ckpfer 2 SPECKLE PATTERN INTERFEROMETRY

Transcription

1 ckpfer 2 SPECKLE PATTERN INTERFEROMETRY

2 2.1 INTRODUCTION The speckle phenomenon had been investigated by many scientists since the time of Newton, who observed the scintillation or twinkling of stars. Speckle patterns which are formed by star light which has propagated through the atmosphere are different in character to those which are formed by diffusely reflected laser light. In the early 1960, holography was developed, and interferometric measurements of diffusely reflecting or opaque objects became feasible. In 1969, speckle interferometry allowed interferometric measurements of diffusely reflecting objects without the need of recording a hologram. With the development of lasers, CCD cameras, computers and frame grabbers, speckle interferometry has become a powerful measurement technique with many applications. With the invention of the laser in 1960, highly coherent light became available, and scientists began to study the phenomenon of speckle, and practical applications began to be reported in literature [1-2]. The surfaces of most materials are optically rough, i.e. the surface height variation is greater than one fourth, of the wavelength of illuminating light. When light with a fair degree of spatial and temporal coherence is reflected from an optically rough surface, the light is scattered in all directions. The reflected waves created by different microscopic elements of the surface interfere and produce random fluctuations in intensity with dark and bright spots. Illumination of a diffuse object by coherent light produces a grainy structure in space. This intensity distribution has a characteristic granular structure and is called speckle pattern [3]. A noisy, random granular pattern called a speckle pattern is observed when looking at or imaging a laser illuminated, diffusely reflecting surface with the eye or with a camera Fig. 2.1(a) and 2.1(b). Fully developed speckles appear only if the height * variations of the surface are greater than the wavelength X of the light. Such surfaces are said to be optically rough. If the object is viewed, each point P on the detector will gain contribution of light coming from a coherence volume, determined by at least the airy spot and the roughness 40

3 of the surface. A summation of these wave packages that illuminates point P is illustrated in Fig. 2.1(c), describing a so-called random walk. As long as the complex amplitude A follows the statistics indicated in the figure, the speckle field is fully developed. Anyone who has seen a speckle pattern in reality will have observed the curious granular appearance. The speckle pattern moves if the head moves, and it seems impossible to focus the eye properly on the illuminated surface. If the speckle pattern is observed through a small hole, and if this hole is smaller than the pupil, the speckles appear larger. Speckles observed on an imaging system, e.g. with the eye or a camera, are called image speckles or subjective speckles. For speckle patterns collected on a screen, the speckle size depends on the area of the surface that is illuminated. The smaller the area, larger will be the speckles. This type of speckles is called far-field speckles or objective speckles. This chapter describes the basic principles of speckles and Electronic (ESPI) with several speckle measurement techniques, such as surface roughness measurement and phase-shifting methods. Temporal and spatial phase-shifting methods yield three-dimensional information. For instance, on deformation or surface contour of the measurement object. The speckle patterns contain information on surface characteristics, e.g. on surface roughness. They are random and can be described in statistical terms. Therefore speckles have the potential to be used for surface roughness measurement [4-7]. 2.2 BASIC SPECKLE PHENOMENON The grainy light distribution, known as speckle pattern, results from self-interference of numerous waves from scattering centers on the surface of the diffuse object, the amplitude and phases of these scattered waves are random variables. We assume that the amplitude and the phase of each scattered wave is statistically independent variables, and also independent of the amplitudes and the phases of all other waves, the phases of these ======================================================= 41

4 b) Fig. 2.1 a) a typical speckle pattern, b) schematic description of how speckles appear in a detector, and c) a random walk in the complex plane

