EFFECT OF R-TABLE MEASUREMENT
DISPERSION ON ROAD LIGHTING QUALITY
CRITERIA

Sébastien Liandrat, Florian Greffier, Christoph Schulze, Enoch Saint Jacques,
François Eymond, Mickaël Ferreira Fernandes, Valérie Muzet

► To cite this version:

Sébastien Liandrat, Florian Greffier, Christoph Schulze, Enoch Saint Jacques, François Eymond, et al.. EFFECT OF R-TABLE MEASUREMENT DISPERSION ON ROAD LIGHTING QUALITY CRITERIA. CIE2025 Scientific Conference, CIE, Jul 2025, Vienna, Austria. hal-05283739v2

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# EFFECT OF R-TABLE MEASUREMENT DISPERSION ON ROAD LIGHTING QUALITY CRITERIA

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Liandrat, S.¹, Greffier, F.², Schulze, C.³, Saint-Jacques, E.⁴, Eymond F.⁴, Ferreira-Fernandes, M.¹,
Muzet, V.⁵

¹ Cerema, STI, F-63000, Clermont-Ferrand, France

² Cerema, EL, F-49130, Les Ponts-de-Cé, France

³ Technische Universität Dresden, "Friedrich List" Faculty of Transport and Traffic Sciences, D-01062, Dresden, GERMANY

⁴ COSYS, PICS-L, Université Gustave Eiffel, F-77420, Champs-sur-Marne, FRANCE

⁵ Cerema, ENDSUM, F-67000, Strasbourg, FRANCE

sebastien.liandrat@cerema.fr

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## Abstract

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Knowing the reflective properties of road surfaces is an important lever for optimizing the performance of lighting installations. Nevertheless, measuring these properties is still a confidential exercise, and the uncertainties associated with *r*-table measurements are rarely evaluated. Based on a cross-test campaign between 3 laboratory gonioreflectometers, we investigated the effect of the dispersion of *r*-table measurements on the quality criteria of a lighting installation. We were able to show that these dispersions were still acceptable, and that characterizing the optical properties of a pavement is an advantage over the traditional use of CIE standard *r*-tables. By carrying out these measurements in different observation geometries, we also showed that reconsidering the standard 1° geometry would offer the possibility of reducing measurement uncertainties. This contributes to current research aimed at better integrating different types of night-time mobility into urban lighting practices.

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**Keywords:** Gonioreflectometer, *R*-tables, Measurement Dispersion, Road Lighting Calculation

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## 1 Introduction

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Street lighting plays an important role in urban night-time environments, particularly in meeting the challenges of safe mobility and public safety. The quality of a lighting installation depends on several factors: the characteristics of the luminaires, the geometry of the installations, but also the reflective properties of the surrounding surfaces. In recent years, the massive renewal of lighting installations, marked by the widespread adoption of LED technology, has improved their energy efficiency offering new opportunities for operators responsible for roads and public spaces. This technological shift not only enhances energy efficiency but also provides a chance to rethink the design of lighting systems to address broader societal challenges, such as reducing light pollution or improving visual comfort for users. We now need to go one step further in the quest for sobriety by taking greater account of the reflective properties of the surfaces to be lit, particularly road surfaces.

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Indeed, road surfaces play a critical role as they directly influence the luminance perceived by users in a given direction. These reflective properties are considered in the design methods for urban lighting systems (CIE, 2010). However, in practice, the photometric properties of road surfaces are often poorly considered. Indeed, although studies have already demonstrated the importance of measuring these properties to optimize the design of lighting installations (Muzet, 2022), the implementation of these measurements remains complex. The challenges start with the logistical constraints of taking measurements in the field or collecting samples before analysis in the laboratory. Gonioreflectometers are rare and expensive, while *in situ* measurement can be difficult to achieve since commercial measuring equipment are not available on site, particularly for the grazing angle of 1°. Moreover, the measurement methodology is sensitive to numerous factors that can influence the results. Measurement uncertainties are therefore often poorly considered, as is their effect on the design of a lighting installation. Among the world, this still leads to favor the use of standard *r*-tables (Gidlund, 2019) defined by the CIE (CIE, 2001).
The standard *r*-tables were developed based on an observation angle of 1°, corresponding to a driver focusing approximately 90 meters ahead. A recent study (Lebouc, 2024) explored the preferred observation geometries for different types of road users, considering their travel modes and speeds. For drivers traveling at 75 km/h, an observation angle of 1° remains appropriate. However, in urban areas, where driving speeds are closer to 25 km/h, or for cyclists, an angle of 3° would be more suitable. For pedestrians, Lebouc (2024) recommends an observation geometry of 5°. Currently, there is limited data on the optical properties of road surfaces under these specific observation conditions, primarily due to the absence of on-site measurement equipment capable of capturing such information.

