The interpretation of holographic interferograms

Holographic interferometry is a very powerful technique for the measurement of small deformations and displacements of opaque solid objects. Unfortunately, the quantitative interpretation of the fringe patterns is somewhat involved, and the large number of papers published on this subject in the past 10 years has caused considerable confusion. This review paper is an attempt to rationalize the field by classifying the many different interpretation schemes into four main techniques, and by offering guidelines for the choice of technique for different applications.     

Spatial filtering of holographic interferograms of lateral shift

With the Fresnel approximation we consider the formation of lateral shift interferograms in diffusely scattering fields during double-exposure recording of Fresnel holograms of a dull screen on the basis of superposition of the objective speckle fields of the two exposures in the plane of the photographic film. It is shown that the interference pattern characterizing the phase distortions of the wave front of radiation, used to illuminate the dull screen, is located in its imaging plane, while the front of the supporting wave is located in the hologram plane. To record them it is necessary to carry out spatial filtering of the diffraction field in the corresponding planes.V. V. Kuibyshev Tomsk State University. Translated from Izvestiya Vyssikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 106–111, August, 1994.     

含冲击波流场干涉图的图像处理方法研究

本文研究了含冲击波流场干涉图的图像处理方法,它包括干涉条纹的快束细化算法,冲击波波阵面的提取算法和时间序列冲击波波阵面的配准算法.根据这些算法,在PC-VISION 100图像处理机上开发了应用软件.实验结果表明,该方法可用于定量计算冲击波的传播速度和压力分布,增加了流场干涉图的用途.     

Analysis of holographic interferograms with a tv picture system

An automatic dual reference beam method for the evaluation of holographic interferograms is presented. Based on the principle of image intensity subtraction, the method employs video electronic recording of the interograms and high speed digital image processing. Quantitative results are given for the bending of a cantilever.     

A relativistic fluid in which shock fronts are also wave surfaces

The equation of state which characterizes the fluid has a corresponding non-relativistic form. The fronts of all shocks that occur in the fluid are characteristics surfaces of the field equations.     

Formation of lateral-shear holographic interferograms in diffusely scattered fields

An analysis in the Fresnel approximation is given of the formation conditions of lateral-shear holographic interferograms in bands of infinite width characterizing the wave aberrations of a microscope optical system over the field in the case of coherent diffuse illumination of a ground-glass screen.Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 71–76, July, 1995.     

High-frequency instability of wave fronts

Experimental evidence is presented that a lateral instability of a wave front, as described earlier in a chemically active medium with the Belousov-Zhabotinsky reaction with decreased excitability, can also occur in a medium with any degree of excitability provided that a high-frequency wave train travels through the medium. The interaction of chemical waves with the boundary of the medium can result in the appearance of wave breaks and spiral waves.     

Dissipation of the excitation wave fronts

An excitation wave in cardiac tissue will fail to propagate if the transmembrane voltage at its front rises too slowly and does not excite the tissue ahead of it. Then the sharp voltage profile of the front will dissipate, and the subsequent spread of voltage will be purely diffusive. This mechanism is impossible in FitzHugh-Nagumo type systems. Here a simplified mathematical model for this mechanism is suggested. The model has exact traveling front solutions, and gives conditions for the front dissipation. In particular, a front will dissipate if it is not allowed to propagate faster than a certain nonzero speed. This critical speed depends only on the properties of the fast sodium current.     

Spatial filtering of holographic lateral-shear interferograms for control of negative-lens aberrations. II

The conditions for lateral-shear interferogram formation in diffusively scattered fields are analyzed taking into account hologram aberrations for the case of transverse displacement of a mat screen and a negative lens before second photoplate exposure. It is shown that the error of control of wave aberrations of the negative lens results at the hologram reproduction stage when the diffusive field is subject to an off-axis spatial filtering. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 58–62, October, 2005.     

Restless rays, steady wave fronts

Observations of underwater acoustic fields with vertical line arrays and numerical simulations of long-range sound propagation in an ocean perturbed by internal gravity waves indicate that acoustic wave fronts are much more stable than the rays comprising these wave fronts. This paper provides a theoretical explanation of the phenomenon of wave front stability in a medium with weak sound-speed perturbations. It is shown analytically that at propagation ranges that are large compared to the correlation length of the sound-speed perturbations but smaller than ranges at which ray chaos develops, end points of rays launched from a point source and having a given travel time are scattered primarily along the wave front corresponding to the same travel time in the unperturbed environment. The ratio of root mean square displacements of the ray end points along and across the unperturbed wave front increases with range as the ratio of ray length to correlation length of environmental perturbations. An intuitive physical explanation of the theoretical results is proposed. The relative stability of wave fronts compared to rays is shown to follow from Fermat's principle and dimensional considerations.     

