New formulas for phase retardance measurements of birefringent plates

Two simple formulas are introduced that allow for simultaneous determination of the phase retardances of two birefringent plates from a single pair of readings of the polarizer and the analyzer at extinction. These formulas are of great importance since they furnish the basis of a model for a simple, timesaving and accurate method for calibrating phase plates in the Senarmont compensator arrangement without requiring an exact λ/4 plate and with almost direct results. The Poincaré sphere representation of polarization states is used to illustrate the model.     

Spectrophotometric calibration of a quarterwave plate

A new photometric method for calibrating a quarterwave phase plate is presented and the underlying physical phenomenon is explained. A mica sheet of thickness about 30 μm was found to introduce quarterwave phase retardance at 515 nm. The accuracy of the method and the sources of error are discussed.     

Hamiltonian structure and gauge symmetries of Poincaré gauge theory

This is a review of the constrained dynamical structure of Poincaré gauge theory which concentrates on the basic canonical and gauge properties of the theory, including the identification of constraints, gauge symmetries and conservation laws. As an interesting example of the general approach, we discuss the teleparallel formulation of general relativity.     

The method of the Poincaré map for compressional and torsional waves in composite rods

A generalized Poincaré map is introduced and used to find the compressional and torsional normal-mode frequencies and wave amplitudes of a one-dimensional rod composed by N coaxial cylinders of different length and radius. The method is approximately 100 times faster and more stable than the transfer matrix method. The Poincaré map method is used in a rod composed of two locally periodic systems, each one with a different length of the unit cell. This system can be used as an almost perfect mechanical noise filter.     

Moiré topography in odontology

For several decades, measurement of optical techniques has been used in different branches of science and technology. One of these techniques is the so-called moiré topography (MT) that enables the accurate measurement of different parts of the human body topography. This investigation presents the measurement of topographies of teeth and gums using an automated system of shadow moiré and the phase shift method in an original way. The fringe patterns used to compute the shape and the shape matrix itself are presented in the article. The phase shift method ensures precisions up to the order of microns. Advantages and disadvantages of using the MT are included. Besides, some positive and negative aspects concerned with the implementation of this technique in odontology are shown in the article.     

Raman spectroscopy of selected borate minerals of the pinakiolité group

The Raman spectra of a series of related minerals of the pinakiolité group have been collected and the spectra related to the mineral structure. These minerals are based upon an isolated BO₃³⁻ ion. The site symmetry is reduced from D_3h to C₁. Intense Raman bands are observed for the minerals takeuchiité, pinakiolité, fredrikssonité and azoproité at 1084, 1086, 1086 and 1086 cm⁻¹. These bands are assigned to the ν₁ BO₃³⁻ symmetric stretching mode. Low‐intensity Raman bands are observed for the minerals at 1345, 1748; 1435, 1748; 1435, 1750; and 1436, 1749 cm⁻¹, respectively. One probable assignment is to ν₃ BO₃³⁻ antisymmetric stretching mode. Intense Raman bands of the studied minerals at 712 cm⁻¹ are attributed to the ν₂ out‐of‐plane bending mode. Importantly, through the comparison of the Raman spectra, the molecular structure of borate minerals with ill‐defined structures can be obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Phase shifting nano-moiré method with scanning tunneling microscope

In this paper, a new nano-moiré method using scanning tunneling microscope (STM) is proposed. This method is capable of measuring nanoscopic deformation of matter. The formation mechanism of the STM moiré fringe and the phase shifting technique used in STM moiré fringes are explained in details. Typical experiments are conducted with the crystal lattices of freshly cleaved highly oriented pyrolytic graphite, are used as specimen grating, to generate STM moiré fringe patterns. Phase shifting is realized in four steps from 0 to 2π by controlling the PZT in the STM system to shift the specimen in the vertical direction. This method provides a new way for disposal of moiré fringes pattern in the nano-moiré measurement.     

Directive metamaterial-based subwavelength resonant cavity antennas – Applications for beam steering

This article presents the use of composite resonant metamaterials for the design of highly directive subwavelength cavity antennas. These metamaterials, composed of planar metallic patterns periodically organized on dielectric substrates, exhibit frequency dispersive phase characteristics. Different models of metamaterial-based surfaces (metasurfaces), introducing a zero degree reflection phase shift to incident waves, are firstly studied where the bandwidth and operation frequency are predicted. These surfaces are then applied in a resonant Fabry–Perot type cavity and a ray optics analysis is used to design different models of ultra-compact high-gain microstrip printed antennas. Another surface presenting a variable reflection phase by the use of a non-periodic metamaterial-based metallic strips array is designed for a passive low-profile steering beam antenna application. Finally, the incorporation of active electronic components on the metasurfaces, allowing an electronic control of the phase responses, is applied to an operation frequency reconfigurable cavity and a beam steering cavity. All these cavity antennas operate on subwavelength modes, the smallest cavity thickness being of the order of λ/60. To cite this article: A. Ourir et al., C. R. Physique 10 (2009).     

Mixed polarization in determining the film thickness of a silicon sphere by spectroscopic ellipsometry

The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed, and a method to eliminate this effect is proposed. Based on the simulation result of the SE measurement on a silicon sphere by ray tracking, we find that the sphere makes the parallel incident beam of the SE be divergent after reflection, and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory. By settling an aperture in front of the detector of the SE, we can almost eliminate the error. For the silicon sphere with a diameter of 94 mm used in the Avogadro project, the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method. The principle of the method and the results of the experimental verification are presented.     

