Red blood cell (RBC) anomalies are significant symptoms for identification of health disorders and several blood diseases, which involve the modification of the parameters and biophysical characteristics of such cells. An optical system was implemented using a Mirau interferential objective to evaluate the micro-topography of Red Blood Cells in Papanicolaou test (PAP). The phase-shifting algorithm called 8-Bell6 was applied to evaluate the phase map. The phase ambiguity is removed by using three light-emitting diodes (LEDs) emitting at three different wavelengths: 459.7, 512.8 and 637 nm. The micro-topography is evaluated for one of the RBC observed in the sample. Profiles of two perpendicular diameters to each other are showed. The relative error for measurements made with this optical system is 2.9%.
An optical system is proposed for wavelength measurement and detection using phase vortices produced by an integrating glass disc. This optical system is based on a modified digital holographic configuration used previously for measurement in Particle Image Velocimetry (PIV) but adapted here for the detection of phase vortices generated by an integrating glass disc. Phase vortices are detected from speckle patterns that are produced using a tunable light with a wavelength of 632 ± 2 nm emitted by a Littrow monolithic tunable external cavity laser, and after multiple reflections in the integrating disc combined with a reference beam and a speckle interferogram is obtained that recorded by a CCD camera. The Fourier transform method is used for speckle phase generated in the proposed optical configuration and analyzed with a vortex detection method that produces a singularities pattern for each wavelength.
The ever-increasing requirements of product quality and reliability demand more efficient measuring and test methods
that must be online, nondestructive, wholefield and without contact. Optical methods seem to be ideal for such purposes.
The interferometric technique of ESPSI (Electronic Speckle Pattern Shearing Interferometry), or Shearography, is a
coherent-optical measuring and test method that is similar to holographic interferometry. However, this method displays
many advantages for industrial applications, due to its relative insensitivity to environmental disturbances. Shearography
measures the gradient of the deformation, not the deformation itself as holography does. Consequently, shearography
measures strain information directly. Based on the above, Shearography was adapted for the surface strain measurement
in graphene-reinforced composite materials; the information was evaluated at each point from our sample observed area.
Defect inspections with shearography on fiber-reinforced plastics parts, widely used in aircrafts, ships, chemical and oil
and gas industries, are often performed outside of the lab. An optical system capable of measuring the strain fields in and
out of plane was developed based on electronic speckle interferometry. The obtained interferogram images were
processed using the phase-stepping technique. A specific specimen geometry and an optical arrangement based on the
Michelson interferometer are proposed to measure the deformation along two orthogonal axes due to sensibility in and
out of plane. The advantages of the system include its high sensitivity and stability. The experimental setup and approach
for estimating the strain fields was validated using a membrane based on polylactic acid reinforced with cellulose
microcrystalline as sample with and without graphene.
In this work, we present a novel Panoramic Fringe Projection system (PFP) to retrieve the three-dimensional topography of quasi-cylindrical objects along their full length and around the entire circumference. The proposed procedure uses a 45° concave conical mirror to project a circular sinusoidal fringe pattern onto a specimen placed coaxially to the mirror and at the same time to image the modulated fringe pattern diffused from the object surface. In order to obtain the required sensitivity, an axicon is used to create a divergent fringe pattern with constant pitch. By processing the phase map, information on the radius over the full 360° surface of the sample can be obtained by using a single-view series of images captured from a single camera. To verify the feasibility of the PFP technique, a tubular sample with shape discontinuities has been tested. The proposed method demonstrated to be able to retrieve the accurate topography of quasi-axial-symmetric samples with complex geometries for a large variety of applications.
The structured light technique is useful to evaluate the topography of an object. By using the Fourier transform, the
phase of a fringe pattern is obtained from a single image. With the phase information and the sensibility vector of the
optical system, the value z(x, y) at each point of the object can be determined. It is known that color is a subjective
sensation, and it changes depending on the observer. In order to make an association of real color and texture, it is
necessary to calibrate and profile the optical devices involved in the process. Thus, we ensure that the color detected by a
camera is the same displayed on the monitor and perceived by the observer, so it is possible to associate the color of the
target object in addition to the evaluation of topography.
