基于数字非线性锁相环的相干态相位估计

基于量子理论获取相位参数的导航机制,理论上可以突破经典物理极限对导航精度的限制.利用量子零拍探测对相干态光场相位进行测量时,通常需要相位与之正交的本振光才能使测量精度达到量子标准极限.由于导航信号相位的高非线性特点,想要利用传统的线性锁相环获取完全满足条件的本振光具有一定的难度.为此,本文设计了一种基于容积准则的非线性锁相环,实现了在非正交本振光的条件下对相干态相位进行精确测量的功能.首先,利用相干态的Wigner函数推导了其相位在量子零拍探测的输出结果,设计了量子相位估计的非线性数字锁相环框架.然后基于正交单纯形容积准则设计了非线性滤波算法实现锁相环功能,该锁相环通过对本振相位进行多次状态更新,最终实现非线性迭代估计.实验结果表明,本文方法突破了本振光相位需与相干态相位正交的局限性,避免了传统量子锁相环方法引入的线性化误差,实现了对相干态相位的准确、稳定估计.     

Multiple-surface interference fringes analysis basing on wavelength-modulated phase shifting interferometry

Phase-shifting interferometry is widely used for high-precision surface measurements, but has difficulty in dealing with parallel optical plates. In this paper, an advanced method is proposed to simultaneously measure surface distributions of parallel optical plates from multiple surface interference fringes. The basic theory behind the technique is by applying wavelength-modulated phase shifting interferometry (WMPSI) to get enough frames of multiple surface interference fringes. In the procession of wavelength-modulated phase shifting, the phase variation for one point of the surface is traced and is processed by Fourier transform, and then the frequency spectrum of every surface can be separated from each other. Therefore, it allows extraction of front surface, back surface and thickness variation from multiple surface interference fringes with high precision.     

Self-mixing interferometry based on nanometer fringes and polarization flipping

Self-mixing interferometry (SMI) based on nanometer fringes and polarization flipping is realized. The interferometer comprises a single-mode He-Ne laser and a high-amplitude reflectivity feedback mirror. The nanometer fringes are obtained by tilting the external feedback mirror. The fringe density is 35 times higher than that derived with conventional two-beam interference, and each fringe corresponds to a λ/70 displacement in external cavity length. Moreover, polarization flipping occurs when the external feedback mirror moves in the opposite direction. Such movement can be used to easily distinguish displacement direction. Experimental results show an optical resolution of displacement measurement of 9.04 nm with a range of 100 μm. The proposed SMI presents promising application prospects in precisely measuring displacement and calibrating other micro-displacement sensors because of its optical wavelength traceability.     

Comparison of phase recovery methods in spiral speckle pattern interferometry correlation fringes

Spiral interferometry can be used as a solution to the problem of sign ambiguity presented in the conventional speckle pattern interferometric technique when the optical phase needs to be reconstructed from a single closed fringe system. Depressions and elevations of the topography corresponding to the object deformation are distinguished by the direction of rotation of the local spiral fringe pattern. In this work, we implement and compare several methods for optical phase reconstruction by analyzing a single image composed of spiral speckle pattern interferometry correlation fringes. The implemented methods are based on contour line demodulation, center line demodulation, Spiral Phase Quadrature Transform and the 2D Riesz transform with multivector structure. Contour line and center line demodulation approaches are exclusively dedicated to images containing a fringe system with spiral structure. The others are based on the 2D Riesz transform, these being well known approaches in conventional interferometry. We examine simulated experiments and analyze some of the emerging drawbacks for solving the phase reconstruction problem by using different mean values of speckle size and background noise levels. We also discuss several numerical procedures that may well improve the efficiency and robustness of the presented numerical implementations. The performance of the implemented demodulation methods is evaluated by using a universal image quality index and therefore a quantitative comparison is also presented.     

Accurate nonlinear phase step estimation in phase shifting interferometry

We propose a new method for the accurate estimation of nonlinear response of the PZT to the applied voltage. The method uses discrete chirp Fourier transform for the coarse estimation followed by a fine search method for the accurate estimation of the phase step and nonlinearity. The method can be extended to the cases of extraction of multiple phases in the configurations involving multiple PZTs such as holographic moiré in the presence of nonlinearity. The robustness of the proposed method is verified by comparing with Cramér-Rao lower bound. Experimental results prove the method’s feasibility.     

