Generalized Hyperinterpolation on the Sphere and the Newman—Shapiro Operators

Hyperinterpolation on the sphere, as introduced by Sloan in 1995, is a constructive approximation method which is favorable in comparison with interpolation, but still lacking in pointwise convergence in the uniform norm. For this reason we combine the idea of hyperinterpolation and of summation in a concept of generalized hyperinterpolation. This is no longer projectory, but convergent if a matrix method A is used which satisfies some assumptions. Especially we study A partial sums which are defined by some singular integral used by Newman and Shapiro in 1964 to derive a Jackson-type inequality on the sphere. We could prove in 1999 that this inequality is realized even by the corresponding discrete operators, which are generalized hyperinterpolation operators. In view of this result the Newman—Shapiro operators themselves gain new attention. Actually, in their case, A furnishes second-order approximation, which is best possible for positive operators. As an application we discuss a method for tomography, which reconstructs smooth and nonsmooth components at their adequate rate of convergence. However, it is an open question how second-order results can be obtained in the discrete case, this means in generalized hyperinterpolation itself, if results of this kind are possible at all. March 9, 2000. Date revised: October 2, 2000. Date accepted: March 8, 2001.     

Listen to the chemical and histological information in biological tissue

Photoacoustic imaging (PAI), as an emerging biomedicine diagnostic technique that has been developed quickly in the past decade, inherits the high spatial resolution of ultrasonography in imaging deep tissue and the high sensitivity of optical imaging in evaluating tissue chemical and physiological information. In this paper, after introducing the basic principles of PAI including both photoacoustic tomography and photoacoustic microscopy, we will review some recent progress of PAI in biomedicine and demonstrate the capability of PAI in detecting the chemical compositions and in evaluating the histological microstructures in biological tissue.     

Detection of Wave Front Set Perturbations via Correlation: Foundation for Wave-equation Tomography

We discuss the mathematical aspects of wave field measurements used in traveltime inversion from seismograms. The primary information about the medium is assumed to be carried by the wave front set and its perturbation with respect to a hypothetical background medium is to be estimated. By a convincing heuristics a detection procedure for this perturbation was proposed based on optimization of wave field correlations. We investigate its theoretical foundation in simple mathematical case studies using the distribution theoretic definition of oscillatory integrals.     

Drawing parameters optimization for birefringence reduction in optical fibers

The impact of the drawing process on the stress-induced birefringence in optical fiber is experimentally analyzed. By means of the photoelastic tomographic technique, residual internal stresses are measured in fiber samples drawn under different conditions of temperature, drawing tension and speed. From measured residual stress distributions, the stress-induced birefringence and beatlength are mathematically derived and compared, proving that an effective birefringence reduction can be obtained by a proper choice of drawing parameters.     

托卡马克等离子体辐射诊断中的线积分辐射率

在托卡马克等离子体辐射诊断中,通过阿贝尔反汪或层析分析从线积分辐射率中得到的空间分布,是辐射率在束线宽度范围内的平均值的分布,束线宽度限制了诊断的空间分辨能力。当探测器无穷小的近似条件不成立时。束线宽度显著大于探测器中心对光栏孔径张角决定的宽度,并且在给定束线截面内各点辐射对探测信号的贡献差别可能变得重要从而导致辐射率的宽度平均成为带权重的平均。     

辐射源旋转台阶成像技术

 提出了用旋转台阶对辐射源成像的方法。对台阶响应曲线微分可得到辐射源2维出射强度沿台阶方向的1个投影,通过旋转台阶体,可得到完整的正弦图,从而可用层析重建算法重建出辐射源区的强度分布。用钨合金台阶体在1个60Co源上进行成像实验,从400个角度的台阶响应数据重建出60Co源活性区图像,表明该方法是可行的。此方法可推广到大孔径圆孔台阶体,用于测量X射线焦点等小尺寸辐射源的尺寸。     

Using hydrogels in microscopy: A tutorial

Sample preparation for microscopy is a crucial step to ensure the best experimental outcome. It often requires the use of specific mounting media that have to be tailored to not just the sample but the chosen microscopy technique. The media must not damage the sample or impair the optical path, and may also have to support the correct physiological function/development of the sample. For decades, researchers have used embedding media such as hydrogels to maintain samples in place. Their ease of use and transparency has promoted them as mainstream mounting media. However, they are not as straightforward to implement as assumed. They can contain contaminants, generate forces on the sample, have complex diffusion and structural properties that are influenced by multiple factors and are generally not designed for microscopy in mind. This short review will discuss the advantages and disadvantages of using hydrogels for microscopy sample preparation and highlight some of the less obvious problems associated with the area.     

Ground Layer Adaptive Optics

We will introduce the present knowledge of the turbulence profile and in particular we will emphasise the existence of a turbulence layer close to the ground. Then we will present the concept of Ground Layer Adaptive Optics and will provide estimates of performance expected from such systems and their potential for astronomical applications. Finally we will provide practical implementation concepts for two instruments at the VLT, MUSE and HAWK-I using multi-Laser Guide Stars and a large Deformable Secondary Mirror. The latter will also be described as its use is optimum for GLAO systems. To cite this article: N. Hubin et al., C. R. Physique 6 (2005).     

时域光声谱技术及其在生物组织检测中的应用

当强度调制的光束照射于吸收物质,周期性热流使周围的介质热胀冷缩而激发声波,这种将光能转化为声能的现象称为光声效应。基于光声效应的时域光声谱技术将光学和声学有机地结合,为生物组织的无损检测技术提供了新的检测手段。该技术能够实现类似光学技术的高对比度和近似于声学技术的高精度和穿透深度,在生物医学检测中具有广阔的应用前景。文章介绍时域光声谱技术的原理及其在生物组织成分检测和层析成像检测中的应用。