On the other hand, 3D visualization is possible by using a stereoscopic system that provides two different images of the
same object (one for each eye). One possible technique is that known as the anaglyph method, based on the binocular
disparity of two images obtained with different color filters. Each one of the images is taken with complementary colors
(red-blue or red-green), and the tri-dimensional shape can be seen through the use of special glasses; this way, each eye
sees an image from its own angle. Object topography is obtained with the fringe projection technique, and then one
image is selected and pseudo colored; then, the second image is taken, slightly changing the perspective of the tridimensional
display and pseudo coloring it with a complimentary color. A computational algorithm is developed to
evaluate and visualize the object in real time.
This communication describes some details of polarization modulation that are useful in phase-shifting interferometry when applied to phase profile measurements of phase objects. Since non-destructive optical techniques allow surface measurement with high accuracy, a Mach-Zehnder configuration coupled to a 4-f arrangement using phase gratings placed on the Fourier plane was implemented to analyze phase objects. Each beam of the interferometer goes through a birefringent wave plate in order to achieve nearly circular polarization of opposite rotations, with respect to each other. The interference of the fields associated with replicated beams, centered on each diffraction order, is achieved varying the spacing of windows with respect to the grating period. Experimental results are presented for cases of four and nine simultaneously captured interferograms.
Nowadays, the trends of miniaturization of sensors and inspection devices have been of major importance in science and
technology. The characterization of microchips, integrated circuits, MEMS, and micro-sensors is important to determine
their proper operation. Due to their element small size may have structural fails for improper handling of them. This
paper proposes the use of a Michelson interferometric objective for the determination of topographical features in
materials at micro and nanoscale level. The main advantage of this method is its non-invasive nature that allows testing
in soft materials without damage. The Michelson interferometric microscope objective with a magnification of 5X
illuminated with a 632nm He-Ne laser is used. Fringes that allow the study of the topography of these structures are
properly analyzed. The acquisition of the interferograms was performed by a CCD, which are handled by the method of
phase-stepping. An integrated circuit of a CCD as target is used. A reconstruction of the microscopic topography of the
sample produced results with a statistical error in the topography of 12nm. Application of this method is to conduct
quality control tests in manufacture of electronic components such as micro-chips and integrated circuits.
This paper describes a micro-topography measurement system using a Mirau interferometric microscope objective. Such
system is a non-invasive, full-field, economical, and compact. The interferometer device consists of a beam splitter that
permits send a portion of the light to the sample surface and other part to a reference surface. Reflected light from these
surfaces are combined to form interference fringes which are captured by a CCD camera. For each local point on the
surface target, there is a distance from the Mirau microscope objective lens. Then, each fringe provides the locus of
points of equal phase in the interferogram image. Contour lines corresponding to the surface target topography are
extracted from the interferograms using digital image processing. Phase-stepping technique have been used in order to
have a phase map which is unwrapped and mapped to a full-field microscopic data topography of the surface target.
Object target is mounted on computer controlled stage with capability of linear movements of the order of nanometers.
With this, the phase-stepping technique was done. For calibrating, a step-in-shape made of thin film on a glass substrate
is built up. The obtained depth resolution is of 15 ± 4 nm, employing the interferometric system. Experimental results
were compared with an Atomic Force Microscope, (AFM) giving an overall error of 17 nm on a 33μm × 45μm field of
view. An application for integrated optics on-chip quality control is suggested.
In this work we present a parallel polarizing phase shifting interferometer based in a Double Cyclic Interferometer
(DCSI) to analyze transparent samples. This system has the advantage of generating four beams that can interfere
properly; this can reduce the number of captures needed in phase shifting interferometry. The interferometric system
generates two π-shifted interferograms, which are recorded by the CCD camera in a single-shot. For the processing of
the optical phase data map, a parallel phase shift can be generated by placing a linear polarizer covering two patterns.
