Speckle pattern interferometer

We describe in this paper a speckle interferometer constituted by two partially diffusing plates. They are illuminated by a laser and the resulting intensity distribution is observed in the image plane of the source. Each speckle of this plane (Fourier plane) is modulated by a ring system whose interference order depends on its phase. Since the observation plane is a Fourier plane, a longitudinal or lateral shift of one of the diffusers results only into a change of the modulating fringes, the speckles themselves remaining unchanged. A photographic plate which records successively the intensity distribution lying in the Fourier plane before and after the considered shift, exhibits after processing a system of Moiré fringes, the shape of which depends on the nature of the translation given to the diffuser between the exposures.     

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.     

Laternal-shift interferogram formation on two-exposure recording of a focused-image specklegram

It is shown theoretically and experimentally that on reproduction of a two-exposure record of a focused groundglass-image specklegram, a lateral-shift interferogram formed in the far diffraction zone in bands of infinite width characterizes the axial wave aberrations of the lens with which the record was made. The interferometer has twice the sensitivity at a given lateral shift, and the form of the interference pattern does not depend on the off-axis wave aberrations of the lens. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 14–20, March, 1997.     

Speckle reduction by a rotating aperture at the fourier transform plane

Statistical properties of the time-averaged speckle-reduced pattern at the image plane of a coherently illuminated uniform diffuse object are theoretically and experimentally studied. The diffuse object is assumed to be approximated by a deep random phase screen and zero-mean circular complex Gaussian statistics is also assumed to hold for the formation of speckles. The time-averaging process is performed by using a rotating aperture at the Fourier transform plane of the object. A theoretical study of the speckle reduction is conducted for a rotating Gaussian soft aperture at the Fourier transform plane. Expressions are analytically derived for the mean, autocorrelation function, power spectrum, and contrast of the time-averaged speckle pattern at the image plane. In particular, the contrast of the time-averaged speckle pattern is theoretically evaluated and its characteristics are discussed in detail. The theoretical results for the contrast are experimentally confirmed using a TV/film recording system. Excellent agreement between theoretical and experimental results is obtained.     

Optical method of determination of stress at a point

A method of determining stress at a point is suggested here. The effect of bending of a wave front that is due to variations of the refractive index is used to measure different aspects of stresses. A Fourier lens with a cross slit at its front focal plane is used to form interference fringes at planes near its back focal plane. The sample, illuminated by a plane-parallel coherent beam of light, is placed close to a cross slit, and the change in fringe pattern due to axial shift of the spectrum planes of the slits is measured to relate it to the state of stress.     

Diffraction of a Gaussian light beam at the right-angle edges of a plate and the interference pattern in the shadow region

A circular Gaussian beam of monochromatic laser radiation is normally incident to the plane of a right-angle thin metal plate and diffracts at the edges of the plate angle. It is revealed that two main fragments of a composite diffracted wave with cylindrical wave fronts whose axes are mutually orthogonal occur and interfere with each other in the shadow region behind the plate. This is found from the characteristic interference pattern on a flat screen behind the plate. This interference pattern consists of intensive curvilinear, wedge-shaped bands that are located symmetrically in pairs with respect to the bisector of the direct central angle of the circular shadow sector.     

Effect of primary aberrations on transverse displacement of laser speckle patterns

The effect of primary aberrations on the transverse displacement of laser speckle patterns in the real image plane due to transverse displacement of an object is studied in the approximation of Fourier optics. Primary aberrations cause: (i) a complementary displacement of the speckle pattern; and (ii) its decorrelation. The main features of complementary displacements are as follows: (a) the overall complementary displacement is the sum of complementary displacements caused by each one of the primary aberrations; (b) the complementary displacement caused by the spherical aberration is uniform in the image plane; (c) spherical aberration and curvature of field cause complementary displacements that are parallel to the object's displacement; (d) the complementary displacement caused by distortion is always zero on the optical axis; (e) the complementary displacement caused by distortion is free of decorrelation; (f) complementary displacements are non-proportional to the object's displacement; and (g) complementary displacements depend on the position of the illuminating source with the exception of the complementary displacement caused by distortion.     

Spatial Filtering of Lateral-Shear Interferograms in the Case of Double-Exposure Recording of a Lens Fourier Hologram of a Mat Screen. II

Distortions of lateral-shear interferograms in fringes of infinite width due to hologram aberrations are analyzed in a third approximation for a complex field amplitude. The interferometer sensitivity range in the field is shown to increase in the case where a Fourier hologram of a mat screen is recorded using a negative lens, two identical subjective speckles of two exposures are superimposed in the hologram plane, and errors of control are eliminated.     

