Interferometry for ellipso-height-topometry: Part 2: Measurement of the ellipsometric data, material identification, and correction of the measured height

Ellipso-height-topometry, EHT, as introduced by Leonhardt, et al. [Interferometry for ellipso-height-topometry, part 1, Optik 113 (2003) 513-519; Topometry for locally changing materials, Opt. Lett. 23 (1998) 1772-1774]; [Ellipso-height topometry, Optik 112 (2001) 413-420] is an extended topometry where topographies of the surface height H(x,y), the ellipsometric parameters Ψ(x,y) and Δ(x,y) (and optionally the intensity distribution I(x,y)) of the surface are measured on the same pixel raster and with high resolution. Thus, we can dispose over a set of (mutually coherent) topographies, and further topographies of quantities of interest can be calculated from this set: the local change in the complex refractive index N(x,y)=n(x,y)−k(x,y)i of bulk surfaces, the thickness distribution t(x,y) of locally changing (discontinuous) films and overlayers, and a correction of the optically measured local height H(x,y). The height error ΔH(x,y) can be calculated from the ellipsometric data and the true height h(x,y)=H(x,y)−ΔH(x,y) is thus obtained. ΔH(x,y) can assume large values when overlayers of oxidations or residues from lubrication oil or from processing are present. Much more information about the surface is gained with this concept.In part 1 of this work a z-scanning interferometric scheme with oblique incidence over the entire object field has been introduced, with the advantages of white-light interferometry, but with the additional capability of measuring material information to supply a complete set of topographies for extended topometry. In addition, very useful coherence properties for interferometry with oblique incidence were presented and discussed which allow to shape the interferogram in a simple way without any additional devices. In this part we derive the theory of the ellipsometric measurement and present first results by complete sets of two different samples.     

Noise-Limitations of Coherence Imaging Based on Wavefront Folding Interferometry

Noise-limitations of the coherence imaging system based on the wavefront folding interferometer are studied. The signal-to-noise ratio SNR in two kinds of noise-limiting cases, the photon-noise-limit and the detector-noise-limit, is derived and are compared with the experimental results. The experimental demonstration is conducted using a wavefront folding interferometer and a single slit that provides the light source. An ensemble of ten sets of data are measured under the same conditions and the statistics of the retrieved images are computed from them. It is verified that the experimental results generally agree with the theoretical expectations.     

Coherence theory and coherence phenomena in a closed spin‐1/2 system

A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence Ξ, and discuss in some detail a general coherence theory and its elementary results. As expected, decoherence is understood as a statistical process that is caused by the dynamics of the system, similar to the growth of entropy. It appears that coherence is an important measure that helps to understand quantum properties of a system, e.g., the decoherence time can be derived from the coherence function Ξ(t), but not from the entropy dynamics. Moreover, the concept of decoherence time is applicable in closed and finite systems. However, in most cases, the decay of off‐diagonal elements differs from the usual exp(‐t/τ_d) behaviour. For concreteness, we report the form of decoherence time τ_d in a finite Heisenberg model with respect to the number of particles N, density n_ρ, spatial dimension D and ? in a η/r^?‐type of potential.     

Coherence and wavefront characterization of Si‐111 monochromators using double‐grating interferometry

A study of the coherence and wavefront properties of a pseudo‐channel‐cut monochromator in comparison with a double‐crystal monochromator is presented. Using a double‐grating interferometer designed for the hard X‐ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel‐cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.     

Self-Inconsistencies of the U(1) Theory of Electrodynamics: Michelson Interferometry

The Michelson interferogram from perfectly reflecting mirrors does not exist in the U(1) gauge theory of electrodynamics, which is therefore seriously flawed. The adoption of an O(3) internal gauge field symmetry allows these flaws to be remedied self-consistently and leads to several developments in electrodynamics, enriching the subject considerably.     

光源对相干层析系统特性的影响

在分析相干层析系统成像机理的基础上，从理论上研究了光源对系统成像特性的影响，在考虑干涉条纹的强度用概率函数处理的条件下，由分析得出相干层析成像系统相当于一个复振幅的线性空间不变系统，从而给出相干函数和光源的功率谱密度之间的关系。通过对使用不同光源的系统相干传递函数比较，得出了采用具有较大线宽的低相干光源，系统的空间分辨率更好，可使测量更精确的结论。本文的工作为光学相干层析成像系统的优化设计提供了理论依据。     

Interferometry for Ellipso-Height-Topometry part 3: Correction of the aspect errors and reduction of the dispersion of the ellipsometric parameters

Ellipso-Height-Topometry, EHT, is an extended optical topometry, where both the topographies of the surface height H(x,y) and the ellipsometric local parameters Ψ(x,y) and Δ(x,y) of surfaces with locally changing materials are measured on the same pixel raster with high resolution and using the same data sets. Further quantities can be calculated from these measurements on the base of locally confined surface models: the local refractive index, the thickness t(x,y) of overlayers or films, or other parameters of layered systems.     