To gain a better understanding of these issues, a cross-testing campaign was carried out between three laboratory gonioreflectometers belonging to different organizations. The main results of this campaign, detailed in another article (Schulze, 2025), investigates the accuracy of *r*-tables measured with these different instruments for several observation angles. Based on these measurements made on different samples, this article presents lighting calculations that were implemented to assess the impact of measurement dispersion on the quality criteria of a lighting installation. These lighting calculations were carried out using the standard geometry of 1°, but also with observation angles of 3° and 5° to represent the different road users in urban environment.

After a review of road lighting basics, the first part of this article presents the cross-testing campaign carried out and the lighting calculations made. In the results section, we first look at the dispersions associated with the measured *r*-tables and their impact on lighting calculations, in particular on the quality criteria of a road lighting installation. Secondly, we compare the lighting calculations carried out using the measured *r*-tables and the CIE standard *r*-tables that would be traditionally used for characterised pavements. The final section contains the conclusions and perspectives.

## 2 Road lighting basics

In road lighting, the nominal position of the grid on which the calculations are performed is defined by CIE (2019). In the longitudinal direction, the calculation field shall enclose two luminaires in the same row. In the transversal direction, the calculation field is positioned between two lane markings and can include several driving lanes as shown in Figure 1 on the left.

<figure><img src="image_2.png" /><figcaption>Figure 1 – Calculation grid points in road lighting (left) and angles of observation α, deviation β and incidence ε for photometric characteristics calculation (right).</figcaption></figure>

For luminance calculation, the position of the observer (symbolized with a green smiley in Figure 1 on the left) is 1,5 m above the road surface and at 60 m ahead the field of the relevant area. In the transverse direction, the observer shall be positioned in the centre of each lane in turn.

From these luminance values, the following photometric parameters are computed (CIE, 2019):

* The average luminance ($L_{ave}$) is the arithmetic mean of the luminance at the grid points in the field of measurement.

* The overall uniformity ($UO$) is the ratio of the lowest luminance, occurring at any grid point in the field of measurement, to the average luminance.

* The longitudinal uniformity ($UL$) is the ratio of the lowest to the highest luminance on points in the longitudinal direction along centre line of lane.
The reflection properties of the road surface are used for the computation of a lighting installation (CIE, 2001). The most characteristic parameter is the luminance coefficient q, which is the ratio between the luminance L in cd/m², which the observer sees, and the illuminance E in lux which is incident on the surface (Equation 1).

$$q(\alpha, \beta, \varepsilon) = \frac{L(\alpha, \beta, \varepsilon)}{E(\beta, \varepsilon)} \qquad (1)$$

The standardised observation angle α (see Figure 1 on the right) is constant at 1°, which corresponds to a distance of 86 m for an observation height of 1,5 m.

Since the 1980s, for practical reasons the luminance coefficient was replaced by the reduced luminance coefficient r in cd.m⁻².lux⁻¹, which is derived from q (Equation 2).

$$r(\beta, \varepsilon) = q(\alpha = 1^{\circ}, \beta, \varepsilon) \cdot (\cos \varepsilon)^3 \qquad (2)$$

A table of reduced coefficients, called r-table, was defined, where the luminance coefficients r are given for 580 combinations of fixed lighting angles β and tan ε (see Figure 1 on the right). The r-table is the standard format for describing the optical properties of road surfaces for road lighting applications. A representation of the reflexion indicatrix of an r-table is represented on the Figure 2.

<figure><img src="image_3.png" /><figcaption>Figure 2 – Representation of an r-table as a photometric solid.</figcaption></figure>

Other indicators are also defined in CIE 144:2001 to describe globally the reflective properties of road surfaces.

