A. A. Merkin

Modulation-spectrum method for measuring the amplitude and phase characteristics of optical time-dependent signals

A solution to the phase problem in optics is considered for time-varying signals, in particular, of extremely short duration. The modulation-spectrum method is used to obtain information concerning amplitude and phase variations of the optical signal. The intensity distribution is directly, detected for the spectrum of the signal itself and of the signal additionally modulated in a special way. The modulation should provide a visualization of the phase information. The intensity distribution obtained makes it possible to calculate the structure of the initial signal. Three approaches toward analyzing the signals are considered in the paper. The first one is to analyze, the signal whose characteristics vary in time. The second one is to study temporal optical characteristics of the medium or the object under investigation by using a probing radiation of a prescribed structure and measuring the parameters of the radiation passed through the object. The third way is to determine simultaneously the structure of the signal that varies in time and the structure of the transfer function responsible for the influence of the medium, object, or optical system on the propagating signal.

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.

Analysis of amplitude and phase characteristics of two-dimensional optical fields using the modulation-spectrum method

A solution to the phase problem in optics is considered within the context of the registration and analysis of two-dimensional stationary optical fields transformed by an object under study or fields forming an image. The modulation-spectrum method put forward by the authors is used for obtaining information on the amplitude and phase distributions of a light field. To solve the problem the intensity distribution is directly detected for the spatial spectrum or the image, of a signal and for those additionally modulated in a special way. The modulation should provide a visualization of the phase information. The intensity distributions obtained make it possible to calculate the two-dimensional structure of the initial signal. It is essential that the method require no, iteration procedures in solving the problem. This allows one to expect speeding up of the processing and analyzing of the information. Three variants of optical schemes for the analysis of light fields are considered in the paper. The first one uses an additional spatial modulation in the plane of the investigated field, the spectrum of spatial frequencies being recorded. In the second case, the spatial modulation is performed at the input of the processing scheme, the spatial spectrum being registered likewise. In the third variant of the scheme, the spatial modulator is placed at the plane of spatial frequencies, and the image is registered.

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.

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.

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.

Analysis of the amplitude and phase structure of optical nonuniformities in transmitting media with registration in the spatial frequency 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. Stationary media and objects can be tested along several directions The three-dimensional structure of the optical nonuniformities under study can be analyzed using preliminary information on the symmetry of the medium or the object. To obtain information on the amplitudes and phases of the light field and on their change resulting from the testing of the object, the modulation-spectral method is used. To solve the problem, the intensity distribution is directly detected for the spatial spectrum of the field and for that of the field additionally modulated in a special way. The modulation is performed in the plane of the analyzed filed. It should provide a visualization of the phase information contained in the light field. The obtained intensity distributions and the known initial field make it possible to calculate the two-dimensional structure of the analyzed field and therefore the effect of the optical nonuniformities of the medium or of the object on the field. It is important that the method requires no iteration procedures in solving the problem. This allows one to expect substantial speeding up of the processing and analyzing of the information if compared with the known methods. The paper deals with two variants of the influence of the medium or object on the testing radiation. The first one is connected with the spatial modulation of the field and is described by multiplication. In the second case, the effect of the object leads to redistribution of the radiation in the studied plane and is described by the operation of 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.

Measurements of Time-Varying Characteristics of Optical Signals and Inhomogeneities of Tested Substances with Additional Phase Modulation

The problem of investigation of the amplitude and phase structure of a time-varying probing optical signal and the structure of time-varying inhomogeneities of a substance tested by this signal is considered. The analysis is concerned, in particular, with determination of the structure of signals and processes with resolution in the pico- and femtosecond range. The scheme used for the analysis is based on registration of four spatially separated spectra of the studied radiation. The spectra are formed in a four-channel scheme with a twin-wave Michelson interferometer and a spectral device. Modulators based on electrooptical crystals (perovskites) are placed in the channels. The sum spectra are formed: without modulators, with the effect of either of the modulators, and with both of them affecting the radiation. The effect of the studied substance implies either modulating the radiation (in this case it is described by multiplication) or redistributing the radiation (then it is described by convolution).

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.