Quantitative analysis of pulsed ultrasonic beam patterns using aschlieren system

The acoustic output from pulsed ultrasonic transducers has traditionally been analyzed with a hydrophone. Recently, a new faster technique has been developed using the principles of optical diffraction. This schlieren method allows the direct two-dimensional visualization of the ultrasonic beam as a pulse train. In order to obtain quantitative information in the form of temporal-average acoustic intensity, however, tomographic reconstruction has to be performed. In this study, tomographic reconstruction was achieved by acquiring 250 images over a 180° angle. Automation of the measurement was obtained by using a frame grabber, a stepper motor, and digital delays all controlled by an IBM-compatible computer. Comparisons of the schlieren results to those obtained by a hydrophone are made in terms of both the -3 dB beamwidths and axial profiles. The results demonstrate that the schlieren method may be a more time efficient alternative for the characterization of ultrasonic transducers     

Quantitative Fourier analysis of schlieren masks: the transition from shadowgraph to schlieren

In a schlieren setup, a lens system forms an image of the refractive index fluctuations of a transparent sample onto a matrix detector while an intensity mask is positioned in the Fourier plane of a collecting lens to perform the required spatial filtering. In the absence of the mask, the resulting technique is that of a shadowgraph. The two methods provide different information about the refractive index of transparent fluids and can be used both for visualization purposes and scattering measurements. Here, we describe the effect of the intensity mask on the technique transfer function, i.e., its ability to detect different spatial frequencies and show how the special cases of shadowgraph, schlieren, and the transition between the two can be derived. We also present experimental data that agree well with our predictions.     

Modeling the influence of edge effects on refraction of a laser beam by a temperature inhomogeneity

The influence of edge effects on refraction of a laser beam in flat-layered optical inhomogeities of finite dimension is modeled. An algorithm for numerical calculation of the trajectory of a geometrical optical beam in an arbitrary two-dimensional inhomogeneous field of indices of refractions is developed. A comparison is performed with the results of a calculation of the beam for the case of a temperature inhomogeneity, taking into account edge effects and with edge effects ignored. __________ Translated from Izmeritel’naya Tekhnika, No. 7, pp. 28–31, July, 2008.     

Modeling of Thermal-Wave Fields in Radially Inhomogeneous Spherical Solids Using the Green Function Method

A theoretical model for evaluating solid multilayered spherical solids heated by a frequency-modulated light beam using the Green function method is presented. The specific thermal-wave Green function corresponding to the composite structure has been derived. The characteristics of the thermal-wave field with respect to the thermophysical, geometrical, and measurement parameters are presented. Unlike the quadrupole method, the Green function method is capable of evaluating thermal-wave fields at any point of multilayered structures with arbitrary intensity distributions of the incident laser beams. This study establishes applications of thermal-wave fields in both cylindrical and spherical samples using the Green function method and is of importance in characterizing radially inhomogeneous spherical solids.     

Focusing properties of high charge number vortex laser beams

We investigate experimentally and numerically the propagation characteristics of laser beams formed by imparting an azimuthal phase lphi to a Gaussian beam, where l is an integer. We find that when high-l beams of a finite extent are focused through a lens, the beams achieve peak intensity and are most sharply defined before and after the focal plane. Additionally, in these regions of highest intensity the effect of aberrations on the beam quality is greatly reduced, which we also demonstrate experimentally and numerically. We present a simple geometrical picture that provides excellent estimates of the beam radius and propagation distance to the plane of peak intensity.     

Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond

We describe monochromatic light propagation in uniaxial crystals by means of an exact solution of Maxwell's equations. We subsequently develop a paraxial scheme for describing a beam traveling orthogonal to the optical axis. We show that the Cartesian field components parallel and orthogonal to the optical axis are extraordinary and ordinary, respectively, and hence uncoupled. The ordinary component exhibits a standard Fresnel behavior, whereas the extraordinary one exhibits interesting anisotropic diffraction dynamics. We interpret the anisotropic diffraction as a composition of two spatial geometrical affinities and a single Fresnel propagation step. As an application, we obtain the analytical expression of the extraordinary Gaussian beam. We then derive the first nonparaxial correction to the paraxial beam, thus giving a scheme for describing slightly nonparaxial fields. We find that nonparaxiality couples the Cartesian components of the field and that the resultant longitudinal component is greater than the correction to the transverse component orthogonal to the optical axis. Finally, we derive the analytical expression for the nonparaxial correction to the paraxial Gaussian beam.     

Propagation of a partially coherent beam from an unstable resonator through turbulent atmosphere

The influence of atmospheric turbulence on the propagation of a partially coherent beam from an unstable resonator was studied numerically. The resonant mode of the unstable resonator is obtained by iterative calculation using the Huygens–Fresnel formula. Also, using the extended Huygens–Fresnel integral, the intensity distribution of a propagating laser beam is calculated for different conditions. The influence of turbulence on the profile of partially coherent beams of an unstable resonator is studied. The effects of geometrical parameters of the resonator on the far-field beam profile are investigated. The results show that an unstable resonator with higher magnification has a superior far-field beam profile under partial coherency and turbulence conditions.     