Lateral-shear interferograms registered with double-exposure recording of a gabor lens hologram

An analysis is made of the results of a double-exposure recording based on superposing the subjective speckle fields of a Gabor hologram with a negative lens located in the plane of the amplitude scatterer. It is shown that when the hologram is reconstructed a lateral-shear interferogram is formed in this plane and on the optic axis if the diffraction field is spatially filtered, and an interference pattern having twice the interferometer sensitivity for a fixed lateral shear is localized in the plane of the hologram. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–54, March, 1998.     

Measurements of axial displacements undergone by a diffusing object in speckle photography

The speckles of the image plane of an object are both radially shifted and decorrelated when the object is axially translated through an amount ?. We demonstrate that this radial shift, which is related to the position of the pupil of the optical system, disappears when the pupil lies in the back focal plane of the imaging lens. However, if the irradiance of the image plane is twice recorded on a photographic plate which is laterally shifted through ζ_H between the exposures, the minimum value of the contrast of the Fourier fringes exhibited by the plate after processing, gives the value of ? if ? is less than a particular value, ?_M which will be defined. Also we propose a new speckle measurement method in which the fringes are automatically removed when ? is greater than ?_M. We record the image of the object illuminated in convergent light through an amplitude diffuser placed in the Fourier plane of the object. The mean speckle speckle size of the diffuser is equal to the mean size of the speckles generated by the object in its Fourier plane.     

高斯型弱散射屏产生的像面散斑场的分布特性研究

弱散射屏产生的远场散斑由一个中央亮斑和一个分布于亮斑周围而与正态散斑类似的散斑结构, 根据弱散射屏远场的散斑图样, 人们假设弱散射屏产生的像面散斑为均匀背景与正态散斑两者相干叠加的结果, 但这种假设与实际像面散斑存在歧异, 基于上述情况, 本文利用4f高通滤波光学成像系统, 研究了高斯型弱散射屏产生的像面散斑场的统计特性, 得出只有表面均方根粗糙度与入射光波的波长相差不多时上述假设才是可行的结论. 关键词： 弱散射屏 f光学成像系统')" href="#">4f光学成像系统 像面散斑     

Formation of interference patterns during double-exposure recording of lens Fourier speckles

Within the Fresnel approximation we consider the formation of a speckle interferogram, sensitive to the inclination of the wave front or the derivative of the normal displacement of the object during its coherent illumination by either a diverging or converging spherical wave. This results in recording a Fourier transform speckle pattern of light diffusely scattered by the surface into the plane of the photographic place. It is shown, both theoretically and experimentally, that the sensitivity varies according to the variation of the Fourier transform scale.V. V. Kuibyshev Tomsk State University. Translated from Izvestiya Vyssikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 100–105, August, 1994.     

载频调制大剪切电子散斑干涉系统

大剪切电子散斑干涉技术不需要引入参考光，具有条纹质量好等特点。提出将干涉场的载频调制技术引入到大剪切电子散斑干涉中，可形成具有载频调制功能的新的电子散斑干涉系统。该系统具有对测量环境的隔振振动要求低，能方便定量求解物体的变形场等优点。首先讨论大剪切载频的调制机理，然后利用中心加载、周边固定的圆盘进行典型实验，设计了可用计算机控制且可对参考物进行精确偏转的步进电机系统，进而实现了对电子散斑干涉场的自动控制调制。最后，利用傅里叶变换法对调制条纹进行解调，解调出变形场的相位，并通过相位与位移的转换计算，得到精确的物体变形场。实验结果证明，该系统能够调制电子散斑干涉场，求解物体的位移场。     

Correlation of speckle patterns generated by laser point source — Illuminated diffusers

In this paper it is shown that, when a ground-glass transilluminated by a diverging or converging beam is axially translated, there exists a particular plane in which the corresponding speckle pattern remains correlated. Consequently, under some experimental conditions on this incident beam and the geometry of the optical setup, a speckle pattern generated by a set of two parallel ground-glasses suffers no decorrelation when one of them is axially or laterally translated.     