We analyze the cases of four patterns with arbitrary shifts captured in two shots. The unwrapped phase is processed by
Kreis methods. Experimental results obtained by the proposed interferometer are presented.
In this work we present a different method to reduce shot noise in phase imaging from digital holograms. An averaging
process of phase images reconstructed with different reconstruction algorithms of the complex amplitude of a phase
object in digital holographic microscopy. We obtain an improved phase image reaching a 29% of shot noise reduction.
We use a single object complex amplitude that is needed to perform our proposal. Also show the corresponding
simulations and experimental results. As phase sample test we used a micro-thin film step surface made at home of 100
nm high of TiO2 on a glass substrate of 4.7 mm thickness, our system was calibrated and traceable to an Atomic Force
Microscope results.
A Mach Zehnder (MZ) interferometer was implemented to analyze a phase object using polarization phase-shifting
interferometry. The Mach Zehnder interferometer produces two beams with circular polarization of opposite rotations
one respect to the other. The system is coupled to a 4-f system with phase grating in the Fourier plane, interference of the
fields associated with replicated beams centered on the diffraction orders is achieved by a proper choice of the beams
spacing with respect to the gratings period. The optical configuration allows obtaining n-interferograms in one shot. The
configuration presented does not require micro-polarizer arrays or additional software to eliminate noise caused by
vibration, as the system is stable itself and uses conventional polarizing filters. Considering the object under study a thin
phase object, experimental results are presented.
An interferometric method to measure the slope of phase objects is presented. The analysis was performed by
implementing of a polarizing phase shifting cyclic shear interferometer coupled to a grating interferometer. This system
can obtain four interference patterns with adjustable phase shifts and variable lateral shear. In order to extract the slope
of a phase object, is analyzed the optical phase applying the classical method of phase extraction.
Electronic speckle pattern interferometry is a useful technique in the measurement of displacement fields and
topography. Traditionally, arrangement with dual collimated illumination to topography measurement is used. In this
case, the object analysis is limited to the size of optical collimating lens. In the case of large objects, an optical system
with divergent illumination can be used. It is known that displacement fields and the phase are related by the sensitivity
vector. At once, to compute the sensitivity vector, illumination sources position and superficial shape need to be
considered. The last condition becomes an impediment to surface contouring. In a published work1, a simple iterative
algorithm based on the Gauss-Seidel technique is presented to compute contouring measurement. In the present work,
the uncertainty associated to the measurement of the topography is calculated by using the Monte Carlo method.
The development of this work is important in the morphological study of plant parts, specifically in the study of the
cuticle of fruits or leaves. The implemented optical technique for fringe projection can identify potential fracture zones
which damage the presentation of the fruits impacting business as well as producing them. Specifically, we obtained
information on the thickness of a cuticle corresponding to the abaxial surface of a leaf of apple (Malus domestica) of the
variety Golden Delicious.
Three-dimensional object topography is obtained by using the fringe projection technique. In fringe projection technique,
digitalization is done when black and white lines are projected over the sample object and the image is captured by the
CCD. It is applied the phase shifting method to evaluate the phase of the projected fringes. In this paper it is proposed a
method in which red, green and blue fringes are projected sequentially. It is obtained the topography to each color (RGB)
and finally the three obtained shapes are averaged. By using this method, we obtain information about color, texture and
topography details of the object.
Stereo Vision is a powerful tool used to make a 360° scan of an object in order to obtain topography details
or getting the spatial position of interest points, but the process could be slow due to the computing time. In this
work we present the alternative of using high reflective markers, which are used as reference points to track an
object movement. The advantage of these markers is that their detection is faster than a full scene correlation and it
is done by comparing the position of the centroids of each marker without using pixel-pixel analysis.
We measured the topography of lens by using a technique of diffuse reflection (fringe projection technique) and by a
method based on specular reflection technique (similar to Placido disk system). The obtained results with both
techniques are compared with those obtained with a spherometer. The retrieval of the three-dimensional shape of the
lens is an issue of great interest for wide medical application, particularly in ophthalmology.