Using higher steps phase-shifting algorithms and linear least-squares fitting in white-light scanning interferometry

White-light scanning interferometry (WLSI) has been a well-established tool for measuring the profile of objects. Since the white-light source is continuous in spectrum, the phase ambiguity problem can be avoided. Specimens with discontinuous profile can therefore be possibly measured by WLSI. In this paper, using higher steps, i.e. nine and eleven steps, phase-shifting algorithms (PSAs) based on local linear conditions of envelope function were proposed. The actual zero optical path difference position was retrieved by extracting the phase value and phase compensation. Maximum intensity peak positions at five points were used to calculate the center wavelength of the light source by both phase unwrapping and linear least-squares fitting. Both simulated and experimental results showed that the proposed nine- and eleven-step PSAs have good linearity and robustness to accurately measure the profile and center wavelength of the light source.     

Resolution improvement for enhancing interference fringes of digital holograms with near infrared illuminance

A new resolution improving method of enhancing the interference stripes, which can achieve better reconstruction of the recorded object of infrared digital holography has been proposed in this paper. The experiment is conducted under near infrared illuminance. We create poor quality holograms with very low-resolution interference stripes and enhance it with our new method. The processed holograms have much higher-resolution interference stripes. This method is based on interpolation theory, and we make it works fast, stable and easy to apply. Both the forward and backward interpolation of the oriental and portrait direction of the source pixels have been calculated, and have been used to realize the final aim of resolution improvement. During the experiment, since the responsivity of the CCD is not satisfied with the illuminance laser, which is by design, we also give specific analysis on the experimental setup of our work to make sure the object information can be fully recorded by the optical setup but cannot be reconstructed because of the low-resolution and unobvious of the interference stripes. After the resolution improvement process of the original hologram, the object information can then be fully reconstructed, which is very clear in the paper. Figures and dataflow give evidence and demonstrate the good performance of our method.     

散斑错位干涉术条纹的形成与特性分析

通过相关计算及滤波分析,建立了散斑错位干涉术条纹强度的统计分布,从而得到了这类条纹更为一般的特征属性.     

Optical phase locking of two extended-cavity diode lasers with ultra-low phase noise for atom interferometry

We present a phase coherent laser system with ultra-low phase noise with a frequency difference of 6.9 GHz. The laser system consists of two extended-cavity diode lasers that are optically phase-locked with electrical feedback to the injection current of a slave laser. The bandwidth of the optical phase-locking loop is extended up to 8 MHz. We achieve the residual phase noise of two phase-locked lasers of below ?120 dBrad²/Hz in the offset frequency range of 100 Hz–350 kHz and a flat phase noise of ?127 dBrad²/Hz from 700 Hz to 20 kHz. These results are, to the best of our knowledge, the lowest phase noise level ever reported with two extended-cavity diode lasers.     

Generalized phase shifting interferometry based on Lissajous calibration technology

The feasibility and limitation of directly using the Lissajous figure and ellipse fitting technology to correct the phase extraction error in generalized data reduction algorithm (GDRA) for phase extraction of randomly phase-shifted interferograms are analyzed and discussed. By combining Lissajous calibration technology, which represents the transformative process of Lissajous ellipse to circle (ETC), with advanced iterative algorithm (AIA) we propose a novel generalized phase shifting algorithm (GPSA), and here it is abbreviated as ETCI method. The phase distribution and phase shifts that extracted from randomly phase shifted interferograms by use of ETCI are more accurate and the whole process is far faster than AIA. Additionally, proposed method is less sensitive to non-uniform background intensity and modulation amplitude. Numerical simulations are conducted to evaluate the performance of ETCI, and some influential factors are elaborated. The experimental results further indicate proposed method is suitable for truly random phase shifted interferograms.     

Homomorphic partial differential equation filtering method for electronic speckle pattern interferometry fringes based on fringe density

Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a homomorphic partial differential equation filtering method for interferometry fringe patterns. The diffusion speed of the equation is determined based on the fringe density. We test the new method on the computer-simulated fringe pattern and experimentally obtain the fringe pattern, and evaluate its filtering performance. The qualitative and quantitative analysis shows that this technique can filter off the additive and multiplicative noise of the fringe patterns effectively, and avoid blurring high-density fringe. It is more capable of improving the quality of fringe patterns than the classical filtering methods.     

