D. V. Lyakin

Wiener–Khintchin theorem for spatial coherence of optical wave field

The application of the Wiener–Khintchin theorem for determining the functions of the transversal and longitudinal spatial coherence of the optical field, depending on the parameters of the angular and temporal frequency spectra of the field, is considered. Based on the Wiener–Khintchin theorem, the possibility to derive the van Cittert–Zernike theorem for transversal and longitudinal spatial coherence of the optical field of a spatially incoherent quasi-monochromatic light source is shown. An expression for the dependence of the longitudinal coherence length of the optical field on the width of the frequency and width of the angular spectra of the field is obtained. The results of the interference experiment confirming the dependence of the longitudinal coherence length on the parameters of angular and frequency spectra of the field are presented.

Longitudinal coherence length of an optical field

Longitudinal coherence of an optical field depending on the parameters of its frequency and angular spectra is considered. Expressions for the function and length of longitudinal coherence depending on the width of the frequency and angular spectra are obtained. The competitive influence of the angular and frequency spectra of the field on its longitudinal coherence is discussed. Experimental studies using a longitudinal shearing Michelson interferometer that proves theoretical results are performed.

The effects of temporal and longitudinal spatial coherence in a disbalanced-arm interferometer

During the interference of optical fields possessing broad frequency and angular spectra in an oscillating-mirror Michelson interferometer, the presence of a film introducing an additional optical path increment in one of the arms leads to a mutual shift (recession) of the signals of temporal and longitudinal spatial coherence. This phenomenon leads to breakage of the mutual coherence of the interfering fields. In the presence of two light sources, this effect can be used for the independent determination of the thickness and refractive index of the film.

Changes in longitudinal spatial coherence length of optical field in image space

The laws of variation in the length of spatial longitudinal coherence (LC) and the width of the LC interference pulse of the optical field of an extended spatially incoherent source are established in the image space behind a collecting lens that occurs in the output arm of the scanning (oscillating-mirror) Michelson interferometer. The LC length (and the interference pulse width) varies nonmonotonically and exhibits a local minimum, the magnitude and position of which on the longitudinal axis of the system are determined by the source size and position and depend on the lens aperture diameter.

Effect of decoherence of optical field with broad angular spectrum upon propagation through transparent media interfaces

The effects of the decoherence of a narrow-band optical field with a broad angular spectrum upon propagation through a plate of a transparent medium placed in one of the arms of the Michelson interferometer are established.

Laser interferometer with fine-focused beams to monitor the spatial position of an object

Analogies with interferometers using a light source with low temporal coherence are used to analyze the principles of the construction of laser interferometers with averaging over the photodetector aperture, whose sensitivity to the position of an object being monitored at the maximum of the output signal is as good as that of low-coherence interferometry and tomography.

Influence of the frequency spectrum width on the transverse coherence of optical field

Transverse spatial coherence of the optical field depending on parameters of angular and frequency spectra is considered. Expressions for the function and length of the transverse coherence in relation to the widths of the angular and frequency spectra are obtained. Experimental studies with a modified high-power Young interferometer that prove theoretical results are performed.

Mutual spatiotemporal coherence of optical fields in an amplitude-splitting interferometer

We have considered cross correlations of wave perturbations formed by optical fields at different points of space at the exit of an interferometer with the splitting of the amplitude of the initial wave field. Expressions for the longitudinal spatiotemporal cross-correlation function of perturbations on the optical axis of a Michelson interferometer have been obtained and analyzed. We have determined spatial and temporal intervals in which the wave fields excite mutually coherent perturbations in the exit channel of the interferometer in the free space and in the image space of the lens system. We have found that, in the free space, mutually correlated perturbations arise simultaneously in identical longitudinal intervals, whereas, in the image space, they arise at different times in spatial and temporal intervals varying along the optical axis of the lens. The influence of cross correlations of the wave fields on the interferometer signal has been analyzed.

Low-coherent autocorrelation interferometry of layered media

Anew technique of low-coherent interferometry is discussed. In the method, the optical field reflected from the layered medium is directed into a longitudinal share scanning interferometer for autocorrelation analysis. The object under analysis is outside the interferometer and the reference beam is not used. Theory, results of numerical simulation, and experimental data are presented.

Digital Speckle Photography of Subpixel Displacements of Speckle Structures Based on Analysis of Their Spatial Spectra

We have investigated the capabilities of the method of digital speckle interferometry for determining subpixel displacements of a speckle structure formed by a displaceable or deformable object with a scattering surface. An analysis of spatial spectra of speckle structures makes it possible to perform measurements with a subpixel accuracy and to extend the lower boundary of the range of measurements of displacements of speckle structures to the range of subpixel values. The method is realized on the basis of digital recording of the images of undisplaced and displaced speckle structures, their spatial frequency analysis using numerically specified constant phase shifts, and correlation analysis of spatial spectra of speckle structures. Transformation into the frequency range makes it possible to obtain quantities to be measured with a subpixel accuracy from the shift of the interference-pattern minimum in the diffraction halo by introducing an additional phase shift into the complex spatial spectrum of the speckle structure or from the slope of the linear plot of the function of accumulated phase difference in the field of the complex spatial spectrum of the displaced speckle structure. The capabilities of the method have been investigated in natural experiment.