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Precise measurement of extremely small tilt angles is of immense importance in various scientific and technological applications. Interferometry has always been a tool of great importance in such applications. Most of the conventional interferometric techniques use a Michelson configuration and the problem with this interferometer is that it is extremely sensitive to environmental turbulances and vibrations. In our privious works, we had introduced a cyclic interferometer for the measurement of tilt angles which showed excellent stability against environmental turbulances and vibrations as well as twice the sensitivity. Also, with the introduction of multiple reflections, sensitivity as low as 5 micro radian had been achieved by us. To improve the sensitivity further, we had employed phase shifting techniques. The cyclic configuration being a same path interferometer, we used a polarizing phase shifting technique. For acieving this, we developed a new scheme of polarizing phase shifting techique which is rather simpler compared to those reported in the literature. With this we could precisely measure angles as low as 2 nano radians. However, in these measurements we found that the precise alignment of the quarter wave plate plays an important role in the visibility of the fringes which affects the accuracy of measurement. In this work, we numerically investigate the effect of the misalignment of the quarter wave plate on the visibility of the fringes and consequently on the accurcy of the measurement.

High-accuracy tilt or roll angle measurement is required for a variety of engineering and scientific applications. A cyclic interferometer with multiple reflections has been developed to measure small tilt angles. To accomplish this task, a novel and simple method, phase shift by polarization, was developed. The results of these studies show that the multiple reflection cyclic interferometers can be used to measure object tilts on the order of 0.2 nano-radians. We develop the theory for polarization phase step and show that accurate measurements can be made with the cyclic interferometer.

Accurate measurement of angles is extremely important in various metrological applications. Interferometry has always been an excellent technique for accurate measurements. Several methods have been proposed for accurate tilt measurement using interferometric techniques. Almost all of them use the Michelson configuration which is extremely sensitive to environmental vibrations and turbulences. We know that a cyclic interferometer is extremely stable. Even though it is not sensitive to displacement changes, it is twice sensitive to tilt compared to that of a Michelson interferometer. We have enhanced the sensitivity to measure tilt using multiple reflections in a cyclic interferometer. Since the input beam is collimated, we have studied the effect of aberration of the input beam on the accuracy of tilt measurement. Experimental results on this study are presented in this paper.

The field of speckle metrology has seen a surge in development in the past 10 years owing to advancements in digital cameras and computing power. For instance, a variety of digital speckle correlation (DSC) processes can now be performed in almost real time and therefore speckle techniques has found applications in nondestructive testing (NDT), biology, and medicine. New techniques in terms of optical arrangements and in extracting phase data have been introduced for measuring out-of-plane and in-plane motions in digital speckle interferometry (DSPI) and digital speckle shear interferometry (DSSPI). DSC, DSPI, and DSSPI have also been combined to extend the range of measurements. In addition, quantitative analysis in speckle interferometry has seen a plethora of new software developments for conducting real-time, accurate, complicated, fast, and repeatable measurements with ease. In addition, different methods to process speckle fringes have made analysis equivalent to that of classical interferometry, yet can be applied to all types of real-world specimen. Keywords: speckle photography; digital speckle correlation (DSC); digital image correlation (DIC); digital speckle pattern interferometry (DSPI); digital speckle shear pattern interferometry (DSSPI); speckle fringe analysis; temporal speckle pattern interferometry; speckle phase extraction; biospeckles; white light speckles; speckles in medicine

Summary Recently a new method to measure object shape and deformation using temporal evolution of speckles in speckle interferometry was reported. The principle behind the method is that certain parameter sensitive to shape or deformation is changed continuously and the fluctuations in the intensity of the speckles are recorded in a large number of frames. The phase data for the whole object deformation is then retrieved by inverse Fourier transformation of a filtered spectrum obtained by Fourier transformation of the signal. In this paper a theoretical evaluation of the amplitude of the signal for inplane sensitive interferometer that uses dual beam illumination is presented. It is shown that signal to noise ratio is better when the speckle size is smaller than the pixel size contrary to the normal assumption that the speckle size be matched to the pixel size.

