**2.1. Image processing algorithms**

This section deal with a brief description of the recognition procedure algorithm to analyse the prism profile structure. First, a diagram with a description of the recognition procedure to extract the inclination of the lines from the image and to calculate the radio of the peak prism is given (Fig.3), secondly, a more detailed description will follow.

**Figure 3.** Structure of the recognition procedure and extraction process performed.

In order to investigate the light behavior in the system the effect of accuracy of prismatic structures and peak defects has been examined; computer analyses such as changes of prism angle and plane shape were carried out. By analyzing the image processing prism structure and by using morphological operations measurement of the inclination angle with high accuracy can be achieved. To execute the processing, the prismatic film profile showed in figure 4 is employed (the optical microscope used to obtain the prism image is Motic SMZ-143 equipped with a digital camera Moticam 2000).

**Figure 4.** Prism structure used to analyse the parameters of the prism (57X)

158 Dielectric Material

prismatic film (2.5X).

**2.1. Image processing algorithms** 

**Figure 2.** Prismatic film used to distribute light. a) Surface area detail of prisms structure (25X), b)

This section deal with a brief description of the recognition procedure algorithm to analyse the prism profile structure. First, a diagram with a description of the recognition procedure to extract the inclination of the lines from the image and to calculate the radio of the peak

prism is given (Fig.3), secondly, a more detailed description will follow.

**Figure 3.** Structure of the recognition procedure and extraction process performed.

Firstly, a threshold is applied to the input image in order to make it binary. The threshold value is determined from a grey-level histogram of the image, later the edge is separated from the background (Fig.5.b).

**Figure 5.** (a) Cropped image before the digital processing used to obtain the dimensions of micro prism structures. (b) Edge detected images resulting from the Canny Method (white), the line after Hough transforms (red), and the estimation to calculate the radius of the prism´s peak (blue).

The edge map is used to determine the existence of lines around the regions. This edge description is obtained from the operator Canny (Canny, 1986) this operator is consider as an optimal edge detector to find boundaries between poorly defined objects as well as hard edges. The Canny method finds edges by looking for local maxima of the gradient of the image; the gradient is calculated using the derivative of a Gaussian filter. The method uses two thresholds, to detect strong and weak edges, and includes the weak edges in the output only if they are connected to strong edges.

Natural Lighting Systems Based on Dielectric Prismatic Film 161

After performing probabilistic Hough Transform, two lines are obtained determining and ensuring the right angle prism used to guide the incident light. Figure 5 shows in blue color the plot of the inclination angle of the prism through the digital processing. The main peaks are located in the Hough transform matrix. The left slope is calculated to be an apex angle of -45.38º and the right slope has an apex angle of 44.50º forming a total angle of 89,88º (Fig. 6 (b)), after that, an approximation was made to relate the prism rounding radius with the slope values and the contour of the vertex profile. The circle obtained used to achieve the radius of the prism vertex is showed in red color (Fig. 5 (b)). The prism base obtained has a width of 400 µm and the radius value obtained is 13.78 µm; this result could be affected by

The lightguide structure analysed is a prismatic hollow tube with the thin polycarbonate film with right angle prism sections. The prism light guide transmits light by total internal reflection, which gives higher efficiency and homogeneous light distribution through the guide. Prismatic sheeting developments have provided further improvements in sunlight systems (Fig. 7), boosting efficiency for specific incidence angles with regard to the

**Figure 7.** Prismatic light tubes are used for transporting and distributing natural light. Experimental

Light travels mainly in the hollow air space inside the guide and bounces off by total internal reflections (TIR) when the input light is highly collimated. This configuration has an angular acceptance cone, which is not an isotropic distribution in the space determined by the refractive index of the prismatic film, if the refractive index of the dielectric material is

setup in the School of Optics (Complutense University of Madrid)

the pressure exerted to make the cut of the prism film.

**3. Prismatic lightguide analysis** 

aluminum guides.

Later, we use the Hough transform (Fig.5. (b) and Fig.6) to detect the parameters that controls the accuracy of the right angle at the vertex of the prism (Hough, 1962).

**Figure 6.** (a) The Hough transform of the prism image. (b)The red square shows the peaks of data in the Hough matrix. ρ is the distance from the center and θ the angle at which the sum of intensities in the image peaks, it is thus the slope of the line along with the position.

Originally, the Hough Transform was proposed to extract straight lines in the particle tracks recognizing procedure. Nowadays, the Hough transform is a technique which is used to insulate features of a particular shape within an image. In this case, the Hough transform is used to identify the parameters of the line and it uses the parametric representation of a line which is fits to a set of given edge points. It takes as input the grey scale image, and produces as output an image showing the positions of tracked intensity discontinuities. The output of the edge detector defines where features are in the image, and the Hough transform determine what the features are and how many of them exist in the image. The main advantage of the Hough transform technique is that it is tolerant of gaps in feature boundary descriptions and is minimal unaffected by image noise. The result of the Hough transform is stored in a matrix that often is considered an accumulator (Fig. 6 (a)). One dimension of this matrix is the angles θ and the other dimension are the distances ρ, and each element has a value telling how many points/pixels are positioned on the line with parameters (ρ, θ). So the element with the highest value shows the line that is most represented in the input image.

After performing probabilistic Hough Transform, two lines are obtained determining and ensuring the right angle prism used to guide the incident light. Figure 5 shows in blue color the plot of the inclination angle of the prism through the digital processing. The main peaks are located in the Hough transform matrix. The left slope is calculated to be an apex angle of -45.38º and the right slope has an apex angle of 44.50º forming a total angle of 89,88º (Fig. 6 (b)), after that, an approximation was made to relate the prism rounding radius with the slope values and the contour of the vertex profile. The circle obtained used to achieve the radius of the prism vertex is showed in red color (Fig. 5 (b)). The prism base obtained has a width of 400 µm and the radius value obtained is 13.78 µm; this result could be affected by the pressure exerted to make the cut of the prism film.