5 waves are uniformly distributed between -n and n. This pattern observed due to free-space propagation is termed as objective speckle pattern. Its properties are extensively covered in Goodman [8]. 2.3 AVERAGE SPECKLE SIZE The speckles in the pattern are not well defined but have a structure. However, we associate with the speckle, an average size and this is considered under the cases of objective and subjective speckle pattern Objective Speckle Pattern A speckle pattern is formed in free space when a diffuse object is illuminated by a coherent wave is called the objective speckle pattern [9]. The speckle size in an objective, speckle pattern is given by _ aob - D Where D - size of the illuminated area of the object, X - wavelength of laser light z - distance between the object and the observation plane, Fig.2.2(a). The speckle size increases linearly with the separation between the object and the observation plane Subjective Speckle Pattern A speckle pattern formed at the image plane of a lens is called the subjective speckle pattern. It is due to interference of waves from several scattering centers in the resolution area of the lens. In the image of this resolution area, the randomly dephased impulse response function is added, resulting in a speckle [10]. Therefore, the speckle size is governed by the well-known Airy formula. Xb ~ D Where D - diameter of the lens, b - Image distance, Fig.2.2 (b). By introducing the/-number F# (=/ ) of the lens. The average speckle size is expressed as follows: oi = (l + m)xf # ======================================================= 43

6 Recording Recording

7 Where we have introduced magnification m {= b/a = (b -f)/f} of the lens. Where, F# =f/d and a is the distance between object and lens. It is thus seen that the speckle size can be controlled by the magnification m and F# of the lens. Hie control of speckle size is often used in speckle metrology to match the speckle size with the pixel size of the CCD array detectors. 2.4 MEASUREMENT OF SURFACE ROUGHNESS The surface roughness can be regarded as variation of the surface height. There exists a great variety of distributions of surface height variations and a large number of parameters to characterize the surface roughness that might be considered. Since the speckle is a random phenomenon, only random and isotropic roughness will be considered. Thus the roughness can be characterized in a statistical manner. The most obvious parameter is the average roughness, R. N N 1=1 5 also called the center line average (CLA) roughness. This is the average of the surface height derivations Ari of N data points. This parameter is often used in manufacturing industry. The root-mean-square (rms), a. f j jv \l/2 ft is commonly used in the optical industry Statistics of Speckle Pattern The statistics of speckle patterns derived in detail by Goodman [2]. Assuming that the laser light is perfectly monochromatic and perfectly polarized, that the surface is rough compared to the wavelength of the laser light, and that the elementary scattering areas of the surface are unrelated. Following statistical properties can be derived. The probability density function of the intensity I follows a negative exponential law,

8 P(I)- 1 </>' f % exp 7T to The angular brackets indicate die average value over an ensemble of macroscopically similar, but microscopically different rough surfaces. The most probable intensity is zero and causes the very high contrast observed in the speckle pattern. In the case of far-field speckles, i.e. free space propagation geometry, the width of the autocorrelation function of the intensity distribution provides a reasonable measure of the average width of a speckle. The average size of a speckle can be taken proportional to, The speckle size depends on the wavelength of the illumination of light X, the illuminated area of the surface with a diameter q, and the distance z between the surface and the observation plane, and which is parallel to the illuminated surface. This indicates that the speckle size increases when the illumination area decreases [11] Speckle contrast The surface is rough compared to the wavelength, and the incident light is perfectly coherent, so that the standard deviation is equal to the mean intensity{/), and the speckle contrast is equal to unity [2]. C to where C is the speckle contrast If the roughness of the surface is smooth compared to the wavelength of the light, the speckle pattern is partially developed, and the speckle contrast is less than unity. If the roughness of the surface is increased, the speckle contrast is also increased until it approaches unity, as the roughness of the surface approaches one fourth of the wavelength of the light. If die coherence of the light source is reduced, the speckle contrast depends on the surface roughness. ======================================================= 46

9 2.4.3 Correlation techniques The radially fibrous structure observed in polychromatic speckle patterns on the far field can be analyzed to determine the surface roughness. Since this structure will vanish more and more with increasing surface roughness. The spatial autocorrelation function Cs of the speckle intensities in the observation plane describes the radially fibrous structure, also called speckle elongation [12] with location vectors *, {1,2} h(v W? \~h(r Vrft? The angular brackets denote the average over the pixels of the regions with respective centers 3c, of the speckle size. With increasing the surface roughness, the decorrelation (means the distribution of speckles in restricted area) of the monochromatic speckle patterns is intensified, and the speckle elongation of the total intensity pattern will gradually decrease. The two dimensions lx and ly of the speckles in the x- and y- direction of the observation plane can be determined by the widths of the spatial autocorrelation function in the jc- and y- direction. The correlation coefficient C12 of the speckle intensities I\ and I2 of two different speckle patterns is defined by, where the angular brackets denote the ensemble average. The theory applied for different roughness measurement techniques is far from being complete. 2.5 SURFACE RUOGHNESS STUDIES OF DIFFUSER Introduction When any object is illuminated with laser light the granular appearance of the object can be seen and this is called as laser speckle. This 47

