Applicability Evaluation of a Laser Light-Mater Interaction Based Computational Tool on Status Identification of Applied Micro-Structured Coatings

The current work aims at evaluating a proposed method based on a computational tool developed using Object-Oriented Programming to identify the status of micro-structured surfaces. In this case, these are micro-structured coatings with riblet microstructure developed by Fraunhofer Institute–IFAM, by building a graphical reproduction of the analyzed surface and calculating an expected laser reflection intensity acquired by a laser sensor device, the proposed method is assessed by using the simplest case: a flat surface, and an optimal case: an intact riblet surface. The results corroborate the calculations to be applied to further steps from more complex cases of degradation and to diverse riblets geometries. Based on Huygens-Fresnel and Fraunhofer diffraction theories, the calculations developed and demonstrated in this paper improved the nondestructive tests to support the status identification of the micro structured coatings, e.g. riblet structures based on shark skin used in shipping and aerospace industries. This work is assured required quality of the riblet coating identifying the number of structures and expected geometry using implemented calculations to foresee the laser reflection intensity acquired by a laser sensor device with 3 detectors, for instance, a riblet structure could be graphically reproduced, analyzed and completely identified based on the application of the theoretical optics applied on this work.


Introduction
Status identification of structured surfaces used in aviation industry, e.g. shark skin, called tiny ribs (riblets), is an option to support the quality assurance and keep desired performance of these coatings. Riblets are used as an alternative to decrease drag and consequently save fuel and reduce Greenhouse gas (GHG) emissions [1]. These riblets are part of strategical and technological possibilities to fulfill the decision taken by European Union that CO 2 emissions from the aviation and shipping industry must be reduced by 10% and 20% respectively, in a period of medium to long term [2], for instance, due to climate change caused by GHG emissions [3].
Quality assurance using Non-destructive tests (NDT) is a powerful tool in terms of reliability, costs and easiness. NDT improvements are related to safety of aviation components and structures. The NDT technique refers to testing methods, specially used to analyze structural parts or objects without harming or affect future usefulness. The main goals of NDT are to identify hidden defects or damages. Furthermore, NDT material properties can be evaluated and the structure geometry can be measured [4]. According to the American Society for Testing and Materials [5], the concept of NDT is based on the "development and application of technical methods that examine materials and components, in order to detect, measure and evaluate discontinuities, defects and other imperfections. Integrity, properties and composition assessment and measure geometrical characteristics are evaluated by NDT as well". In special attention to riblet structure coatings, geometrical characteristics and integrity are important parameters to keep the desired functionality. Among the methods of possible tests to be applied to this specific analysis of coatings based on riblet structures, nondestructive testing tends to be powerful for this application.
There is a large range of NDTs available and especially for those applied in aviation industry; it is relevant to consider, for instance, health monitoring tests using Fiber Bragg Grating (FBG) sensors are used in order to be applied to durability tests of a composite wing structure. FBG sensors could be detecting toughly visible impact damages due the distortion of the spectrum by the strain change [6].
Characterization of micro structured surfaces has to be achieved in nanoscale level. Research on characterization of surfaces is being made using full field polarized light-scattering, and experimental findings have reached a good agreement with theoretical predictions considering different surface roughness [7]. Development of NDT includes concepts of non-contact devices, such as the one proposed by Imlau et al. [8], and it can be an alternative to evaluate the conditions of structured surfaces. Researchers from Osnabrück University presented a sensor development based on the intensity distribution principle of the scattered light generated by a laser beam incidences normal to the riblet layer [9]. In this work, the calculations based on Huygens-Fresnel diffraction theory applied on riblet surfaces, was implemented in a code based on Mathematica software, showing the expected applicability of the proposed method.
The laser light behavior prediction is a relevant step for the implementation of this proposed technique. The calculations based on Huygens-Fresnel and Fraunhofer diffraction theories are the initial step to fulfill the computational tool implementation and to provide a knowledge database to be compared to experimental measurements.
The application of non-destructive testing must be taken into account in order to achieve the main objective, identifying the structural geometry of the coating based on riblet structure with the functionality of drag reduction. The purpose of this work in the beginning is graphically reproducing the original riblet structure geometry, which will be the basis for all calculations and data analysis and ensure the quality of the coating characteristics.
This work aims at introducing a method to validate the computational tool outputs in order to build a reliable computational tool to support analysis and make decisions in aviation industry production and maintenance. The "Introduction" section presents the state of the art related to non-destructive tests, micro structured surfaces and applications and optics theories applied to develop the proposed method. Section "Experimental part" expounds about the original geometry used to define the riblet surface and the main parameters to set the algorithm calculations, the development techniques and theoretical foundation will be detailed as well. Section "Results and Discussions" discuss the main results obtained in cases explored and defined previously, and "Conclusions" explain the contributions of the work to improve a robust computational tool able to identify micro-structured surface status.

