Precision inspection of transparent component quality

In this work, a method using transmission interferometry is proposed to detect micro defects (streaks, inclusions, air bubbles, grooves, cracks, etc.) present in transparent materials surface. This technique is non-destructive and non-contact for the analysis of transparent and optical components whose surfaces vary from a few mm2 to larger sizes. The purpose of this method is to provide a means as simple as possible and to identify defects with low contrast, and in particular barely visible defects, and to differentiate between the defects. The transmission system generates interference fringes by the superposition of two microscopic periodic structures. According to the principle of the method, the image of the periodic microscopic structure, transmitted by the laser beam, traverses the sample. It then superposed on the reference microscopic structure; to generate the interference fringes, which materialize the presence of defects in the material. Changes in the shape of interference fringes inform the presence and dimensions of defects. This technique makes it possible to clearly identify microscopic and submicroscopic defects, thanks to the high resolution of the system. The optical device used allows high defect magnification of up to 1000 times. This control and measurement method allows for real-time inspection. It provides high detection resolution, allowing better observation of defects, which facilitates the automation of measurements and controls. Therefore, the proposed method can be suitable for the detection of surface defects in transparent optical objects such as optical films, lenses, and prisms.


Introduction
Transparent materials play an important role in many areas. They are used in optical devices and precision instruments and are also used in various industries. They are often used to create products that require high material quality and reliability, such as airplane and automobile windshields or high-precision optical elements such as lenses used to guide laser beams in medical surgery applications. Transparent objects such as glass and lenses are commonly used in optical systems, and their surface quality greatly affects the performance of host systems. When transparent materials are difficult to inspect by the human eye and defect identification and quantification is not easy in these materials. It is necessary to make the defect more visible, which requires the implementation of appropriate methods, as there are many methods developed to inspect objects that are not applicable to transparent objects. However, research has been conducted to develop inspection methods suitable for transparent objects where the appropriate inspection technology can make transparent objects and structures visible and detect surface defects affecting the shape or anomalies of the index of refraction, material cracks, spalling, and impurities [1][2][3][4][5][6][7].
During inspection, the integrity of the component must be preserved. Therefore, many techniques non-destructive diagnosis have been developed to inspect different transparent objects. Each of them pays much more attention to the shape and size of the test object, as well as on the region where the defect is located with acquired detection accuracy [8][9][10].
Holographic microscopy and diffractive microtomography of transparent samples were studied by Debailleul et al. [11].
Chaki et al. [12] presented a multi-technique approach for non-destructive diagnosis of structural composite materials using ultrasound, guided wave, acoustic emission, and infrared thermography. Kolkoori et al. [13] used a novel X-ray backscatter imaging technique for non-destructive testing of aerospace materials.
Recently, inspection of transparent objects is under development, such that a new machine vision method is proposed to test the quality of transparent objects with varying light scattering using a frangi filter [14], a reflection-based approach for reconstructing transparent objects using laser scanning [15].
Interferometry is also a beneficial approach for quality inspection transparent objects such a non-invasive measurement.
method for transparent objects using digital holographic interferometry based on iterative least-squares phase unwrapping [16], a new type of digital holographic microscopy based on a modified lateral shearing interferometer (LSI) is proposed for the detection of micrometer or nanometer-scale defects on transparent target objects [17].
Interferometric technique was used for controlling wedge angle and surface flatness of optical slabs [18]. However, a focal length measurement by fiber point diffraction longitudinal interferometry was proposed [19].
Moiré techniques could potentially be applied include process monitoring and quality control, non-destructive evaluation and testing, maintenance, strain measurement, and medicine [20], where a wide range of measurement and control and make it possible to achieve high measurement precision [21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The thickness measurement is an important factor in glass quality inspection. However, the Moiré technique is a typical method for quality control. It is a non-destructive technique used for measuring the thickness distribution of transparent plates [35].
A well-developed digital phase-shifting shadow moiré (DPSSM) method was used to measure the light guide plate's (LGP's) surface topography without painting [36].
Therefore, the aim of this work which is adressed in this paper is to develop an experimental setup for optical inspection by transmission. It is a precision transmission system especially designed for the defect detection of transparent objects. Therefore, we have developed an accurate and immediate control method based on moiré technique and interferometry, to expand the possibilities of non-destructive identification capable to detect the presence of elements affecting the quality of optical components, because their existence sometimes brings disastrous consequences, which can disturb the function of the optical system [37].
The technique proposed here does not require any preparation of the inspected material. It allows an instantaneous characterization, either in terms of shape or homogeneity, of the size of the particles. This technique can provide an addition to what is achieved by the existing Moiré techniques [38]. The experimental setup used has characteristics such as the following: • Very high precision detection • For precise control of relatively small surfaces of and most critical surfaces • Allows the observation and the detection of defects in real time • What allows a profit of precision, time, and money • Offers performances extremely important which give possibilities of detecting defects of form of a micrometric size with a speed in control The Moiré method is recommended for the reason that the potential of Moiré techniques, in particular, comes from their low cost and simplicity, their portability and versatility, lack of risk, and their ability to provide fullfield intuitive information. Furthermore, Moiré fringes can have a more direct application in interferometric optical testing [17].