A novel nondestructive testing (NDT) method is reported in which temporal evolution of the speckles in speckle interferometry is used to measure large object deformations. The basic principle of the method is that continuous object movement introduces fluctuations in the phase of the speckle and is recorded as intensity modulation. Acquiring a large number of frames of the object motion, the phase data for the whole object deformation are then retrieved by the Fourier transformation technique. The method is capable of measuring more than 100 μm in-plane and out-of-plane deformation with speckle interferometry and more than 500 μm for speckle shearing interferometry. The authors discuss the NDT results obtained with the three methods and make some relative comparisons of each.

Measurement of in-plane displacements of a diffuse object by observing the temporal fluctuation of the speckle pattern in a dual-beam illumination speckle interferometer is illustrated. To conceive the temporal changes the object is displaced in its plane continuously. A high-speed camera is used to acquire a number of frames of the image of the object motion sequentially. Through Fourier transformation and inverse Fourier transformation of the frames stacked together, the total phase is determined. Finally, the magnitude of the in-plane displacement of the object motion is extracted. The range of displacement that can be measured using this novel method lies between few microns and over 100 μm on the upper end. Theory together with experimental results are presented in this paper.

Measurement of tilt plays an important role in metrological applications and consequently, several methods have been proposed in the recent past. Classical interferometric methods can measure angles with high accuracy but are easily susceptible to external turbulences. We propose to use a cyclic interferometer to measure tilt in which the sensitivity to tilt measurement is double when compared with that of the classical Michelson interferometer. Since the counter propagating beams travel identical paths, the interferometer is insensitive to external vibrations and turbulence and thus can be used under harsh environmental conditions. The novelty in the technique lies in creating multiple reflections in the tilt mirror to enhance the measurement accuracy by the way of increasing the sensitivity. This paper presents the basics of the interferometer and experimental results to quantify the increase in sensitivity. By increasing the number of reflections, it is shown that sensitivity can be further improved to measure tilt angles below 5 μ rad .

In this paper we extend and study the method for generating contours of diffuse objects employing a dual beam illumination coupled with electronic speckle pattern interferometry. The sensitivity and the orientation of the contour planes are analyzed. A novel method for tilting the planes of contours and experimental results incorporating phase shifting and fringe analysis are also presented. The theoretical and the experimental results show good agreement.

We describe an optical arrangement that increases the sensitivity to in-plane displacement in an electronic speckle-pattern interferometric system. This is accomplished by oblique illumination and observation along the direction of illumination. An anamorphic prism placed in front of the object is used to correct for the eccentricity in the image caused by the oblique observation. The sensitivity to in-plane displacement can be increased to a maximum of approximately λ/2. Experimental results including phase stepping are presented.

The effect of the pulse width of a pulsed laser in the studies of speckle velocimetry and transient vibration analysis is discussed. Because of the motion of the object during an exposure, a sine function is obtained by using the pointwise filtering method. This function modulates the halo along with the Young's fringes. It is shown that for high object velocities the sinc function modifies the halo distribution; as a result, the error in calculating the fringe position increases. An aperture geometry for which the autocorrelation halo is made constant in certain regions is proposed in which the intensity variation in this region is the result of the modulating sinc function only. A closed-form solution for the shift in the position of the fringes in this region is obtained. Experimental results of the simulation are presented.

A new arrangment for an electronic speckle pattern interferometer is reported in which an off-axis reference beam is used, thereby eliminating alignment problems.

Presentation d'un interferometre inverseur employant des composants holographiques. Il est tout a fait adapte au controle optique a chaque fois qu'une detection isolee du coma est necessaire

L'utilisation d'un reseau holographique juste devant le plan image fournit le cisaillement (dedoublement du front d'onde) et conduit a des figures de franges de courbure et de pente

In this paper we discuss a method of wavefront phase detection by differentiation of the interferometric fringes. We show that only one phase step is required to determine the wavefront phase. In the process of differentiation, Moire fringes are formed. Conditions on the angle of tilt introduced between the interfering beams to overcome the formation of Moire fringes are also presented. The method is shown to be suitable for techniques such as null optical testing or interferometric methods where comparison is made between a master and a test. We present in this paper the theory of the method and experimental results obtained for both specular and speckle interferometric fringes.

A quasi-equal-path electronic speckle pattern interferometric system that uses the polarization property of a diffusing object is presented. The fringe pattern is extremely stable with high visibility. Phase stepping in this arrangement is accomplished by translating the glass plate used for obtaining the reference beam. The only alignment that is necessary is that for obtaining a uniform field of view. This experimental arrangement demonstrates high efficiency of laser power usage. An equation for longitudinal alignment tolerance is also obtained.

