Diffraction effects in the radiometry of coherent beams

High-accuracy radiometry requires an optical beam in which all the light is contained within the radius of the smallest detector to be calibrated. We analyze a common configuration of the optical components used to prepare such a beam and show that diffraction rings are formed in the far field although the irradiance is zero along the limiting aperture's edge. The beam profile is calculated and used to find the radius of the smallest detector that can be calibrated with this beam.     

Blood-flow measurements with a small number of scattering events

Results of simulations of the diffraction of a laser beam by a small blood vessel imbedded in scattering tissue are presented. The form of the spectra of biospeckle intensity fluctuations is analyzed. The Doppler shift of intensity fluctuations of scattered light is investigated as a function of the laser beam radius, the radius of the blood vessel, the depth of the vessel in the tissue, and the scattering characteristics of flowing blood. A formula that serves as the basis for a method of absolute measurements of blood-flow velocity is derived.     

Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity's integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to rho2n, where p is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n = 2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.     

Propagation characteristics of a diffracted M2 beam

The propagation characteristics of a beam diffracted by a circular aperture are investigated. The beam-quality factor M2 defined by an 86.5% power-content radius is given theoretically and experimentally as a function of the truncation ratio. It is found that the theoretical limit of M2 is 2.37 times as great as that of an incident beam as the truncation ratio approaches 0. For a weakly diffracted beam a simple formula giving M2 is derived. Although M2 does not increase much with diffraction, the influence of diffraction should be taken into account in beam brightness.     

Numerical simulation of a laser resonator with an in-phase doughnut-like output beam

A numerical model of the toric concave mirror laser resonator is founded by using the eigenvector method. Numerical calculation shows that an in-phase doughnut-like beam mode with high beam quality can be obtained in this resonator, whose diffraction loss is the lowest, and whose intensity distribution covers the whole resonator mirror. Systematical simulations indicate that, different from the spherical stable resonator, the effects of Fresnel number of the resonator and curvature radius of the toric concave total reflector on output beam quality is not very obvious. Under the condition of curvature radius of 15 m, the M ² factor of the output beam of this resonator with a large range of Fresnel number from 6.2 to 12.6 is from 1.3 to 1.9. Furthermore, the diffraction loss is close to 1.0% or less than 1.0%. Under the condition of Fresnel number of 7.07, the M ² factor of the output beam of this resonator with curvature radius from 6 to 30 m is from 1.60 to 1.24, and the diffraction loss is close to 1.0% or less than 1.0%.     

Diffraction of Gaussian beams by periodic and aperiodic rulings

The diffraction of Gaussian beams by periodic and aperiodic rulings is considered. The theory of diffraction is based on the Rayleigh-Sommerfeld integral equation with Dirichlet conditions. The transmitted power and the normally diffracted energy are analyzed as a function of the beam radius. Two methods to determine the Gaussian beam radius by means of periodic and aperiodic lamellar gratings are proposed. One is based on the maximum and the minimum transmitted power, and the other one considers the normally diffracted energy. Small and large Gaussian beam radii can be treated with these two methods.     

光干涉绝对重力仪衍射修正

针对绝对重力仪的衍射修正进行研究计算。在光干涉绝对重力仪测量原理基础上,分析并得到激光的高斯特性给重力加速度测量带来的影响。利用90/10刀口法测算激光特性参数(束腰半径),推算得到光衍射(激光的高斯特性)引入的重力加速度值相对修正量。结果表明:激光束腰半径为1.158 6 mm,使用该高斯激光束给重力加速度值引入的偏差,其相对修正量为7.56×10^-9。该方法适用于光干涉绝对重力衍射修正量的计算。     

Analytical far-field divergence angle of a truncated gaussian beam

Approximate, but accurate, analytical expressions for the far-field divergence angle of a Gaussian beam normally incident on a circular aperture are derived. A first equation is obtained based on the concept of Gaussian transform, in which the Bessel function present in the far-field diffraction integral is approximated by a Gaussian function. Refining this approach yields another simple, practical closed-form formula with such a level of accuracy that we propose that it can be used as an exact reference. All approximations hold for any combination of Gaussian beam width and aperture radius.     

