Signal processing method of phase correction for laser heterodyne interferometry

A novel signal processing method of movement direction identification and phase correction is presented for laser heterodyne interferometry. Based on the reference signal, four intervals with phase difference of 90° each other are set up. The real-time movement direction identification and the integer fringe counting are realized by detecting the times that the rising-edge of the measurement signal crosses the intervals. The phase correction approach is proposed in detail to solve the fraction phase compensation when the initial phase difference is not equal to the zero phase difference. Three experiments of the stability test, the nanometer and micrometer displacement tests on bi-directional movement were performed to demonstrate the usefulness and feasibility of the presented signal processing method.     

A white-light interferometer using a lamp source and heterodyne detection with acousto-optic modulators

A heterodyne technique for white-light interferometer with a lamp source, which uses two acousto-optic modulators, is developed for high-sensitivity detection of weak light. By using converging input beams input into a Michelson interferometer with spherical mirrors, the spectral dependence of the modulators is canceled, and the white-light heterodyne interference fringes are generated at 200 kHz. Using a tandem interferometer, the object surface which has a low surface reflectivity of less than 10⁻⁴ was detected with a good signal-to-noise ratio.     

Investigation on the maximum signal handling capability of fiber optic interferometric sensor based on the digital heterodyne demodulation scheme

The maximum signal handling capability (MSHC) is an important parameter for the fiber optic interferometric sensor (FOIS) system. It is restricted by the heterodyne frequency (HF) and the digital quadrature demodulation algorithm (DQDA) in the digital heterodyne demodulation scheme. In this paper we systematically investigate the MSHC of the FOIS based on the digital heterodyne demodulation scheme through comparison of the HF-determined MSHC and DQDA-determined MSHC. When discussing the DQDA-determined MSHC, two widely used methods are included, which are arctangent and differential-cross multiply (DCM). The comparison results reveal that the arctangent-determined MSHC is 12 dB larger than the DCM-determined MSHC. The HF-determined MSHC is between the two types of DQDA-determined MSHC. If the DQDA is arctangent, the MSHC of the system is the HF-determined MSHC. If the DQDA is DCM, the MSHC of the system is the DCM-determined MSHC. Experiments are carried out and the results are consistent with the theoretical analysis. The conclusion in this paper can help us to estimate the MSHC of the FOIS system based on the digital heterodyne demodulation scheme more accurately and provide a useful guideline for the design of the FOIS system with large demodulation dynamic scale.     

A phase quadrature interferometer for measuring the small optical rotation angle of a chiral medium

The passage of a linearly polarized beam through a chiral material and a phase retarder will induce a phase difference between the s and p polarizations of the beam. In this study, a phase quadrature interferometer is designed to measure the phase difference variation proportional to the optical rotation. The proportionality constant (or measurement sensitivity) can be greatly enhanced by setting the retardation of the phase retarder close to 0° or 180°. The experimental results demonstrate that with our system we can obtain a measurement resolution for the rotational angle of better than 3.5° × 10⁻⁴. This method has several advantages such as a simple optical setup, easier operation in real time, and low cost. In addition, due to the common-path arrangement, surrounding noise can be eliminated.     

Application of passive quadrature phase demodulation for the detection of laser ultrasound

In this paper we describe a laser ultrasound detection scheme based on a new passive phase demodulation technique. Typical laser interferometers suffer from the loss of sensitivity because of phase drifts resulting from the mechanical movements of optical components and normally require closed loop stabilisation control. Through the use of a custom-designed grating mask, the present design completely eliminates the need for any feedback control by simultaneously sampling the interferometer output in the four quadrants of the optical phase circle. The signals are then processed to reproduce the actual waveform of the ultrasound pulse. The operation of the proposed technique is demonstrated through the detection of laser-generated ultrasound waves propagating inside an aluminium block.     

On the research of avalanche photodiodes-based heterodyne in FM/cw laser rangefinder

An avalanche photodiodes (APDs)-based heterodyne technique for FM/cw laser rangefinder (FM/cw LRF) is described. Based on a modified APDs model, the properties of heterodyne are theoretically analyzed and experimentally demonstrated under different illumination intensities and multiplications, both the amplitude and the signal to noise ratio (SNR) of the difference frequency signal are inversely proportional to the unmultiplied current at a high multiplication and are proportional to the square of multiplication at a low multiplication.     