Nowadays, the implementation of an accurate non-destructive technique for the measurement of mechanical
properties in small samples has become a main subject of interest due to the recent development of MEMS
and intelligent materials, which need a safe procedure for their characterization.In this work we study a non-destructive
method for determining the Young's modulus of an aluminium circular plate. Our technique is based
on Electronic Speckle Pattern Interferometry (ESPI), a mechanical loading setup, and digital processing, which
allows to obtain accurate values of Young's modulus for the sample agreeing those values from the literature.
It is measured the topography of a large object by using structured light. The type of fringes generated are equivalent to
the produced by divergent beams. In this case the relation between the phase and the height is not linear. In this work it
is proposed an iterative estimation to the topography measurement. It is taken in account the variation of period in xdirection
of the projected grating and the perspective problem of CCD camera. The shape obtained is compared with the
measurements realized with a commercial scanner. The stop criterion value c in the algorithm was chosen of .1 mm. This
value corresponds to resolution in z of commercial scanner. To this case, three iterations are enough to reach the value of
c. It is observed that after three iterations, the value of z is approximately the same. It is obtained a great discrepancy to
the topography measurement when does not use correction in perspective and in the period variation due to divergent
projection of the fringes. The main contribution of this work is show that it is important consider the variation of period
and the perspective problem in the measurement of the topography to large objects.
In this work, a dual illumination beam system is used to obtain the strain intensity factor in mode one (mode I) to
mechanical elements during tension testing. The displacement field is obtained by means of a phase stepping technique,
and deformations are calculated by the Stokes differentiation method. Results are compared using a finite element
analysis technique.
Non-destructive optical techniques for 3D shape measuring are fundamental in science, engineering, medicine, and
industry. Such 3D data offer advantages over 2D data: shape data are invariant against alteration of the illumination and
object motion. One of the major and easy methods to obtain 3D shape is from its contours. There exist several optical
techniques for contouring, but the easiest to put into operation is by using linear structured light projection. The present
work focuses on the implementation of linear structured light projection techniques for static and dynamic 3D contouring
at macro- and micro-levels. Linear structured light as a fringe pattern is projected on the surface to be contoured. White
light and laser-illuminating Talbot image are used in order to project the fringe pattern. Projected fringe pattern is
captured by a conventional or high-speed CCD camera for image digitalizing and further analysis. Fourier transform
method is employed as a tool to obtain a contour-wrap optical phase map. The simple experimental arrangement is
adapted for static or dynamic conditions of the surface to contour. Samples that are under harmonic vibration conditions,
for example, their vibrating frequency is tuned with that of the capture CCD camera to obtain the mode shape. In the
static case one can obtain the topographical comparison before and after the surface subject to a static load or simply its
topography. Examples, at micro and macro levels, of static and dynamics surface conditions are shown.
We use the projected fringes technique to follow the changes induced in the topography of metallic sample sheets
subjected to uniaxial tensile tests. Since in-plane strains are associated with out-of-plane deformations, the monitoring of
thickness variation of the tensile specimens can be used to detect necking and shear band formation. A sequence of
images of the fringe pattern was captured and processed by means of the Fourier transform technique. We measured the
material behavior in the elastic and plastic zones during its elongation until fracture took place. We present experimental
results for stainless and hot rolled steel sheets.
Studies on adaptive lenses formed of two transparent elastic surfaces with a transparent liquid medium between them
have focused mostly on the characterization, analysis and the optical performance of the proposed lenses. No attention,
however, has been given to the mechanical design to generate a user-friendly functional mounting as well as being
adaptable to conventional optical systems. This work, therefore, presents the design and manufacturing processes of the
parts of the mounting for a biconvex adaptive lens with a 20 mm diameter. It also presents an analysis of the membranes
used as elastic surfaces as well as images formation of the proposed lens.
