Simultaneous Determination of the Amplitude-Phase Structure of an Optical Signal and a Transfer Function with the Influence of the Medium Given by a Modulation Function

We consider a solution to the phase problem in optics as applied to registering and analyzing amplitude-phase structures of 1) d optical fields that form or transfer images and 2) transfer or spread functions of the medium where optically inhomogeneous fields propagate or those of the systems forming fields and producing distortions. The influence of the medium is characterized by the modulation function and is described by the operation of multiplication. In order to measure the amplitude and phase field characteristics and transfer or spread functions, we use an original development of the modulation-spectral method proposed earlier by the authors. There are two variants of optical schemes considered. They include identical parts designed to form the light field to be processed. Using the first optical system, one forms the spectrum of spatial frequencies and introduces the first additional space modulation in the plane of spatial frequencies. The second optical system is placed in the same plane to form the image of the investigated field in the input plane of the developing scheme after passing the transmitting medium. In the first variant, the second part of the scheme contains at the input the third optical system forming the spatial spectrum in the registration plane. At the input of this scheme, the second additional spatial modulation is introduced. In the second variant, the third optical system forms the image of the developing scheme input plane in the registration plane. The second additional spatial modulator is placed in the spatial frequency plane of the third optical system. In the output, in both cases four independent two-dimensional intensity distributions are registered, which allow one to solve the formulated problem.     

Analysis of Two-Dimensional Optical Fields Using an Additional Shift

A solution to the phase problem in optics is considered within the context of registration and analysis of two-dimensional stationary optical fields transformed by the object under study or fields forming an image. To obtain information on amplitude and phase distributions of the light field analyzed, a method of registration of two intensity distributions is used. The first distribution corresponds directly to the amplitude distribution. The other is formed for the sum of the initial field and the field shifted along a certain direction. The intensity distributions obtained allow one to calculate the two-dimensional structure of the field under study. It is noteworthy that the method requires no iteration procedures in solving the problem. This leads to speeding up of the processing and analysis of the information. Two variants of optical schemes for the analysis of light fields are considered. The first one corresponds to registration of the image of the analyzed plane and the second to registration of the spectrum of the spatial frequencies.     

Measurement of the amplitude and phase structures of an optical field and the transfer function for describing the effect of a medium in the form of a modulating function

The phase problem in optics is solved as applied to the detection and analysis of the amplitude and phase structures of two-dimensional optical fields forming or transmitting an image and the amplitude and phase structures of the transfer or instrumental functions of either the media containing optical inhomogeneities or the systems forming fields and involving instrumental distortions. The effect of the medium is characterized by a modulating function and described by a multiplication operation. Two variants of the optical scheme are considered. In each variant, the spatial-frequency spectrum is formed by the first optical system and the first spatial modulation is introduced in the spatial-frequency plane. The second optical system is arranged in the same plane. This system images the field under investigation into the plane located at the exit of the transmitting medium. In the first variant of the optical scheme, the second spatial modulation is introduced in the same plane. The third optical system forms a spatial-frequency spectrum in the detection plane. In the second variant of the scheme, an image of the plane positioned at the exit of the probing medium is formed in the detection plane by the third optical system. The second spatial modulation is introduced in the spatial-frequency plane of the third optical system. In both variants, four independent two-dimensional intensity distributions that make it possible to solve the problem posed are detected at the exit.     

How to Determine the Amplitude-Phase Structure of a 2D Optical Field and a 2D Complex Transfer Function, with the Effect of the Medium Described by Convolution

We consider the solution to the phase problem in optics in application to registration and analysis of the amplitude–phase structure of twodimensional optical fields that form or transmit images, as well as the amplitude–phase structure of transfer and spread functions of media, in which light propagates, or those of systems that form fields or images. The idea of our method is to introduce two additional modulators that visualize phase information. We consider two variants of optical schemes designed for analyzing the amplitudephase characteristics of twodimensional optical fields as well as twodimensional complex transfer and spread functions. These schemes are special because the twodimensional structure of the fields is transmitted at a distance in a disturbing medium or system and four independent twodimensional intensity distributions are to be registered in the course of processing the twodimensional fields. To solve the problem, the first additional modulation preceding the transmitting medium is introduced in the scheme. Then the spectrum of spatial frequencies is formed by the optical system. The second additional spatial modulation is applied either in the optical system plane (the first variant of the scheme) or in the plane of spatial frequencies formed by the optical system (the second variant). A separate optical system is used for registration in the plane of spatial frequencies in the first variant of the scheme and in the image plane in the second variant. The intensity distributions obtained make it possible to solve the problem.     