A simple electronic speckle-shearing-pattern interferometer, in which the image of an object is focused and sheared with a split lens onto a diffuser, is described. The sheared images on the diffuser are focused by a television camera and then digitized and processed in a host computer. The results obtained for two basic types of shearing, lateral and radial, are presented.

We present two new methods for measuring small out-of-plane displacement. These methods are descendents of Leendertz's method in speckle interferometry but provide fringes of good contrast.

Recently, a new method to measure object shape and deformation with temporal evolution of speckles in speckle interferometry was reported. In this method, certain parameters, sensitive to shape or deformation are changed continuously, and the fluctuations in the irradiance of each speckle is recorded. The information over the whole object deformation is retrieved by Fourier-transformation techniques. We present a detailed theory and analyze the influence of decorrelation due to longitudinal and lateral size of the speckles. It is also shown that the method can be used to measure small deformations (less than 5 µm) with higher resolution. Further, the nonlinearity of the camera is shown to enhance the sensitivity.

Michelson interferometer is one of the most popular optical interferometric systems used in optical metrology. Typically, Michelson interferometers are used to measure object displacement with wavefront shapes to one half of the laser wavelength. As testing components and device sizes reduce to micro and nano size, a sensitivity of half the wavelength of light cannot be used to measure several hundred picometer displacement. Multiple-reflection interferometers have been proposed and are used to increase the sensitivity in a Michelson interferometer; however, when altering the number of reflections, the system alignment becomes cumbersome. We describe some of the problems associated with the current multiple-reflection interferometer and introduce a setup for matching path lengths to increase the resolution and allow for the reduction of the stringent requirement on the coherence length of the lasers used. Theoretically, we show that more than 1000 reflections can be achieved. Experimental results of up to 100 reflections are presented in this paper.

Speckles are a three-dimensional self interference pattern formed by a large number of random coherent waves. This results in a granular structure in free space or can be observed to be superposed on the image of the object and sets a fundamental limitation in high-resolution hologram microscopy and coherent imagery. Essentially, speckles are a randomly coded pattern that carries information about the object surface, and also has the rare distinction of being a nuisance and simultaneously a useful tool for measurement. Emergence of better measurement capabilities, newer recording media, faster computers and interfaces, and software has revitalized speckle metrology and has resulted in many fascinating new developments. Scores of books and review articles cover the myriads of applications and developments, and this chapter is intended to provide a concise and precise account of speckles starting from its infancy to the latest developments such as temporal speckle pattern interferometry or digital holography. Attractiveness of speckle methods lies in their ability to measure: large deformations, displacements with variable sensitivity to in-plane and out-of-plane, displacement derivatives, shape of a three-dimensional object, surface roughness, and dynamic displacement. Speckle techniques can nowadays be used to measure a wide range of displacement, sensitivities ranging from 0.25 µm to 150 µm for in-plane and 0.05 to 150 µm for out-of-plane displacements and with shearing techniques to over a 1000 µm. Keywords: speckle; speckle photography; speckle interferometry; electronic speckle pattern interferometry; digital holography

Lateral shear interferometry operating in the convergent beam mode has been used for testing optical components. This method is simple and phase information of the wavefront has conventionally been extracted using phase stepping techniques. We propose to use defocus, which introduces uniform tilt as a means of extracting phase information via two procedures, namely spatial phase stepping and spatial frequency carrier method. Experimental results are presented that show the wavefront phase extracted with defocus before and after the focal point of the lens.

Multiple wavelength interferometry is used to increase the range of unambiguity beyond that of single wavelength interferometry. In wavelength scanning interferometry, the frequency of the intensity modulation induced by the wavelength change is determined independently for each image pixel. The tuning range determines the resolution of measurements, while the tuning step limits the range of the measurements. Laser diodes can be tuned, but an external cavity is needed for a larger mode hop free wavelength variation. Polished and optically rough surfaces can be analyzed in the same manner. Acquisition times of a few seconds and high resolutions were obtained. In a new development, the application of temporal evaluation of speckles for deformation and shape measurement will be discussed. It turns out that spectral and temporal phase analysis can be very useful for many applications in optical metrology.