Acousto-optic interaction of a Gaussian laser beam with an ultrasonic wave of cylindrical symmetry

We present experimental studies of the interaction between a narrow Gaussian laser beam and a standing cylindrical ultrasonic wave. As a theoretical approach, a Fourier-optics-based successive diffraction model is used. Depending on the ratio of the Gaussian laser beam diameter to the first nodal diameter of the cylindrical ultrasound, light refraction or diffraction is observed. We experimentally investigate the time-averaged light intensity as well as the modulation of light in the far field of light refraction-diffraction by a cylindrical ultrasound. It is revealed that significant focusing appears if the phase front of the incident light is curved. The focusing effects of the acousto-optic system depend on the width of the laser beam and curvature of the phase front. Finally, possible applications are discussed.     

Noncontact Laser Inspection Based on a PSD for the Inner Surface of Minidiameter Pipes

A new noncontact laser-inspection technique based on a position-sensitive detector (PSD) to inspect the inner surface of minidiameter pipes is proposed, and the corresponding sensor is developed. A light spot is projected onto the pipe inner wall after the laser beam is reflected by two mirrors. At the same time, four current signals are produced when the light spot is read by the 2-D PSD. According to the magnitude of the current signals and the structure parameters of the sensor, the spot position on the inner wall can be calculated in a local 3-D coordinate system. With a micromotor, the surface of the whole inner wall can be scanned by the laser beam. This way, the coordinates of all the sample points in the section are obtained. After that, several reasonable data-processing methods are used, such as data segmentation and least squares fitting. Finally, the section curve can be reconstructed. The radius and defects of the section can also be obtained. Driven by a micropipe robot, the sensor can inspect a long curved pipe. The inspection system based on this technique can detect the inner surface of minidiameter pipes, which has an inner diameter of 9.5–10.5 mm and a curvature radius of more than 100 mm. The measurement accuracy of this inspection system for the inner diameter and surface defect reaches $pm$0.1 mm.      

Formation of a sub-wavelength longitudinally polarized beam using a radially polarized controllable dark-hollow beam

On the basis of vector diffraction theory, the tightly focusing properties of radially polarized controllable dark-hollow (CDH) beams are examined theoretically. Calculation results demonstrate that by choosing the initial parameters of the proposed light beams suitably, a sub-wavelength (0.422λ) longitudinally polarized light beam with high beam quality (82.2%) can be formed without any filters. Meanwhile, we find that a relatively long depth of focus benefits from larger beam order. The dependence of the focal spot size on the parameters such as truncation parameter, variation constant, and beam order is also explored in detail. Moreover, an alternative method to generate the CDH beams is proposed.     

Apodizing of an achromatic lens by a gray-glass negative lens element

The apodizing performance of a plano-concave lens made of gray glass was analyzed numerically. It was found that apodizing performance depends solely on the edge transmittance of the lens (a zero center thickness is assumed here) for any reasonable ratio of radius of curvature of the concave surface and the lens radius. If a modest increase in the size of the central diffraction peak and light losses introduced by such a lens can be accepted, it is possible to reduce energy diffracted into diffraction rings approximately tenfold.     

低合金超高强度钢HC950LA典型零件应用及回弹控制

目的以低合金超高强度钢HC950LA为对象,研究其在汽车座椅滑轨零件上的典型应用及回弹控制。方法通过V弯试验分析HC950LA在不同弯曲角度下的最小弯曲半径,根据试验结果优化滑轨零件折弯圆角设计,使HC950LA满足滑轨零件的成形性要求,并通过试制滑轨零件,在成形过程中研究回弹控制进行方法。结果 HC950LA沿着垂直于轧制方向的折弯性能较好,成形模具半径可以小至1 mm,满足滑轨零件成形需求。使用HC950LA试制座椅滑轨零件,通过优化产品折弯圆角设计、模具型面调整及改变零件弯曲时的应力分布状态对零件进行回弹控制,零件回弹控制效果明显。结论低合金超高强度钢HC950LA冲压座椅滑轨零件成形性良好,满足零件精度、性能要求。     

Transverse intensity distributions of a broadband laser modulated by a hard-edged aperture

By means of the Huygens-Fresnel diffraction integral, the field representation of a laser beam modulated by a hard-edged aperture is derived. The near-field and far-field transverse intensity distributions of the beams with different bandwidths are analyzed by using the representation. The numerical calculation results indicate that the amplitudes and numbers of the intensity spikes decrease with increasing bandwidth, and beam smoothing is achieved when the bandwidth takes a certain value in the near field. In the far field, the radius of the transverse intensity distribution decreases as the bandwidth increases, and the physical explanation of this fact is also given.     