10 is having a random spatial variation of the intensity. The speckle intensity is varied from object to object due to debonds, flaws and roughness present on the object. When such object is illuminated by a monochromatic light or a beam of light is reflected from a surface, then the rough surface can be observed as coherent components which are arising from different microscopic elements. Laser speckle is thus useful to study the roughness of any material object which is not optically flat Speckle pattern interferometry can be potentially used with the help of any photorefractive material to observe the flaws in the materials. The speckle structure can be used to study the amplified and de-amplified images for the comparison between them [13] Experimental The holographic experimental set can be modified with high digital CCD to study the roughness in the materials. The experimental arrangement is shown in Fig.2.3, consists of He-Ne laser (5mW) which is transmitted through a beam splitter without any expansion and directed on a BaCaTiO;, photorefractive material. The refracted beam from the same source is allowed to pass through a diffuser and through the photorefractive material which captured in a P.C. via CCD-camera (Qimaging Retiga- 1300) Results Using CCD-camera, it is possible to record the amplified and deamplified laser speckle. This is analyzed with the help of frame grabber card. The photorefractive crystals are having very high diffraction efficiency. Hence we can be able to obtain laser speckle beams which are amplified or de-amplified to large extent. The amplified images of the diffusion having different roughness are shown in Fig. 2.4 (a) and (b). The de-amplified images are shown in Fig. 2.5 (a) and (b).these two images are ======================================================= 48

11 subtracted point wise by using H-Digital software and subtracted images are shown in Fig. 2.6 (a) and (b) Discussion The amplified images of the diffuser show speckles of high intensity and the distribution of the magnified points in the speckles are equally spaced. The variation of speckle intensity is same throughout all the images. As compared with the magnified images and de-magnified images the resultant speckle pattern shows irregularities in the speckle intensities. All the speckle points are not equally spaced. The subtraction of demagnified images and magnified images is done by using H-Digital software developed by VSSC Tiruanantpuram. Then the resultant speckle pattern gives us the information regarding the roughness of the diffuser. Such pattern clearly shows the variation in the contrast of the laser speckles as compared to the images shown in Fig. 2.4 (a) & (b) and are shown in Fig. 2.5 (a) & (b). PC Fig.2.3 Experimental setup for studying surface roughness 49

12 Fig. 2.4 Amplified images of the two diffusers (a) most rough (b) less rough Fig. 2.5 De-amplified images of the two diffusers (a) most rough (b) less rough Fig. 2.6 Point wise subtracted images of the two diffusers (a) most rough (b) less rough 50

13 The speckle methods used for deformation measurement and vibration analysis are placed under the following categories: 1. Speckle Pattern Photography Speckle Shear Interferometry 4. Electronic Methods 1-3 employ photographic medium for recording and method 4 employs electronic detection. 2.6 SPECKLE PATTERN PHOTOGRAPHY The object may be illuminated obliquely or normally. Consider an image of the object, as shown in Fig. 2.7 (a), on photographic plate capable of resolving the speckle pattern, and the first exposure was recorded. The object was loaded and another record of the displaced speckle pattern is made on the same plate. In this way it is possible to record two speckle patterns, one of them translated locally by d. We need to find out d at various locations on the plate and then generate the deformation map. It was pointed out earlier that the speckle displacement has poor sensitivity for axial displacements. Hence, speckle photography is used mostly to measure in-plane displacements and in-plane vibration amplitudes [14-15]. Let us first examine the specklgram (negative film or plate) realized by making a single exposure. The intensity recorded is given by/(je,y)= «(jt,;y) 2. The amplitude transmittance of this negative (specklgram) is expressed as follows: t(x,y)=t0-pn(x,y) Where t0 - bias transmittance, ft - constant, and T - exposure time. Since the speckle pattern consists of a grainy structure, each grain being identified by a 8 function, the intensity 1 (x, y) could also be expressed as follows: l(x,y) = JJl(x',y')>(x-x',y- y')dx'dy