The average luminance coefficient Q0 represents the degree of lightness of the measured surface. It is computed as the average of the luminance coefficients over the specified solid angle Ω₀ which only depends on the specific values of β and tan ε defined by the r-table format (Equation 3).

$$Q0 = \frac{1}{\Omega_0} \int q d\Omega \qquad (3)$$

CIE 144:2001 gives a methodology and a specific table of weighting factors for approximating Q0 values by numerical integration. Note that these integrals can also be solved more directly using the trapezoidal method (Boucher et al., 2023).

The specular factor S1 represents the degree of specularity of the observed surface. It is defined as the ratio between the reduced luminance coefficients of two specific illumination conditions (Equation 4).

$$S1 = \frac{r(\beta=0, \tan \varepsilon=2)}{r(\beta=0, \tan \varepsilon=0)} \qquad (4)$$

In CIE 144:2001, a classification system groups different surfaces according to the value of the specular factor S1. Surfaces within a class are represented by a predefined r-table as well as typical values of Q0 and S1. In France the R classification system is mainly used with its four-standard r-tables R1, R2, R3 and R4.
124 **3 Materials and Methods**

125 **3.1 Cross-testing campaign**

126 The cross-testing campaign was carried out using three laboratory gonioreflectometers belonging to
127 three different organizations: one from Technical University of Dresden (Germany), one from University
128 Gustave Eiffel (France) and one from Cerema (France). A detailed presentation of these devices can be
129 found in (Schulze, 2025). In line with CIE recommendations (CIE, 2001), each of them is commonly
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131 A set of 5 stabilized road pavement samples (see Table 2) was characterised: one very old clear concrete
132 (Core A), one very old asphalt mix (Core B) and three 3-years-old asphalt concretes (Cores C to E), one
133 of which has a synthetic binder (Core D). These samples were characterized from 3 angles of
134 observation α: 1°, 3° and 5°. Each measurement was carried out 3 times in order to take into account the
135 impact of reproducibility of the measurements, in particular to address the alignment of the samples,
136 which can have a significant effect on the measurement.

<table><caption>137 **Table 2 – Description of the measured road samples.**</caption><thead><tr><th>Core A</th><th>Core B</th><th>Core C</th><th>Core D</th><th>Core E</th></tr></thead><tbody><tr><td>Cement concrete</td><td>Bituminous pavement extracted in a tunnel</td><td>Classic thin asphalt concrete</td><td>Synthetic binder thin asphalt concrete</td><td>Classic thin asphalt concrete</td></tr><tr><td>More than 10 years old</td><td>More than 20 years old</td><td>3 years old</td><td>3 years old</td><td>3 years old</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

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139 **3.2 Road lighting calculations**

140 For each sample, we have 9 *r*-tables per angle of observation tested. These *r*-tables are used in road
141 lighting calculations based on the 7 reference situations of the CIE 140:2019 report (CIE, 2019). These
142 reference situations describe different types of roads with various characteristics (width of relevant area,
143 number of lanes) and lighting arrangements (position of the luminaires and spacing between them,
144 mounting height, overhang, tilt, type of lamps, etc.). The aim is to study how the differences between
145 the 9 *r*-table measurements affect the dispersion of the quality criteria (average luminance, overall
146 uniformity, longitudinal uniformity) of a lighting installation. For an observation angle of 1°, lighting
147 calculations are carried out conventionally. For observation angles of 3° and 5°, we use the concept of
148 mobile observation, which consists in building the calculation grid from successive observations
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150 To assess the acceptability of the dispersions obtained, we compare them in a second series of
151 calculations at 1°, still based on CIE reference situations, with the differences between the quality
152 criteria obtained with the average *r*-tables derived from measurements and those obtained with the
153 standard *r*-tables, traditionally used to dimension a lighting installation. The aim here is to assess
154 whether the dispersions inherent in any measurement process remain acceptable, particularly in the face
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156 **4 Results**

157 **4.1 Dispersion of *r*-table measurements and relative importance for lighting calculations**