干涉法测量多层透明膜系反射率

应用干涉法实现透明膜系反射率的测量。将待测膜系镀在两薄玻璃片，并构成F-P干涉仪，根据透射光谱的自由谱宽和干涉峰的半宽值，计算出膜系反射率，避免了光源波动对测量结果的影响。在实验所用膜系的反射率小于98％时，测量误差小于0．09％。     

应用干涉原理检测激光晶体夹具的应力

详细介绍了激光干涉原理,在此基础上,引入了一种简单实用的板条激光器夹具应力检测方法,从而减小了应力对板条激光器带来的不利影响。实验结果表明：夹具对板条各个方向产生的应力均匀,通过初步实验得到了6.94 W的1 064 nm连续光输出。     

Quantum uncertainty relations of Tsallis relative α entropy coherence based on MUBs

In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.     

An L‐shaped nanoprobe for scanning electrochemical microscopy–atomic force microscopy

We present an L‐shaped nanoprobe for scanning electrochemical microscopy–atomic force microscopy (SECM–AFM) capable of imaging the surface topography and the electrochemical activity of nanostructures of interest. Owing to the geometry of the protrusive peak in the L‐shaped probe, the distance between the probe electrode and the substrate is maintained precisely at ～100 nm during surface scanning. The reduction in electrode‐to‐substrate distance significantly improves the positive feedback current on top of the electrochemically active nanomaterials. The L‐shaped nanoprobe successfully acquired simultaneous a topographical image and an electrochemical current image of individual carbon nanotubes (CNTs) in a two‐dimensional (2D) CNT network.

     

On perturbed oscillators in 1–1–1 resonance: the case of axially symmetric cubic potentials

Axially symmetric perturbations of the isotropic harmonic oscillator in three dimensions are studied. A normal form transformation introduces a second symmetry, after truncation. The reduction of the two symmetries leads to a one-degree-of-freedom system. To this end we use a special set of action–angle variables, as well as conveniently chosen generators of the ring of invariant functions. Both approaches are compared and their advantages and disadvantages are pointed out. The reduced flow of the normal form yields information on the original system.We analyse the 2-parameter family of (arbitrary) axially symmetric cubic potentials. This family has rich dynamics, displaying all local bifurcations of co-dimension one. With the exception of six ratios of the parameter values, the dynamical behaviour close to the origin turns out to be completely determined by the normal form of order 1. We also lay the ground for a further study at the exceptional ratios.     

相干性对X光全息图分辨率的影响

分析计算了Ｘ光束的相干性对Ｘ光全息图分辨率的影响，结论是Ｘ光无透镜傅里叶变换全息术所要求的相干长度和分辨率与样品尺雨戌二次线型关系；Ｘ光同轴全息术所要求的相干长度和分辨率的平方以及样品到全息图的距离成正比。     

双频激光泵浦光纤放大器中的原子相干效应

用密度矩阵的方法从理论上分析了不同频率的两个激光场混合泵浦的光纤放大器中，由光场诱导的原子相干效应。并由此引入相干修正因子，通过修正的速率方程讨论了两光场与原子的相干作用对放大器增益的影响。     

Preparation and Characterization of Activated Carbon – nFe3O4, Activated Carbon – nSiO2 and Activated Carbon – nZnO Hybrid Materials

The preparation and physicochemical characterization of activated carbon, nano metal oxides, and activated carbon – nFe₃O₄, activated carbon – nSiO₂ and activated carbon – nZnO hybrid materials has been undertaken. The materials have been characterized by scanning and transmission electron microscopy, x‐ray diffraction, CNH analysis and Fourier transform infrared spectroscopy. Surface area and porosity, ash content, pH, and point of zero charge were also measured. The results showed that the surfaces of activated carbon, nSiO₂, activated carbon – nFe₃O₄, activated carbon – nSiO₂ and activated carbon – nZnO are suitable for the sorption of cationic complexes while the surfaces of nFe₃O₄ and nZnO are favourable to the sorption of anionic complexes of heavy metals. Results also showed that the composition of the activated carbon and nano metal oxides increased the surface and micropore areas of nano metal oxides due to the large number of micropores and crevices on the surface of the hybrid materials.     

NMR dipolar constants of motion in liquid crystals: Jeener–Broekaert, double quantum coherence experiments and numerical calculation on a 10-spin cluster