Principle of the control method
In this work, the Moiré technique is used in a precision optical device for controlling transparent component quality. A schematic principle of the experimental setup is shown in Fig. 1, where the He-Ne 35-mw laser beam 1 is enlarged by the lens system (2, 3), passes through the diaphragm 4, and arrives on the transmission linear grating 5 (test periodic structure).The lens system (6,7) realizes the double Fourier transformation to project the image of the grating 5 on the plane of the sample 8. The image of the grating 5 traverses and crosses the sample 8 and undergoes a double Fourier transformation by the lens system (9,10), for projecting the test grating image on the plane of the linear transmission grating 11 (reference periodic structure), with a magnification of 1/1 (test structure and reference structure are identical). The grating 11 is rotated in its plane by an angle θ. The superposition and the crossing of the two gratings generate the moiré effect, which consists of parallel and equidistant straight lines alternately bright and dark on the plane of the reference grating 11. The system (12,13,14) projects the Moiré fringes on observation plane 15 with a magnification mag. The CCD camera 16 captures the image projected on the observation plane 15 and transmits it to the computer 17 for the acquisition and automatic processing of the image.

Detection process of the technique
The analysis of the sample is held in the following order. Initially, the setup must be adjusted without the sample, in such a manner that only superposition of image test grating with reference grating; the Moiré fringes are observed on the observation plane 15. Figure 2a shows thus are parallel and equidistant straight lines alternately bright and dark.
In the next step the sample is placed into position 8 ( Fig. 1), the image of the microscopic structure of the test grating conveyed by the laser beam, palpates and passing through the sample thickness, and then comes to be superposed on the plane of the reference grating 11, to generate Moiré fringes. If the test grating image does not undergo any variation, the Moiré fringes are parallel and equidistant straight lines (Fig. 2b), either the sample does not show any anomaly, or the defects are inferior than the detection resolution and are not highlighted. However, if the test grating image undergoes a variation by the presence of defects, this is materialized by the change in the Moiré fringe shape (Fig. 2c). The detected microscopic size defect is instantly materialized by moiré figures on a macroscopic scale with a magnification up to 1000 times. Magnification is defined by the ratio D obs /P. It is the quotient between the moiré fringes pitch on the observation plane D obs and the pitch of the finest grating P, which favors the defect detection and measurement.

Detection of defects
The experimental setup according to Fig. 1 is able to detect the type of defect present in different transparent samples tested as follows.

Transparent film
A film for optical use is controlled. In the first stage, the Moiré fringes were obtained at initial state of the transparent film shown in Fig. 3a. The Moiré fringes are parallel and equidistant straight lines. What explains that this film does not present any anomalies. In the second stage, the film has undergoes a small deformation according to the indication of the Fig. 3b; in this case, the Moiré fringes ( Fig. 3c) obtained are deformed in the area where the deformation was produced; these fringes thus directly materialize the deformation caused on the transparent film. Figure 4a shows the moiré fringes of a glass plate without defects; however, the Moiré fringes of a glass plate about defects such as hollow, groove, roughness, and imprint are collected separately in Fig. 4b-e.

Indentation technique
The indentation technique has been investigated and widely applied to detect and to determine the material mechanical properties such as stiffness and hardness;besides, the indentation method is also a nondestructive testing method [39]. The principle of the indentation test consists in applying an indenter of known shape (ball, cone, or pyramid) on the surface of the material to be tested. Under the action of the indentation load, the indenter sinks into the material, producing elastic and plastic deformations in the contact area. When the indenter is removed, a redundant indentation remains. The higher the applied load, the larger the size of the indentation [40].
The application of the indentation load can be continuous or discontinuous. In the first case, the residual indentation is observed after the indenter removed using an optical microscope. For continuous indentation, the load applied progressively and the displacement of the indenter tip measured in real time as a function of the load.
The test of instrumented indentation is currently largely used for various applications and to different scales (macro-, micro-, and nanometer). For loads not exceeding 1 kgf, the indentation hardness is often called microindentation. Nanoindentation refers to a hardness test with a load less than 1 N, and the size of the indentation is in the nanometer scale. Currently, Vickers, Knoop indenters are frequently used in microindentation tests [41].  For both microindentation and nanoindentation, considerable care and experience are necessary to obtain good accuracy. Indentation is a good alternative test for brittle materials. Knoop indentation tests are a standard method for material characterization due to the fact that they provide an easy, inexpensive, non-destructive, and objective method of evaluating basic properties from small volumes of materials [42].
The residual surface deformation after spherical indentations was first investigated using phase-shifting moiré and Twyman-Green interferometry [41]. In this work, the interest was holding for experimental indentation Knoop tests.

