The information of ambiguity

The phase space characteristics of a quantum state are best captured by the Wigner distribution. This displays transparently the diagonality information of the density matrix. The complementary function offering transparently the off-diagonal elements is captured by a function called the S-function, or the ambiguity. In carrying the maximal information about the quantum coherences it represents the uncertainties or ambiguity of the diagonal information. Mathematically this is manifested in its role as the phase space moment generating function. Formally it complements the information in the Wigner function. These formal relations provide the starting point for the present investigations. As a measure of quantum uncertainties, ambiguity may be used to define a probability measure on the off-diagonality. The mathematical and physical consistency of this view is presented in this paper. For a pure state, we find the extraordinary result that such distributions are their own Fourier transforms. The physical interpretation of this distribution as a carrier of classical signal fuzziness suggests the introduction of heuristic approximations to the observational uncertainties. We illustrate the properties and interpretation of the ambiguity function by some specific examples. We find that for smooth, ‘Gaussian-like’ distributions, the heuristic considerations provide good approximations. On the other hand, representing quantum interferences, the ambiguity serves as the most positive probe for the ultimate quantum structures which have been called sub-Planckian. They are interesting because it has been argued that such structures are physically observable.     

Efficient reconstruction of two-dimensional complex amplitudes utilizing the redundancy of the ambiguity function

In a previous paper [Opt. Commun.225, 19-30 (2003)] we presented a method to reconstruct two-dimensional complex amplitudes by using the ambiguity function of one-dimensional intensity scans, obtained from two optical setups involving cylindrical lenses. We demonstrate that the internal redundancy of the ambiguity function can be utilized to improve the efficiency of this method even further. We show that the phase reconstruction errors can be minimized with an appropriate algorithm, and we present experimental data that illustrate the efficient reconstruction of a two-dimensional phase element.     

Vibration measurement by temporal Fourier analyses of a digital hologram sequence

A method for whole-field noncontact measurement of displacement, velocity, and acceleration of a vibrating object based on image-plane digital holography is presented. A series of digital holograms of a vibrating object are captured by use of a high-speed CCD camera. The result of the reconstruction is a three-dimensional complex-valued matrix with noise. We apply Fourier analysis and windowed Fourier analysis in both the spatial and the temporal domains to extract the displacement, the velocity, and the acceleration. The instantaneous displacement is obtained by temporal unwrapping of the filtered phase map, whereas the velocity and acceleration are evaluated by Fourier analysis and by windowed Fourier analysis along the time axis. The combination of digital holography and temporal Fourier analyses allows for evaluation of the vibration, without a phase ambiguity problem, and smooth spatial distribution of instantaneous displacement, velocity, and acceleration of each instant are obtained. The comparison of Fourier analysis and windowed Fourier analysis in velocity and acceleration measurements is also presented.     

Wavelet analysis of speckle patterns with a temporal carrier

A novel temporal phase-analysis technique that is based on wavelet analysis and a temporal carrier is presented. To measure displacement on a vibrating object by using electronic speckle pattern interferometry, one captures a series of speckle patterns, using a high-speed CCD camera. To avoid ambiguity in phase estimation, a temporal carrier is generated by a piezoelectric transducer stage in the reference beam of the interferometer. The intensity variation of each pixel on recorded images is then analyzed along the time axis by a robust mathematical tool, i.e., a complex Morlet wavelet transform. After the temporal carrier is removed, the absolute displacement of a vibrating object is obtained without the need for temporal or spatial phase unwrapping. The results obtained by a wavelet transform are compared with those from a temporal Fourier transform.     

Defocus transfer function for circularly symmetric pupils

We present a two-dimensional function that graphically illustrates the effects of defocus on the optical transfer function (OTF) associated with a circularly symmetric pupil function. We call it the defocus transfer function (DTF). The function is similar in application to the ambiguity function, which can be used to display the OTF associated with a defocused rectangularly separable pupil function. The properties of the DTF make it useful for analyzing optical systems with circularly symmetric pupils when one is interested in the OTF as a function of defocus. In addition to presenting these properties, we give examples of the DTF for systems with clear, bifocal, and annular pupil functions.     

