Pitch-modulated phase grating and its application to displacement encoder

Abstract

A binary phase grating with modulated pitch is investigated for a simple displacement encoder. The grating consists of a binary phase grating to eliminate the zeroth-order diffraction, and the pitch of the grating is modulated to compensate the higher harmonics of the encoder displacement signal. Therefore, an undistorted sinusoidal signal as a function of displacement is obtained by simply superimposing a conventional binary grating on the pitch-modulated phase gratings for any air gap between the gratings. The characteristics of the proposed gratings and the encoder signal are investigated by the Fresnel diffraction theory. The proposed grating has been fabricated lithographically, and the signal was examined experimentally. Considering these results, the proposed technique can suppress interpolation error and will be useful for an encoder in precision machining.     

Two-dimensional grating light modulator for projection display

A novel two-dimensional (2D) phase grating light modulator for projection display is proposed. It consists of an upper moveable grating, a bottom mirror, and four supporting posts between them. After the driving voltage is applied to the modulator, the upper grating will move down, which induces a phase difference and, therefore, leads to a controlled variation of its diffraction pattern. Optical characteristics of the modulator and the modulator array are analyzed with Fourier optics theory. The analysis shows the incident light will be switched from its zero order diffraction fringe to the first order diffraction fringe when the phase difference between the moveable grating and the bottom mirror changes from 2 pi to pi. The diffraction pattern of the light modulator array is the coherent superposition of all single modulators. A 16 x 16 modulator array is fabricated by surface micromachining technology. The test result shows that the device works well when it is actuated by a voltage with a 1 kHz frequency and 10V amplitude. Both theoretical analysis and experiment results indicate that the 2D phase grating light modulator has potential application in a projection display system.     

基于EMD算法的光栅莫尔条纹信号去噪方法研究

针对计量光栅莫尔条纹信号的质量问题,提出了基于经验模态分解（EMD）算法对非平稳光栅莫尔条纹信号模型的去噪方法。建立非平稳的光栅时变信号模型,利用EMD算法不需要定义滤波器参数的自适应性优点,对添加不同噪声的多组光栅信号模型进行了滤波分析的仿真实验,其信噪比和均方根误差两项指标优于均值滤波、小波阈值去噪方法。对两路正余弦理想信号添加高次谐波分量,通过对比EMD算法抑制高次谐波前后的李萨如图形,验证了该方法在去噪过程中对光栅莫尔条纹信号正弦性误差补偿的良好效果。     

Sensitivity analysis of grating parameter estimation

An optimization method for the sensitivity of diffraction efficiency measurements is presented. I define the sensitivity as the estimation precision of the grating parameters. The optimization method called sensitivity analysis for fitting scans all the possible measurement configurations and selects the configuration that yields the best sensitivity. The scan is made over the domain of the experimental parameters of the arrangement, such as the azimuth angle of the grating and the orientation angles of the analyzer and the polarizer. These parameters can be freely varied, and among the multitude of possible combinations there is one configuration that provides optimum sensitivity. Comparison with experimental results reveals a qualitative agreement between theory and practice.     

基于干涉解调技术的光纤激光器水声传感系统

分析了基于Michelson干涉解调技术的光纤激光器水声传感的原理,在一段掺铒光纤中写入具有π相移的光纤光栅构成光纤激光器,水声压力作用在激光器上引起激光工作波长的变化;采用基于3×3耦合器的偏振无关的非平衡光纤Michelson干涉仪将激光波长变化转化为干涉仪的相位变化;干涉仪的输出由光电探测器转换后使用DSP进行信号解调.针对3×3耦合器分光比不对称的问题,本文提出利用实时调整幅度的2路干涉信号进行解调的方案,该方案不需要3×3耦合器有严格的分光比,消除了外界环境对解调输出的非线性影响.水声探测实验表明,光纤激光器水声传感系统的声压灵敏度为-166.5 dB(参考值1 rad/μPa),解调结果与水声信号具有良好的线性关系.     

新型绝对零位粗光栅的研究

本文在总结国内外粗线纹光栅绝对零位实现方法的基础上，提出了一种新型绝对零位粗光栅的方案。它克服了传统粗化栅采用栅动开关作为附加零位标志的缺点，将零位标志直接刻制在粗光栅尺上，采用编码识别的方法，用专用自扫描光电二极管列阵ＣＧ２００Ｓ提取粗定位信号，结合列阵自扫描起始信号Ｓ及其调相测量信号ＭＳ的边沿触发脉冲，产生高精度绝对零位脉冲。既保证了系统精度，又解决了粗光栅与绝对零位一体化的问题。为进一步研制     

Grating light reflection spectroscopy for determination of bulk refractive index and absorbance

