2 THREE-DIMENSIONAL SURFACE ANALYSIS 2.1 Measurement of high gloss surfaces

Capturing the three dimensional topography of a high gloss surface is challenging due to the optical properties of these surfaces and requires a technology that can cope with mirroring surfaces as well as with transparent top layers which may be used in the multi-layer buildup of the coating. Due to the wavelength of the relevant structures and the distortion of single characters on the surface the measured area needs to have an adequate size, which means at least some centimeters in x- as well as in y-direction.

As the existing parameters do not meet the requirement of showing a high correlation to human perception, an algorithm needs to be developed to analyze the surface data. For further analysis in this project, the data captured should be processible with standard calculation software such as MATLAB.

In test measurements the phase stepped deflectometry was identified as a suitable technology. Here a periodic grid is projected on the surface and its reflection is captured by a sensor. As every distortion of the ideal surface will lead to a variation of the ray path and results in a displacement of the point´s position on the sensor the slope in each surface point can be calculated by a phase shifted repeated projection of the pattern [4]. On this data mathematic operations like differentiating and integrating can be applied to calculate the curvature and the three-dimensional topography of the surface [5]. This three-dimensional data is saved in a 3D matrix and used for further processing.

2.2 Topographic elements

Topographic elements known from geology can also be applied on technical surfaces. They are described in [6] and can be classified in the categories of point, line or area elements, according to their expanse. Figure 1 gives an

Figure 1: Topographic elements of a surface.

The peaks and sinks are point elements, inclines and slopes are line elements and hills and dales form the category of area elements.

As these elements due to their influence on the reflective properties strongly affect the human perception [7] they form the basis for the analysis of the surface data.

The motif parameters for the profile method described in [8] are also based on the definition of hills and dales but are only applicable on two dimensional profiles. For the further analysis this definition was transferred into the description of a three dimensional motif or pattern recognition. Following the concept used in [8] this should be a dale surrounded by watershed lines. As hills and their shapes seem to be the more prominent characteristics of high gloss surfaces this definition was inverted and the further analysis uses a three dimensional motif consisting of a hill and its surrounding dales.

2.3 Data analysis

For the data analysis the matrix with the three dimensional surface data is loaded into the calculation software MATLAB where filters and algorithms are established to identify the relevant topographic elements. Prior to the analysis itself some pre-operation are applied on the data. To enable a visual comparison of the processed data and the image output of the original measurement device the matrices are flipped horizontal to standardize the position of the point of origin. Next approximately ten millimeters are cut on either side of the measurement field as due to the reflective properties of the surfaces failures may occur close the edges.

Development of an Algorithm for Measuring the Quality of High Gloss Surfaces Correlated to Human Perception

Now the matrix contains the vertical coordinate in microns corresponding to the pixel position on the sensor of the measurement device. To enable the use of standard length units the resolution of the matrix is calculated and all further calculations work with x- and y-coordinates in millimeters.

The data analysis aims at extracting short wave surface deviations like orange-peel or lacquer sinking. They differ in form and frequency from others like roughness or waviness of the substrate. Signal noise and very short waved components of the profile are suppressed by applying a low pass filter on the data. For the filter operation an areal robust Gaussian filter according to [9] is chosen. This filter is chosen as it is especially suitable for surfaces containing single, pulse like distortions [10] like spots or pinholes, which can be found on high gloss surfaces.

The chosen filter is described by the following Gaussian weight function:

(1)

Table 1: Explanation of variables according to [9].

Variable Explanation

s The Fourier transform of the discrete representation of the weight function

π Number pi

x The distance from the center (maximum) of the weight function in x-direction

y The distance from the center (maximum) of the weight function in y-direction

λc Cut-off wavelength γ Constant (0,7309)

For the implementation of the filter the Gaussian weight function is truncated at a value of Lc = 0.5 which is recommended for general applications in [11].

According to [8] a cut-off wavelength should be chosen referring to [10]. It is also stated, that structures with wavelength smaller than one third of the cut-off length are eliminated. The smallest structures in lacquer surfaces that affect the perceived quality show wavelength in the size of 0.02 mm to 0.06 mm [12]. To ensure that they are not eliminated by the filtering operation a cut-off wavelength of λc = 0,025 mm is chosen. No form correction or high pass filtering is applied on the data as the analysis works with relative heights corresponding to the definition of the three dimensional motif.

According to the definition of topographic elements hills can be identified by

matrix a maximum can be defined as a point, where the local slope changes from positive to negative. These maxima are identified in the data matrix by a crosswise search in rows and columns, with the peaks being a maximum in both directions. These points are stored in a separate matrix.

The hills on high gloss surfaces do often show a kind of double peak, as shown in figure 2, which cannot be distinguished from common viewing distances. Thus the number of peaks is reduced by combining adjacent peaks.

Figure 2: Double peaks on high gloss surface with orange peel.

This approach is also based on the analysis of two dimensional motif parameters [8] where small peaks are suppressed by combining them with larger ones. For the combining operation a threshold is required which has to depend on the concrete topography, as the distance between the peaks depends on the kind and size of the different characteristics. Thus the Euclidean distance between all the adjacent peaks and their cumulative frequency are calculated. The threshold is defined as 95% of the cumulative frequency. Thus all the peaks with a smaller distance are combined while single peaks are separated via the top 5%.

Development of an Algorithm for Measuring the Quality of High Gloss Surfaces Correlated to Human Perception

Applying the change of sign of the slope for identifying the peaks ensures that also small hills, which are positioned in larger valleys, are found. This cannot be ensured applying a threshold height for the peak search. As on high gloss surfaces a lot of characteristics with different wavelengths and amplitudes overlay, a threshold based search can easily mask out those elements, e.g. a small orange peel inside a larger sanding line might not be found.

Besides the peaks also the surrounding valleys need to be identified for a comprehensive description of the single hill. They are identified by searching the adjacent minima of each peak along the x- and y- axis. After determining the peak and the surrounding valleys the characteristic size of each hill can be calculated. The height of the hill is the difference between the z-coordinate of the relevant maximum and the average z-z-coordinate of the surrounding minima. The rectangular area of the hill is calculated based on the distance of the minima along x- and y- axis.

These characteristic sizes are used to calculate the specific value for describing the hill: the ratio of hill height to hill area (hill height/area). As this ratio also describes the gradient of the hillsides, it gives an indication for the reflective properties of the surface and with this also for the perceived quality. This specific value for each hill is presented in an Excel sheet together with a number of additional figures like x-, y- and z- coordinate of the peak or the mean slope along x- and y- axis. In this list, hills with a very high ratio of hill height/area are filtered as they do often form irregular characteristics like spots, which are not subject of the on hand analysis.

After deleting these outliers a mean value is calculated and added to an additional Excel sheet that includes the mean values for all measurements on one sample.

Additional results of the MATLAB routine are 3D plots of the original surface and the filtered surface as well as a contour line plot in which the relevant maxima are marked. These plots are mainly used for the visualization and verification of the algorithm.

3 EVALUATION OF THE MEASUREMENT PROCESS