Interferometry using a single wavelength delivers the surface topography and surface heights of optically polished surfaces. However, discrete steps and holes cannot be determined, the sensitivity is fixed, and the analysis of optically rough surfaces is not possible. Some of these limitations can be overcome by using two or more wavelengths. In wavelength scanning interferometry, the frequency of the modulation induced by the wavelength change is determined independently for each image pixel. The tuning range determines the resolution of measurements, while the tuning step limits the range of the measurements. Laser diodes can be tuned, but an external cavity is needed for a larger mode hop free wavelength variation. Polished and optically rough surfaces can be analyzed in the same manner. In a new development, the application of temporal evaluation of speckles for deformation and shape measurement will be discussed. It turns out that spectral and temporal phase analysis can be very useful for many applications in optical metrology. Experimental results will support the methods discussed.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Absolute interferometry can be a powerful tool for distance and shape measurement. Two and more wavelengths can be used to increase the range of unambiguity in interferometry. Furthermore it leads to the possibility to apply interferometric methods to measure optical rough surfaces. A continuously tunable laser in a two beam unequal path interferometer is used to overcome the ambiguity problem of classical interferometric methods. While the laser wavelength is tuned continuously, the variation of the interference intensity is recorded sequentially. At each image pixel the frequency of the signal modulation is analyzed, giving the absolute depth information for the corresponding object point. The wavelength tuning step governs the depth of measurement whereas the tuning range determines the depth resolution to be obtained. The method can be applied for optical as well as for technical surfaces. In the latter case, the intensity variation is observed independently in each speckle. However, the resolution of the measurement of optically rough surfaces is limited by the surface roughness. The continuous tuning of the wavelengths is performed with a diode laser with external cavity where a frequency variation of 30 nm can be obtained without mode hops within one second. Furthermore a novel method to measure the shape and steps heights by rotating the object and using temporal evaluation of the speckles' modulation is presented. Currently a temporal Fourier- transformation is used, similar to the evaluation method used in wavelength scanning interferometry.

Previously, we reported a simple method to obtain lateral shear in both the x - and y -directions using a multiplexing technique. The phase data was extracted using the inherent spatial carrier fringes formed due to the tilt in the two sheared beams. In this article, we report that an error in phase map is introduced when the band-pass-filtered Fourier transform (FT) spectrum is not centered prior to performing the inverse FT to obtain the phase. We also found that intentionally introducing aberrations when capturing dynamic fluctuations in the wave front, resulted in controlling the spread of the Fourier spectrum.

Current methods in shear interferometry provide shear only along one direction at a time. We propose a method in which interferograms with shear along the x, y, and xy directions can be obtained simultaneously from a single exposure recording via the concept of spatial multiplexing. The method utilizes holographic lenses, which have been recorded on a single plate with their optical centers translated along the x and y directions. The phase information is extracted through the Fourier transform method. In addition, this technique also provides a method to obtain interferograms with shear in multiples of the original shear along the x and y axis in one single frame capture due to the nonlinearity inherent in the phase holographic lens.

Testing with lateral and radial shears is becoming standard in optical shops. Of late, holographic optical elements have proven to be easy and simple to set up, and can be used in both a collimated and convergent beam. However, there is very little work on making quantitative measurements using a symmetric radial shear. We demonstrate a simple method of obtaining both asymmetric and symmetric radial shears, and use the inherent tilt in the wavefronts to perform spatial Fourier transformation to extract phase maps. This radial shear interferometer is also suitable for static and dynamic situations.

In this paper further discussions on some new methods proposed in an earlier paper on phase stepping interferometry is detailed. These studies reveal that certain algorithms are more sensitive to miscalibration and nonlinearity and can be better candidates to detect the presence of phase shifter miscalibration or nonlinearity. A simplified approach to the understanding of the error and its reduction/elimination in phase shifting interferometry are also presented.

Testing with a single holographic lens or grating in a collimated beam is normally not possible because of the inherent tilt caused in the wavefront. The tilt between the two beams in shearing creates a large number of linear fringes which overshadow the information about the wavefront. However, here, we show that we can use this tilt to make quantitative measurements which was otherwise not possible. In the novel method, we obtain shear in a relatively simple way, and at the same time we extract phase information using spatial Fourier transform technique. This technique is suitable for making quantitative measurement of wavefront and disturbances in turbulent conditions. Here, we demonstrated the real-time phase measurement capacity of the interferometer, a result of one such application is shown.

