V. A. Zubov

Application of speckle interferometry to the analysis of refractive-index gradients in flows

A version of a scheme of speckle interferometry is considered, which is intended for the analysis of the distribution of refractive-index gradients in optically transparent media. The application of this approach to problems of hydrodynamics and gas dynamics makes it possible to determine the structure of the distribution of optical inhomogeneities in liquid and gaseous flows. The method is based on the recording of patterns of two speckle structures obtained in the plane of spatial frequencies by using illumination with an auxiliary speckle structure. One speckle structure is formed in the absence of an object, and the other one is formed by transilluminating an object. In comparison with other known phase methods, the speckle-interferometry methods make it possible to change the measurement sensitivity in a wide range and substantially simplify the interpretation of the results obtained.

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.

Optical-Information Transfer Through Perturbing Media and Determination of the Transfer Function

A version of the solution of the problem of simultaneous determination of the structure and characteristics of a two-dimensional signal and of two-dimensional complex transfer or instrumental functions is considered. The solution is based on measurements of four independent intensity distributions for spectral representation of a signal: Isr(Wx, Wy) for a signal subjected to the transfer function, Ismrn(Wx, Wy) for a signal affected by additional specially produced modulation and the transfer function, Isrn(Wx, wy) for a signal of the form Isr(Wx, Wy) with a certain additional modulation at the output, and /5mm(wx,u/y) for a signal of the form Ismr(Wx, Wy) with a certain additional modulation at the output. The intensity distributions obtained in the work make it possible to calculate the amplitude and phase components of the signal being analyzed and the transfer function. Additional modulations should provide visualization of phase information in one form or another.Linear amplitude modulation, which represents a particular form of spatial modulation, is analyzed. For this case, concrete expressions making it possible to calculate the amplitude and phase characteristics of the spectra of the signal being analyzed and the transfer function and, therefore, the characteristics of both the signal itself and the transfer function are obtained.

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 and analysis of optical inhomogeneities with steep refractive-index gradients in stationary transparent media by speckle-interferometry methods

A version of a scheme of speckle interferometry is considered, which is intended for the analysis of the stationary distribution pattern of steep refractive-index gradients in optically transparent media. The application of this approach to problems of hydrodynamics and gas dynamics allows one to determine the structure of distribution of optical inhomogeneities in liquid and gaseous flows or media. The method is based on the recording of patterns of two speckle structures obtained in the plane of image formation of the object by an optical system when the object is illuminated by radiation having an auxiliary speckle structure. The patterns correspond to the two positions of an object shifted somewhat in the direction of the optical axis of the system. Contrary to the common methods of speckle interferometry, only the state of the object being investigated for two different conditions of illumination by the probe radiation is used for the detection in this case. The difficulties arising in the measurements of the objects with steep refractive-index gradients by the known methods of speckle interferometry are accordingly practically eliminated in the scheme under consideration. In comparison with the schlieren phase methods, this method offers higher possibilities in the variation of sensitivity.