Determination of the 2D amplitude-phase structure of an optical field and the transfer function in the case of a convolution-like effect of a medium

A solution of the phase problem in optics as applied to the simultaneous detection and analysis of the phase-amplitude structure of image-forming or image-transmitting 2D optical fields and the phase-amplitude structure of probed media or objects, transfer or instrumental functions of signal-transmitting media, or field-or image-forming systems is considered. The effect of media or objects is described by the operation of convolution. The essence of the method applied is the introduction of two additional modulators, which in some way perform the function of visualizing the phase information. Optical schemes of two types are considered. In both cases, the first additional modulation precedes the action of a medium or an object. The second additional modulation takes place either in the plane immediately behind the probed medium (first type of scheme) or in the plane of spatial frequencies formed by the optical system (second type of scheme). In the first variant, the plane of detection is that of the spatial frequencies; in the second variant, it is the plane of the image formation. The resulting intensity distributions yield a solution to the problem.     

Testing and Analysis of the Structure of Transmitting Media or Objects with Registration of the Field Structure in the Image Plane

A solution to the phase problem in optics is considered within the context of the registration and analysis of the amplitude–phase structure of optical nonuniformities in stationary transmitting media or in investigated objects. To solve the problem, the object or the medium is tested by radiation with a known structure. For a certain selected direction of testing, the structural change due to the interaction with the object is registered. To obtain information on the amplitudes and phases of the testing light field, an original development of the modulationspectral method put forward by the authors is used. To solve the problem, the intensity distribution is detected in the image plane both for an unmodulated field and for that subjected to an additional twodimensional modulation specially formed in the plane of spatial frequencies. The modulation should provide a visualization of the phase information contained in the light field. The intensity distributions obtained make it possible to determine the twodimensional structure of the testing field at the output of the medium or the object. In the proposed variant of the method, the testing field should not be affected in the investigated plane. The interpretation of the results is easier, since it is the image that is registered. The two intensity distributions can be registered simultaneously, provided the light beam is divided into two channels after the optical system. It is significant that the method requires no iteration procedures in solving the problem. This allows one to expect speedingup of the processing of the information and analyzing it in almost real time. Two variants of optical schemes are considered in the paper. The first one deals with media or objects with a modulation effect described by multiplication by a complex function characterizing the effect. In the second case, the effect of the object leads to redistribution of the radiation in the investigated plane and is described by the operation of convolution of the testing signal and the function characterizing the effect.     

Modulation-spectral method for analyzing the amplitude-phase structure of optical inhomogeneities of objects

An original solution to the phase problem in optics is considered as applied to the problems of recording and analysis of the amplitude-phase structure of optical fields used for studying fine structures and inhomogeneities in steady-state objects producing effects to fractions of the wavelength period. The problem is solved by probing objects using radiation with a known structure. Intensity distributions of the probing field are detected at the exit from the object by using the modulation-spectral method directly for the spatial frequency spectrum and for the spatial frequency spectrum subjected to additional modulation formed in a special way, which is realized in the plane under study and provides visualization of the phase information contained in the light field in some form. The intensity distributions obtained make it possible to calculate the two-dimensional amplitude-phase structure of the field analyzed and, hence, the fine structure of the optical inhomogeneities of the object analyzed for the chosen probing direction. For steady-state objects, probing in a number of directions is possible. Information on the bulk structure of the inhomogeneities under study can be obtained by using the information available on the symmetry of the object. Two variants of action of the medium on probing radiation are considered. In the first one, the action is related to spatial field modulation (described by the multiplication operation); in the second one, the action leads to redistribution of radiation in the plane studied (described by the convolution operation).     

