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).     

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.     

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.     

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.     

Analysis of the amplitude and phase structure of transmitting media with probing field registration in the image plane

The problem of obtaining information on the amplitude and phase internal structure of a medium in which radiation propagates is considered. The information is extracted by probing the medium; the information on the amplitude and phase distribution of the probing field behind the transmitting medium in the plane of image formation is analyzed. A modified version of the modulation-spectral method proposed earlier by the authors is applied. In this version, there is no need to act on the probing field in the plane under investigation. The interpretation of results is simplified since the image is registered. Two versions of the schematic solution are analyzed. The first version corresponds to the experimental scheme intended for media that produce a modulating action on radiation and is described by multiplication by a complex function characterizing the action. The second version corresponds to the case when the action of the medium leads to a redistribution of radiation and can be presented by the convolution of the probing signal and the function describing the action.     

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.     

Spectrum-modulation method for measuring the amplitude and phase characteristics of time-varying optical signals and transfer functions

The solution of the phase problem in optics, as applied to the determination of the amplitude and phase characteristics of optical signals varying in time and of the transfer functions of media transmitting the signals, is considered. The solution of this problem is based on using the spectrum-modulation method. In particular, the possibility of studying ultrashort processes is considered. The analysis was performed by probing the medium with an optical signal of an arbitrary structure. To obtain the information required, we used a four-channel optical arrangement with a spectral instrument, which records the intensity distributions directly for the signal under study after it passed through the medium; for the signal that was preliminary modulated in the specific manner and then passed through the medium; for the signal that was additionally modulated after passing through the medium; and for the signal that was additionally modulated both before and after passing through the medium. Each of these modulations should provide, to some extent, visualization of the phase information. Two variants of analysis were considered. In the first variant, the influence of the medium to be analyzed on the radiation considered is represented as modulation of the latter in time. The second variant is associated with studying the medium, whose influence on the signal brings about time-redistribution of the radiation and is described by a convolution operation.     

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.     

聚焦光在亚表面损伤介质中的散射特性

针对光学元件的亚表面缺陷,结合基于激光共焦层析的亚表层检测方法,建立聚焦光束在亚表面损伤介质中的传输模型,并采用有限元分析方法,仿真研究K9玻璃光学元件亚表层缺陷对聚焦光束的散射调制特性,特别对颗粒状和微裂纹两类特殊缺陷的光学调制特性进行研究和分析,探索了波长、缺陷大小、缺陷折射率及缺陷方向对聚焦光束散射特性的影响规律,通过分析包含亚表面损伤缺陷信息的光场分布图和强度变化曲线,获得了亚表面损伤缺陷的信息,并对其进行评价。     

Influence of the Brownian movement on the motion of nanoand micro-particles in the inhomogeneous optical field

The motion of light scattering particles of the Mie and Rayleigh micro- and nano-range type in the inhomogeneously-polarized optical field, with allowance made for the Brownian movement, is analysed in the paper. The spatial modulation of polarization in the observation plane determines the spatial modulation of the volume energy density. That is why the velocity and the resulting optical force, which cause the motion of the testing particles, change according to the degree of coherence of the interacting fields. The influence of the forces which arise in the viscous medium and cause the Brownian movement upon the mechanisms of manipulating and trapping testing particles by the optical field is studied.     

Speckle diagnostics of multiple scattering media with the use of frequency-modulated laser radiation

A method for probing randomly inhomogeneous multiple scattering media with the use of frequency-modulated laser radiation is considered. The method is based on analysis of the dependence of the blinking index of time-averaged speckles formed upon scattering of the probing radiation in a medium on the frequency modulation depth of the probing radiation. In the case of a binary frequency modulation, the blinking index of the detected speckle-modulated radiation is determined by the cosine Fourier transform of the probability density of the optical path-length difference of partial components of the scattered field in the probed medium. The values of the probability density of the optical path-length difference reconstructed with the use of the proposed method from the measured blinking index of speckles for model scattering media (fluoroplastic layer and layer of TiO₂ particles on a glass substrate) are in a good agreement with the results of statistical simulation of the probing radiation transfer in multiple scattering media.     

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.     

Axial radiation force exerted by general non-diffracting beams

The axial radiation force exerted by a general non-diffracting beam on an object of arbitrary shape in lossless medium is analyzed. The object may be on or off the beam's axis. The analysis is based on the plane-wave representation of the beam using an azimuthal function and conical angle. The analytical expression relates the force to axial projections of the extracted and scattered momentum. Using an extended optical theorem, the extinction is related to the scattering at the forward direction of the beam's plane wave components. The axial force is expressed using the scattering amplitude and known angular functions.     

Calculation of radiation field in semi-transparent medium with consideration of incident collimated radiation

The mathematical model of radiation field in a semi-transparent medium formed under the action of incident collimated and diffusion radiation was developed and implemented numerically. To solve the problem, the approach on the basis of modified average flux method was developed. Method testing via comparison with results of other authors has proved its high reliability and accuracy. As an example, the effect of different factors on radiation field was analyzed: self-radiation of medium, scattering anisotropy, and bottom reflectance.     

Synthesis of multifrequency optical holograms of rotating objects

A two-channel system for synthesizing two-dimensional complex multifrequency optical holograms of rotating objects was developed. In the object irradiation (longitudinal) direction, a hologram is synthesized due to multifrequency laser radiation, and in the transverse direction, the synthesis is provided by object rotation. The object image is reconstructed in the plane coinciding with the plane of its rotation. The resolution of the synthesized hologram in the longitudinal direction is determined by the frequency bandwidth of the laser radiation, and in the transverse direction, the resolution is determined by the initial laser-radiation frequency and the angle of object rotation during the time of hologram synthesis. Using a digital simulation, the degree of isoplanarity of the multifrequency system for synthesizing holograms of rotating objects and its noise immunity under conditions of phase noises were analyzed.