A novel approach for characterizing the nonlinear phase steps of the PZT in interferometry

We propose a novel approach to estimate the phase distribution in the presence of nonlinear response of the PZT. The proposed method is an outcome of two different concepts based on the discrete chirp Fourier transform (DCFT) and the maximum-likelihood estimator for the estimation of nonlinear phase step. The robustness of the proposed method is tested for various magnitudes of nonlinearity and harmonics. Comparison of our proposed method with the bench marking algorithm by Hibino et al.'s six and nine sample algorithm in the presence of noise shows that our method is highly efficient.     

Phase-shifting interferometry with feedback control using heterodyne phase detection

A phase-shifting interferometer with feedback control using heterodyne phase detection was developed. A composite heterodyne phase detection method for obtaining feedback signals was proposed. Interference fringe stabilization and accurate pi/2 phase shifts under micrometer-order vibrations were successfully demonstrated using a digital high-speed lock-in amplifier.     

相移干涉术及广义相移数字全息干涉术

在基础光学框架内说明了传统的相移干涉术及近年来发展的广义相移数字全息干涉术的基本原理;前者要求特殊值等步长相移,而后者则可以采用任意未知相移值.着重介绍了广义相移干涉术中的物波恢复算法,以及基于衍射场统计特性的未知相移提取算法.从一个侧面沟通了基础光学与近代光学之间的关系.     

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.     

Generalized linear prediction method in phase-shifting interferometry in the presence of noise

The effectiveness of phase-shifting interferometry (PSI) techniques employing piezoelectric device PZT in the estimation of phase depends largely on the accuracy with which the phase shifts are imparted to the device and the noise influencing the measurement. Several effective algorithms have been proposed to compute the phase shifts imparted to the device and subsequently obtain the phase using least-squares estimation technique. In this paper, we propose a generalized approach, which accurately estimates the phase shifts in the presence of noise. The method is based on the idea of linear prediction and explores the fact that sampling more data frames yields a reliable phase step estimate in a least-squares sense. We also compare our method with a commonly used generalized phase-shifting method based on histogram analysis and show that our proposed approach is highly effective. We also present simulation and experimental validations of our proposed method.     

Deterministic phase unwrapping in the presence of noise

We present a new Fourier-based exact solution for deterministic phase unwrapping from experimental maps of wrapped phase in the presence of noise and phase vortices. This single-step approach has superior performance for images with high phase gradients or insufficient digital sampling approaching 2pi/pixel and therefore performs as a fast and practical solution for the phase-unwrapping problem for experimental applications in applied optics, physics, and medicine.     

Identification of nonlinear recording error in phase shifting interferometry

The phase shifting method for quantitative fringe pattern analysis provides high accuracy if stringent requirements on the component interferogram recording are met. In the paper the issue of detection and identification of error sources in the two-beam interferogram phase shifting experiment is discussed. The phase shift angle histogram and lattice-site representation are applied for that purpose. Special attention is paid to possible nonlinear recording of component interferograms in the presence of linear and nonlinear phase step errors. Four and five step phase shifting algorithms are considered. The superiority of the lattice-site representation is shown. In the case of phase steps equal to π/2, however, the lattice-site representation of shift angles for five frame algorithm does not allow to detect recording nonlinearity. The four frame counterpart shows to be very helpful in this respect. Its properties related to the fringe pattern profile under study, including a defocused Ronchi grating, are discussed.     

Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps

A new approach to reconstructing the object wave front in phase-shifting interferometry with arbitrary unknown phase steps is proposed. With this method the actual phase steps are first determined from measured intensities with an algorithm based on the statistic property of the object phase distribution in the recording plane. Then the original object field is calculated digitally with a derived formula. This method is simple, accurate, and capable of retrieving the original object field, including its amplitude and phase distributions simultaneously, with arbitrary and unequal phase steps in a three- or four-frame method. The effectiveness and correctness of this approach are verified by a series of computer simulations for both smooth and diffusing surfaces.     

Probability density functions of the nonlinear phase noise

Probability density functions are given for nonlinear phase noise in a photonic communication system in which the information is encoded in the optical phase, both unconditioned and conditioned to the detection of a given amount of pulse energy. It is shown that the reach of a transmission system is increased by approximately 41% by ideal postcompensation of the nonlinear phase noise.     

Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects

A general method of extracting the arbitrary unknown and unequal phase steps in phase-shift interferometry from interferograms recorded on the diffraction field of an object and then reconstructing the object wave front digitally with our derived formulas is proposed. The phase steps are first calculated based on the statistical nature of the diffraction field and are further improved by an iterative approach. This method is simple, highly accurate, and usable for any frame number N (N > or = 3) and for both smooth and diffusing objects, as is verified by a series of computer simulations.     

Effect of dispersion on nonlinear phase noise

The variance of nonlinear phase noise is analyzed by including the effect of intrachannel cross-phase modulation-induced nonlinear phase noise. Consistent with Ho and Wang [IEEE Photon. Technol. Lett.17, 1426 (2005)] for a lightwave transmission system but contrary to the conclusions of both Kumar [Opt. Lett.30, 3278 (2005)] and Green [Opt. Lett.28, 2455 (2003)] with different initial conditions, the variance of nonlinear phase noise does not decrease much with the increase of chromatic dispersion. The results are consistent with each other after a careful reexamination.     

Asymptotic probability density of nonlinear phase noise

The asymptotic probability density of nonlinear phase noise, often called the Gordon-Mollenauer effect, is derived analytically when the number of fiber spans is large. Nonlinear phase noise is the summation of infinitely many independently distributed noncentral chi2 random variables with two degrees of freedom. The mean and the standard deviation of those random variables are both proportional to the square of the reciprocal of all odd natural numbers. Nonlinear phase noise can also be accurately modeled as the summation of a noncentral chi2 random variable with two degrees of freedom and a Gaussian random variable.     

Effect of chromatic dispersion on nonlinear phase noise

We consider the combined effects of amplified spontaneous emission noise, optical Kerr nonlinearity, and chromatic dispersion on phase noise in an optical communication system. The effect of amplified spontaneous emission noise and Kerr nonlinearity were considered previously by Gordon and Mollenauer [Opt. Lett. 15, 1351 (1990)], and the effect of nonlinearity was found to be severe. We investigate the effect of chromatic dispersion on phase noise and show that it can either enhance or suppress the nonlinear noise amplification. For large absolute values of dispersion the nonlinear effect is suppressed, and the phase noise is reduced to its linear value. For a range of negative values of dispersion, however, nonlinear phase noise is enhanced and exhibits a maximum related to the modulation instability found in amplitude fluctuations. Nonlinear phase noise is quenched by these effects even in dispersion-compensated systems; the degree of suppression is sensitively dependent on the dispersion map. We demonstrate these results analytically with a simple linearized model.     

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.     

Comment on "Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps"

We comment on the recent Letter by Cai et al. [Opt. Lett. 28, 1808 (2003)] in which an approach to phase-shifting interferometry with arbitrary phase steps was proposed. Cai et al. based their method of phase shifting on the idea that the intensities of the reference and object beams can be measured previously, which actually makes the whole posterior phase-shifting procedure absolutely unnecessary. Their method is also based on the statement that the phase of the Fresnel diffraction pattern of a test object if generally a spatially random distribution, which in most situations is wrong.     

Intermittency of intermittencies at the phase synchronization boundary in the presence of noise

The intermittent behavior at the boundary of phase synchronization in the presence of noise is investigated. It is shown that in a certain range of the coupling parameter and noise intensity, the system experiences the intermittency of needle’s eye- and ring-type intermittencies. The basic results are demonstrated with two unidirectionally coupled Ressler chaotic oscillators.     

Effect of nonlinear gain on the phase noise of Y-branch lasers

Effect of nonlinear gain on the phase noise of modulated grating Y-branch (MGY) lasers is investigated by experiments and simulations. The phase noise is first characterized by measuring the frequency modulation noise spectrum of the MGY laser, and some interesting phenomena are observed. In order to understand the underlying physic mechanism of those phenomena, simulations are performed with taking Langevin noise sources and nonlinear gain terms into account. Simulated results show that, in the presence of the nonlinear gain, fluctuations of side-modes can bring excess phase noise to the lasing mode, especially when the side-modes are on the long-wavelength side of the main mode. Furthermore, it has been found that the phase noise hopping phenomenon can be induced by a bi-stable state of the laser, which is also closely related to the nonlinear gain. The investigation is helpful for explaining the complicated phase noise characteristics of the MGY laser.     

Effect of dispersion on nonlinear phase noise in optical transmission systems

An analytic expression for the variance of nonlinear phase noise that uses a first-order perturbation technique is obtained. The results show that for highly dispersive transmission systems, amplified spontaneous emission-induced phase noise due to self-phase modulation becomes much smaller than that for the systems with no dispersion.