去斜聚束式 SAR 方位模糊度分析及仿真

方位向模糊度是衡量其成像质量的一个重要指标. 而传统的条带模式 SAR 方位模糊度计算方法对于聚束成像模式来说并不适用. 通过分析方位模糊度的来源及聚束工作模式下回波信号的特点,定义了聚束模式 SAR 的方位模糊度函数,并针对星载去斜条件讨论了方位模糊度函数的变化,采用实际的卫星和雷达参数的仿真结果为系统设计提供了可靠的理论依据.     

Netted radar sensitivity and ambiguity

The performance of netted radar is evaluated in terms of a netted version of the radar equation and the ambiguity function. A software simulation has been developed to allow assessment of netted radar sensitivity and ambiguity properties in both two-and three-dimensional space. Simulation results demonstrate that coherent netted radar sensitivity depends not only on the radar parameters, but also on the numbers, locations and specification of transmit and receive nodes. The netted radar ambiguity function is affected by a combination of many factors. In addition to those that determine the form of the monostatic ambiguity function, the locations of transmit and receive nodes as well as the position and velocity of the target all are shown to play an important role in evaluating system performance. As a result of these dependencies, it is shown that there is severe degradation of range and Doppler resolution when a target crosses sufficiently close to a transmit-receive baseline.     

Optical realization of the ambiguity function of real two-dimensional light sources

We propose a setup that can generate the sectional ambiguity function of a two-dimensional real light source. The setup is easy to implement; the theoretical analysis and experimental results are given.     

Enlarging the depth of focus by filtering in the phase-space domain

The ambiguity function was employed as a merit function to design an optical system with a high depth of focus. The ambiguity function with the desired enlarged-depth-of-focus characteristics was obtained by using a properly designed joint filter to modify the ambiguity function of the original pupil in the phase-space domain. From the viewpoint of the filter theory, we roughly propose that the constraints of the spatial filters that are used to enlarge the focal depth must be satisfied. These constraints coincide with those that appeared in the previous literature on this topic. Following our design procedure, several sets of apodizers were synthesized, and their performances in the defocused imagery were compared with each other and with other previous designs.     

多Agent系统中含糊性的处理方法

为了能够正确理解含糊语句所传达的信息概念，分析了含糊性如何影响对话双方的知识，尤其是含糊语句产生后，谈话双方彼此了解的情况。提出基于Kripke结构的多agent系统中含糊性的处理方法，多gent系统的信息状态用Kripke结构表示，并用tell函数来实现系统间的通信，而tell的应用受到Grice原理的约束。此方法能够正确地把由含糊子句传递信息中的语义含糊和感觉含糊区分开来，因而对于研究多agent系统具有一定的实用价值。     

Conjugate phase plate use in analysis of the frequency response of imaging systems designed for extended depth of field

We unveil a relationship between generating a point spread function with a pair of conjugate phase elements and visualizing the modulation transfer function (MTF) of a single phase element for a variable focus error, at a tunable spatial frequency. We show that the defocused MTF of a pair of conjugate phase elements can be expressed as the modulus of the second order ambiguity function of a single phase element. Finally, we propose a tunable wavefront coding technique with a pair of quartic (4th power) conjugate phase elements.     

随机调相连续信号的模糊函数特性及在医学超声成像上的应用前景探讨

传统的脉冲式医用超声成像系统的模糊函数由于存在周期性的速度模糊和距离模糊，影响了图像的质量和分辨力。本文借鉴噪声雷达理论，证明了随机调相连续波信号具有最优的模糊函数特性，并据此提出了随机调相医用超声成像系统的设计思想。这一思想的提出为克服速度模糊和距离模糊，提高图像质量和分辨力，设计新一代医用超声成像系统提供理论依据。     

Unique measurement of the parameters of a twisted-nematic liquid-crystal display

The parameters of a twisted-nematic liquid-crystal display (TN-LCD) are measured with no ambiguity when we measure the intensity transmittance of a system that simply consists of a TN-LCD, two polarizers, a quarter-wave plate, and a monochromatic beam. First we show analytically that the director angle can have a 90 degree ambiguity and the twist angle of the liquid-crystal molecules a 180 degree ambiguity. Then we uniquely measure the parameters by fitting the theoretical predictions to the intensity transmittance measured with and without the quarter-wave plate and by using the quasi local-adiabatic condition. The birefringence of the TN-LCD is measured next as a function of the applied voltage. We design a phase spatial light modulator by using the measured parameters and measure the phase delay of the output beam to excellent agreement with the theoretical prediction.     