14 When this specklegram is placed in a setup as described in Fig. 2.7 (b) and illuminated by a parallel beam of light, the amplitude transmitted is given by u0 (jc, y)t(x, y), where w0(jt,;y) is the amplitude of the illuminating plane wave. The specklegram will diffract the light over a reasonably large cone, depending on the speckle size. Fig. 2.7 (a) Speckle photography - in-plane displacement Specklegram Fig. 2.7 (b) Singly exposed specklegram illuminated by a collimated beam 52

15 Let us consider a double-exposure specklegram. In the first exposure, an intensity distribution /, (x,y) is recorded. The object was then deformed and the second exposure I2{x,y) is recorded on the same plate. The deformation causes the speckle pattern to shift locally. Therefore, the intensity distribution I2(x,y) can be expressed as follows: i2 (*. y) = JJ/(* > y )> (*+dx - x. y+dy - y Where dx and dy are the components of d along the x and y directions respectively. The total intensity recorded is, = J l(x', -x',y- y')+ ^(x + dx-x,y + dy- y'^bcdy' Again if this double-exposure specklegram is illuminated by a collimated beam, one obtains, at the focal plane of the lens, a central order and the superposition of halos belonging to the initial and final states of the object. Mathematically, the amplitude transmittance of the double-exposure specklegram is t(x, y) = t0-pt {^(x, y)+12 (x, y)} The amplitude at the Fourier transform plane is given by y)] = t8s(ji,v)- plsfa (x, y)+ I2(x, y)} Where 3 signifies Fourier transform. For simplicity, we now confine ourselves to one dimension; hence we write the total intensity as follows: It (x) = JJ/(x')[5(jc - x')+s(x + dx- x')]dbc'dy' Therefore the magnitude of dx may be obtained from the fringe width measurement. However, if dxis not constant, each value of dx will produce its own fringe pattern Limiting factors in speckle pattern photography The factors which limit the measurement of displacements by speckle pattern photography have been considered in references [16-18] and are briefly discussed here. ======================================================= 53

16 1. Image formation considerations The relationship between the motion of the speckle pattern in the recording plane and the object motion is determined by the location of the recording plane; hence, errors in the interpretation of the fringes will arise when the photographic plate is incorrectly located and when the focus varies across the field of view. The latter will occur when, for instance, a flat object is viewed by a large aperture lens since the image will be curved. Consequently, parts of the speckle pattern in the photographic plate will be slightly defocused and will be sensitive to tilt as well as to in-plane displacement. 2. Sensitivity To observe fringes in a speckle photographic system, the displacement of the object must be such that the displacement of the speckle pattern in the recording plane is greater than the speckle size in that plane; thus the minimum in-plane displacement or out-of-plane tilt which can be detected is determined by the speckle size. When the recording plane is located to give sensitivity to one form of motion, other motion will in general tend to decorrelate the speckle pattern reducing the visibility of the fringes. 3. Object size The maximum area which can be inspected in one view is limited only by the laser power available; however, when a large object is imaged onto a small area, errors due to lens aberration may again arise. 2.7 SPECKLE PATTERN INTERFEROMETRY Although the speckle phenomenon is itself essentially an interference phenomenon, when a reference beam is added to the speckle pattern to code its phase, the technique is then termed as speckle interferometry. Another class of speckle methods with sensitivity comparable to that of holographic interferometry is speckle interferometry. Speckle interferometry was first applied to measure in-plane displacements ======================================================= 54