158 From a set of 9 *r*-tables (3 measurements x 3 gonioreflectometers) associated with a sample for a given
159 observation angle, it is possible to evaluate the dispersions associated with the *r* values by dividing the
160 standard deviation of the 9 values by their mean for each angular combination (β, tan ε). The results are
161 then multiplied by 2 to obtain 95% confidence intervals in the analysis of these dispersions. Figure 3
162 illustrates this operation for core B by giving the dispersions of *r* values in tabulated form (left) and
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then representing them by a photometric solid (right). Unsurprisingly, the highest dispersions are found in the lower part of the solid, corresponding to the graziest angles of incidence, where the alignment of the sample has the greatest impact. The last 8 lines of an *r*-table (tan ε > 8, see red box and ellipse in Figure 3) concern angles of incidence of light greater than 83°. Note that 188 values in the *r*-table are generally not measured and are set to 0 (see lower right quadrant in figure 3 on the left) in accordance with CIE recommendations (CIE, 2001).

<figure><img src="image_4.png" /><figcaption>Figure 3 – Representation of *r* value dispersions for core B</figcaption></figure>

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171 Although certain dispersions appear to be significant, their impact on lighting calculations is not
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176 need to consider the occurrence with which *r* values are used. Depending on the geometric characteristics
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179 values have been weighted by their respective contribution in luminance, i.e. taking into account their
180 intrinsic values and the number of times they are used in the 7 reference situations of CIE 140:2019
181 (CIE, 2019) cumulated.

<figure><img src="image_5.png" /><figcaption>Figure 4 – Representation of *r* value weighted dispersions for core B.</figcaption></figure>

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In Figure 5, following the same approach, we look at the influence of the angle of observation on the weighted dispersions. The results obtained show a reduction in these dispersions as the observation angle increases. The same trend is therefore expected in the lighting calculations that will be presented in the next part.

<figure><img src="image_6.png" /><figcaption>Figure 5 – Representation of *r* value weighted dispersions for core B at the 3 observation angles used for measurements.</figcaption></figure>

## 4.2 Dispersion of road lighting quality criteria

Tables 2, 3 and 4 show the quality criterion dispersions associated with each sample, based on lighting calculations performed with the *r*-tables measured at observation angles of 1°, 3° and 5°. In each lighting situation, we obtain 9 values for average luminance (*L*<sub>ave</sub>), overall uniformity (*U*0) and longitudinal uniformity (*U*1). The dispersions are then evaluated as the ratio of the standard deviation of the values to the mean of the values, multiplied by two to represent 95% of the possible values. The dispersions from each situation are then averaged to obtain a characteristic dispersion per sample. The last column of each Table provides a summary of all samples.

<table><caption>Table 2 – Dispersions of road lighting quality criteria at 1° for the 5 sampled road surfaces</caption><thead><tr><th></th><th>Core A</th><th>Core B</th><th>Core C</th><th>Core D</th><th>Core E</th><th>Average of cores</th></tr></thead><tbody><tr><td>Dispersion of L<sub>ave</sub></td><td>36 %</td><td>30 %</td><td>10 %</td><td>9 %</td><td>14 %</td><td><strong>20 %</strong></td></tr><tr><td>Dispersion of U0</td><td>11 %</td><td>21 %</td><td>14 %</td><td>12 %</td><td>12 %</td><td><strong>14 %</strong></td></tr><tr><td>Dispersion of U1</td><td>16 %</td><td>14 %</td><td>10 %</td><td>11 %</td><td>12 %</td><td><strong>13 %</strong></td></tr></tbody></table>

<table><caption>Table 3 – Dispersions of road lighting quality criteria at 3° for the 5 sampled road surfaces</caption><thead><tr><th></th><th>Core A</th><th>Core B</th><th>Core C</th><th>Core D</th><th>Core E</th><th>Average of cores</th></tr></thead><tbody><tr><td>Dispersion of L<sub>ave</sub></td><td>23 %</td><td>29 %</td><td>18 %</td><td>11 %</td><td>13 %</td><td><strong>19 %</strong></td></tr><tr><td>Dispersion of U0</td><td>5 %</td><td>17 %</td><td>9 %</td><td>8 %</td><td>8 %</td><td><strong>9 %</strong></td></tr><tr><td>Dispersion of U1</td><td>10 %</td><td>9 %</td><td>10 %</td><td>6 %</td><td>7 %</td><td><strong>8 %</strong></td></tr></tbody></table>
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<table><caption>Table 4 – Dispersions of road lighting quality criteria at 5° for the 5 sampled road surfaces</caption><thead><tr><th></th><th>Core A</th><th>Core B</th><th>Core C</th><th>Core D</th><th>Core E</th><th>Average of cores</th></tr></thead><tbody><tr><td>Dispersion of L<sub>ave</sub></td><td>20 %</td><td>10 %</td><td>9 %</td><td>8 %</td><td>12 %</td><td><strong>12 %</strong></td></tr><tr><td>Dispersion of U<sub>0</sub></td><td>4 %</td><td>18 %</td><td>6 %</td><td>9 %</td><td>8 %</td><td><strong>9 %</strong></td></tr><tr><td>Dispersion of U<sub>1</sub></td><td>7 %</td><td>9 %</td><td>9 %</td><td>6 %</td><td>7 %</td><td><strong>8 %</strong></td></tr></tbody></table>