An optical sensing technique is described and evaluated for sensitivity to changes in refractive index and absorbance of model sample matrices. A binary dielectric/metal transmission diffraction grating is placed in contact with a sample and utilized in reflection mode; thus, the light captured and analyzed does not pass through the sample. This particular condition creates thresholds at which a particular transmitted diffraction order is transformed from a traveling wave to an evanescent one. The positions of these thresholds depend upon the complex dielectric function of the sample, the period of the grating, and the wavelength and incident angle of light striking the grating. Experimental evidence directly supports the theoretical predictions regarding responses to both the real and imaginary portions of the refractive index: the reflection coefficient derivative wavelength peak position shifts linearly with changes in the real part of the refractive index, and the derivative peak amplitudes exhibit a square-root dependence on absorbance. Refractive index sensitivity to a series of ethanol/water solutions is demonstrated with detectable changes in index as small as 2 × 10(-)(6). Absorbance sensitivity is shown via the differentiation of methylene blue samples having equivalent 1 cm path length absorbances between 0.459 and 244 AU. In a single reflection measurement, GLRS offers a large dynamic range for absorbance detection, allows simultaneous determination of bulk refractive index in optically dense media, and provides a platform for performing continuous process analysis.     

用改进的小脑模型神经网络实现光栅信号连续细分

光栅测量系统常用硬件进行信号细分，存在细分数不高、硬件复杂等问题。为此，研究了一种神经网络细分方法，即利用一种改进的小脑模型神经网络的泛化能力实现光栅信号的连续细分。该小脑模型神经网络采用直接权地址映射技术，将光栅样本信号直接映射到联想存储器，对非样本信号经联想泛化即可实现连续细分。仿真实验结果表明，仅用少量样本即可达到很高的细分精度。     

光栅信号质量检测及电路实现

对光栅信号的质量指标，主要是对光栅到莫尔条纹信号质量指标进行了分析，并通过采用谐波分析法，对光栅信号质量进行动态综合检测的电路进行了实现。这对计量光栅的发展和长光栅的检测，具有一定的现实意义。     

Optics for modulating multiple beams using an asymmetric multilevel phase grating and a multichannel acousto-optic modulator

Asymmetric multilevel phase gratings for generating even numbered beams have been designed, assuming that their phase patterns are formed by overlapping plural binary-phase patterns, each of which has an arbitrary phase height. The grating for four beams, which produces uniform and high intense diffraction orders of the minus first to the plus second order, is fabricated. The efficiency is 75.5%, although the theoretical efficiency is 79.9%. It is also demonstrated that the optics in which the beams from the grating are fed into a multichannel acousto-optic modulator through a Fourier-transform lens makes their successful modulation possible for pulse signals of 20-ns pulse duration.     

Method for enhancing temperature sensitivity of fiber Bragg gratings based on bimetallic sheets

We designed what is believed to be a novel structure based on bimetallic sheets to enhance temperature sensitivity of fiber Bragg gratings. The two ends of bimetallic sheets were fixed by bolts, and a fiber Bragg grating was longitudinally affixed to one of the sheets whose expansion coefficient was larger than that of the other. The theoretical and experimental results show that the temperature sensitivity of the fiber Bragg grating was enhanced dramatically by the structure. For example, the temperature sensitivity reached 0.08014 nm/ degrees C when the bimetallic sheets were made of aluminum and iron, which are more than eight times that of a bare fiber Bragg grating. Moreover, it was experimentally demonstrated that the structure has excellent linearity, reversibility, and stability.     

Characterization of the phase modulation property of a free-space electro-optic modulator by interframe intensity correlation matrix

Characterization of a phase modulator or phase shifter has always been an integral part of phase-modulating or phase-adjusting applications. We propose a simplified approach to characterize a phase modulator by investigating the performance of phase shifts from grabbed interferograms using the phase extraction method. After reviewing some phase analysis techniques, the interframe intensity correlation (IIC) matrix method is introduced to the investigation. The proposed strategy is illustrated by the measurement of a free-space electro-optic modulator (EOM). Placing the modulator in one arm of a Michelson interferometer, the global phase shifts are estimated by the IIC method from the phase-stepped interferograms. Experimental results demonstrate the tested EOM has a phase modulation response of at least 2π rad with a π/20 rad modulation precision for λ=1064 nm. In addition, our method is applicable to various types of phase modulator or phase shifter calibration, e.g., electro-optic phase modulator, spatial light modulator, or piezoelectric transducer (PZT).     

Two-wavelength phase-shifting interferometry with a superimposed grating displayed on an electrically addressed spatial light modulator

A two-wavelength moire phase-shifting interferometer that uses a superimposed grating has been developed. The optical phase shifts for the two wavelengths are given by digital phase shifts of a superimposed grating displayed on a liquid-crystal spatial light modulator. A phase shift of the moire fringe is achieved by equal phase shifts with opposite signs in the two gratings. A moire phase-shifting interferometer with no moving parts and no requirement for calibration of the value of the phase shifts was obtained. Our experimental result shows measurements of the profile of a step object with a 2.65-microm synthetic wavelength.     

