Optical Bilinear Transformations: General Properties

Because of the quadratic relation between the optical field and intensity, an inherent non-linearity exists in almost all optical systems. A class of non-linear transformations which we call bilinear (quadratic with memory) is defined; its properties and relevance to optical imaging systems are discussed. For space-invariant systems, a generalized transfer function is defined which characterizes the bilinear system completely. We also examine the approximate linearization of bilinear systems for low-contrast images, and the propagation of noise through such systems. Special emphasis is given to the partially coherent system which is but a special case of this general bilinear system.     

Effect of losses on phase noise

Abstract

We study the effect of losses on the phase noise of single-mode field states. The losses are described by the standard loss master equation, and it is used to find an upper bound for the increase in the phase noise as a function of time. We compare the time dependence of the phase noise of an initial coherent state to that of a state that initially has very small phase noise. Both states have the same initial mean photon number. While the small-phase noise state is more susceptible to losses, the difference between its behaviour and that of the coherent state is not great.     

Coherent resonance in klystron oscillator at self-excitation threshold

The phenomenon of coherent resonance in a nonlinear dynamical system based on a delayed-feedback klystron (DFK) oscillator has been experimentally studied. The application of an external white noise signal to the DFK oscillator at the self-excitation threshold leads to the appearance of a resonant response in the system, the maximum of which is attained at a definite power of the external noise. It is demonstrated for the first time that the coherent resonance in response to an external harmonic signal in the microwave range allows the signal-to-noise ratio at the output of a regenerative ring amplifier to be significantly increased.     

Measurement of Microphonic Noise

In the course of designing an airborne radar system, there is inevitably a requirement that the equipment does not generate microphonic noise over a specified level. The level of interest can be such that accurate measurement can be difficult. This paper compares three measuring systems: a simple microwave bridge system, the commercially available Allscott system, and a coherent system conceived and developed after the above two systems were found inadequate. Also presented are results of tests performed on typical microwave components.     

Scattering coherent and partially coherent space-time pulses through few-mode optical systems

We consider the spatiotemporal behavior of coherent and partially coherent, pulsed, few-mode optical systems. It is shown that there is some set of orthogonal space-time pulses at the input reference surface that maps in one-to-one correspondence with some set of orthogonal space-time pulses at the output reference surface; we call these pulses eigenfields. The spectrum of the coupling coefficients determines the amount of information that can be transmitted within a given period of time. The eigenfields are unique for a given system and can be used to propagate a field that is in any state of spatial and temporal coherence. They can also be used to account for the spatial and temporal coherence of internally generated noise and to calculate the powers, fluctuations, and correlations that would be recorded by multimode detectors. Our technique is ideal for modeling the behavior of pulsed imaging arrays and interferometers.     

两个宽带噪声矢量场模型的空间相关特性

针对宽带噪声矢量场的空间相关特性问题,文章讨论了各向同性噪声模型和表面噪声模型。在高频近似条件下,根据射线声学理论和简谐平面行波满足的欧拉公式,采用时域建模方法分别建立了宽带各向同性噪声和表面噪声矢量场模型。给出了噪声场相关函数的积分表达式和竖直方向空间相关系数的解析表达式。数值分析结果表明,相较于窄带噪声矢量场,宽带噪声矢量场各分量空间相关系数振荡幅度更小,随空间两点间距的增大更快地趋近于零;噪声源指向性对表面噪声场竖直方向上的空间相关特性的影响显著。相较于已有的宽带噪声空间相关系数计算方法,文中模型无需使用傅里叶合成方法,可通过时域建模直接获得宽带噪声空间相关函数。     

Restoration of bilinearly distorted images. 3: Constrained least-squares method

A constrained least-squares solution based on a second difference smoothing measure is obtained for images which are distorted by a bilinear (quadratic and with nonzero memory) system in the presence of additive signal-independent noise. Results are applied to a partially coherent diffraction-limited imaging system. It is found that the optimum weight given to the smoothness factor is larger for a coherent (nonlinear) system than for an incoherent (linear) system. However, the restoration quality improves as the imaging system approaches incoherence.     

Design and calibration of a noise measurement system

The setup principle and calibration method of a noise measurement system for frequencies from dc to 10 kHz are described. This system measures the current noise power spectral density of some device, and consists of a low-noise current preamplifier, a voltage preamplifier, and a dynamic signal analyzer which implements the fast Fourier transform (FFT). The noise aspects of the whole system can be modeled as a serial noise voltage generator and a parallel noise current generator at the input port, plus a system free of noise. The cross correlation of the two noise generators is an imaginary number because the system input stage is composed of some junction field effect transistors (JFET's). Via the thermal noise measurement of several resistors, we derive the magnitudes of the noise generators in addition to the input impedance and the total system gain. The imaginary cross correlation is obtained by the noise measurement of pure capacitance. With a well-calibrated procedure, we can measure the noise power down to 2×10^-27 A²/Hz. Two systems with different input stages were calibrated with the same procedure and the noise measurement results of the various resistance values with the two systems all agree well with theoretical values. One of these with an input stage which has a much smaller noise current generator shows great improvement in the noise measurement of the high-impedance device     