Knoop indentation detection
In this part, we will rely on the experimental tests of indentation to predict their effect on the Moiré fringes. They were performed with indentor Knoop. The first case is used, where the application of the indentation load is continuous. The image of the print for the various tests of indentation was seen by optical microscope. The tests of indentation were carried out under various loads. Like in the first step, the glass plate serves as the object under study. The Moiré fringes take of glass plate before the indentation are presented in Fig. 5. The Moiré fringes are parallel and equidistant straight lines. After the first step, on the glass plate was applied an indentation using the Knoop indenter Tukon 2500. This indentation has magnified by objective microscope 50x/0,55. Indentation images were collected respectively with force loads of 0.05 kgf, 0.2 kgf, and 0.8 kgf Figs. 6a, 7a, and 8a. The topography of the indented surface has described by deformation of the structure of the moiré fringes shown by the Figs. 6b, 7b, and 8b according to the loads applied, respectively.

Discussion
The Moiré fringes shown in Figs. 3c and 4b-e are distorted in their structure as the defect is located on the surface under test. This distortion depends on the position and size of the defect present. However, these results show that the moiré fringes materialize the type of defect and that they can differentiate them distinctly.
The results given by Figs. 6b, 7b, and 8b show that the Moiré fringes presenting the indentation as a function of the loads, deforming at the place where the indentation was produced by the application of the indenter. It is observable that the change in the shape of the Moiré fringes responds as a function of the change in the applied indentation load. As the load increases, the fringes become more and more deformed. The change in the Moiré fringe shape is materialized by the test grating image undergoes a variation by the presence of defect. When a grating is projected onto the surface of an object, it is deformed by transmission according to the shape of the object, which makes it possible to obtain information on the surface condition of the object. However, the reference grating is superimposed on this distorted grating, thus generating the Moiré fringes which present an interference pattern [43]. In the literature, gratings are printed inside the transparent specimen [44]. On the other hand, here, the superposition of the image of the distorted grating with the reference grating is achieved by optical contact between the gratings by transmission compared to the literature [45]. The optical contact between the gratings is by reflection.
The results of the Moiré fringes showing the indentation are important. They increase the accuracy of the results of the indentation domain, and they are complementary to the results found in the literature. In perspective, to apprehend a comparative study between the mechanical properties of transparent objects with the optical properties of the moiré fringes. In this way, to increase the precision of the results to characterize mechanically the examined material, by determining its local properties.

Formulation
To validate the method suggested in this work, it is necessary to evaluate the size of defect present on the sample surface. The special attention is given on the defect created on the surface of the sample presented in the Fig. 4a and b. Then, two states were considered (Fig. 9), before and after the creation of the defect. Figure 10 shows the explanatory geometrical diagram of the setup to determine the mathematical relations for the calculation of the defect on the transparent surface. The calculation principle is based on the Ligtenberg principle applied to a reflective surface [46]. This diagram shows the space between the test grating and the sample (projection space or control space). The beginning is with a surface before loading, the light rays coming from point E of grating G of pitch p, arrive at point M on the observation plane. The normal EH of the grating is perpendicular to the sample surface at point H. Point E is projected onto the surface to be inspected at point E′, such that the angle HEE' is defined by α.
After loading, the normal undergoes a rotation of angle β to give EH′. EE′ is also rotated by an angle β defined by E′E″. The angle HEE″ is defined by (α + β). The grating The phase of the object is 2πm and that of reference is 2πk; the difference in phase between the two states is as follows: where Δφ = φ ob − φ ref , φ ob is the object phase (after loading) and φ ref is the reference phase (before loading).
n is the fringe number; it can written through Eq. (4) as follows: From Eq. (3) and Eq. (5), it results to the relation below given by According to the diagram (Fig. 10), β presents the angle of the deformation slope between X and Z, which presented as dz/dx. The calculation was performed from the experimental setup and gave as a result the relation Eq. (6) quantifying the defect.
The MATLAB software was used to obtain the curves of Fig. 11; this one presents the intensity of the fringes according to the ordinate, and the abscissa X indicating the number of fringes and the distance between them. Along this axis, the distance between the fringes is given with this software in pixels. The maximum curves correspond to light fringes and the minimum to dark fringes. The distances are taken between the maxima and minima according to the following steps: the figure of the Moiré fringes before the creation of the defect (Fig. 9a) is transformed into gray; then, plotting the interfringe curve that is obtained according to Fig. 11a. The same process applied to the Moiré fringes of Fig. 9a was applied to the Moiré fringes after the creation of the defect . 9b); the curve of the interfringe obtained for this case is presented in Fig. 11b. Figure 11c shows the superposition of the two curves of Fig. 11a and b, respectively, in order to compare between them. The difference between them is located in the area where the defect was created. It is represented by a dotted rectangle in the interval between 80 and 180 pixels.

