaussian profile of a laser beam propagating in the liquid crystal. Many diffraction ring patterns under different electric and optical fields are compared and are analyzed. Some novel phenomena have been discovered. We have found that the diffraction ring pattern at a high electric field is much different from that at a low electric field. Rings in a pattern should be asymmetrical to one axis, and the outer ring interval should be wider. For the homogeneous NLC film it is possible that a second set of diffraction rings may occur when the electric field or the maximum optical field is larger than the tricritical field. The numerical result for the deformed wave-front profile of a Gaussian-profile laser beam passing through the NLC film is calculated. The results can explain these novel phenomena of diffraction ring structures.

Acoustic emission source location in bidirectionally reinforced composites, Part 2: Wavefront profile and elastic modulus correlation : Ibitolu, E.O.; Summerscales, J. Composites evaluation. Proceedings of the 2nd international conference on testing, evaluation and quality controll of composites- TEQ, 87, Guildford (United Kingdom), 22–24 Sep. 1987. pp. 128–136. Edited by J. Herriot. Butterworths, 1987

Acoustic emission source location in bidirectionally reinforced composites, Part 2: Wavefront profile and elastic modulus correlation : Ibitolu, E.O.; Summerscales, J. Composites evaluation. Proceedings of the 2nd international conference on testing, evaluation and quality controll of composites- TEQ, 87, Guildford (United Kingdom), 22–24 Sep. 1987. pp. 128–136. Edited by J. Herriot. Butterworths, 1987

Acoustic emission source location in bidirectionally reinforced composites, Part 2: Wavefront profile and elastic modulus correlation : Ibitolu, E.O.; Summerscales, J. Royal naval engineering college, Plymouth (United Kingdom), RNEC-RP-87033, 12 pp. (Sep. 1987)

Acoustic emission source location in bidirectionally reinforced composites, Part 2: Wavefront profile and elastic modulus correlation : Ibitolu, E.O.; Summerscales, J. Royal naval engineering college, Plymouth (United Kingdom), RNEC-RP-87033, 12 pp. (Sep. 1987)