Continual deformation analysis with scanning phase method and time sequence phase method in temporal speckle pattern interferometry

If a laser beam illuminates a continual deformation object surface, it will lead to a temporal speckle pattern on the observation plane. Recording this time-dependent speckle pattern the deformation of the surface of an object can be obtained. Two methods, scanning phase method (SPM) and time sequence phase method (TSPM), have been introduced for measuring the displacement caused by the deformation in temporal speckle pattern interferometry (TSPI). Their principle is that by capturing a series of speckle interference patterns related to the object deformations, the fluctuations in the intensity of the interference patterns can be obtained. Through scanning these fluctuations and estimating both the average intensity and modulation of the temporal speckle interference patterns, the phase maps for whole-field displacements are calculated. In this way one is capable of quantitatively measuring continual displacements simply using a conventional electronic speckle pattern interferometry (ESPI) system without phase shifting or a carrier. The elaboration on the new methods is given in this paper and experiments are performed to demonstrate their performance with a conventional ESPI system.     

Spatial filtering of the diffractional field of a double-exposure hologram of a focused scatterer image. Part I

Interferometer sensitivity to a transverse or longitudinal displacement is analyzed for the case of diffusively scattering plane surface. It is shown that the sensitivity does not change when an off-axis spherical reference wave is used instead of a flat one at the stage of hologram recording. However, localization of interference fringes in the Fourier plane, where a pupil image of a positive lens is filtered (the lens was used for recording a hologram of a focused scatterer image), is not accompanied by a parallax phenomenon. In addition, in the case of controlling the longitudinal displacement of the scatterer, the interferometer sensitivity threshold is decreased. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 21–30, August, 2007.     

大剪切电子散斑干涉的载频调制与位移场测量

将电子散斑干涉场的载波调制引入到大剪切电子散斑干涉中,通过对参考物的微小偏转引入载波条纹;利用傅里叶变换法,解调出了变形场的相位,从而实现了物体变形场的精确测量。讨论了大剪切载频的调制机理,理论分析表明,调制条纹的空间频率与参考面偏转的角度成正比;因此,控制参考面的偏转角度可实现不同位移量系统的调制。利用中心加载周边固定圆盘进行了典型实验,实验结果证明在大剪切电子散斑干涉技术中可以通过参考面的旋转高质量地实现电子散斑干涉条纹的调制,求解位移场。该系统具有系统简单,不需要专门引入参考光,条纹质量好等优点。该技术可扩展电子散斑干涉的应用范围,有一定的实际应用价值。     

Reduction of speckle in an image by a moving aperture - second order statistics

In an earlier paper the second-order statistics of time-averaged speckle were investigated for the case of speckle formed in the Fraunhofer plane when an aperture was moved over the surface of a uniformly illuminated diffuse object. In this paper it is the intention to substantiate a claim that was made in that paper that the same treatment will also apply to time-averaged speckle in an image plane when an aperture is moved in the pupil plane of the imaging lens. The optical system is allowed to have aberrations of any degree of severity, and the object is allowed to have non-uniform brightness, subject to the condition that the brightness variations are slow in comparison to the size of the (aberrated) point spread function. The treatment makes use of the usual assumption that a very large number of independent scattering points in the object contributes to any one point in the image: for this assumption to be realistic, however, it will be shown that the point spread function of the lens must be of a size that restricts us either to systems where the numerical aperture in object space is low or, alternatively, to systems where the aberrations are severe.     

天文望远镜像差对斑点成像技术的影响

着重研究了采用斑点成像技术处理天文望远镜图像时,光学系统固定像差对图像恢复结果的影响。在详细研究各种恢复天文图像振幅和相位的理论和方法的基础上,建立了一个包括Labeyrie振幅恢复方法和KnoxThompson相位重构方法的恢复扩展目标的斑点成像处理模型,分析了光学系统固定像差对系统传递函数相位分布和目标相位重构的影响：天文目标通过大气成像,固定像差将会被淹没在大气湍流随机起伏中,像差对相位重构没有显著影响。处理图像结果表明,斑点成像技术能同时消除大气湍流和望远镜系统固定像差的影响,得到高分辨力的扩展目标图像。还提出了一种消除光学系统像差的方法。     

Simultaneous measurement with one-capture of the two in-plane components of displacement by electronic speckle pattern interferometry

We present the simultaneous measurement of the two in-plane displacement components by electronic speckle pattern interferometry with three object beams and without an in-line reference beam. Three interference fringe patterns, corresponding to three different sensitivity vectors, are recorded in a single interferogram and separated by means of the Fourier transform method. Then, two interference fringe patterns are selected to obtain the in-plane displacement components.