Computer simulation of schlieren images of rotationally symmetric plasma systems: a simple method

Schlieren techniques are commonly used methods for quantitative analysis of cylindrical or spherical index of refraction profiles. Many schlieren objects, however, are characterized by more complex geometries, so we have investigated the more general case of noncylindrical, rotationally symmetric distributions of index of refraction n(r,z). Assuming straight ray paths in the schlieren object we have calculated 2-D beam deviation profiles. It is shown that experimental schlieren images of the noncylindrical plasma generated by a plasma focus device can be simulated with these deviation profiles. The computer simulation allows a quantitative analysis of these schlieren images, which yields, for example, the plasma parameters, electron density, and electron density gradients.     

平顶多高斯光束通过球差透镜的聚焦特性

利用广义惠更斯-菲涅耳衍射积分公式,研究了平顶多高斯光束通过球差透镜的聚焦特性。推导出轴上光强分布的表达式,并对轴上光强进行大量的数值计算及分析。研究结果表明,当平顶多高斯光束的阶数N一定时,透镜的球差将在很大程度上影响光束的聚焦特性;当透镜的球差一定时,N值的改变将影响轴上最佳聚焦点的位置;当无球差时,轴上最佳聚焦点并不在几何焦点处,轴上最佳聚焦点位置随着N值增加向几何焦点靠近,例如当阶数N由0增大为1时,则归一化最佳聚焦点由0.91增大到0.98。     

Simulation analysis of the restraining effect of a spatial filter on a hot image

Based on the restraining effect that spatial filtering has on the frequency spectrum of a beam, from the small-scale focusing theory of Bespalov and Talanov (B-T theory) we derive an expression for the pinhole diameter of the spatial filter corresponding to the fastest growing frequency. Then, compared with the theoretical pinhole diameter of the spatial filter, the restraining effect of the spatial filter on a hot image with different pinhole diameters is numerically investigated. The numerical results show that, if the pinhole diameter is larger than the theoretical one, the hot-image intensity will remain steady; once the pinhole diameter becomes smaller than the theoretical one, the hot-image intensity will begin to decrease. Moreover, as the pinhole diameter decreases, a more prominent restraining effect can be obtained. But reducing the diameter of the spatial filter would lead to greater beam energy loss. The parameters of the spatial filter must be chosen to guarantee that the scheme fulfills the demand for low beam energy loss and a satisfactory restraining effect simultaneously.     

Phase-shifting schlieren: high-resolution quantitative schlieren that uses the phase-shifting technique principle

A quantitative autocalibrated high-resolution schlieren technique for quantitative measurement of reflective surface shape is proposed. It combines the schlieren principle with the phase-shifting technique that is generally used in interferometry. With an appropriate schlieren filter and appropriately tailored setup, some schlieren fringes are generated. After application of the phase-shift technique, the schlieren phase is calculated and converted into beam deviation values. Theoretical and experimental demonstrations are given. The technique is validated on a reference target, and then its application in a fluid physics experiment is demonstrated. These two examples show the potential of the phase-shifting schlieren technique that in some situations can become competitive with interferometry but with a much better dynamic range and with variable sensitivity. The technique can also be used to measure refractive-index gradients in transparent media.     

Optimization of the output beam homogeneity of short-pulse KrF amplifiers

The output beam of short-pulse excimer amplifiers exhibits an inhomogeneous spatial intensity distribution caused by diffraction effects at laser windows and mirrors. Theoretical and experimental studies show that the amplification parameters of a KrF amplifier can be optimized with respect to the output beam homogeneity by proper choice of the energy density in the amplifier. The homogenized intensity distribution is obtained at the plane of the output window of the amplifier and can be transferred by optical imaging onto a target plane. It is shown that the amplification parameters for the best output homogeneity are close to the ones previously found for optimal energy extraction efficiency.     

Application of bacteriorhodopsin films in an adaptive-focusing schlieren system

The photochromic property of bacteriorhodopsin films is exploited in the application of a focusing schlieren optical system for the visualization of optical phase information. By encoding an image on the film with light of one wavelength and reading out with a different wavelength, the readout beam can effectively see the photographic negative of the original image. The potential advantage of this system over previous focusing schlieren systems is that the updatable nature of the bacteriorhodopsin film allows system adaptation. I discuss two image encoding and readout techniques for the bacteriorhodopsin and use film transmission characteristics to choose the more appropriate method. I demonstrate the system principle with experimental results using argon-ion and He-Cd lasers as the two light sources of different wavelengths, and I discuss current limitations to implementation with a white-light source.     