A novel method of phase differences extraction is applied in order to study vibrations on a homogenous cantilever. It is
achieved considering fringe patterns with carrier frequency and slow varying respect to the time. The technique is based
on the Fourier-transform method and by the quotient of the two adjacent frames of the patterns. Fringe pattern is
obtained by fringe projection on a fixed end homogenous cantilever, undergoing harmonic vibration. With this
technique, we can obtain profiles of different vibrating modes of the cantilever for frequencies less than that of the
camera frame rate (33.3 ms). In this communication theoretical analysis and experimental profile modes are shown.
Electronic speckle pattern shearing interferometry (ESPSI), also known as digital shearography, is a hole-field non-destructive, optical technique used to measure approximately the field of displacement derivatives. The accurate measurements of these derivatives have several problems one of them is that of ESPSI results are approximately equal to the derivatives, they are equal to the derivatives only if the shear distance tends to zero, hence, if experimental data rendered by ESPSI are taken directly as equal to the derivatives, the measurements may carry an important shearing error. Other error, ESPSI yields values relative to a reference value at a specific location of the field that can be very difficult to determine accurately. In this paper, we propose a general procedure to compensate the shearing error and to introduce the reference by adding two quantities to the values rendered by ESPSI. As an example, we measured a displacement derivative field induced on a metallic sheet specimen by applying tensile load.
We report on the errors obtained by comparing the in- and out-of-plane displacements calculated from the sensitivity matrix with all its components and when it is considered only the component of the largest contributing of each one of the three interferometers. Divergent illumination is considered in the sensitivity vectors evaluation to measure displacement vector components. This analysis is made for a flat elastic target by using of Electronic Speckle Pattern Interferometry (ESPI).
We present a non-contact system for obtaining three-dimensional objects topography. The described system combines the fringe projection technique and the Talbot effect which is knowed like Talbot interferometry. In fringe projection technique, the digitalization is realized when black and white lines are projected over the object and this image is captured by the CCD. In Talbot interferometry, the object is collocated on one of the grating auto-image planes. The deformed grating image is captured by the CCD and superposed with other reference one that can be physical or computer generated (virtual/synthetic) for obtaining a moire pattern which gives information about the object topography. The topography of a coin and phalangeal articulation are obtained by using of this technique. The Spatial Synchronous Detection and Fourier Method were incorporate to retrieve the phase.
The Large Millimeter Telescope (LMT)1 is a 50 m diameter millimeter-wave telescope designed for principal operation at wavelengths between 1mm and 4mm. The LMT secondary mirror will have a diameter of approximately 2.6 meters and focal ratio of .35. The purpose of this study was to implement the incoherent fringe projection technique and the spatial phase synchronous method to measure the secondary mirror mold profiling. The obtained topography is compared with the conic surface generated synthetically. We considered that mold should be hyperboloid surface with paraxial curvature of 1764.9 mm and conic constant of -1.1474. We will discuss the preliminary results where it is obtained a RMS of 0.624 cm.
The optimization of an automatic laser cutting system is reported. This CO2 laser system assisted by an O2 gas jet is used in the cutting of Constant Velocity (CV) joint for the automotive industry. The experimental parameters varied in order to obtain cuts with low roughness were the laser power, cutting speed and oxygen pressure. A mathematical model is presented which explains many of the features of the qualitative optimization realized.
It is described an Electronic Speckle Pattern Interferometer (ESPI) used for Young's modulus measuring of a new PVC material. The technique considers the construction of a small tensile testing machine that is good enough to apply loads on the polymeric specimens. A dual-illumination ESPI system is built up to measure specimen in-plane micro-displacements under the tension loads. For Young's modulus measuring, strain is required and determined by the force per area unit. Since the specimens have irregular traversal section, the self-imaging or Talbot-projected fringe technique is implemented for determining such a transversal section all along the specimen. Experimental results by using these optical techniques are shown, as well as, the measure of a new polymer Young's modulus.
Implementation of a structured light projection technique for measuring the relief of objects, or object areas, of
micrometric size (approximately 500 μm x 500 μm), is described. It is well-known that when a fringe pattern is projected
on an object, the fringes are deformed according to the topography of its surface. This deformed fringe pattern is a
modulated optical signal that allows us to measure the relief of the object. Through one of the oculars of a stereomicroscope,
previously focused on the object under study, the fringe pattern of one the Talbot self-image is projected.