相移长周期光栅在EDFA增益平坦中的应用

对相移长周期光栅进行了理论分析,在此基础上,运用传输矩阵法对它的透射光谱进行数值计算,分析了相移量大小、平均折射率变化以及光栅长度等结构参数变化对相移长周期光栅透射谱的影响,并根据这些变化规律适当调节它的结构参数,使其透射光谱与平坦EDFA的目标光谱在一定程度上相符。平坦后的EDFA增益谱在34nm范围内最大波动不超过±0.7dB。根据此方法设计的增益平坦滤波器只包含一个器件,体积小,便于制造和封装,具有很好的市场应用前景。     

Environmental sensitivities of quartz oscillators

The frequency, amplitude, and noise of the output signal of a quartz oscillator are affected by a large number of environmental effects. The physical basis for the sensitivity of precision oscillators to temperature, humidity, pressure, acceleration and vibration, magnetic field, electric field, load, and radiation is examined. The sensitivity of quartz oscillators to radiation is a very complex topic and poorly understood. Therefore, only a few general results are mentioned. The sensitivity to most external influences often varies significantly both from one oscillator type to another and from one unit of a given type to another. For a given unit, the sensitivity to one parameter often depends on the value of other parameters and on history. Representative sensitivity to the above parameters is given.     

Design of binary diffraction gratings of liquid crystals in a linearly graded phase model

We report on a linearly graded phase model for the design of binary diffraction gratings of liquid crystals (LCs) associated with the periodic interfacial effect. The binary nature of the LC grating is produced by use of periodic striped domains in an alternating homeotropic and hybrid geometry. In our graded phase model the diffraction patterns and the diffracted intensities of the LC binary grating is primarily governed by three length scales: the cell thickness and two distortion parameters scaled by the grating period at two domain boundaries. The experimental data agree well with theoretical predictions made in our linearly graded phase model as well as the elastic continuum theory.     

Tracking generator of calibrated harmonics

A tracking generator of calibrated harmonics has been tested at the Istituto Elettrotecnico Nazionale Galileo Ferraris. This system acquires the sinusoidal input supplied by a precision ac calibrator, and the internal DSP produces, by means of a digital-to-analog converter (DAC), an output signal combination of calibrated harmonics components, which is added to the sinusoidal signal of the calibrator. In this way, an ordinary 12-bit DAC can produce a precision signal with an assigned THD less than 10%. Some algorithms for generating the signal and for tracking with high accuracy the internal reference to the external input signal have been developed, which allow the frequency and phase difference to be recovered within 10/sup -4/ rad in less than 0.1 s.     

Reduction of the grating lobes of annular arrays used in focusedultrasound surgery

An annular array with variable focus, used in focused ultrasound surgery, generates grating lobes responsible for undesirable lesions. It is known that the amplitude and the location of the lobes depend on both the geometry and the frequency of the transducer. A new procedure based on the use of a wide-band CW signal, i.e., a signal phase modulated by a pseudorandom code, is proposed to reduce the amplitude of these lobes. The theoretical study enables us to determine the location and the amplitude of these lobes and to simulate the effect of the transmitted signal bandwidth. In particular, a simple analytical relation gives the intensity ratio between the grating lobes and the main lobe. This equation shows that this ratio is inversely proportional to the number of rings and to the bandwidth of the transmitted signal. A system was developed and tested with two transducer arrays of 35- and 150-mm diameter, respectively. The simulations and experiments demonstrate the validity of the theoretical study and the efficacy of the proposed procedure. In conclusion, it is possible to reduce the grating lobes without geometric modification of the array by increasing the bandwidth of the transmitted signal     

Talbot effect by a photorefractive volume phase grating

In our proposal a light intensity distribution generated by an incoherently illuminated planar amplitude grating is projected into a photorefractive crystal. This 3D distribution is mapped as an index refractive perturbation via the photorefractive effect thereby generating a volume phase grating. The self-imaging phenomenon in the Fresnel field of this volume phase grating coherently illuminated is theoretically and experimentally analyzed. A model to simulate this volume grating that considers the 3D light intensity distribution formed in the crystal combined with the photorefractive grating formation theory is proposed. A path-integral approach to calculate the self-image patterns which account for the inhomogeneous propagation through the photorefractive grating is employed. The experimental and theoretical results show that the self-images location coincides with that of the self-images generated by planar phase grating of the same period. Moreover, the self-images visibility depends on three parameters: the exit pupil diameter of the incoherent recording optical system, the external electric field applied on the crystal, and the crystal thickness. To study the visibility behavior, a phase parameter which includes the three mentioned parameters is proposed. The self-images visibility shows the typical sinusoidal dependence found in planar phase grating. A good agreement between theoretical and experimental results is observed.