Transverse superresolution technique involving rectified Laguerre-Gaussian LG(p)⁰ beams

A promising technique has been proposed recently [Opt. Commun. 284, 1331 (2011), Opt. Commun. 284, 4107 (2011)] for breaking the diffraction limit of light. This technique consists of transforming a symmetrical Laguerre-Gaussian LG(p)? beam into a near-Gaussian beam at the focal plane of a thin converging lens thanks to a binary diffractive optical element (DOE) having a transmittance alternatively equal to -1 or +1, transversely. The effect of the DOE is to convert the alternately out-of-phase rings of the LG(p)? beam into a unified phase front. The benefits of the rectified beam at the lens focal plane are a short Rayleigh range, which is very useful for many laser applications, and a focal volume much smaller than that obtained with a Gaussian beam. In this paper, we demonstrate numerically that the central lobe's radius of the rectified beam at the lens focal plane depends exclusively on the dimensionless radial intensity vanishing factor of the incident beam. Consequently, this value can be easily predicted.     

Novelty filter that uses a bacteriorhodopsin film

We propose a new novelty optical filter that uses a bacteriorhodopsin film. This filter is based on the time-dependent nonlinear diffraction efficiency of real-time holograms recorded in the film. As soon as the signal beam carrying a pattern is diffracted by the polarization hologram recorded in the bacteriorhodopsin film, it begins to erase the hologram and suppresses the diffraction of the beam at the position of the stationary part of the pattern. This filter enhances only leading edges of moving patterns. In this system undesired scattered light, which is orthogonally polarized to the diffracted beam, is discriminated by a polarizer.     

Smallest flattop focus by polarization engineering

Spatial engineering of polarization as a new method of beam shaping is analyzed by using scalar diffraction theory. For the one-dimensional case, it is shown that the smallest flattop far-field distribution can be obtained by adopting a linear polarization that changes direction as a linear function of location in the pupil plane. The resulting light field is functionally equivalent to a cosinusoidal function modulation of the wavefront but maintains high efficiency. This polarization beam shaping technique proves to be highly useful in applications where diffraction effects need to be taken into account. The extension of this technique to two-dimensional beam shaping is also demonstrated.     

Light coupling into an optical microcantilever by an embedded diffraction grating

By measuring the excitation efficiency of an optical waveguide on a diffraction grating one can accurately register the changes in the incidence angle of the exciting light beam. This phenomenon was applied to detect ultrasmall deflections of silicon dioxide cantilevers of submicrometer thickness that were fabricated with corrugation on top to act as diffraction grating couplers. The power of light coupled into the cantilevers was monitored with a conventional photodetector and modulated using mechanical vibration of the cantilever, thus changing the spatial orientation of the coupler with respect to the incident light beam. The technique can be considered as an alternative to the methods known for detection of cantilever deflection.     

Polarization-dependent diffraction efficiency of a photorefractive volume grating and suppression of this efficiency

In terms of refractive-index ellipsoid of a uniaxial crystal, the relationship between the diffraction efficiency of a volume grating and the polarization state of a readout beam is theoretically analyzed. The direction of a refractive light beam and the corresponding refractive-index modulation will both be changed by a variation of the polarization state. In the polarization state of the readout beam, which may lead to a strong variation in the diffraction efficiency of the volume grating. This kind of polarization-dependent diffraction efficiency of a volume grating in an anisotropic crystal is extremely disadvantageous for some applications. A method to suppress the polarization-dependent diffraction efficiency by use of double volume gratings is presented, and experiments with LiNbO3:Fe crystal are also demonstrated. The experimental results indicate that this method can well suppress the polarization-dependent diffraction efficiency of a volume grating. Furthermore, the diffraction properties of the double volume gratings are almost independent of the polarization state of the readout beam. The relative values of the diffraction peaks are calculated on the basis of the relationship between index modulation and the state of polarization. The experimental values are in good agreement with the theoretical analyses.