编码栅在光信息处理中的应用

本文从编码栅对光源、物函数、谱函数的调制原理出发,从三个方面分析了编码栅在光信息处理中的作用及应用实例。     

基于正交调制的偏振光谱成像系统研究

为了同时获取目标的全偏振二维图像信息和其光谱信息,设计了一种基于正交调制的偏振光谱成像系统。该系统由光学接收模块、相位调制器、Wollaston棱镜、Savart偏光镜、检偏器以及成像模块组成。其可以将原始光信号分解成两束相互正交的偏振光,并且分别成像在CCD焦平面的上下两部分上,从而构成两幅偏振图像。两组图像的叠加可以将干涉条纹的数据相互抵消,从而获得目标的纯图像信息,两组图像的相减可以将目标灰度图像相互抵消,从而获得目标的纯干涉条纹。通过理论分析与计算得到了光强分布函数和光谱变化形式。实验在稳定的光源环境中采用高对比度目标与背景板,完成了全偏振图像的实时采集。经相位校正和切趾处理改善了干涉图像的畸变,又通过去低频滤波和阈值滤波抑制了图像中背景噪声的影响,从而实现了对目标图像的提取及偏振光谱的复原。该系统具有稳定性高、光谱分辨率可调、信噪比高、可识别能力强等特点,对在复杂背景中提取目标图像、光谱及偏振态信息具有重要意义。     

Correction to: Generation of amplitude- and phase-modulated signal beam with a phase-only spatial light modulator and its detection by the transport of intensity equation method for holographic data storage

This study evaluates a novel holographic data storage (HDS) that uses a phase-only spatial light modulator (SLM) for the multilevel complex amplitude modulation of a signal beam and the transport of intensity equation (TIE) method to detect the signal beam without interferometry, to increase the capacity of the HDS, simplifying its optical system, and improving the stability of the signal beam modulation and detection. Both the amplitude and phase of the signal beam were modulated by a computer-generated hologram displayed in a phase-only SLM, a 4-f optical system, and a pinhole placed in the Fourier plane. The complex amplitude-modulated signal beam generated by this scheme does not always perfectly match the target complex amplitude, and deviations from the amplitude and phase of the target complex amplitude may exist. It is unclear whether the TIE method, which is sensitive to the state of the beam intensity and the phase distributions to be detected (such as zero-intensity points and phase discontinuities), can accurately detect a signal beam whose complex amplitude is modulated by the modulation scheme with a phase-only SLM. Here, we demonstrate via numerical simulations and experiments that several methods of complex amplitude generation using a phase-only SLM can achieve multilevel modulation of the amplitude and phase of a signal beam and are suitable for detection by the TIE method in HDS.

     

冷铷原子样品中高效静态光信号的生成与调制

为了提高光信息处理元件的性能,实现高效率光信号的静止与存储,本文建立了由双向耦合场耦合的冷铷（87Rb）原子的四能级双Λ型能级机制,并对此机制在生成静态光信号时要求的高效性、持续时间,控制耦合场所需的操作条件以及对信号场强度的相位调制等进行了研究。首先,选取四能级双Λ型87Rb冷原子精细能级,用一对反向传播的行波激光场对能级进行近共振耦合,并沿耦合场方向输入一个正向弱光信号进行探测。接着,通过适当的绝热开启、关闭耦合场,存储光信号和生成高保真度静态光信号。然后,通过选取87Rb原子的不同精细能级结构,得出实现静态光所需满足的必要条件。最后,采用相位调制法对光信号进行处理。结果表明：生成的静态光信号具有高效性,过程持续时间约为80μs;相位调制法可以周期调节静态光脉冲的强度。在此机制下生成的静态光信号满足高效性、易于全光调节和长时效性等要求。     

无衍射特殊光束的产生与三维表征

无衍射光束(如贝塞尔光束、艾里光束)因具有无衍射、自愈合的特性, 在很多领域都有广泛的应用. 本文提出使用纯相位型空间光调制器对光场的复振幅进行调控, 从而可以产生多种复杂模式的无衍射光束, 如强度可独立调控的多个零阶贝塞尔光束, 两个高阶贝塞尔光束干涉生成的花瓣状无衍射光束, 具有多个主瓣的加速光束等特殊的无衍射光束. 通过在待测焦场附近放置一个平面反射镜, 使其沿光轴快速扫描光场, 并由数字相机同步拍摄反射回来的一系列二维光场强度分布信息, 可实现对无衍射光束三维光场强度分布的快速测量和表征. 本实验方法和技术可以快速产生各种复杂的特殊光场并获得其精确的三维可视化重建效果, 在光学显微、光学俘获、光学微加工等领域有潜在的应用价值.     