In this paper we discuss an oblique incidence and observation electronic speckle-pattern interferometer, in which we use an anamorphic prism in front of the object. A collimated beam traveling through the prism is partly reflected at the base of the prism. The reflected light is the reference beam and the transmitted light illuminates the diffuse object, thereby generating the object beam. In this scheme the object and the reference beams are collinear. A new scheme that uses two prisms and permits phase stepping is also presented.

In this paper a comparison of different techniques to obtain vibration patterns by phase stepping on an electronic speckle pattern interferometer (ESPI) is made. The theoretical evaluation of the contrast of the fringes shows that the (pi) phase step method gives good contrast; however, the four step method gives the same contrast along with better pictorial representation. Speckle averaging on the other hand also increases the contrast of the fringes apart from smoothing of speckles. Experimental results corroborating the theoretical predictions are also presented.

The design and system performance of an infrared phase-stepping interferometer is reviewed. This instrument is capable of measuring rms surface roughness with a repeatability of 0.02 waves. The instrument uses a 4-bucket unwrapping algorithm. Calibration of the interferometer and removal of inherent system aberrations are discussed along with the system performance, including repeatability and accuracy. The interferometer is an all-reflective optics design to permit use at any wavelength, accommodating both far- (10.6 micron) and near- (5 micron) infrared sources. Testing applications include infrared windows and surface testing.

In this paper we discuss a fiber optic electronic speckle pattern interferometer (ESPI) for obtaining 3D information about surface deformation. Phase stepping is introduced by stretching the fiber wrapped around a piezo-electric transducer. Two schemes to stretch the fiber are discussed. Also calibration of the phase step is critical in phase measurement techniques for obtaining good phase plots. In this paper we outline a method used for calibrating the stretcher. We also discuss the error in the phase caused by temperature changes.

Fiber optic Mach-Zehnder interferometric sensors for the measurement of various physical parameters such as pressure temperature and magnetic fields are well known and documented. This paper deals with the construction of a fiber optic sensor incorporating He-Ne and diode lasers. Preliminary experimental results for temperature sensing are reported.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper we discuss a fiber optic phase measuring Electronic Speckle Pattern Interferometer. The phase stepping is obtained by stretching the reference arm fiber. We also outline briefly the theory of determining the phase by differentiating the interferogram. Preliminary results obtained with four bucket and differentiation algorithms are presented. 2.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We outline a novel method for determining the shape of an object by use of temporal Fourier-transform analysis in dual-beam illumination speckle interferometry. The object whose shape is to be determined is rotated about an axis, and a number of frames of the image of the object motion are acquired. Temporal in-plane displacement that is due to the object rotation is related to the shape of the object and is retrieved from this large set of data by Fourier transformation. With this method one can determine the absolute height of the object with variable resolution, thereby allowing shapes of objects with large and small slopes to be determined. The theory of the method along with experimental results is presented.

A method to measure the derivative of displacement using time variation changes in the object together with Fourier transform analysis in speckle shear interferometry is presented. The concept of the method is that the object is deformed continuously and a large number of sheared images of the object motion are acquired using a high speed CCD camera. The derivative of the object deformation is then retrieved from this large set of data using Fourier transformation. The method is capable of obtaining information for object displacements over 500 ?m, which is a very difficult task when using conventional electronic speckle pattern shearing interferometry. Theory as well as some of the experimental results with the new method are delineated. ? 1993 society of Photo-Optical Instrumentation Engineers.

We propose two methods to perform shearing in electronic speckle pattern shearing interferometry (ESPSI). These new methods of shearing make the setup compact and easy to align. The first system we propose consists of two parts: (1) the object is imaged onto an interme- diate ground glass and (2) the image on the ground glass is in turn imaged onto the photosensor of a CCD camera. A holographic grating placed in front of the ground glass screen is used to shear the two images and to introduce phase stepping. The separation between the grating and the ground glass plate is used to control shearing. In the second method, two identical holographic gratings separated by a dis- tance introduce shearing and the distance between two gratings can be used to control the size of shearing. Phase shifts to be employed for phase measurements are introduced by displacing the grating. © 1997 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(97)03409-0)

A modification of a dual-beam illumination arrangement for electronic speckle pattern interferometry (ESPI) that leads to a twofold increase in the sensitivity to in-plane displacements is described. For each of the two illumination beams, the scattered light is observed along the direction of illumination, and these two components of the scattered light are then combined. The error in perspective caused by oblique observation can be almost corrected for by using two right-angle prisms in front of the object being studied. Experimental results including phasestepping are presented and compared with the results predicted by theory.

