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.     

Encircled energy for systems with truncated-Gaussian apertures of different Fresnel numbers. II. Maximizing beam energy concentration on a target

In Part I of this study [J. Opt. Soc. Am. A24, 2023 (2007)] the Q(2n) functions of E. Wolf and the Y(n) functions of H. H. Hopkins have been generalized for evaluating the fraction of the total energy in systems with focused truncated Gaussian beams by apertures of different Fresnel numbers and different ratios of aperture radius to beam radius. The generalized special functions provide a mathematical basis for a rigorous study of maximizing beam energy concentration on a target. This subject is addressed under two subtitles: (1) active focusing of a Gaussian beam onto a distant target and (2) optimizing photodetection in a focused field.     

Geometrical analysis of an optical fiber bundle displacement sensor

The performance of a multifiber optical lever was geometrically analyzed by extending the Cook and Hamm model [Appl. Opt. 34, 5854-5860 (1995)] for a basic seven-fiber optical lever. The generalized relationships between sensitivity and the displacement detection limit to the fiber core radius, illumination irradiance, and coupling angle were obtained by analyses of three various types of light source, i.e., a parallel beam light source, an infinite plane light source, and a point light source. The analysis of the point light source was confirmed by a measurement that used the light source of a light-emitting diode. The sensitivity of the fiber-optic lever is inversely proportional to the fiber core radius, whereas the receiving light power is proportional to the number of illuminating and receiving fibers. Thus, the bundling of the finer fiber with the larger number of illuminating and receiving fibers is more effective for improving sensitivity and the displacement detection limit.     

Approximate method for the generalized M2 factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams

On the basis of the truncated second-order moments method in the cylindrical coordinate systems and the expansion of the hard-edged aperture function into a finite sum of complex Gaussian functions, an approximate method used to calculate the generalized beam propagation factor (M2 factor) is proposed. The approximate analytical expressions of the generalized M2 factor for rotationally symmetric hard-edged diffracted flattened Gaussian beams defined by Gori [Opt. Commun. 107, 335 (1994)] and Li [Opt. Lett. 27, 1007 (2002)] are derived, respectively; we show that it depends on the beam order N and the beam truncation parameter delta. Some typical numerical examples are given to illustrate its applications that we compare by using the obtained analytical method and the numerical integration method.     

Normal vector method for convergence improvement using the RCWA for crossed gratings

The rigorous coupled wave analysis (RCWA) is a widely used method for simulating diffraction from periodic structures. Since its recognized formulation by Moharam [J. Opt. Soc. Am. A12, 1068 and 1077 (1995)], there still has been a discussion about convergence problems. Those problems are more or less solved for the diffraction from line gratings, but there remain different concurrent proposals about the convergence improvement for crossed gratings. We propose to combine Popov and Nevière's formulation of the differential method [Light Propagation in Periodic Media (Dekker, 2003) and J. Opt. Soc. Am. A18, 2886 (2001)] with the classical RCWA. With a suitable choice of a normal vector field we obtain a better convergence than for the formulations that are known from the literature.     

Time-resolved laser-induced incandescence of soot: the influence of experimental factors and microphysical mechanisms

We present a data set for testing models of time-resolved laser-induced incandescence of soot. Measurements were made in a laminar ethene diffusion flame over a wide range of laser fluences at 532 nm. The laser was seeded to provide a smooth temporal profile, and the beam was spatially filtered and imaged into the flame to provide a homogeneous spatial profile. The particle incandescence was imaged onto a fast photodiode. The measurements are compared with the standard Melton model [Appl. Opt. 23,2201 (1984)] and with a new model that incorporates physical mechanisms not included in the Melton model.     

Nonparaxial fields with maximum joint spatial-directional localization. I. Scalar case

In paraxial optics, the spatial and angular localization of a beam are usually characterized through second moments in intensity. For these measures, Gaussian beams have the property of achieving a minimum angular spread for a given spatial spread (or beam waist). For wide-angle fields, however, the standard measures of spatial and angular localization become inappropriate, and new definitions must be used. Previously proposed definitions [J. Opt. Soc. Am. A 17, 2391 (2000)] are adopted, and the scalar monochromatic wave fields that achieve a minimum angular spread for a given spatial spread are found.     

Rayleigh scattering limits for low-level bidirectional reflectance distribution function measurements: corrigendum.

In previous research [C. C. Asmail et al. Appl. Opt. 33, 6084-6091 (1994)] an estimate was given of the low-level bidirectional reflectance distribution function (BRDF) limit due to Rayleigh scattering from the air molecules within the detector field of view. Although the underlying model was correct, a fault in the derivation led to a conclusion that contains an erroneous angular factor. A cosine factor in the equivalent BRDF derived by Asmail et al. [Appl. Opt. 33, 6084-6091 (1994)], which was considered unphysical in that treatment, is incorrect and can obscure the correction in certain circumstances. The treatment below calculates the scattered flux from the gas molecules in the field of view and compares it with the flux scattered from a sample in the same incident beam.     

Polarization properties and fractional-power analysis of coated and uncoated parallel-slab multireflection beam splitters

The polarization properties of coated and uncoated parallel-slab multireflection beam splitters are investigated. In a recent study [Opt. Lett. 21, 1709 (1996)] it was shown that the parallel-slab beam splitter is a basic optical component of the parallel-slab division-of-amplitude photopolarimeter. The ellipsometric parameters and the fractional powers for multireflected components generated by this system are analyzed. Interesting new observations with respect to the polarization properties at the Brewster angle of incidence and the distribution of powers among the multireflected components are presented.     