Modulation properties of spatial three-waveguide system using weakly coupled mode theory

Based on the weakly coupled mode theory, the modulation properties of three-waveguide system are analyzed in general. We examine the modulation behavior for two cases that a voltage is applied on the beamlaunched waveguide or non-beam-launched waveguide. The analytical intensity distributions in both cases are given. Applications of the spatial multi-waveguide coupling systems include spatial light modulators,optical switches, optical interconnection, and spatial optical signal processing.     

电光调制在被动综合孔径成像探测中的应用

介绍了一种新型被动综合孔径成像探测方法:视场辐射信号被接收和放大后,通过电光幅度调制将其幅度和相位信息加载到光波上,经光纤传输在末端形成阵列,通过光学系统直接成像,将视场实时恢复出来.该方法可实现工作在微波、毫米波和太赫兹波段的高分辨力实时成像探测的目的.深入分析了电光调制器在综合孔径成像探测中的应用,建立电光调制模型,讨论了在小信号调制下的电光幅度调制近似理论.通过数值计算与仿真分析,得到综合孔径成像探测中电光调制器的调制信号强度限制的有关结论.结果表明,利用上变频电光调制技术和光信息处理,所得到的成像仿真图的半峰全宽和信噪比性能都优于传统的基于下变频技术的成像仿真结果.     

The measurement of amplitude and phase characteristics of time-varying optical inhomogeneities in transparent media

The solution of the phase problem in optics is considered as applied to the problems of studying time-varying amplitude and phase characteristics of a medium with the use of the spectral modulation method, in particular, for ultrashort times. The analysis is carried out by way of transilluminating the medium or the object under study with a probing optical signal with a known structure. The information required is extracted by directly recording intensity distributions for the spectrum of the probing signal transmitted through the medium and for the spectrum of the signal transmitted through the medium and subjected to additional modulation formed in a special way. The modulation should provide, to some extent, a visualization of the phase information. Two varyings of the analysis are considered. The first varying is related to the action of the medium under study on probing radiation in the form of its temporal modulation. The second varying is associated with the study of media whose action on radiation leads to redistribution of radiation in time and is described by convolution.     

Acoustic tomography of the nonlinear parameter by a small number of transducers

A wave approach to solving the problem of reconstructing the acoustic nonlinear parameter distribution by a simple transmitting-receiving system with broadband modulation of primary waves is proposed. The approach uses the effect of sound scattering by sound, which makes it possible to employ a complicated time processing of signals instead of spatial processing and, consequently, to reduce the number of transmitting and receiving transducers. The possibility of practical implementation of a two-dimensional tomographic scheme based on coherent correlation processing of broadband quasi-random signals at combination frequencies is analyzed. Results of model numerical experiments on reconstructing complicated spatial distributions of the nonlinear parameter are presented.     

超声驻波波面的激光相关成像

本文利用傅氏光学概念分析激光通过声驻波后的远场光场,不但被分解成空间频谱,而且在空间频谱中又有时间频谱。以此为依据,分析了超声驻波成稳定像的原理和过程:通过时间互相关过程,得出不同空间频谱中同时间频率光的非零相关值;再由不同时间频率的非相干光进行强度线性叠加,最后形成超声驻波波面的稳定像。从而澄清了声驻波成像中的一些理论上的混淆,找到了成像的新途径,实验上也得到了证实。     

利用4400系统构造具有光学多道分析功能的信号处理系统

基于4400系统,通过引入光电二极管列阵作为传感器,构造了具有光学多道分析功能的信号处理系统。利用该系统对实际的激光空间分布进行了描绘,给出了高斯场分布的相应参数。通过进一步观测p偏振光在K9玻璃上下表面反射光强比(γ)的角度调制曲线,获得了玻璃表面层的光学参数。实验结果表明,该系统测量精度高,可应用在激光时间信号及空间场分布的表征与测量领域。