**3. Results**

### *3.1. Calibration Constant K*

All images had to be captured without saturating the pixels of the camera detector. With this in mind and after several tests, we found that a good compromise was to take images with a maximum exposure time *t* = 1 s and ISO 1600. The luminance of the light source had to have the same order of magnitude as the lighting levels of the road. The luminance of the source when the tests were performed with the photometer (see Figure 2) was *L* = 1.22 cd/m<sup>2</sup> (the light source consumed an electric power of 47 W). When Equation (1) was applied, the calibration constant of the airborne camera was *K* = 0.964.

As a demonstration of the consistency of the camera calibration, in Figure 7 we can see the luminance value of the light source. Figure 7 shows the relative coordinates of the position in pixels of the light source in the image and the magnitude of its luminance in mCd/m2.

**Figure 7.** The image processing tool IRIS gives the luminance values at mCd/m<sup>2</sup> emitted by the ground surface. The red circle depicts the position of the light source and the arrow shows the relative coordinates in pixels (*X* = 2121, *Y* = 1547) and the luminance value *L* = 1215 mCd/m2.

### *3.2. Luminance Measures from Orthoimages*

As mentioned in Section 2.2, the standard procedure for measuring the luminance of the road is not to place the photometer in a vertical position perpendicular to the road surface, but rather to place it horizontally 60 m from the area to be measured, and at a height of 1.5 m. Both methods do not give exactly the same result. Since the surface of the asphalt is not perfectly Lambertian [28], the reflection of the light is a combination of specular and diffuse reflection. This signifies that the light is reflected on the asphalt differently, depending on the direction.

Based on this argument, we calculated the relationship between the measurement from above using an orthoimage (Figure 8) and the measurement obtained with the standard procedure (photometer in an almost horizontal position). For this purpose and as shown in Figure 9, we calculated the average luminance of all the pixels enclosed in the red box. In each image (ortho and horizontal), the statistical analysis of the calculation surface showed that that there was an approximate ratio of 1.06 between the average luminance obtained with the horizontal image and the average luminance obtained with the ortho image. This means that the luminance of ortho images had to be multiplied by a factor of 1.06 to obtain the luminance value, according to the standard road measurement procedure.

**Figure 8.** Aerial photo image of the area where the light source and the wattmeter were placed. Depending on the electrical power demanded by the source, we were able to deduce the luminance emitted.

**Figure 9.** Average luminance and other statistical values (at mCd/m2) of the calculation area from the aerial image or orthoimage (**a**) and the image where the standard procedure was applied (**b**).

## *3.3. Examples of Application*

The application examples were the study of lighting and energy efficiency of various streets in Deifontes, a town in southern Spain. Specifically, we studied the level of lighting, uniformity, energy consumption, energy efficiency, and energy class (A, B, C, etc.). The results indicated which improvements should be addressed to make the installation more sustainable while maintaining its functional requirements.

As a first step, the image processing software IRIS was used to transform an image in RAW format (Figure 10) into another that showed the reflected light (luminance) of the pavement, due to the information stored in each pixel. The transformation process involved obtaining the value *Y* for each pixel. Accordingly, Equation (2) was applied, followed by Equation (1) to obtain the vertical luminance value for each pixel. The next step involved multiplication by the correction factor 1.06 to obtain the real luminance value, according to the measurement process in the standard (Figure 11).

**Figure 10.** Orthoimage of a street obtained by the airborne camera. The image is in RAW format and had not ye<sup>t</sup> been treated with the image processing software.

**Figure 11.** Orthoimage treated with IRIS software and visualized with DS9. The figure shows the luminance values for each pixel and a statistical analysis of the corresponding lighting values of the road (only for the calculation area in the red polygon).

Any astronomical image viewer, such as IRIS or DS9 [29], can give the value of the magnitude in each pixel of the image, as well as a statistical result for all pixels in a large area. These statistical values provide average luminance or illuminance values as well as others that help to calculate lighting quality parameters, such as uniformity in a street or highway.

An example of this is depicted in Figure 11, where the minimum luminance (*Lmin* = 0.11 cd/m2) and the average luminance (*Lave* = 0.52 cd/m2) are obtained. These data made it possible to deduce that the luminance uniformity ( *Lmin/Lave*) in the street sector was 0.22. Obviously these results are not significant because the magnitude values must be calculated for the whole street and not only for one section, but in this case it is an example of the procedure described above.

There are other kinds of lighting whose magnitude of illumination is illuminance. Although luminance and illuminance are two different concepts (light emitted in one direction and light received from all directions), it is possible to relate them by taking certain margins of error into account because, in most cases, pavement characteristics are not known. However, such errors are acceptable in the field of lighting. The relationship between luminance and illuminance is shown in the following equation [15]:

$$L\_{\text{new}} = q\_0 E\_{\text{new}} \tag{5}$$

where *Lave* and *Eave* are the average magnitudes in cd/m2; and lx respectively, and *q*0 is the average luminance coefficient. If nothing is known about the reflection properties of the pavement, a coefficient *q*0 = 0.07 cd/m2/lx can be applied [15].

In the following example, the procedure was simultaneously performed on several streets, captured in a single image (Figure 12). Using the previously described procedure, we calculated the luminance values in each pixel and averaged them to obtain the lighting levels of each street.

**Figure 12.** Aerial image in RAW (**left**) and georeferenced (**right**) format

With the luminance values in each pixel, it was easy to calculate the average luminance reflected by the pavement of each street. Equation (5) was applied to obtain the average illuminance value (see Figure 13).

**Figure 13.** Average luminance (**left**) and illuminance (**right**) levels of some streets.

Another parameter obtained, which is directly related to the quality of street lighting, was the uniformity of the illuminance. This was possible because we knew the minimum illuminance in each street. Figure 14 shows this parameter represented in QGIS together with the position and electrical power of the luminaires.

**Figure 14.** Illuminance uniformity (**left**) and luminaires position (**right**).

With respect to the energy parameters, Table 2 shows the electricity consumption, the surface to be illuminated, and the average illuminance levels. Equations (3) and (4) were used to calculate the energy efficiency of the installation in each street. The electricity consumption data were obtained from the smart electric meters located in the streetlight control boxes.

**Table 2.** Lighting and electrical parameters of each street used to calculate the energy efficiency of the installation.


Since we knew the electric power installed in a particular street, it was then possible to calculate its real electricity consumption (from data provided by the smart electric meter). This was done by applying the following equation:

$$P\_{M\_T} \frac{P\_j}{P\_T} = P\_{M\_j} \tag{6}$$

where *PMT* is the measure of the total electrical power (provided by the smart electric meter); *Pj* is the known installed power in the "*j*" street; *PT* is the known installed power in all the streets connected to the smart electric meter; and *PMj* is the real electrical power calculated in the "*j*" street. This real electrical power includes the losses of the distribution lines and the actual electricity consumption of lamps and auxiliary equipment of all street lights.