Expansion of an arbitrarily oriented, located, and shaped beam in spheroidal coordinates

Within the framework of the generalized Lorenz-Mie theory (GLMT), the incident shaped beam of an arbitrary orientation and location is expanded in terms of the spheroidal vector wave functions in given spheroidal coordinates. The beam shape coefficients (BSCs) in spheroidal coordinates are computed by the quadrature method. The classical localization approximation method for BSC evaluation is found to be inapplicable when the Cartesian coordinates of the beam and the particle are not parallel to each other. Once they are parallel, all the symmetry relationships existing for the BSCs in spherical coordinates (spherical BSCs) [J. Opt. Soc. Am. A11, 1812 (1994)] still pertain to the BSCs in spheroidal coordinates (spheroidal BSCs). In addition, the spheroidal BSCs computed by our method are verified by comparing them with those evaluated by Asano and Yamamoto for plane wave incidence [Appl. Opt.14, 29 (1975)]. Furthermore, formulas are given for field reconstruction from the spheroidal BSCs, and consistency is found between the original incident fields and the reconstructed ones.     

Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam

The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by a collimated plane wave [J. Opt. Soc. Am A 19, 1537 (2002)], but also by an elliptic and astigmatic Gaussian beam when two different fractional orders are considered. Simulations and experimental results are presented.     

Effects of misestimated far-end boundary values on two common lidar inversion solutions

Solutions of the lidar equation in both the Klett [Appl. Opt. 20, 211 (1981)] and the Fernald [Appl. Opt. 23, 652 (1984)] approaches include the effect of errors in the estimated boundary value at the far end. In the present study an attempt is made to formulate the effect of the error in the boundary value on the solution of the lidar equation. Using a modified extinction coefficient, we can simplify and unify the error expression of the lidar inversion solution. From the unified error expression and numerical experiments, we found that (a) in the case of overestimation of the boundary value, the discrepancy between the estimated value and the real value decreases near the lidar more rapidly than in the case of underestimation; and (b) the error for the Fernald solution converges to zero more rapidly than the error for the Klett solution, but the convergence of the Fernald solution sometimes shows oscillatory behavior, whereas the convergence of the Klett solution is always monotonic.     

Generalized in-line digital holographic technique based on intensity measurements at two different planes

In-line digital holography based on two-intensity measurements [Zhang Opt. Lett. 29, 1787 (2004)], is modified by introducing a pi shifting in the reference phase. Such an improvement avoids the assumption that the object beam must be much weaker than the reference beam in strength and results in a simplified experimental implementation. Computer simulations and optical experiments are carried out to validate the method, which we refer to as position-phase-shifting digital holography.     

Aberration correction in an adaptive free-space optical interconnect with an error diffusion algorithm

Aberration correction within a free-space optical interconnect based on a spatial light modulator for beam steering and holographic wavefront correction is presented. The wavefront sensing technique is based on an extension of a modal wavefront sensor described by Neil et al. [J. Opt. Soc. Am. A 17, 1098 (2000)], which uses a diffractive element. In this analysis such a wavefront sensor is adapted with an error diffusion algorithm that yields a low reconstruction error and fast reconfigurability. Improvement of the beam propagation quality (Strehl ratio) for different channels across the input plane is achieved. However, due to the space invariancy of the system, a trade-off among the beam propagation quality for channels is obtained. Experimental results are presented and discussed.     

基于改进萤火虫算法的有限元模型修正

针对标准萤火虫算法后期收敛速度慢、收敛精度低、易陷入局部最优解的问题,提出了参数自适应策略的改进萤火虫算法,建立了基于改进萤火虫算法的有限元模型修正方法。通过隔代随机吸引度因子扩大了算法搜索路径,提升了算法遍历性,避免计算陷入局部最优;通过自适应步长因子使得算法寻优过程中能随迭代次数逐渐减少随机搜索范围,从而提高收敛速度。单、多峰测试函数计算结果表明,改进算法显著提高了收敛速率与收敛精度;简支梁数值算例与某刚构桥实桥有限元模型修正结果表明,简支梁参数最大误差由初始的66.7%降低至修正后的1.08%,刚构桥频率最大误差由14.47%降低至3.25%。所提方法具有良好的更新精度,适用于大型复杂结构的有限元模型修正。     

Reflectance of pigmented polymer coatings: comparisons between measurements and radiative transfer calculations

Solar reflectance spectra of pigmented coatings have been obtained from spectroscopic measurements involving integrating sphere attachments. We demonstrate that measured and computed reflectances of an extended four-flux model [Appl. Opt. 37, 2615 (1998)] whose average path-length parameters (APP's) and forward-scattering ratios (FSR's) are explicitly evaluated from a multiple-scattering approach at the front or back interface of the particulate coatings display fairly good agreement. The agreement of these properties in a standard four-flux model [Appl. Opt. 23, 3353 (1984)], which neglects the spectral dependence of the APP and FSR, is found in the near infrared. Good agreement between these two four-flux approaches over the solar spectral range is obtained when the mean values of the APP's and FSR's are used in the standard model.