Beam shaping of focused partially coherent beams by use of the spatial coherence effect

We demonstrate that when a partially coherent beam with a Gaussian intensity distribution is focused by a lens, the desired partially coherent flat-topped intensity distribution or doughnut-shaped intensity distribution at the geometrical focus can be generated by choice of appropriate form of spectral degree of coherence. We provide a novel approach to beam shaping of a partially coherent beam and offer new schemes for their potential applications such as material processing, optical therapy, and optical tweezers.     

Fresnel Diffraction of Gaussian Beams by a Circular Aperture in Gradient-index Media

Abstract

This work presents a method of evaluating the intensity distribution of a Gaussian beam in a weakly inhomogeneous medium when it has been truncated by a circular aperture. An analytical expression for the diffracted field is obtained in terms of Bessel functions.     

Droplet profiles obtained from the intensity distribution of refraction patterns

A noninterferometric method for obtaining profiles of axially symmetric transparent liquid droplets is described. The drops are illuminated along the symmetry axis by a uniform parallel beam whose intensity distribution is recorded at the focal plane of a lens placed behind the drop. In some conditions and within the geometrical optics approach, it is possible to reconstruct the profile of the drop from this intensity distribution except for the length scale factor, which, if necessary, may be provided by an additional simple measurement. Because of CCD cameras and digital image processing, this method is an interesting alternative technique for measuring drop profile shapes with considerable accuracy when interferometry is unwieldy. We also analyze the diffraction features of the intensity distribution to clarify the extent that they affect the approach that we used and to establish additional information that they may provide.     

涡旋光束轨道角动量在大气湍流传输下的特性分析

从拉盖尔-高斯涡旋光束表达式出发,基于瑞利衍射理论,通过研究涡旋光束在大气湍流中传输时的旋转相干函数的变化规律,总结了涡旋光束在大气湍流中传输时各轨道角动量之间的串扰情况,使用了拓扑荷数探测概率描述串扰规律,并推导了拓扑荷数探测概率的解析表达式。研究了涡旋光束通过湍流后的拓扑荷数的分布情况,并将结果与涡旋光束通过大气随机相位屏的数值仿真结果进行了对比,给出了理论与仿真的拓扑荷数的探测概率随湍流强度以及初始涡旋光束拓扑荷数大小的关系图对比,验证了推导的拓扑荷数探测概率解析表达式的正确性。通过该表达式可进一步研究大气湍流与涡旋光束相互作用从而影响涡旋光束轨道角动量散射的本质,为涡旋光束的空间光通信中选择合适的拓扑荷数间隔,以及在不同湍流强度下选择合适束腰大小以减少串扰带来的误码率提供了理论依据。     

Evolution properties of the intensity distribution of an anisotropic Gaussian Schell-model beam in a turbulent atmosphere

An analytical expression for the cross-spectral density of an anisotropic Gaussian Schell-model (AGSM) beam propagating in a turbulent atmosphere is derived, which is featured by its clear physical meaning. The evolution properties of the intensity distribution of an AGSM beam in a turbulent atmosphere are studied thoroughly. It is found that owing to the anisotropy of the source coherence, the intensity distribution can have many different evolution processes; but under the influence of the turbulent atmosphere, it will finally take on a circular shape. The effects of lowering the source coherence on the circularization speed of the intensity distribution are also investigated. It is found that, when the anisotropy of the source coherence is taken into account, lowering the source coherence can accelerate or decelerate the circularization of the intensity distribution. We propose and demonstrate five kinds of conditions, and, under each condition, lowering the source coherence has a unique and definite effect on the circularization speed of the intensity distribution. In particular, we give an analysis about the equivalence between the problem studied in one of our five conditions and that in the work of Cai and He [Appl. Phys. Lett. 89, 041117 (2006)] and show that their relevant conclusion is incorrect.     

Wigner distribution function in nonlinear optics

Transformation laws for the Wigner distribution function, the radiant intensity, the radiant emittance, and the first- and second-order moments of the Wigner distribution function through an inhomogeneous, Kerr-type medium have been derived as well as for the beam quality factor and the kurtosis parameter. It is shown that the inhomogeneous Kerr-type medium can be approximated from the Wigner-distribution-function transformation-law point of view with a symplectic ABCD matrix with elements depending on the field distribution.     

The effect of the geometrical optical phase on the propagation of Hermite-Gaussian beams through transversal and parallel dielectric blocks

When an optical beam propagates through dielectric blocks, its optical phase is responsible for the path of the beam. In particular, the first order Taylor expansion of the geometrical part reproduces the path predicted by the Snell and reflection laws whereas the first order expansion of the Fresnel phase leads to the Goos-Hänchen shift. In this paper, we analyze the effects of the second order Taylor expansion of the geometrical phase on the shape of the optical beam and show how it affects the transversal symmetry of Hermite-Gaussian beams. From the analytical expression of the transmitted beam, it is possible to determine in which transversal and parallel dielectric blocks configuration the transversal symmetry breaking is maximized or when the symmetry is recovered. We also discuss the axial spreading delay.