Predicting phase steps in phase-shifting interferometry in the presence of noise and harmonics

A novel method for estimating pixelwise phase step values in phase-shifting interferometry is presented. The method is based on the linear prediction property of the intensity fringes recorded temporally at a pixel on the charged-coupled device. The salient features of the method lie in their ability to handle linear miscalibration errors, to compensate for the presence of harmonics in an optical configuration and detector nonlinearity, and to allow for the use of arbitrary phase steps. The robustness of the proposed method is studied in the presence of noise and a comparison with several benchmarking algorithms is performed. The simulation results show the efficiency of the algorithm in retrieving the wrapped phase.     

Rotational invariance of two-level group codes over dihedral and dicyclic groups

Phase-rotational invariance properties for two-level constructed, (using a binary code and a code over a residue class integer ring as component codes) Euclidean space codes (signal sets) in two and four dimensions are discussed. The label codes are group codes over dihedral and dicyclic groups respectively. A set of necessary and sufficient conditions on the component codes is obtained for the resulting signal sets to be rotationally invariant to several phase angles.     

Overall gloss evaluation in the presence of multiple cues to surface glossiness

Human observers use the information offered by various visual cues when evaluating the glossiness of a surface. Several studies have demonstrated the effect of each single cue to glossiness, but little has been reported on how multiple cues are integrated for the perception of surface gloss. This paper reports on a psychophysical study with real stimuli that are different regarding multiple visual gloss criteria. Four samples were presented to 15 observers under different conditions of illumination in a light booth, resulting in a series of 16 stimuli. Through pairwise comparisons, an overall gloss scale was derived, from which it could be concluded that both differences in the distinctness of the reflected image and differences in luminance affect gloss perception. However, an investigation of the observers' strategy to evaluate gloss indicated a dichotomy among observers. One group of observers used the distinctness-of-image as a principal cue to glossiness, while the second group evaluated gloss primarily from differences in luminance of both the specular highlight and the diffuse background. It could therefore be questioned whether surface gloss can be characterized with one single quantity, or that a set of quantities is necessary to describe the gloss differences between objects.     

Measuring ultrashort optical pulses in the presence of noise: an empirical study of the performance of spectral phase interferometry for direct electric field reconstruction

We have measured the performance of a real spectral phase interferometry for direct electric field reconstruction (SPIDER) apparatus operating under suboptimal conditions. We analyzed the errors in SPIDER's measurements of the temporal phases and intensities of 50-fs ultrashort laser pulses as a function of the additive noise in the detected signal. It was found that SPIDER performs exceptionally well, particularly in the case of additive noise. Specifically, a signal with 10% noise yields a pulse that has a mere 2% error in its intensity profile and a phase that differs from the nominal value by 0.2 rad. Furthermore, we quantified SPIDER's performance with limited detector resolution and as a function of signal averaging.     

Asymptotic approach to a theory of multiple spin echoes in the low-temperature phases of3He

We discuss the phenomenon of multiple spin echoes induced by tipping angle-dependent frequency shifts. A general expression for the echo amplitudes neglecting diffusion effects is given as a spatial integral over a periodicity interval. The asymptotic behavior of this formula in the limit of many echoes is discussed and compared with the exact solution and experimental results.     

A new approach to the definition of power components in three-phasesystems under nonsinusoidal conditions

A method has been proposed for the definition of active and nonactive power components in three-phase systems under nonsinusoidal conditions. The method is more attractive than others since it is not a mere extension of methods employed in single-phase systems, but comes from the application of a quite powerful and synthetic mathematical tool specifically studied for the representation of three-wire three-phase systems in any possible condition: the Park transformation and the Park vectors. It is proven that the application of this method leads to the definition of two quantities, the real and the imaginary power, that are measurable in a quite simpler way than those proposed by other theories. The two satisfy all properties typical of the electrical power and are directly related, under sinusoidal and balanced conditions, to the active and reactive powers. It is shown how this method fits with other proposed methods that can be regarded in terms of this more general theory     

Maximum likelihood for target location in the presence of substitutive noise

We consider the optimal likelihood algorithm for the estimation of a target location when the images are corrupted by substitutive noise. We show the relationship between the optimal algorithm and the sliced orthogonal nonlinear generalized (SONG) correlation. The SONG correlation is based on the application of a linear correlation to corresponding binary slices of both the input scene and the reference object with appropriate weight factors. For a particular case, we show that the optimal strategy is a function of only the number of pixels for which the gray values in the noisy image match the ones of the reference image when the substitutive noise is uniformly distributed. This is exactly what a particular definition of the SONG correlation does.     

Design parameter selection in the presence of noise

Themethod of imprecision is a design method whereby a multi-objective design problem is resolved by maximizing the overall degree ofdesigner preference: values are iteratively selected based on combining the degree of preference placed on them. Consider, however, design problems that exhibit multiple uncertainty forms (noise). In addition to degrees of preference(imprecision) there areprobabilistic uncertainties caused by, for example, measuring and fabrication limitations. There are also parameters that can take on any valuepossible within a specified range, such as a manufacturing or tuning adjustment. Finally, there may be parameters which mustnecessarily satisfly all values within the range over which they vary, such as a horsepower requirement over a motor's different speeds. This paper defines a best set of design parameters for design problems with such multiple uncertainty forms and requirements.     