The deformed fringe patterns are observed by the other ocular, in which a CCD camera is mounted to digitize them.
Digitized fringe patterns are demodulated by means of a second virtual reference grating. As a result, a moire fringe
pattern is obtained delivering a wrapped phase map when is digitally processed by means of a phase recover technique.
Phase recovery techniques for obtaining the wrapped phase maps are phase-shifting and spatial phase synchronous.
Experimental results and the conditions, under which the topography of an object section is determined, are shown. Also,
comparisons over quality between the phase recovery techniques are discussed.
When it is carried out to perform a three dimensional evaluation of displacements and strains, it has been proposed some optical systems which uses three illumination beams or the use of three sensors. The different sensitivity vectors components associated to each illumination beam; let us permit to calculate the displacement in each direction by sensitivity matrix. In the present work, simple geometries of interferometers are discussed. It is showed the sensitivity components for each source in the case of optical set-up with three divergent illuminating beams, where we analysed the sources position that makes possible measure the u, v and w components with a maximum weight factor in each direction respecting to set-up total sensitivity. The sources position is one on x-axis, the second on y-axis and the third near to z-axis. From the theoretical predictions is proposed an interferometer which is based on the ESPI technique which has the sources configuration calculated. Experimental results of displacements are presented to an elastic surface when a rotated load is applied in the centre of the target.
A fringe normalization procedure is presented in this paper. The main idea of the computer algorithm is to normalize the fringe pattern using spline interpolation functions. To achieve this, two splines are fitted using the maximum and minimum irradiance peaks detected over each fringe image line. Then, each pixel in the fringe image is interpolated and normalized by using of the values of the max and min splines. The fringe contrast is enhanced with an error around 1%. Preliminary results are presented.
It is described a technique where different views of an object are connected to recover its three-dimensional form in a field of vision of 360°. The object is placed on a rotary motorized platform and projected a linear fringe pattern. In each angular object displacement, the projected fringe pattern is captured by a camera CCD. Each pattern is digitally demodulated providing information of depth. The format of the digital matrix, this is, the image type, is changed for one of triads (x, y, z). This way, a cloud of independent points of their position in the matrix is constructed. As a reference, one point in each cloud (known it a priori), is taken. All the clouds are rotated and displaced until the reference point taking its corresponding position. Different mixed clouds of points (views) are ordered in a single triad matrix that describes the complete surface of the object surface target. Finally a mesh of quadrilaterals is built up that makes possible to generate a solid surface.
A feasibility study for amplitude and frequency vibration measurement in aerial electricity transmission cable has been made. This study was carried out incorporating a fringe projection method for the experimental part and horizontal taut string model for theoretical one. However, this kind of model ignores some inherent properties such as cable sag and cable inclination. Then, this work reports advances on aeolic vibration considering real cables. Catenary and sag are considered in our theoretical model in such a way that an optical theodolite for measuring has been used. Preliminary measurements of the catenary as well as numerical simulation of a sagged cable vibration are given.
Displacement measurements by optical interferometry are affected by errors in the determination of the phase-difference and in interferometer sensitivity. In this paper, we perform an uncertainty analysis of displacements measured by in-plane ESPI with spherical wavefronts. The displacements were induced by applying uniaxial tensile load on a nominally flat elastic sample. Our attention was focused on the quantification of the effect of eventual errors in the sensitivity vector determination. We found that the displacement uncertainty depends on the geometry of the optical arrangement, and on the dimensions of the illuminated field. Moreover, the displacement uncertainty increases with the deformation.
The optimization of an automatic laser cutting system is reported. This CO2 laser system assisted by an O2 gas jet is used in the cutting of Constant Velocity (CV) joint for the automotive industry. The experimental parameters varied in order to obtain cuts with low roughness were the laser power, cutting speed and oxygen pressure. A mathematical model is presented which explains many of the features of the qualitative optimization realized.