The combined effect of signal decorrelation and random noise on the variance of time delay estimation

Tissue motion and elasticity imaging techniques commonly use time delay estimation (TDE) for the assessment of tissue displacement. The performance of these techniques is limited because the signals are corrupted by various factors including electronic noise, quantization, and speckle decorrelation. Speckle decorrelation is caused by changes in the coherent interference among scatterers when the tissue moves relative to the ultrasound beam. In time delay estimation, the effect of noise is usually addressed through the signal-to-noise ratio (SNR) term. Decorrelation, often a significant source of error in medical ultrasound, is commonly described in terms of the correlation coefficient. A relationship between the correlation coefficient and the SNR was previously derived in the literature, for identical signals corrupted by uncorrelated random noise. In this paper, we derive the relationship between the peak of the correlation coefficient function and the SNR for two jointly stationary signals when a delay is present between the signals. Recently, an expression for the Cramer-Rao lower bound (CRLB) has been derived in the literature for partially decorrelated signals in terms of the SNR and the correlation coefficient. Since the applicability of the CRLB is determined not only by the SNR, but also by the correlation coefficient, it is important to unify the expression for the CRLB for partially correlated signals. In this paper, we derive an expression for the CRLB in term of an equivalent SNR converted from the correlation coefficient using an SNR-p relationship, and show this expression to be equivalent to the expression for CRLB. We also corroborate the validity of the SNR-p expression with a simulation. Using this formulation, correlation measurements can be converted to SNR to obtain a composite SNR. The use of this composite SNR in lieu of those in the CRLB expression in the literature allows the extension of the literature results to the solution of the common TDE problems that involve signal decorrelation.     

Internally coded time-hopping coherent ultra-short light pulse code division multiple access scheme with optical amplifier and its performance analysis using additive noise model

The internally coded time-hopping coherent ultra-short light pulse code division multiple access (CULP CDMA) scheme (recently introduced) with an optical amplifier is described and its performance in fibreoptic communication systems is analysed. In accordance with the important role of optical amplifiers in optical communication systems, a preamplifier at the input of the receiver is used in order to compensate the losses because of the spectral encoder, spectral decoder and optical fibre path. The authors evaluate the bit error rate of the system considering the effects of the multiple access interference, noise because of the optical amplifier and thermal noise using saddle point approximation, and compare the results with those of the conventional CULP CDMA system with and without an amplifier. The numerical results indicate a substantial improvement in the performance of the coded system in comparison with the uncoded one. In addition, the negative effect of amplifier noise in the proposed scheme is much less than that of the conventional CULP CDMA system.     

A fast BDD algorithm for large coherent fault trees analysis

Although a binary decision diagram (BDD) algorithm has been tried to solve large fault trees until quite recently, they are not efficiently solved in a short time since the size of a BDD structure exponentially increases according to the number of variables. Furthermore, the truncation of If–Then–Else (ITE) connectives by the probability or size limit and the subsuming to delete subsets could not be directly applied to the intermediate BDD structure under construction. This is the motivation for this work.This paper presents an efficient BDD algorithm for large coherent systems (coherent BDD algorithm) by which the truncation and subsuming could be performed in the progress of the construction of the BDD structure. A set of new formulae developed in this study for AND or OR operation between two ITE connectives of a coherent system makes it possible to delete subsets and truncate ITE connectives with a probability or size limit in the intermediate BDD structure under construction. By means of the truncation and subsuming in every step of the calculation, large fault trees for coherent systems (coherent fault trees) are efficiently solved in a short time using less memory. Furthermore, the coherent BDD algorithm from the aspect of the size of a BDD structure is much less sensitive to variable ordering than the conventional BDD algorithm.     

Measurement and system impact of multipath interference from dispersion compensating fiber modules

Dispersion compensating modules (DCM) are key components in long distance and high-speed fiber-optic transmission systems. However, many types of DCMs exhibit multipath interference (MPI) that acts as noise in transmission and degrades the bit error rate of the system. Further, MPI generated in DCMs is mostly due to forward scattering and mostly of the coherent type. This type of MPI cannot be correctly measured using conventional measurement techniques that use electrical spectrum analysis to measure post-detection noise. We demonstrate an accurate and simple method of MPI measurement using a swept wavelength system apparatus. We discuss the strengths and limitations of this measurement method and show system results of Q penalty due to MPI from concatenated DCMs.     