17 by Leendertz [19]. The basic theory was borrowed from holographic interferometry, since the phase difference introduced by deformation is governed by the equation,s = (k2-kl)d. When the object is illuminating with two beams with directions symmetrical to the object normal and observation are made along the optical axis. The arrangement generates fringes that are contours of constant in-plane displacement. These fringes are called correlation fringes. Speckle interferometers can be used to study deformations of object surfaces that scatter light. These methods are based on the coherent addition of scattered light from the object surface with a reference beam that may be a specular or scattered field not necessarily originating from the object. The schematic setup for measuring in-plane displacement [20] is shown in Fig. 2.8(a). The object is illuminated by two plane waves incident symmetrically at angles 0 and -0 with respect to the optical axis. The image of the object is made on the photographic plate. The object is deformed, and a second exposure is made on the same plate. The intensity distribution at a point in the observation plane before the object is deformed can be expressed as; A (*. y)=io+ir+ WOT COS0or where, <j)or = $,-0r is the random phase, I0 =a20, Ir=a2r. where, a0 ar and are the amplitudes and phases of the object and reference beams at a coordinate point (x, y) respectively. The intensity distribution after the object is deformed is given by *,(*.> )= K + ', +2VV>"k, +«) where, Sis the phase change introduced due to the deformation of the object. These two intensity distributions are recorded in a photographic plate that is converted to amplitude transmittance upon processing. When the phase change S is (2m+l) n, then there is no correlation between the two speckle fields. When the phase change is 2mn, then die two speckle fields are correlated. ======================================================= 55

18 X Kg. 2.8 (a) In-plane displacement measurement by Speckle Interferometry Kg. 2.8 (b) Out-of-plane displacement measurement by Speckle Interferometry ======================================================= 56

19 An interferometer for measuring out-of-plane displacement [21] is shown in Fig. 2.8(b). It is the Michelson interferometer in which one of the mirrors has been replaced by an object under study. This therefore has a reference wave that is smooth or specular. The lens L2 makes an image of the object at the recording plane. The record consists of interference between the smooth reference wave and speckle field in the image of the object. 2.8 SPECKLE SHEAR INTERFEROMETRY (SHEAROGRAPHY) Shear means to shift, when an object is imaged via two identical paths and the images are perfectly superposed. Then there will be no shear even though there are two images. Since the imaging is via two independent paths, the images can be independently manipulated. In speckle shear interferometry, a point in the image plane receives contributions from two or more points on the object. One of the most commonly used methods of shearing employed is the Michelson interferometer, where the object is seen via two independent paths, as shown in Fig. 2.9 (a). For linear shear, pair of the plane parallel plates is used, Duffy s arrangement with a wedge for shearing is shown in Fig. 2.9 (b). A speckle shear interferometer consists of an imaging element and a shearing element. The imaging lens is used as either a single aperture or a multi-aperture system. Let us now consider a situation when the contributions from two object points (x, y) and (x +Ax0, y) are received at the same image point. Here Ax0 is called the object plane shear and is related to the image plane shear Axj through the magnification of the imaging lens. The waves from the two points at any image point can be represented by a{e,b' and a^' 2; one wave acts as a reference for the other. The intensity distribution fr is given by /, = a2 + a22 + 2a,a2 cos0, where 0 = 0, -02

20 Fig. 2.9 (a) Michelson interferometer for shearing Fig. 2.9 (b) Duffy s arrangement with a wedge for shearing 58

21 When the object is deformed, these waves arrive at the image point with additional phases 8: and S2. Thus the intensity distribution l2 is, 12 = a* + a22 + 2axa2 cos(0 + 5), and 8 =8l-82 The phases 5, and S2 are different because the deformation vectors at the two sheared points are different. The phases <5j and 82 are expressed as si =$2~ki)-L{x>y) and S2 = (*2 *1 ) L(x + Axa, y) where L(x,y) and L(x+Ax0,y) are the deformation vectors at the two points (x,y) and (jt + Ax0,y), respectively. The phase difference 8 can then be expressed as 8 = 2 n du. _ dw sin0 + (l + cos0) ox ox The total intensity recorded is given by /1(x,y)+/2(x,y) hence the amplitude transmittance of the double-exposure specklegram is y)=t0-pt {h(x> y)+h (*> y)} One obtains a fringe pattern representing the derivatives of the displacement components. 2.9 ELECTRONIC SPECKLE PATTERN INTERFEROMETRY (ESPI) Introduction The speckle size is governed by the number of the imaging lens. Furthermore, by adding a reference beam coaxially, the speckle size is doubled. It is therefore possible to record the speckle pattern using a standard television camera. Video processing can be used to generate correlation fringes equivalent to those obtained photographically. This method is known as Electronic (ESPI) [22-23]. The minimum speckle size is typically in the range 5 to 100 /Jtm so that 59