Mixed polarization in determining the film thickness of a silicon sphere by spectroscopic ellipsometry

The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed,and a method to eliminate this effect is proposed.Based on the simulation result of the SE measurement on a silicon sphere by ray tracking,we find that the sphere makes the parallel incident beam of the SE be divergent after reflection,and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory.By settling an aperture in front of the detector of the SE,we can almost eliminate the error.For the silicon sphere with a diameter of 94 mm used in the Avogadro project,the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method.The principle of the method and the results of the experimental verification are presented.     

A study on the digital moiré technique with circular and radial gratings

A digital moiré technique with circular and radial gratings is proposed to measure in-plane displacement and strain distributions of soft materials in a polar coordinate system. By introducing the coordinate-transform technique, the concentric circles and radial lines in the Cartesian coordinate system are converted to cross gratings in a polar coordinate system. Then, the digital moiré fringes are generated using logical and filter operations on the one-bit binary images. Finally, the in-plane displacement distributions are obtained by means of the four step phase-shifting procedure. Also, the measurement principles and the basic procedures of the new digital moiré technique are explained in detail. An application for rubber sheet with a single-edge crack is studied, and the experimental results show that the presented method is feasible.     

Phase shifting SEM moiré method

A new phase shifting scanning electron microscope (SEM) moiré method is proposed in this paper. The phase shifting technique is realized in four steps from 0 to 2π by shifting electron beam in the y-axis direction controlled by the SEM system. It is successfully applied to determine the residual strain of a deformed holographic grating with a frequency of 1200 lines/mm in an electronic package. As a further application, it is used to measure the virtual strain of a MEMS structure with a 5000-line/mm grating and to determine the phase distribution of a SEM moiré formed with a 6000-line/mm grating fabricated by electron beam lithography. The experiments show the feasibility of this method. It provides a new way for disposal of fringes pattern in sub-micro moiré method.     

A simple method to unwrap the geometrically discontinuous phase map and its application in the measurement of IC package

Research on the techniques to unwrap the geometrically discontinuous phase map is an active area during the past decade, various algorithm are developed. Basically, these algorithms need a prior knowledge about the spatial extension of the discontinuity area in the sample for correct phase unwrapping, manual mask is often involved and negate the sense of automatic processing to fringe patterns. More ever, current phase unwrapping algorithms are either computationally complex or highly time consuming. In this paper, a refined method is proposed to deal with the geometrical discontinuity problem in an improved automation sense: suppression of background noise and recognition of discontinuity area in the phase map can be finished in the same time, and discontinuous phase map can be unwrapped in a simple way to avoid the effect of discontinuity area. An example of electronic package with complex shape and structure is used to verify the efficiency of this method.     

Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform

A new approach based on the moiré theory and wavelet transform (WT) is proposed for measuring the micro-range distance between a charge-couple-device (CCD) camera and a two-dimensional reference grating. The micro-range distance is determined by measuring the pitch of the moiré pattern image, which is digitized by a CCD camera. A one-dimensional WT algorithm is applied to estimate the pitch of the moiré pattern. Experimental results prove that this technique is very efficient and highly accurate. The moiré range finder is an economic technique for measuring a micro-range distance.     

Theoretical analysis of the effect of coating polarization on the second harmonic generation of an Nd:YVO4/KTP laser

Jones calculus is used to analyze the effect of the polarization characteristics of the output mirror coating of a V-shaped Nd:YVO4/KTP laser on the second harmonic generation. The reflection-induced phase retardance (RIPR) of the coating can quench the second harmonic generation. When the optical axis of Nd:YVO4 makes a π/4 angle with the incident plane of the output mirror and the fast axis of KTP in the incident plane, the RIPR induced reduction of coupling factor of the second harmonic generation is less than 1% if the phase retardance is smaller than 25°. If the polarization direction of the fundamental wave coincides with the eigen-polarization directions of the incident plane, the effect of the reflection-induced phase retardance on the conversing efficiency can be avoided.     

Shadow Moiré method for the determination of the source position in three-dimensional shearography

Shearography is a full-field non-contact optical technique used for characterisation of surface strain. In a multi-component system, the displacement derivative components are measured using a number of illumination positions. These components are then transformed into a three-dimensional coordinate system, using a knowledge of the source positions. This process is highly sensitive to errors in the knowledge of the source position. Shadow Moiré, with either linear or circular gratings, can be used to measure angle of illumination, with the measurement sensitivity and accuracy variable by changing the grating pitch. Circular gratings have a measurement range determined by multiple fringe analysis and linear gratings have a different measurement range determined by sub-fringe analysis. In this paper vertical linear, horizontal linear and circular gratings are combined to extend the measurement range and the accuracy of the measurement of the source position in two directions. Using this method the source position was measured to an accuracy of ±3%.     

对轴误差对光纤陀螺输出的影响

理论分析并试验研究了Y波导保偏尾纤与保偏光纤线圈之间熔接点的对轴误差对光纤陀螺输出的影响.根据简化的光纤陀螺光路误差模型,对光纤陀螺的输出相位误差与光路中主要耦合点的对轴误差的关系进行了理论推导和仿真分析,并利用一个实际的闭环光纤陀螺试验研究了主要熔接点的对轴误差变化对光纤陀螺零偏和零偏稳定性的影响.结果表明,Y波导保偏尾纤与保偏光纤线圈之间的对轴误差是引起光纤陀螺输出误差的重要因素,必须尽量减小.