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.     

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.     

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.     

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.     

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。     

Interference of speckle fields in the diffraction zone of a focused spatially modulated laser beam by a random phase screen

The processes of formation of average-intensity interference fringes upon diffraction by a random-phase object of a laser beam having interference fringes and focused on the surface of the object are considered. The dependences of the fringe contrast on the parameters of scattering inhomogeneities of the object and the parameters of the focused laser beam are established in analytical form for various diffraction regimes. Practical possibilities of a method of probing of scattering objects in problems of measuring the parameters of inhomogeneities and problems of interference-pattern formation in optical systems with scattering media are discussed.     

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.     

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.     

Localization of inhomogeneities in diffuse optical tomography based on late arriving photons

An algorithm for localizing inhomogeneities in pulsed diffuse optical tomography is proposed and implemented. A distinctive feature of this technique is the formation of an initial approximation to the spatial distributions of the absorption and scattering coefficients in a biomedical object under study based on the angle-dependent homogeneity index, HI(a). The method allows one to determine the approximate optical structure of the object using late arriving photons and thus solve more rapidly the inverse problem. The suggestion that all absorbing and scattering inhomogeneities in an object under study are spherical also simplifies and enhances image reconstruction.     

Use of spatial filtering in imaging through a randomly inhomogeneous medium

The possibility of improving the image quality of a coherently reflecting object, viewed through a randomly inhomogeneous medium, is investigated theoretically. Three cases of coherent illumination of the object by a plane wave are considered: illumination by unperturbed wave, illumination and viewing through different inhomogeneities of a medium, illumination and viewing through the same inhomogeneities. The spatial spectrum of the average intensity is investigated. It is shown that, when the fluctuations of the intensity in the plane of the receiving lens aperture are strong, the use of a suitable spatial filter located in the focal plane of the lens always gives an improvement of the image, but the quality of the image is better when illuminating and receiving optimal systems coincide.     

Use of spatial filtering in imaging through a randomly inhomogeneous medium

Abstract

The possibility of improving the image quality of a coherently reflecting object, viewed through a randomly inhomogeneous medium, is investigated theoretically. Three cases of coherent illumination of the object by a plane wave are considered: illumination by unperturbed wave, illumination and viewing through different inhomogeneities of a medium, illumination and viewing through the same inhomogeneities. The spatial spectrum of the average intensity is investigated. It is shown that, when the fluctuations of the intensity in the plane of the receiving lens aperture are strong, the use of a suitable spatial filter located in the focal plane of the lens always gives an improvement of the image, but the quality of the image is better when illuminating and receiving optimal systems coincide.     

Backscattering response from periodic spatial patterns in random media

Abstract

In wave-based remote sensing or radio-location of distant objects in a random medium, a high-frequency electromagnetic wave is scattered by object discontinuities, and portions of the scattered radiation can traverse the same random inhomogeneities as the initial incident field. The statistical dependence of the forward–backward travelling events results in an anomaly in the backscattered intensity pattern that carries information about the scattering object. The quality of this information depends on the ability to resolve the fine-structure elements. In this work we investigate the resolving properties of periodic spatial objects by using the random propagators of the stochastic geometrical theory of diffraction.     

Lensless imaging of an arbitrary object

A new class of imaging systems that do not require the use of lenses or similar optical devices is introduced and theoretically investigated. In particular, it is demonstrated that, if an arbitrary plane object is illuminated by an appropriate spherical wave front (generated from a monochromatic point source), then a magnified image of the object intensity distribution can be observed in any transversal plane along the light-propagation direction within the far-field (Fraunhofer) diffraction region. The phenomenon is based on the fact that, under certain conditions, the spherical wave front can modify the energy's angular spectrum of the field distribution in the object plane such that this spectrum replicates the spatial intensity distribution of the object.