22 a standard television camera may be used to record the pattern, of all the whole-field interferometric techniques. Electronic speckle pattern interferometry is the most practical tool for in-situ engineering measurements. The major feature of ESPI is that it enables real-time correlation fringes to be displayed directly upon a television monitor without recourse to any form of photographic processing, plate relocation etc. Intensity correlation in ESPI is observed by a process of video signal subtraction or addition. The availability of fast PCs and large-density CCD detectors makes the technique of electronic detection very attractive. In fact, ESPI is an alternative to HI and perhaps will replace it in the industrial environments. The reasons for the enormous interest in ESPI include (1) non contact measurement with sub-micrometer accuracy, (2) the possibility to reach remote areas; (3) data storage on video taps for analysis at a later stage, (4) quantitative analysis performed using phase stepping, (5) easy operation, (6) variable sensitivity, and (7) real-time operation. Advances in the development of CCD cameras and image processing units have propelled ESPI to the forefront of both scientific and engineering applications. Researchers have developed ESPI to measure out-of-plane and in-plane deformation, contouring, stress analysis, and vibration analysis Historical development of ESPI ESPI is a measurement technique that utilizes a laser interferometer, a CCD camera detector and digital processing to generate speckle correlograms at television (TV) frame rate. The live images of correlograms fringes provide real-time whole-field visualization where each fringes typically represents a contour of the required measurand. Several different names have been used to describe the technique such as TV holography, digital speckle pattern interferometry and electro-optic holography. However, the name ESPI still remains the most popular internationally since it was first coined by Butters and Leendertz [24]. ======================================================= 60

23 Earlier ESPI systems used a He-Ne laser as a source. The semiconductor lasers used now possess good thermal stability and give out radiation of long coherence length [25]. They are therefore used in ESPI systems, making such systems portable; commercial using semiconductor lasers. It may be of interest to know that ESPI has been performed in the far-infrared at C02 wavelength [26]. In classical interferometry two coherent beams are generated via a beam splitter, normally referred to as the object beam and reference beam. The reference beam is often considered as fixed whilst the optical path length of the object beam is varied either by changing the physical length of the beam or by transmission through a region of different refractive index. From the last 15 years the major advances were made principally mainly by two research groups in London. These were at the Department of Mechanical Engineering, Loughborough University in England and the Department of Physics, Norwegian Technical University of Trondheim, Norway. Towards the end of the 1980s, there was a proliferation of researchers in the area as the technique was adopted to incorporate software programmable computer-based digital-image-processing techniques rather than hardwired dedicated electronics. While throughout the 1990s there have been further refinements of the technique, a greater need has since been placed on the integration of ESPI into routine delivery of information as part of a larger measurement process or system of measurements Basic principles of ESPI The complete ESPI system constructed with bulk optical components is shown in Fig In the arrangement shown, the position of the two interfering coherent beams is such that the interferometer is sensitive to out-of-plane motion of the object surface. The collimated light emanating from the laser is divided into the reference beam and the object ======================================================= 61

24 beam, where the reference typically has 5% of the intensity of the object beam. Test Object Fig An ESPI system constructed from bulk optics

25 The object beam is spread over the area of interest on the objects surface. The test object is imaged by a lens onto a light-sensitive spatial array of pixel elements, such as CCD camera. The reference beam is also conditioned to illuminate the camera s sensor; in this example a common lens is used to expand both beams. A second beamsplitter is placed in front of the CCD to combine the two beams. The beamsplitter is normally selected to transmit > 90% of the object beam and reflect <10% of the reference beam [27]. The CCD detects the interference between the two beams at each pixel across the camera. At the detector, the intensity J, due to the interference of the object and reference beams is obtained as, Where 7dc is the background intensity, Jm is the intensity modulation of the interference fringes and (0D+$r) represents the optical phase difference between the two waves (denoted as the object and reference wave) Out-of-plane sensitive ESPI The ESPI system that is sensitive to motion in the direction of the interferometer camera is depicted in Fig (a). Here the illumination and viewing directions are parallel giving a 2n = 180 phase shift for an out-of-plane object displacement of A/2. The optical signal scattered from the object surface may be weak and the amplitude arriving at the CCD is further reduced by the small lens aperture (to obtain necessary speckle size). In practice the beam splitters BSi and BS2 are selected to give ~ 90% transmission in compensation. The object and reference beam need to combined in front of the CCD camera. A beam splitter wedge was used in the arrangements but it gives unequal optical path lengths across the field of view; hence, a beam splitter cube is preferred.