Effect of aberrations in formation of holographic lateral shear interferograms under high measurement sensitivity

Analysis of the effect of aberrations of a system for recording and optical processing of holograms, as well as of inhomogeneities in hologram bases, on fringe distortion is performed for different methods of holographic shearing interferometry. Different dependences of the degree of fringe distortion in lateral shear interferograms on the measurement sensitivity are revealed. A method of excluding aberrations in formation of shear interferograms is proposed for the cases of single-and double-exposure holograms. Experimental results are reported.     

Shear strength of metals behind shock fronts

Results are presented from a numerical modeling of experiments, conducted by J. Lipkin, R. Asay, L. Chabildas, and J. Wise, in which shock-compressed aluminum and polycrystalline beryllium were loaded again by shock waves. Reproduction of the experimental structures of the impulses in the calculations made it possible to determine the stresses acting in the materials during the primary and secondary shock loading, as well as to study the dynamics of the secondary shock load. It is shown that resistance to plastic strain is maintained in aluminum and beryllium behind the front of weak shock waves with intensities up to 10 GPa. The shear strength of the material behind the front does not correspond to the shear stresses at the Hugoniot elastic limit. For aluminum alloy 6061-T6 and beryllium, shear strength behind the fronts of shock waves with amplitudes up to 10 GPa is lower than in the elastic precursor but is greater than the static yield point of the material in the initial state.V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 62–66, October, 1995.     

全息光刻中的驻波效应研究

对光刻胶内光强分布进行了计算与模拟, 结果表明, 来自基底的反射光与入射光干涉, 光强在垂直基底的方向上呈现强弱周期性变化, 即驻波效应. 进一步的分析与实验结果表明, 随着基底反射率的增加, 驻波效应变得严重, 进而影响光栅掩模的槽形、占宽比并限制线条高度. 为减弱驻波效应的影响, 尝试了使用减反射膜降低基底反射光强度, 实验结果表明, 在基底与光刻胶之间增加一层减反射膜吸收来自基底的反射光强度, 减弱驻波效应的效果显著. 关键词： 全息光刻 驻波 减反射膜     

Improvement of the sensitivity of measurements in the formation of holographic interferograms of wedge plates

We consider the method for improving the sensitivity of measurements in the formation of aberration-free interference images of wedge plates, which do not require a priori knowledge of the position of the wedge edge. It is shown that the sensitivity in the measurement of the wedge angle in real time interferometry is doubled in the case of recording on the reference hologram of the wedge plate followed by its reconstruction by the object light wave that has passed through the wedge plate rotated through 180° relative to the normal. It turns out that recording of a pair of holograms of the wedge plate, one of which is the image of the wedge plate turned through 180° relative to the normal to the plate, makes it possible to increase the sensitivity of measurements by more than an order of magnitude by eliminating the systematic components of measuring errors due to complete compensation of aberrations. The results of experimental testing of the method are considered.     

The structure of shock fronts in various gases

The optical reflectivity of shock fronts in A, N₂, O₂, CO, CO₂, N₂O, CH₄, Cl₂ and HCl have been studied. The thickness of shock fronts in A up to the Mach number M = 1·55 is in agreement with the theory of Gilbarg and Paolucci. The rotational relaxation time is about 5·5 collisions in N₂ and equal to or less than that in the other gases. However, for stronger shocks N₂ does not appear to reach rotational equilibrium in the shock front and a qualitative theoretical discussion of this phenomenon is presented. In HCl there appears to be over-excitation of rotation in the shock front. There is no vibrational excitation of any of the gases.     

High focal depth with fractional-power wave fronts

We explore the use of phase profiles with fractional power for tailoring modulation transfer functions with high focal depth at high pupil apertures. We present numerical simulations of the images that can be obtained with certain fractional-power profiles.     

Speckle statistics in partially corrected wave fronts

Wave fronts distorted by the atmosphere preserve high-spatial-frequency information. This information can be retrieved by use of adaptive optics systems to correct the incoming wave front. This correction should be as nearly complete as possible. In experiments performed in the visible, only partial compensation is attainable. We provide a theoretical model to predict the intensity statistics of the light in the image center as a function of the number of Zernike polynomials corrected.     

On shock waves and phase-transition fronts in continua

A R I - The canonical formalism that considers simultaneously the second law of thermodynamics and the balance of canonical momentum is used to incorporate the case of shock waves among those...     

Nonlinear hydrodynamic corrections to supersonic F-KPP wave fronts

We study the hydrodynamic corrections to the dynamics and structure of an exothermic chemical wave front of Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) type which travels in a one-dimensional gaseous medium. We show in particular that its long time dynamics, cut-off sensitivity and leading edge behavior are almost entirely controlled by the hydrodynamic front speed correction δU_h which characterizes the pushed nature of the front. Reducing the problem to an effective comoving heterogeneous F-KPP equation, we determine two analytical expressions for δU_h: an accurate one, derived from a variational method, and an approximate one, from which one can assess the δU_h sensitivity to the shear viscosity and heat conductivity of the fluid of interest.