When it is carried out to perform a three dimensional evaluation of displacements, it has been proposed ESPI systems which uses three illumination beams or the use of three sensors. The same technique has been used by digital holography and shearography. The different sensitivity vectors associated to each illumination beam let us permit to calculate the displacement in each direction by sensitivity matrix. In the present work, it is showed the sensitivity components for each source in the case of optical set-up with three divergent iluminating beams, where the sources position makes possible measure the u, v and w components with a weight factor approximately equal respecting to set-up sensitivity.
In the present work, a simple moire interferometer, which commonly is sensitive to in-plane displacement, is studied. In contrast to traditional in-plane moire interferometric technique, we use two spherical wavefronts. This kind of illumination produces a sensitivity vector varying with the position. Therefore, it is capable of detecting in-plane and (a whitish) out-of-plane deformations due to the use of divergent beams. Uncertainty to each component of the displacement vector is calculated and discussed. It is shown each component of the sensitivity vector, which should be examined in the stage of planning an interferometric measurement experiment, have to minimize the required component uncertainty. This analysis is made for a flat and spherical object surface. Experimental results for the displacements of a rigid object are presented, which show the measured displacement components with the highest sensitivity.
Optical non-destructive testing have been broadly used for flaw analysis in engineering structures. The valuable of these techniques has been their easiness to obtain full field information. Likewise, with them one can determine with high precision micro—displacements due to different types of loads. Holographic, moire, and speckle interferometry are the most common optical non-destructive techniques. Particular experimental arrangements can be built to measure in- and out-of-plane displacements. Commonly, in-plane speckle and moire grating techniques use collimated symmetrical beams for target illuminating. However, when the target illumination beams are spherical, a series of errors in the interpretation of the interference fringes appears. Among these errors, under this kind of illumination, are those due to light arising out-of-plane displacement components. These components are of supreme importance when the objects to be analyzed are of considerable size. In this paper, the importance of shape and out-of-plane displacements as factors that introduce error in the interpretation of a phase map obtained from a grating moire and in-plane ESPI interferometers, are evaluated. The analysis is done utilizing the uncertainty of the sensitivity vector varying as a position function on the surface under study. The effect of a slight out-ofplane displacements and surface shape upon the change of the sensitivity vector are numerically analyzed. This numerical analysis shows that serious measurement error can be obtained when these factors are neglected. It shows that the possible errors in the measurement from the ESPI and grating moire interferometers using non-collimated object illumination can be estimate before doing the measurement. A general function of correction in phase map interpretation for any in-plane sensitive interferometric scheme, in spherical illumination, is proposed. Since moire interferometry uses a grating specimen recorded on a mirror-like and prepared with a fine diffraction grating (typically ~12OO lines per millimeter). Gratings are commonly made of photoresist. However, if we want to analyze engineering structures in spherical illumination, in order to have a surface without pre-prepared under polishing, the surface roughness is an important parameter to be characterized. Then, additionally in this work first we analyze the fringe visibility of moire during the fabrication of specimen gratings as a function ofthe surface object roughness.
A well-founded and computationally fast method is presented for filtering and interpolating noisy and discontinuous wrapped phase fields that preserves both the 2(pi) discontinuities that come from the wrapping effect and the true discontinuities that may be present. It also permits the incorporation of an associated quality map, if it is available, in a natural way. Examples of its application to the computation recovery of discontinuities phase fields from speckle interferometry fracture measuring are presented.
Commonly, in-plane sensitive arrangements use tow symmetrical collimated wavefronts for object surface illumination. However, this is a limitation when large objects surface have to be analyzed. In this case spherical illumination is needed. Using this kind of optical set-up, the present work shows results of fracture measuring by using moire and speckle interferometric methods. Non- collimated symmetrical dual-beams, having a sensitivity vector varying with the position are performed. These methods are capable of detecting in-plane and out-of-plane deformations due to the use of divergent beams. It is calculated the error to each component of the sensitivity vector. Experimental result of fracture measurements are shown.
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