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As expected, comparing these values for different angles of observation, we can see that the dispersions decrease as the angle of observation increases. This underlines the difficulty of making reliable measurements in standard grazing geometry at 1°. Sensitivity to alignment is important in this case. The reduction in dispersions, particularly from 1° to 5°, illustrates more reproducible measurements within each laboratory, and closer together. This should encourage current research aimed at reconsidering standard geometry, particularly in urban lighting where the observation angles associated with different types of user seem to be precisely of the order of a few degrees (Lebouc, 2024).

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## 4.3 Differences between measured *r*-tables and standard *r*-tables

The dispersions presented in the previous section might seem significant enough to raise questions about the value of this measurement compared to the conventional use of standard *r*-tables. We therefore check this point for the standard 1° geometry by comparing the quality criteria calculated with the measured *r*-table (average of the 9 measurements on each sample) with those calculated with a standard *r*-table. In line with practice (Gidlund, 2019), we choose *r*-table R1 for samples A and D (diffuse light concrete and asphalt concrete with synthetic binder and light aggregates) and *r*-table R3 for the other samples (rather dark and specular asphalt and asphalt concrete). In Table 5, the relative deviations between the quality criteria are evaluated in each reference situation, taking the measured *r*-table as the reference.

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<table><caption>Table 5 – Deviations of road lighting quality criteria (actual vs. standard *r*-tables)</caption><thead><tr><th></th><th>Core A<br>vs. R1</th><th>Core B<br>vs. R3</th><th>Core C<br>vs. R3</th><th>Core D<br>vs. R1</th><th>Core E<br>vs. R3</th></tr></thead><tbody><tr><td>Deviation for L<sub>ave</sub></td><td>-8 %</td><td>81 %</td><td>-27 %</td><td>39 %</td><td>9 %</td></tr><tr><td>Deviation for U<sub>0</sub></td><td>-5 %</td><td>-30 %</td><td>11 %</td><td>-11 %</td><td>5 %</td></tr><tr><td>Deviation for U<sub>1</sub></td><td>-11 %</td><td>-11 %</td><td>9 %</td><td>11 %</td><td>-2 %</td></tr></tbody></table>

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With the exception of the overall uniformity for core B, there are no major deviations in the values associated with uniformities (U0 and U1), which remain acceptable. As uniformities are correlated with the specularity factor S1 (Greffier, 2021; Sorensen, 1974), we can assume that we have made an appropriate choice regarding the standard *r*-table to be used to represent the reflective properties of our samples. As far as average luminance is concerned, the situation is more problematic, since the deviations when using a standard *r*-table are very random. This confirms that current lighting practices, which are based on the almost systematic use of standard *r*-tables, are a risky exercise when it comes to obtaining the right levels of lighting. If we look more closely at the calculations made for core B (resp. core D), the deviations correspond to 81% (resp. 39%) of excess luminance and as much potentially wasted energy. For core C, the trend is the opposite, the deviation corresponds to 27% of deficient luminance, in which case there is a significant risk of a deterioration in visibility.

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## 5 Conclusion

In this study, a cross-testing campaign of *r*-table measurements on 5 road surface samples was carried out with 3 different gonioreflectometers. For each sample, 3 observation angles and 3 repetitions were carried out. The measurements were then used in lighting calculations to assess the effect of their dispersion on the quality criteria of a lighting installation. In addition, the same quality criteria were

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241 calculated using standard *r*-tables. The differences between the values obtained for the measured *r*-tables
242 and the standard *r*-tables are presented.