Parameter estimation of optical fringes with quadratic phase using the fractional Fourier transform

Optical fringes with a quadratic phase are often encountered in optical metrology. Parameter estimation of such fringes plays an important role in interferometric measurements. A novel method is proposed for accurate and direct parameter estimation using the fractional Fourier transform (FRFT), even in the presence of noise and obstacles. We take Newton׳s rings fringe patterns and electronic speckle pattern interferometry (ESPI) interferograms as classic examples of optical fringes that have a quadratic phase and present simulation and experimental results demonstrating the performance of the proposed method.     

相位梯度条纹假彩色化的色度研究

用色散单棱镜和双棱镜,对谱衍射干涉和傅里叶滤波准光干涉的相位梯度条纹,进行周期性非对称和对称假彩色编码.本文用色度学方法统一计算和分析了编码色的色品,主波长,色度纯,光度和单色含量与相位梯度的关系.导出了各种系统获得最佳编码色的结构参数条件.同时还提出了双棱镜非重叠色散相补的对称彩色编码新方法.     

Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

White-light interference has changes in fringe contrast. When phase-shift techniques are applied to white-light interference, the phase-shift algorithm which can extract the phase accurately under the contrast changes is required. There is often another requirement that the phase shift between frames should not be restricted to π/2. Computer simulations show that the well-known algorithms have non-negligible errors under both requirements. To find an algorithm which will satisfy the requirements, I extract individual terms (I _j ∓ I _k ) in an algorithmic equation by considering symmetry of light intensity against phase, where I _j is light intensity just after the j-th phase shift. Using computer simulations, I search for appropriate coefficients by which the terms are multiplied in the equation, finally finding an algorithm which satisfies both the requirements with the phase shift used.     

Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map

Among different phase unwrapping approaches, the weighted least-squares minimization methods are gaining attention. In these algorithms, weighting coefficient is generated from a quality map. The intrinsic drawbacks of existing quality maps constrain the application of these algorithms. They often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. In order to deal with those intractable wrapped phase data, a new weighted least-squares phase unwrapping algorithm based on derivative variance correlation map is proposed. In the algorithm, derivative variance correlation map, a novel quality map, can truly reflect wrapped phase quality, ensuring a more reliable unwrapped result. The definition of the derivative variance correlation map and the principle of the proposed algorithm are present in detail. The performance of the new algorithm has been tested by use of a simulated spherical surface wrapped data and an experimental interferometric synthetic aperture radar (IFSAR) wrapped data. Computer simulation and experimental results have verified that the proposed algorithm can work effectively even when a wrapped phase map contains intractable error sources.     

Self-mixing interferometry based on sinusoidal phase modulation and integrating-bucket method

In order to realize real-time displacement measurement with high resolution, sinusoidal phase modulation and integrating-bucket method are introduced in the self-mixing interference (SMI) system firstly. The phase of the laser beam is modulated by an electro-optic modulator (EOM) in the external cavity. Theoretical analysis, simulation results and error evaluation are presented. Experimentally, the micro-displacement of a high-precision commercial PZT is reconstructed and the reconstruction accuracy is on the order of nanometers for displacements of a few micrometers.     

外腔锁相二极管激光列阵的超模

利用耦合理论推导了通过外腔反馈实现锁相运行的激光二极管列阵所满足的本征值方程。在忽略非相邻单元间耦合的串联运行方式下,解析求解了包括端面反射的列阵方程的本征值。求出了各阶超模的近场分布,并得到了考虑单个发光单元影响时的远场分布,具体为：当列阵运行于基超模时,近场各个单元间的光场同相,在远场中心位置出现光强主极大;而在其它高阶模式,近场各个单元间光场不同相,远场光强主极大出现在中心位置两侧;远场总体受到单个发光单元近场分布函数的调制。     

Multiple self-mixing interferometry algorithm based on phase modulation for vibration measurement

A novel algorithm based on a phase modulation and demodulation technique for multiple self-mixing interferometry was proposed in this paper. This algorithm can measure nanoscale vibration in real time and enhance the measurement resolution of a multiple self-mixing interferometer twofold compared with that of a self-mixing interferometer. In this paper, the principles of the method were described in detail, and a phase equation for multiple self-mixing interferometry was derived. Experiments were confirmed by conducting a series of experiments with different amplitudes, different signal-to-noise ratios, and different vibration waveforms. The experimental results showed that the algorithm can rapidly demodulate vibration in real time and indicated good agreement between theory and experiment.     

Relation between geometry of localization of interference fringes in classical and holographic interferometry

It has been proven graphically and experimentally that the localization of interference fringes in classical interferometry is a specific case of the localization in holographic interferometry.