Reduced-noise-displacement measurements with a correlated differential photodiode sensor

A measured displacement resolution of <3 nm is demonstrated with a common cathode differential photodetector combined with a laser-diode optical source and a fiber-optic collimator. Resolution, standard deviation, and differences between maxima and minima values for the residuals of the least-squares fit suggest that a coherent laser-diode source temporally correlates photoelectron flux between adjacent detector segments, suggesting reduced signal variance and associated electronic (shot) noise. For otherwise similar systems, the laser-diode source provides approximately an order of magnitude reduction in standard deviation compared with a light-emitting-diode source, which implies an equivalently improved measured (including standard deviation) resolution. Combined variances for correlated and uncorrelated detectors and their measured variances are outlined. The measured resolution is a sum of both the (ideal) mathematical variance based on the detector noise (millivolts) divided by the system sensitivity (millivolts per nanometer, and the standard deviation of the noise (nanometers).     

实时跟踪控制系统中的数字滤波技术

在高精度的实时跟踪控制系统中，由探测器等其他一些因素给系统带来的噪声将不容忽视，数字滤波将是滤除噪声的有效手段，，由于系统实时性和采样频率的要求，本文介绍几种时跟踪系统中常用的数字滤波方法，并对它们在实时跟踪系统中的作用进行了和比较。     

非高斯噪声激励下非线性漂移Fokker-Planck方程的非稳态解及其应用

非高斯噪声广泛存在于各种非线性系统，对非高斯噪声所驱动系统的非稳态演化行为进行研究可以更为深入的了解其内在的演化机理．本文对非高斯噪声和高斯白噪声共同驱动的非线性动力学系统的非稳态演化问题进行研究．首先应用格林函数的 $\Omega$ 展开理论在初始区域对非线性动力学系统进行线性化，然后结合本征值和本征矢理论推导出了该系统 Fokker-Planck 方程的近似非稳态解的表达式，最后以 Logistic 系统模型为例分析了非高斯噪声强度，关联时间及非高斯噪声偏离参数对非稳态解以及一阶矩的影响．研究结果表明，用 Logistic 模型描述产品产量增长时，其非稳态解可更好地反映产品产量在不稳定点附近的演化行为．     

The error performance simulation for DEQPSK systems employing nonlinear phase synchronizers

Abstract

In this paper, we use the importance sampling (IS) method to evaluate the bit error rate (BER) for systems employing nonlinear synchronizers. It is shown by simulation results that the sample sizes required by the IS method for evaluating the BER of systems with nonlinear synchronizers are almost constant for various values of signal‐to‐noise ratio (SNR). This implies that the efficiency of IS to MC method approaches infinity as the SNR becomes very high. It is also shown in this paper that for differential decoding of QPSK signals, the error performance of a system with nonlinear synchronizer of size 15 is close to that of a coherent system.     

Nonparaxial vector-field modeling of optical coherence tomography and interferometric synthetic aperture microscopy

A large-aperture, electromagnetic model for coherent microscopy is presented and the inverse scattering problem is solved. Approximations to the model are developed for near-focus and far-from-focus operations. These approximations result in an image-reconstruction algorithm consistent with interferometric synthetic aperture microscopy (ISAM): this validates ISAM processing of optical-coherence-tomography and optical-coherence-microscopy data in a vectorial setting. Numerical simulations confirm that diffraction-limited resolution can be achieved outside the focal plane and that depth of focus is limited only by measurement noise and/or detector dynamic range. Furthermore, the model presented is suitable for the quantitative study of polarimetric coherent microscopy systems operating within the first Born approximation.     

Extended viewing angle holographic display system with tilted SLMs in a circular configuration

This paper presents an extended viewing angle holographic display for reconstruction of real world objects in which the capture and display systems are decoupled. This is achieved by employing multiple tilted spatial light modulators (SLMs) arranged in a circular configuration. In order to prove the proper reconstruction and visual perception of holographic images the Wigner distribution function is employed. We describe both the capture system using a single static camera with a rotating object and a holographic display utilizing six tilted SLMs. The experimental results based on the reconstruction of computer generated and real world scenes are presented. The coherent noise removal procedure is described and implemented. The experiments prove the possibility to view images reconstructed in the display binocularly and with good quality.     

Dynamics of adaptive optical systems

Dynamic (time) characteristics of adaptive systems are analyzed. A common adaptive system with a finite frequency band (or a finite response time) is described as a dynamic constant time-delay system, where time delay is to be much shorter than the time of coherence radius transfer through an optical beam by a mean wind speed. The questions of coherent beam formation are considered with use of the reference source. The analytical calculation of the Strehl parameter is made on basis of the generalized Huygens-Kirchhoff principle. An adaptive system is considered where the correcting phase is calculated with the use of both its derivatives and the signal, as well as adaptive systems using different time-predicting algorithms of the correcting signal for future time points. The use of a predicted phase front of the correcting wave allows much longer time delays. The stronger the phase distortions in the optical wave, the higher the time gain in comparison with common (with constant time delay) adaptive systems.     

Properties of Output Signal Moments of Optical Processors

General results for the output signal moments are given for both linear and bilinear systems and both space-variant and space-invariant processing. As an example of a bilinear system, a partially coherent system is considered. The properties of intensity moments for a Fourier optical processor and an imaging system with partially coherent illumination are also investigated.