243 Once again, it was shown that the use of standard *r*-tables is a risky exercise, particularly when it comes
244 to controlling average luminance levels. Although there are variations between the measurements made
245 by different gonioreflectometers, using measured *r*-tables to design a lighting installation remains the
246 most appropriate way of controlling the luminance levels to be achieved.

247 More specifically, the quality criteria dispersions associated with *r*-tables measured in the standard
248 geometry at 1° are not neutral, even if they remain acceptable in view of the various uncertainty factors
249 associated with the measurement process, particularly sample alignment under such grazing observation
250 conditions. Measurements taken at 3° and 5° offer much more contained dispersions. This confirms the
251 value of using these new geometries in urban lighting, not only from a metrological point of view, but
252 also to better consider the specific uses of illuminated spaces, which could lead to downward
253 reconsideration of lighting levels (Lebouc, 2024).

254 This work aims to better understand the practical and methodological implications for achieving
255 sustainable and efficient urban lighting installations. By doing so, the study seeks to optimize lighting
256 systems further, ensuring they meet the evolving needs of urban environments while considering energy
257 efficiency and user comfort.

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259 **Funding**

260 This research was funded by the French National Research Agency under the REFLECTIVITY project
261 (ANR-22-CE22-0006).

262 **References**

263 BOUCHER, V., MUZET, V., IACOMUSSI, P. 2023. Mathematical Considerations for Road Reflection Properties. In: *Proceedings of 30th Quadrennial Session of the CIE, 15-23 September 2023*, Ljubljana, Slovenia. Vienna: CIE.

266 CIE 2001. CIE 144:2001. Road Surface and Road Marking Reflection Characteristics. Vienna: CIE.

267 CIE 2010. CIE 115:2010. Lighting of Roads for Motor and Pedestrian Traffic, 2nd Edition. Vienna: CIE.

268 CIE 2019. CIE 140:2019. Road Lighting Calculations, 2nd Edition. Vienna: CIE.

269 GIDLUND, H., LINDGREN, M., MUZET, V., ROSSI, G. and IACOMUSSI, P. 2019. Road Surface Photometric Characterisation and Its Impact on Energy Savings. *Coatings*, 9 (5), doi: 2079-6412/9/5/286.

272 GREFFIER, F., MUZET, V., BOUCHER, V., FOURNELA, F., LEBOUC, L. and LIANDRAT, S. 2021. Influence of Pavement Heterogeneity and Observation Angle on Lighting Design: Study with New Metrics. *Sustainability*, 13, 11789. doi: 10.3390/su132111789

275 GREFFIER, F., MUZET, V., BOUCHER, V., LIANDRAT, S. and SCHULZE, C. 2023. Qd vs Q0 for Scaling of Standard *R*-tables in Road Lighting Design: The Question is Worth Asking. In: *Proceedings of 30th Quadrennial Session of the CIE, 15-23 September 2023, Ljubljana, Slovenia*. Vienna: CIE.

279 LEBOUC, L., GREFFIER, F., BOUCHER, V., NICOLAÏ, A. and RICHARD P. 2024. Exploratory study to define new observation geometries for road lighting design. *Lighting Research & Technology*, 281 0(0). doi: 10.1177/14771535241265720

282 MUZET, V., LIANDRAT, S., BOUR, V., DEHON, J. and CHRISTORY, J.-P. 2022. Is it possible to achieve quality lighting without considering the photometry of the pavements? *Lighting Research & Technology*, 55(4-5), 345-365. doi:10.1177/14771535221111564

285 SCHULZE, C., SAINT-JACQUES, E., LIANDRAT, S., EYMOND, F., FERREIRA-FERNANDES, M., MUZET, V. 2025. Investigating the Accuracy of Road Surface Reflection Characterisation Based on Round-Robin Measurements. In: *Proceedings of the Conference at the CIE Midterm Meeting, 7-9 July 2025, Vienna, Austria*. Vienna: CIE.
289 SORENSEN, K. and NIELSEN, B. 1974. Road Surfaces in Traffic Lighting. *Danish Illuminating Engineering Laboratory Report 9*.