**3. Prismatic lightguide analysis**

160 Dielectric Material

only if they are connected to strong edges.

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

Later, we use the Hough transform (Fig.5. (b) and Fig.6) to detect the parameters that

**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

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

image peaks, it is thus the slope of the line along with the position.

represented in the input image.

controls the accuracy of the right angle at the vertex of the prism (Hough, 1962).

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 aluminum guides.

**Figure 7.** Prismatic light tubes are used for transporting and distributing natural light. Experimental setup in the School of Optics (Complutense University of Madrid)

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

#### 162 Dielectric Material

1.5, as is the case of acrylic plastic, then the input light angle must be approximately less than 27.5º from the guide´s axial direction, even though the acceptance cone can be higher in the meridional plane.

Natural Lighting Systems Based on Dielectric Prismatic Film 163

**Figure 8.** The Coordinate system defines the angles of incidence and observation in the guides.

The photometric profile of the source is an angular distribution adapted to the optimal transmission features of the prismatic film used, and the analysis was restricted to the spectral range between 380 and 780 nm. The CIE Illuminant D65 is the reference light

The spectral reflectance of aluminum is estimated as isotropic over the fence and has been experimentally determined using a Hitachi U-3400 spectrophotometer with special accessories for measuring the specular reflectance at 12° incidence. Experimental spectral

Spectral Reflectance Aluminum AlanRh

400 450 500 550 600 650 700 750

Wavelenght (nm)

Longitudinal section (a) and transverse section (b).

reflectance measured of aluminum is shown in figure 9.

**Figure 9.** Aluminum spectral reflectance.

0.6

0.65

0.7

0.75

0.8

R.U.

0.85

0.9

0.95

1

source.

Two different analysis have been done: Firstly, a theoretical simulation based on the specular reflection model in order to analyse the color characteristics to the output of two guides, rectangular and cylindrical of different lengths, one of them of aluminum material and the other one, internally coated of prismatic film structure this model have been developed by means of a mathematical software as Matlab. Secondly, the prismatic guides proposal evaluates with a ray tracing software through which we show the efficiency for a wavelength evaluated at the end of the guide, this model have been studied with Monte Carlo ray tracing.