Two proton quasi-equilibrium states were previously observed in nematic liquid crystals, namely the and quasi-invariants. Even though the experimental evidence suggested that they originate in a partition of the spin dipolar energy into a strong and a weak part, respectively, from a theoretical viewpoint, the existence of an appropriate energy scale which allows such energy separation remains to be confirmed and a representation of the quasi-invariants is still to be given. We compare the dipolar NMR signals yielded both by the Jeener–Broekaert (JB) experiment as a function of the preparation time and the free evolution of the double quantum coherence (DQC) spectra excited from the state, with numerical calculations carried out from first principles under different models for the dipolar quasi-invariants, in a 10-spin cluster which represents the 5CB (4^′-pentyl-4-biphenyl-carbonitrile) molecule. The calculated signals qualitatively agree with the experiments and the DQC spectra as a function of the single-quantum detection time are sensible enough to the different models to allow both to probe the physical nature of the initial dipolar-ordered state and to assign a subset of dipolar interactions to each constant of motion, which are compatible with the experiments. As a criterion for selecting a suitable quasi-equilibrium model of the 5CB molecule, we impose on the time evolution operator consistency with the occurrence of two dipolar quasi-invariants, that is, the calculated spectra must be unaffected by truncation of non-secular terms of the weaker dipolar energy. We find that defining the quasi-invariant as the subset of the dipolar interactions of each proton with its two nearest neighbours yields a realistic characterization of the dipolar constants of motion in 5CB. We conclude that the proton-spin system of the 5CB molecule admits a partition of the dipolar energy into a bilinear strong and a multiple-spin weak contributions therefore providing two orthogonal constants of motion, which can be prepared and observed by means of the JB experiment. This feature, which implies the existence of two timescales of very different nature in the proton-spin dynamics, is ultimately dictated by the topology of the spin distribution in the dipole network and can be expected in other liquid crystals. Knowledge of the nature of the dipolar quasi-invariants will be useful in studies of dipolar-order relaxation, decoherence and multiple quantum NMR experiments where the initial state is a dipolar-ordered one.     

Microsolvation of morpholine,a bidentate base – the importance of cooperativity

The structure, relative energies, and bonding in morpholine(water)_n (n = 1–4) clusters have been investigated at the Becke, three‐parameter, Lee–Yang–Parr/6–311 + G(3df,2p)//Becke, three‐parameter, Lee–Yang–Parr/6–311 + G(d,p) level of theory. Cooperative effects have been analyzed through the use of structural, energetic, and electron density indexes. Our analysis shows that these effects are crucial to trace the relative stability of the complexes formed. In all cases water molecules prefer to self‐associate forming chains in which each individual molecule behaves as a hydrogen bond (HB) donor and HB acceptor. The chain so formed behaves in turn as HB donor and HB acceptor with respect to morpholine, being the most stable arrangements those in which the NH group of morpholine behaves simultaneously as HB donor and HB acceptor. Higher in energy lie complexes in which the HB acceptor continues to be the NH group, but the HB donor is a CH group, or alternative structures in which the HB acceptor is the ether‐like oxygen of morpholine and the HB donor its NH group. Cooperativity increases with the number of solvent molecules, but there is a clear attenuation effect. Thus, whereas the additive interaction energy on going from dihydrated to trihydrated species increases by a factor of 3, this increase is about half on going from trihydrated to tetrahydrated complexes. Copyright © 2012 John Wiley & Sons, Ltd.     

Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence

The unified theory of coherence and polarization is applied to an investigation of the changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian (EHG) beams propagating through atmospheric turbulence. Based on the extended Huygens–Fresnel principle, the 2×2 electric cross-spectral density matrix of partially coherent EHG beams in turbulence is expressed analytically by using a quadratic approximation of Rytov's phase structure function. The analytical expressions for the degree of polarization, the degree of coherence and the spectrum of partially coherent EHG beams in turbulence are derived, and the corresponding analytical results of electromagnetic Gaussian Schell-model (EGSM) beams can be obtained when the order number of the Hermite polynomial is zero. Some interesting results are obtained, which are illustrated by using numerical examples.     

Capability of a Liquid-Crystal Adaptive Optics System Based on Feedback Interferometry for Retinal Imaging

A modified arrangement of the adaptive optical retinal imaging system that we described previously is proposed to reduce the intensity loss in the system, so that it works properly even when the intensity of light incident on the eye is very weak. Experiments to verify the system performance were conducted using a conventional artificial eye with a specular reflector as a model retina. We observed that an image of a test target (mimicking a retina) blurred by an aberration plate (mimicking the ocular aberrations) was successfully restored in the adaptive optics fashion even when the intensity of the incident light probing the aberration of the eye became about 1.5% of that required in the previous system. Effect of a more realistic artificial eye with a scattering object as a model retina was also examined experimentally. We found that not only the ocular aberrations, but also the retinal scattering cause the wave-front deformations and that our adaptive optics system compensates for both of them simultaneously.     

‘Best-case’ noise performance of feedback interferometers, potential for micromachine applications

We present a theoretical analysis of the noise performance of phase measuring feedback interferometers. We first analyse the operation of this kind of instrument and note that under certain circumstances bistability can occur. The bistable region should be avoided if possible when using feedback interferometry for high-accuracy measurement with low-input powers, as it can give rise to very high-noise levels. We then go on to investigate the effects of shot noise (on the interferometer output signal) and thermal noise (in the feedback loop), and relate these to the phase measurement accuracy of the interferometer. A ‘best-case’ calculation indicates that phase noise of about 0.005λ is possible at input powers in the nanowatt region. In practice, we expect that noise levels will be higher than predicted (particularly at high-input powers) due to the effects of vibration and air turbulence.