New methods that can be used to determine phase in phase-stepping interferometry are presented. It is shown that a combination of some of these methods can be used to reduce the error introduced by phase-stepper miscalibration and nonlinearity. Moreover these new algorithms can also be used to detect the presence of miscalibration or phase-shifter nonlinearity. A simplified approach to understanding the error introduced by miscalibration and nonlinearity of the phase stepper and its reduction in phase-shifting interferometry is also presented.

Two methods to measure the cladding diameter of single-mode fibers are presented. The first method is based on an interference fringe measurement technique. Interference fringe spacing at two different planes is measured to determine the cladding diameter of the fiber. The theory of the fringe formation in the interferometeric arrangement using single-mode fibers is discussed. It is theoretically shown that the far-field overlapping Gaussian field distribution from the fibers shifts the position of the fringe maxima and minima. As a special case of unit fringe visibility the minima positions do not shift, whereas the maxima positions are shifted. In the case of a Lloyd mirror arrangement it is shown that fringes can be obtained from a rough surface as well. A lens is used in the second method to image the two identical point sources that cause the interference. Through the use of the magnification and spacing of the images, the cladding diameter is estimated. It is shown that the accuracy of the fiber cladding-diameter measurement can be enhanced by generating multiple point sources. Consistent results of the fiber cladding diameter have been obtained with the proposed methods. Fiber cladding-diameter measurements with a standard error of less than 0.15 μm can be achieved.

Limitations of a quasi-equal-path electronic speckle pattern interferometric system are discussed. We show that by replacement of the reference glass plate with a plano-concave lens the quasi-equal-path electronic speckle pattern interferometric system can be made more versatile. An arrangement to reduce the aberration in the reference beam is also presented.

A phase-measuring fiber optic electronic speckle pattern in- terferometer (ESPI) was recently constructed and demonstrated. In thisarrangement, phase stepping is introduced by stretching the fiber wrappedaround a piezoelectric transducer. Calibration of the phase step is criticalin phase measurement techniques for obtaining good phase plots. Meth-ods used for calibrating the stretcher are outlined and the drifts in thephase caused by fluctuations in temperature and mechanical stressesare discussed. Ways to minimize this drift are also presented. Subject terms: speckle interferometry; electronic speckle pattern interferometry.Optical Engineering 31(2), 315-321 (February 1992).phase step calibration is important in order to obtain error- free phase maps. Different methods for calibrating the piezoelectric transducer (PZT) in an interferometric arrangement13 as well as in a fiber optic interferometric sensor arrangement14 have been developed. Methods suchas phase-lock, sinusoidal extrema sensing, and employingsoftware routines to evaluate the phase from equations andintensity values are successful with specular interferometricfringes. On the other hand, the ESPI fringes are speckled.Even though good calibration can be obtained with phase-lock and sensing methods

A detailed analysis of the vibration fringes obtained by phase stepping on a time-averaged electronic speckle pattern interferometer is presented. It is shown that the contrast of the fringes remains relatively high for any phase step between 30 degrees and 180 degrees for low electronic noise and fringe density. Also, for the four-phase-stepped method, the vibration fringes have the same contrast as that of the pi-phase-shift method except that the high-frequency speckles are smoothed. The contrast of the fringes obtained with extra phase steps along with incoherent superimposition is shown to be higher than the single- or four-phase-step method. Both theory and experimental results are presented.

The halos formed while filtering from a double exposed specklegram are combined with a shear to obtain moire’ superposition of slope patterns depicting curvature. The shear is provided by a pair of plane mirrors. Further, filtering of this record results in fringes of better contrast.

Radial and rotational slope contours are obtained using speckle shear interferometry and a dual refractive index immersion method. Unlike speckle shear interferometry which compares the deformed state of any object with its normal state and thus brings out the structural defects, the method reported here displays prominently any departures from an otherwise regular profile.

A simple method for obtaining lateral shear using holo shear lenses (HSL) has been discussed. This simple device which produces lateral shears in the orthogonal directions has been used for lens testing. The holo shear lens is placed at or near the focus of the lens to be tested. It has also been shown that HSL can be used in speckle shear interferometry as it performs both the functions of shearing and imaging.