Experimental Part
The implementation of the proposed technique, performing the calculations using Object Oriented Programming (OOP) is based in a code developed in Java language and the support of a consistent Database Management System (DbMS).
In order to be applied in production and maintenance lines on aviation industries, it is necessary to provide specific tools and techniques based on computer science field with the intention of support making decision on quality assurance of the structured coatings.
First step to reach the target is to build a graphical representation of the surface. The original geometry of the riblet structured surface defined in this work is based on the structure developed by Fraunhofer Institute-IFAM, as cited by Stenzel et al. [2]. The model consists in sharp-peaked riblets whose characteristics are presented in Figure 1, with the following characteristics: triangular shape, distance between bottom center riblets (dR), height (h) of the riblet and angle of the riblet tip (α).
The riblets will be generated one by one, following cartesian coordinates in space and will be defined according to Equation (1) and shown in Figure 1: where Figure 1. Sketch of the intact riblet modeling. Xr = riblet width; h = height of the riblet; α = angle of the riblet tip.
The original geometry starts in a plane section, with the half measure of the distance between riblet tips, as: where dR is the distance between riblet bottom centers. In order to contextualize this work, degradation is defined as the "act or process of damaging or ruining something" [10]. Coating degradation is a combination of both chemical and physical processes [11]. In airplanes coatings there is deterioration in the coating performance due to weather and use. Anti-corrosion procedures are not useful to restore the original surface. So the coating needs to be completely stripped and reapplied, thus this process is expensive [12].
Aiming to reproduce the status of the surfaces on airplanes with riblet coating applied, rebuilding the riblet geometry in degraded state is necessary. In this study, a pattern of degradation is considered to be able to validate the output data and a total degradation of the structured coating is the investigated degradation pattern used as test approach to the calculations. A total degradation, considering totally smooth surface of the sample, is the easiest case to validate the calculations and support the further research steps.
In this work, an experimental fast sampling sensor setup using Non-contacting laser probing is being developed, based on the Huygens-Fresnel and Fraunhofer diffraction theories combined with ray tracing calculation methods. This part of the work is the software development to perform analysis and treatment of output data provided by a laser sensor ( Figure 2) defined by Imlau et al. [8]. The computational tool is used to interpret the obtained diffraction patterns and as a way to simulate the structured surface status from a given pattern. Thus, the software is developed to generate consistent information for analysis and decision-making regarding the surface structure and its maintenance.
A previous study developed by Imlau [8] underlying the performed calculations seeks to validate the results obtained in the current work, where the findings can be theoretically grounded by other calculation approaches, for instance using Mathematica software. These parameters were applied in two equations to be validated. The first equation (Equation (1)) is given by the electric field equation and the second equation (Equation (2)) is given by the calculations using Fresnel diffraction theory.
Related to Equation (1), intensity calculated in a point p on detector is obtained by the square of the electric field calculated, as demonstrated on Equation Assumption is made that t ω is a variation between −2π and 2π, and φ is a relation between a reference point on detector and the amount of calculations to the surface, and is assumed that E 0 is equals 1.
Using Equation (2), starting from Fresnel integration, a diffraction pattern is calculated which should be acquired by the detectors. Applying Fresnel integration on the equation, in combination with transcendental functions with complete tables of values, this function can be calculated beyond Euler spiral [14], which is a geometric representation of Fresnel integration in a complex plan.
Nowadays, these integrations can be fast solved using computational tools.
Reis et al. [15] used this approach to characterize a diffraction grid with n nonsymmetric slits and arbitrary widths, and the results can be a base to further steps of this research, which will introduce more detailed structured surfaces, considering variations on intensity patterns acquired by detectors, aiming characterization of the analyzed samples.
Equation (2) assumes that n is the number of reflections to a central detector without interference, and U2 is related to calculations taking into account the last position of reflection on surface for each continuous reflection and U2-1 is related to calculations taking into account the first position of reflection on surface for each continuous reflection, as shown in Figure 3 and described on Equation (4).
To apply the proposed techniques we are setting the software with the main parameters to virtually build a sample with the characteristics used to perform riblets at Fraunhofer Institute-IFAM. The software is able to change these parameters as needed to simulate different types of riblets. The main parameters are: height of the riblet (h); distance between riblets (d), which is related to the distance between bottom centers of the riblets; angle at the tip of the riblet (α), length (x) and the width(y) of the sample.
The structure of the laser beam is filled in the next step. The user should input the parameters to set the laser incidence and the laser reflection will be graphically reproduced. The main parameters are the initial position of the laser (lx0), related to the position on the x axis of the original geometry; the number of the laser beams (lxn); and the distance (ld) between the laser beams; all these parameters are saved to generate a 2D visualization of the sample with the laser beam incidence and the reflection of the beams. In this step all beam incidences and reflections are calculated, which allows building a 2D visualization of the structure ( Figure 4 and Figure 5).  The riblet degradation can be simulated in the next step. At this stage of development, we can set the degradation as a regular degradation with a perfect flat cut on the tip of the riblet.
The percentage of degradation is varied from 0% to 100%, related to the percentage for the exact point on the structure of the riblet where the degradation will start, that is, 100% is the maximum point to degradation. On Figure 6 showed a riblet structure surface with 50% of flat degradation, a completely degraded riblet structure (100% of degradation) and an intact riblet structure.
In the current work, a totally flat surface is analyzed in strict calculations on the central detector, and the main parameters are given as:

Results and Discussions
An initial result applying the calculations presented in this work shows a good agreement with the theoretical approach, at first, taking a completely degraded sample, considering the surface completely flat. To evaluate performed calculations some expected characteristics of the laser light reflection, as symmetry and Figure 6. Sketch of the intact riblet structure in comparison to degraded riblet structures (50% degraded and 100% degraded).
periodicity of the wave were taken into account. In Figure 9 normalized calculations using Equation (1) (Figure 7) and Equation (2) (Figure 8) are shown.
Comparing Figure 7 and Figure 8, the similarity of results performed by both different calculations can be identified. Evaluating the symmetry of both, the findings shown in Figure 9 present a great accuracy comparing the intensity   calculated in relation to detector center, in these evaluation is calculated the difference between the both sides in relation to center of central detector, and if tends to zero, that means there's no difference, then is reached a good symmetry. Figure 9 shows the comparison between the symmetry calculations in relation to calculated intensity, finding expected symmetry level, with variations due the precision used. Even with high calculated intensity, specially observed around detector center, calculated symmetry tends to zero, as expected.
An analysis of the plots presented in Figure 7 and   gaps between the peaks identified are considered hollows.
As observed in Figure 15, it is possible to identify the Fraunhofer pattern, and the area between the central maxima and the first maxima, it is possible to observe the number of riblets on the structure. The number of hollows, between central maxima and 1st maxima, on both sides, represents the number of riblets, in the evaluated case, 9 riblets and as showed on Figure 15, the 9 riblets can be related to 09 hollows.  for further deep surface evaluations. Final evaluation consists in analysis of the calculated intensity performed on lateral detectors. Performing the same methodology applied to evaluate the calculations performed on central detector, symmetry and periodicity are presented on the calculated results. Figure 19(a) shows the entire calculated intensity range on right detector. The values calculated are spaced from 7 µm and the variation of ωt is defined with 40 temporal steps between −2π and +2π. It is possible to observe periodicity of the calculations, confirmed by Figure 19(b), that shows the same calculations in log scale.
A complementation of the initial work presented at this paper, is the evaluation related to the distance between the maxima observed on lateral detector calculations. Applying the Bragg condition to confirm the performed calculations is possible to identify the expected results showed on Figure 20. As applied to evaluate the central detector intensities, on lateral detector is observed a spreading of the intensity related to the applied angle to the calculations. The distance calculated, it is assumed that is on Fresnel pattern, there's a regular variation between each set of maxima, as showed on detailed plot on Figure 20, analizing the highest set of maxima, with the direct incidence of the reflected laser light, return the expected variation of the peaks.

Conclusions
The computational tool intends to perform the calculations to predict a laser and, if taking a small distance between the sample and detector, keeping the Fresnel pattern, also the distance between riblets can be identified. All data calculated via the developed computational tool can be further compared with real measurements.
The structure can be graphically reproduced as an intact riblet structure and vary to diverse levels of degradation. Specifically in this work, maximum degradation of the riblet structure was applied, considering flat degradation on 100% of degradation. This completely smooth surface was implemented and calculated by the proposed technique on the computational tool.
Presented results show that this work can be an alternative for the identification of the status of a structured surface. First evaluations of the proposed calculations, applied on the easiest cases of validation, considering a totally degraded riblet structure, as a flat surface, corroborate the applicability of the proposed technique and start a field study to improve the developed algorithm to be applied in further structured coating analysis.
Analyzing features which cannot be accessed by manual evaluations, periodic micro structured coatings, e.g. riblet structures, the intensities calculated via computational tool show the possibility to compare with experimental measurements performed by the laser sensor device developed in Fraunhofer Institut-IFAM, and identify the main properties of the micro structured surface previously defined. A relation between the calculated intensities specifically to lateral detectors are initial kick off to evaluation of the degradation on riblet structures; evaluation of the distance among the maxima peaks spread on the detector could be a way to identification of further parameters related to type of degradation and level of degradation on riblet micro structure surfaces. The assessment with this proposed methodology to identify riblet structured coatings ensures the application and comparison with the results acquired by the prototype of the laser sensor device developed and described as a potential tool to be used in quality assurance of structured surfaces, specially applied on aerospace industry.