Phase calculation
In order to extract information for characterizing the defect, the phases are calculated [47]. The phase of the surface is Interfringe pixel: (a) before creation of defect, (b) after creation of defect, and (c) superposition of the above two preceding states calculated before creating the defect and after creation of the defect, along the horizontal line blue (Fig. 9b) that runs through the defect.
To obtain more accurate results, the graphs of phase were plotted by the Excel software; they are presented in Fig. 12. The surface phase were calculated by the object interpolated phase (PHIO), after creating the defect, and the reference interpolated phase (PHIR) before creating the defect.
The interpolated phase was used to take the same values of X for the object phase and the reference phase. The interpolated phase difference Δφ calculated between the two states is equal to 0 except at the location where the defect was created (defect area).
The two curves show a similar shape and the slight difference is between 75.10 -3 pixels and 150.10 -3 pixels. The phase difference between the two states (PHIO-PHIR) determines the phase of the defect [16,20,48]. This phase difference allows us to extract the depth of the current defect, the depth at each point of the tested surface and the width of the defect compared to [49] the defect's volume was measured by the difference between two fringes images of fringes (flat surface fringe image and surface fringe image with introduction of defect).
Thus, Fig. 13 shows the curve quantifying the defect in 2D. This curve is plotted by substituting values Δφ in relation of Eq. (6) to obtain the deformation slope dz/dx. According to Fig. 13, the deformation slope is defined by ∆Z along the Z-axis and the defect width defined by X along the X-axis. Then, ΔZ.10 -3 is between 0 and − 0.002.10 -3 pixels, and X is between 75.10 -3 pixels and 150.10 -3 pixels.

Detection resolution of the setup
The used technique and the setup offer a double possibility, which facilitate the defects' amplification (enlargement/ magnification) as well as its detection even if it is small. The double amplification is generated first by the Moiré effect, where the microscopic deformation is materialized by a macroscopic deformation of the Moiré fringes; the second is achieved by optical setup. The control of a specific surface according to the size of the order of diffraction transmitted. It suffices to project the spectrum of diffraction on the surface to be controlled, to move the surface according to the coordinates x and y to position the desired order on the surface to be checked. Depending on the chosen order (+ 1, + 2, + 3, …) of the harmonics distributed according to the Fourier series, the control resolution of the setup is increased; therefore, if only the chosen order is authorized to pass and the zero order.
This technique of topographical control by transmission using diffraction orders is new in literature to inspect the surface of transparent object at increased resolution. Further, the detection resolution it depends on the spatial frequency of the used gratings. It can be easily adjusted by several orders of magnitude, by changing the pitch of grating used. To obtain the height resolution of our setup, we made the second possibility is to use the fringe multiplication technique based on spatial filtering [50].

Conclusion
In this paper, an experimental setup has developed. It is based on a non-destructive and non-contact optical method using the Moiré method and interferometry, which allows inspection of the surface of transparent objects where various microscopic or sub-microscopic defects were detected.
The results provided by Moiré fringes have variation in their structure which materialize the type of defects and allow for a clear distinction between them.
In the case of the indentation, the Moiré fringes obtained were deformed where the indentation was produced by the application of the indenter. The radial forces of indentation show their effect on the form of the Moiré fringes.
The Moiré fringes obtained are thus relevant with the tests of indentation carried out under various loads. Therefore, The method of measuring defects by the setup gave information about defects, which proved the validity of the proposed method. The detection resolution of this setup can reach the nanometer. It depends on the spatial frequency of the gratings used and can therefore be adapted to the size of the defects sought. This simple method, fast and precise control process can be exploited advantageously in research laboratories as well as in industry.
Since industry is one of the sectors that attaches increasing importance to surface quality, such as the surface quality of transparent objects (surface of optical components, defect detection of glass, surface flatness for deposits on glass, etc.). This requires the development of new characterization tools that are more accurate, convenient, reliable, effective, and easy to use with application and less cost. Thus, in this work, the proposed method is easy to install and use, does not require complex equipment, and is less expensive.
Finally, this method has practical application and largely improves capability in inspection the transparent objects, in micrometer or nanometer scale. The results obtained are very satisfactory results with a high degree of accuracy. In fact, it is sufficient to compare a Moiré pattern with a previously recorded pattern and obtain it from a part considered a standard, which allows us a gain accuracy, time, and money. And also, in order to verify the presence or absence of defects by using the system mentioned in this work, it is enough to place the sample to be examined in the path of the laser beam. The achieved magnification can be 1000 times.