Blind turbo-detection in the presence of phase noise

Blind coherent detection of convolutional turbo codes is a hard problem in the presence of strong phase noise. Since the operating signal-to-noise ratio is usually very low, phase synchronisation algorithms suffer from phase ambiguities and cycle slips. A possible remedy is to perform joint phase estimation and decoding on a combined state-space model for the time-varying phase and the component convolutional codes. We demonstrate that joint phase estimation and decoding is in fact mandatory only for one component code, while ordinary BCJR decoding can be used for the second component code. Monte Carlo simulations for the turbo code used in the DVB-RCS standard show that the performances of the proposed scheme are close to decoding with perfect knowledge of the phase.     

Limitations of interferometry due to the flicker noise of laser diodes

Interferometry with laser diodes is a cost-effective way to perform displacement measurement. The tunability of laser diodes is also of great interest in multiple-wavelength interferometry. However, the additional flicker noise in the frequency-noise spectrum of semiconductor lasers may become a limiting factor. Investigations on the limitations due to the 1/f noise of laser diodes are presented for both classical and multiple-wavelength interferometry. Measurements at the limit of the coherence length of laser diodes with the corresponding phase fluctuations are reported. The theoretical results are verified experimentally.     

Image preprocessing for rotation-invariant pattern recognition in the presence of signal-dependent noise

I propose a new method that ensures efficient rotation-invariant pattern recognition in the presence of signal-dependent noise by combining the application of rotation-invariant correlation filters with preprocessing of the noisy input images. The preprocessing uses local suboptimal estimators derived from estimation theory and implies an a priori knowledge of a model describing the noise source. The image noise sources considered are speckle and film-grain noise. Pour different metrics are used to analyze the correlation performance of the circular-harmonic filter, the phase-only circular-harmonic filter, and the binary phase-only circular-harmonic filter, with and without a preprocessing. Computer simulations show that signal-dependent noise can seriously degrade the performance of the phase-only circular-harmonic filter and the binary phase-only circular-harmonic filter. The most severe indication of correlation-performance degradation is the occurrence of false alarms in 15% to 20% of noise realizations of the correlation. Preprocessing increases the correlation-peak signal-to-noise ratio significantly and reduces the false-alarm probability by one to two orders of magnitude.     

Optimal transformations for optical multiplex measurements in the presence of photon noise

Hadamard multiplexing is a measurement strategy that yields best sensitivity improvements over scanning measurements for signal-independent detector noise. The presence of photon noise degrades the performance of Hadamard multiplexing because of the increase of photon noise by the superposition of multiple signals. I derive the reduction of the sensitivity gain of a Hadamard measurement and an upper limit for the gain of any cyclic multiplexing strategy in the presence of photon noise. This upper limit clearly exceeds the reduced Hadamard gain and can be achieved by multiplexing sequences that differ from Hadamard S sequences but also share some similarities with respect to their autocorrelation. Examples of such sequences are given. As the analysis shows, the presence of photon noise limits the gain of multiplexing strategies to a finite value, which depends on the ratio between photon noise and detector noise and cannot be exceeded by increasing the number of multiplexed channels. In addition, only switching multiplex schemes, which superpose either all the light or no light of individual channels, can achieve the upper limit of the gain.     

Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting

We present a new computational algorithm of phase-shifting interferometry that can effectively eliminate the uncertainty errors of reference phases encountered when we obtain multiple interferograms. The algorithm treats the reference phases as additional unknowns and we determine their exact values by analyzing interferograms using the numerical least-squares technique. A series of simulations prove that this algorithm can improve measuring accuracy because it is unaffected by the nonlinear and random errors of phase shifters.     

非一致性噪声条件下的特征空间波束形成

由于水声环境的复杂性,阵列的噪声分布可能是非一致性的。当阵元噪声功率各不相同时,阵列协方差矩阵特征分解得到的特征子空间与真实目标的特征子空间之间存在误差,导致特征子空间波束形成算法的性能衰减。文章提出了一种新的非一致性噪声条件下特征子空间的估计方法,将阵列协方差矩阵对角线置0,进行特征分解估计的特征子空间将不受阵元噪声非一致性的影响。将该方法应用到特征空间波束形成算法,提高了非一致性噪声条件下特征空间波束形成算法的方位分辨能力。仿真和实验结果验证了所提方法的可行性和有效性。     

Susceptibility of systematic error-compensating algorithms to random noise in phase-shifting interferometry

In phase-shifting interferometry, many algorithms have been reported that suppress systematic errors caused by, e.g., nonlinear motion of the phase shifter and nonsinusoidal signal waveform. However, when a phase-shifting algorithm is designed to compensate for the systematic phase-shift errors, it becomes more susceptible to random noise and gives larger random errors in the measured phase. The susceptibility of phase-shifting algorithms to random noise is analyzed with respect to their immunity to phase-shift errors and harmonic components of the signal. It is shown that for the most common group of error-compensating algorithms for nonlinear phase shift, both random errors and the effect of high-order harmonic components of the signal cannot be minimized simultaneously. It is also shown that if an algorithm is designed to have extended immunity to nonlinear phase shift, simultaneous minimization becomes possible.     

Measurement error caused by speckle noise in heterodyne and quasi-heterodyne holographic interferometry

In heterodyne and quasi-heterodyne holographic interferometry, the measuring accuracy is limited by speckle noise. It is important to know the relation between measurement accuracy and speckle noise in both theory and application. This problem has been discussed in the past under the assumption that the speckle noise produces only a small measuring error. However, this assumption is not reasonable in practice. The effect of speckle noise on the measurement accuracy is analyzed by the use of a general statistical method. The results obtained reveal the general relation between the measuring accuracy and system parameters, and thus constitute important guidelines to the application of these techniques.