26 Laser e Beamsplitter BSt 6r Fig.2.11 (a) Arrangement for out-of-plane ESPI CCD & Fig (b) ESPI system configured for in-plane measurement ======================================================= 64

27 In-plane sensitive ESPI Sensitivity to in-plan motion is achieved by illuminating the test object with two beams at equal and opposite angles either side of the viewing direction, see Figure 2.11 (b). In this configuration die correlation fringes obtained are contours of deformation in the X-direction. The sensitivity vector is given by, <l>(x,y) = 47TCOS0 A u where 0is the spatially varying interference phase, 6 is the angle between the illuminating beam and the test surface, A the wavelength of light and u be the component of object deformation parallel to X-axis. In-plane deformation it is particularly useful measurand as, by differentiation. The in-plane strain can be determined. Moore et al [28] developed a system for the simultaneous measurement of both in-plane deformation components and thereby the in-plane normal and shear strain can be determined SPECKLE NONDESTRUCTIVE TESTING (SNDT) The speckle nondestructive testing (SNDT) is similar to holographic nondestructive testing (HNDT). It requires some kind of loading of the object between exposures. The flaws and/or defects in the object are detected by comparison of two states of the object; the comparison is performed by any of the techniques - point wise filtering, speckle correlation etc. Defocused speckle photography has been applied to detect debonding in layer composites [29]. The deterioration of stone surfaces has been studied by speckle photography [30]. Major advantages of ESPI which as an NDT tool has potential are, 1) The technique is not limited to any particular material type. 2) The surface does not need to be carefully prepared, and the technique supplies the information over the full field of view unlike some of the conventional measurement techniques which measure point by point. ======================================================= 65

28 3) The area that can be investigated is limited only by the laser power available. 4) The ability to conduct tests in real time mode, where the object behavior is observed almost instantaneously while it is being stressed Limiting factors of Electronic 1. Measurement Sensitivity The ESPI can be used to represent lines of either in-plane or out-ofplane displacement. The fringe sensitivity for an in-plane interferometer is given by ^2sin0 w^ere ^ wavelength of the light used and Q is the angle of incidence of the illuminating beams. Out-of-plane interferometers may give fringes representing constant displacements at intervals of the order of A, or may be desensitized up to about loopm. It 2 is not possible to detect less than one fringe accurately with a conventional ESPI system so that this represents the minimum sensitivity of the system. 2. Object size limitations The maximum area which can be inspected in one view is limited by the available laser power and the camera sensitivity. There is no reason why a larger area should not be inspected if sufficient laser power is available; and depends upon the mechanical stability of the system and the performance of the system. 3. Depth of field The depth of field of the system is high, and so this is generally there will be no restriction in ESPI APPLICATIONS OF ESPI With the ESPI, measurements can be made using static or dynamic loading. Applications using static analysis include areas such as stress analysis, object contouring, non-destructive testing (NDT), and optical component testing. Dynamic studies that can be carried out in the time- ======================================================= 66

29 average mode, the pulsed mode, or the stroboscopic mode can be used to detect both amplitude and phase of vibration [31].Static and dynamic measurements at high temperature have successfully detected debonds [32]. The ESPI may be used to determine the shape of complicated objects. The techniques are used to obtain object contours in hologram interferometry have been extended to ESPI [13-21]. Recently new techniques have broadened the industrial use of ESPI. In one method the angle of illumination is changed between the two exposures to generate contours [33]. In nondestructive testing or evaluation, different means of applying stress to the object under test along with phase stepping have been employed to detect defects [34-37].

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