非对称空间外差光谱仪自适应频率跟踪处理方法

非对称空间外差光谱技术是一种新型的超高分辨率遥感探测技术,要求后期的数据处理技术也具有相应的超高准确度.从数字信号处理的角度,提出了一种自适应的频率跟踪处理方法,根据信号的空间频率来插值补偿信号的相位偏移,并且递归迭代出最接近真实值的相位信息.经仿真实验对比验证表明,在噪声干扰强度不大的条件下,相较于传统傅里叶变换方法,本文算法对信号频率和相位提取的准确度提高了约100倍以上,能够有效降低非对称空间外差光谱技术的系统误差.     

Ellipse detection and phase demodulation for wood grain orientation measurement based on the tracheid effect

The methods of ellipse detection and phase demodulation for determining wood grain orientation are proposed. These methods are based on the tracheid effect—laser beam impinging upon a wood surface forms an elongated laser spot with its direction indicative of the grain orientation. Experimental results show that the method of ellipse detection is suitable for the grain orientation measurement on planed softwood surfaces, while the method of phase demodulation is capable of extracting the grain orientation precisely from laser images with low signal-to-noise ratio, such as the images on the surfaces of hardwood species or roughsawn materials.     

New uncertainties in QCD—QED rescaling factors using quadrature method

In this paper we briefly outline the quadrature method for estimating uncertainties in a function which depends on several variables, and apply it to estimate the numerical uncertainties in QCD-QED rescaling factors. We employ here the one-loop order in QED and three-loop order in QCD evolution equations of the fermion mass renormalisation. Our present calculation is found to be new and also reliable when compared to the earlier values employed by various authors     

Some investigations in holographic microscopic interferometry with respect to the estimation of stress and strain in micro-opto-electro-mechanical systems (MOEMS)

Holographic microscopy with conjugate reconstruction for the interferometric determination of three-dimensional displacement was used for the investigation of the mechanical behaviour of micromechanic and microelectronic components. An experimental set-up for the exposure of the holographic interferograms is described for the application of the spatial heterodyne technique, for the application of phase shifting, and for electro-optic holography. Three holograms for different illumination directions recorded on one holographic plate were reconstructed conjugately, and spatial-heterodyne technique as well as phase-shift technique were used to evaluate the interferograms. Only by conjugated reconstruction, it is possible to obtain a perfectly optimised interferometer for the static evaluation method. The evaluation of interferograms, which are strongly disturbed by speckle noise, can be performed successfully. A comparison of the results of the application of these techniques is given. The influence of the speckle effect on the resolution was investigated.     

The study of third harmonic demodulation in phase modulation optical heterodyne technique using optical resonator

With the technique of phase modulation optical heterodyne(PMOH), we detected the beat-frequency signal of the reflected wave from a F-P cavity. The frequency of the beat signal was three times of that of the modulation electric field, when the 3rd harmonic of the modulation electric field was used as the phase reference signal. The line shapes of the signal match those of the theoretical calculations, and the dispersion signal has good frequency-discrimination characteristic.     

New demodulation filter in digital phase rotation beamforming

In this paper, we present a new quadrature demodulation filter to reduce hardware complexity in digital phase rotation beamforming. Due to its low sensitivity to phase delay errors, digital quadrature demodulation is commonly used in ultrasound machines. However, since it requires two lowpass filters for each channel to remove harmonics, the direct use of conventional finite impulse response (FIR) filters in ultrasound machines is computationally expensive and burdensome. In our new method, an efficient multi-stage uniform coefficient (MSUC) filter is utilized to remove harmonic components in phase rotation beamforming. In comparison with the directly implemented FIR (DI-FIR) and the previously-proposed signed-power-of-two FIR (SPOT-FIR) lowpass filters, the proposed MSUC filter reduces the necessary hardware resources by 93.9% and 83.9%, respectively. In simulation, the MSUC filter shows a negligible degradation in image quality. The proposed method resulted in comparable spatial and contrast resolution to the DI-FIR approach in the phantom study. These preliminary results indicate that the proposed quadrature demodulation filtering method could significantly reduce the hardware complexity in phase rotation beamforming while maintaining comparable image quality.     