Spatial and temporal spectra of periodic functions for spectrum analysis

Both the spatial and the temporal spectra of reference signals used in interferometric spectrum analyzers affect the system performance. We define a class of bandlimited reference signals that have N discrete frequency components of equal magnitude. We show that the system performance is primarily determined by the aperture weighting function and is much less dependent on the specific signal waveform. The aperture weighting function can be used to match the spectral shape to the photodetector size, which then optimizes the dynamic range. Further, since the spatial aperture weighting is converted to an equivalent temporal weighting, this function can also be used to control spurious temporal modulation products. The analysis is extended to include results for periodic chirp signals such as those produced by VCO or SAW devices and shows that the results are not affected by using a reduced duty cycle. We also find that the effect of using finite as opposed to point photodetectors is to introduce an additional factor to the aperture weighting function. Control of both the spatial and temporal modulation products introduced by the periodic reference is necessary to achieve the expected dynamic range.     

Noise and its effects on photoreceptor temporal contrast sensitivity at low light levels

We studied photoreceptors in the locust (Schistocerca americanus) visual system to determine the extent to which quantal noise and intrinsic neural noise limit temporal sensitivity. Typical computational models of the temporal contrast sensitivity function are deterministic, reflect only filter characteristics, and lack explicit noise sources [J. Opt. Soc. Am. 58, 1133 (1968); Vision Res. 32, 1373 (1992)]. We report here that the temporal contrast sensitivity function, at low light levels, is not simply the reflection of a filter function. Our evidence suggests that, at low backgrounds, noise, in conjunction with temporal filtering, plays a role in shaping the temporal contrast sensitivity function. At a given low adaptation level, quantal noise limits sensitivity at low temporal frequencies, while intrinsic noise limits sensitivity at relatively higher temporal frequencies.     

Extended depth of field through wave-front coding

We designed an optical-digital system that delivers near-diffraction-limited imaging performance with a large depth of field. This system is the standard incoherent optical system modified by a phase mask with digital processing of the resulting intermediate image. The phase mask alters or codes the received incoherent wave front in such a way that the point-spread function and the optical transfer function do not change appreciably as a function of misfocus. Focus-independent digital filtering of the intermediate image is used to produce a combined optical-digital system that has a nearly diffraction limited point-spread function. This high-resolution extended depth of field is obtained through the expense of an increased dynamic range of the incoherent system. We use both the ambiguity function and the stationary-phase method to design these phase masks.     

Temporal statistics of the beam-wander contribution to scintillation in ground-to-satellite optical links: an analytical approach

The beam-wander contribution to the scintillation in a ground-to-satellite free-space optical link is one of major importance. An analytical model, based on the duality between beam wander and angle-of-arrival fluctuations, is proposed for the temporal statistics. The expression of the probability density function of the log-amplitude fluctuations is first obtained. Then, the expressions of the spatial and temporal autocovariances are also obtained. We present plots of the beam-wander contribution to the log-amplitude variance, as a function of the transmitter aperture size and the turbulence accumulated in the propagation path. We also present the angular fluctuation and log-amplitude scintillation spectrum plots for some selected cases.     

Amplitude and phase recovery of rotationally symmetric beams

Two methods are presented for the amplitude and phase recovery of optical beams with rotational symmetry. These are the tomographic method based on the ambiguity function and the one-step wavefront recovery based on the measurement of a phase-space distribution closely related to the Wigner distribution function. The results obtained from these two methods are compared, and the appropriateness of using either one of them for specific situations is discussed.