Nonlinear two-mode squeezing obtained by analysing two-mode exponential quadrature operators in entangled state representation

By analysing the properties of two-mode quadratures in an entangled state representation (ESR) we derive from ESR some complicated exponential quadrature operators for nonlinear two-mode squeezing, which directly leads to wave function of the nonlinear squeezed state in ESR.     

Fringes demodulation in time-averaged digital shearography using genetic algorithms

This paper presents a phase recovery method, based on genetic algorithms, in time-average shearography. It is proved that a single Bessel fringe pattern obtained under a subtraction operation could be enough to calculate the phase. A merit function is solved iteratively using genetic operator like selection, reproduction and mutation. Experimental results are presented in this paper using a simple shearing system based on a Fresnel biprism.     

Fringe-variable interferometry used for the detection of domain structure in LiTaO3

We design a fringe-variable Jamin interferometer to detect the reversed domain of a ferroelectric crystal in real time. In contrast to the Mach-Zehnder interferometer, this setup is compact and tunable in fringe frequency. In experiments, we use it to detect the partly reversed domains of Stoichiometric LiTaO₃ (SLT). Selecting the proper fringe cycle, we can estimate the average phase shift between the original and reversed domains through eyeballing. Furthermore, in the interferogram processing, we use the FFT methods to reconstruct the phase according to the original fringe and deformed fringe, and obtain the phase variance at the domain wall. The results show that the average phase variance at the domain wall is in good agreement with the theoretical value.     

Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams

In this paper methods to simulate the signals in laser interferometers are proposed. The central part deals with the computation of the photocurrent, subsequent phase demodulation and finally the generation of interferometer signals, such as the longitudinal phase readout, differential wavefront sensing signal, differential power sensing and contrast. Here, fundamental Gaussian beams without astigmatism are assumed. The methods are validated in several examples by comparison with experimental data, with analytical results as well as with an intuitively predictable system.     

外差探测系统中马卡望远镜离轴使用的研究

鉴于马卡望远镜离轴能够减小因副镜遮挡引起的光能量损失,分析了马卡望远镜离轴使用时,合作目标和非合作目标发射和接收光路的区别。讨论了马卡望远镜在外差探测系统离轴使用时,发射能量提高,但外差效率下降的原因;在合作目标外差探测系统离轴使用时发射能量提高30%以上,外差效率也有很大提高;通过对散射体目标物和平面镜的测量,分别得到了17%和85%的外差效率,验证了马卡望远镜在合作目标外差探测系统中可以离轴使用。     

A five-point stencil based algorithm used for phase shifting low-coherence interference microscopy

The phase shifting technique is the most widely used approach for detecting the envelope in low coherence interferometry. However, if the phase shifts calibration contains errors, some parasitic fringe structure will propagate into the calculated envelopes and cause imprecision in the envelope peak detection. To tackle these problems, a five-point stencil algorithm is introduced into the phase shifting interference microscopy. Considering the amount of parasitic fringes, envelope peak detection and computational efficiency, the presented approach leads to satisfactory results in performance. In combination with a simple polynomial curve fitting method the proposed algorithm exhibits good performance on envelope peak detection in surface profiling. Both of the simulated results and the experimental results indicated that the presented approach can be taken as an alternative to the currently existing methods used for phase shifting low-coherence interference microscopy.     

近距离激光外差探测光学极限位移分辨率

通过统计理论和维纳-辛钦定理推导出激光外差探测系统光电流的功率谱函数,分析了光电流谱线分布与激光光源线宽、中频信号频率以及信号光相对本振光传输延迟时间的关系,修正了相关文献中光电流功率谱的理论公式.根据信号与噪声理论建立了激光线宽引起的相位噪声的一维概率分布模型,并据此得到了基于激光波长、探测距离以及激光线宽的极限位移分辨率的数学模型.对光电流的功率谱和外差光学极限位移分辨率进行了相关的数值仿真,结果表明延迟时间与相干时间的关系决定光电流谱线分布的情况.当激光波长为532 nm,激光线宽在1 kHz,探测距离为100 m时,光学极限位移分辨率为0.266 nm,相关文献中的实验数据与理论推导结果相符合.