The article is devoted to assessing lighting quality based on lighting engineering design's spatial-angular brightness distribution (LSAD). The main problems of modern lighting design related to the modeling of scenes based on the emissivity equation and restrictions on the use, in this regard, as the main criterion for the lighting quality of Unified Glare Rating (UGR), are considered. The mathematical foundations of the use of LSAD in the practice of lighting engineering design are proposed. The integral equation LSAD is obtained, which allows modeling the brightness at an arbitrary point of the scene volume. A method for solving the formulated equation based on double local estimates of the Monte Carlo method is proposed. The formulated algorithm for calculating LSAD is view-independent: LSAD visualizes the lighting scene at all fixed points. Methods for storing the calculated LSAD are proposed. Based on the LSAD, a new criterion for lighting quality is formulated, which was experimentally tested in a full-scale experiment to evaluate the lighting of Moscow Metro stations. In the experiment, the proposed criterion and UGR were compared. One calculated the quality criteria by the station's photos, and their correlation with observers' assessment was found. Computer models of stations were created, in which quality criteria were also calculated from the experiment viewpoints - obtained good correspondence of the calculations with the estimates of observers.
Modern three-dimensional computer graphics have reached truly phenomenal heights. Programs for visualizing three-dimensional scenes allow us to obtain truly photo-realistic images, which became possible due to the rapid development of computer technology and methods for solving the global illumination equation [8]. One of the practice areas that the development of computer graphics has influenced is lighting engineering. The key task in lighting engineering is the design of lighting installations, which is to find the number, types, and arrangement of lamps. Two decades ago, this was an extremely time-consuming routine engineering calculation. Today at the heart of this process, as in computer graphics, is modelling the solution of the global illumination equation (GIE). However, if a key task in computer graphics is to obtain a "realistic" image, then there is a task of correct calculation of illumination and luminance in lighting engineering. While the designer is guided by normative documents, defining qualitative and quantitative indicators of coverage.
In modern regulatory documents for non-special lighting installations (office, industrial, commercial, etc.), illumination and various parameters derived from it (the ratio of minimum illumination to maximum, etc.) are normalized as a quantitative characteristic. As a rule, all calculations are conducted for illumination on the floor of the room, or an imaginary working plane located at the table's height. However, the illumination is an integral characteristic of the incident light, while the human eye reacts to light reflected from the surface. That is, if you take a completely black surface with a reflection coefficient of zero, then formally, you can get the required illumination on it. At the same time, visually, we will not see anything since the light will not be reflected from the surface. From the point of view of the human visual organ, it is necessary to normalize the luminance. The current situation is quite understandable since the calculation and measurement of luminance were complicated until recently.
This problem is partially eliminated by the introduction of a unified glare rating (UGR) among a variety of qualitative indicators for non-special installations
0, 25 N L2
UGR 8lg i 2 i , (
La i1 pi where Li is the luminance of the glitter source, cd/m2; i is the angular size of the glitter source; pi is the light source position index relative to the sightline; Lа is the adaptation luminance, cd/m2.
Accordingly, the UGR allows expressing the lighting quality in just one figure, making it possible to include it in regulatory documents. Today, when designing non-special LI, the designer is guided by the illumination as a quantitative characteristic and UGR as a qualitative assessment of lighting. UGR answers the question-how comfortable a person will be within the lighting system.
However, the formula (
However, as shown later in the paper, with a certain approach to UGR, such calculations are possible when using luminance images. In this case, based on contrasts, sources of glare can be found, which can be considered individual pixels that contribute to the UGR. Including in the case of sources' hidden location, their glare can be distinguished based on contrasts, which was done for the experiment described later in the article. Moreover, it is the contrast that forms the basis of the new quality criterion we are considering.
A significant step forward in lighting design is DIALux Evo's introduction based on the photon map method. However, it still uses the diffuse approximation and, accordingly, the UGR calculation method has not changed.
Thus, LI is designed by assessing approximately how comfortable a person will be in it and normalize the invisible characteristic-illumination. However, at the beginning of the last century, it was suggested that the luminance spatial-angular distribution (LSAD) plays a key role in the issue of comfort [6]. Note that the lighting quality depends on three main luminance distributions: by space, by spectrum, and by time, and all of them have some relationship. Here and further in work, when we talk about lighting quality only by the distribution over space.
Modelling of lighting installations is based on the equation of global illumination, well known in
computer graphics, first obtained [8]:
1
L(r, ˆl) L0 (r, ˆl)
L(r, ˆl)(r; ˆl, ˆl) (Nˆ , ˆl) dˆl ,
(
The integral equation in the form (
L(r, ˆl)(r; ˆl, ˆl)G(r,r)d 3r , G(r,r) ( Nˆ(r),r r) (r r)3 (r,r) d (r ˆl) d rr0 (r r r ˆl) (r r r0 ˆl) 0 is the equation describing the scene surfaces, ˆl r r0 r r0 , is a function that tracks shading.
Equation (
Consider an equation concerning an arbitrary point in space. Let us define the luminance distribution L(r, ˆl) on some closed surface Σ defined by the equation (r) = 0. We need to determine the luminance distribution LV (r, ˆl) at an arbitrary point r of volume V bounded by the surface Σ. The volume is filled with a completely transparent medium. Following the radiative transfer equation's solution for a transparent medium, the luminance along the beam does not change. Therefore, the luminance at the point r in the direction ˆl will be equal to the luminance of the surface at the point of intersection of the surface with the ray from the point r in the direction ˆl
LV (r, ˆl) L(r ˆl, ˆl) , where ξ is the root of the ray - surface intersection equation (r ˆl) 0 .
One can give the latter relations a more convenient analytical form based on the use of the properties of the δ-function LV (r, ˆl) C01 L(r, ˆl) (r r r ˆl) ˆl
(V ) r r d 3r
r r (r r)2
,
It is related to the integral of the δ-function with a complex argument, where С01 d(r ˆl) d
rr0 r r and ˆl r r fixes the sighting direction of luminance.
Then, by combining the last expression with the global illumination equation (
LV (r, ˆl) L0 (r , ˆl) 1
C01 L(r1, ˆl)(r ; ˆl, ˆl)G(r1, r )((r r r ˆl)) ˆl
r r d 3r
r r d 3r1 (r r )2 ,
(
Equation (
The resulting equation can be decomposed into a Neumann series and solved by local Monte Carlo estimators [2], first proposed in atomic physics [9].
We present the solution (
p2 (xi x)
Building a Markov chain allows estimating the luminance at a given point in a given sighting direction on the scene surface. In the theory of the Monte Carlo methods, such an estimate is usually called a local estimate.
It is not possible to construct a local estimation for the LSAD equation since it contains two
r r
additional δ-functions: ((r r r ˆl)) and ˆl r r , which depend on the desired direction ˆl
. In practice, this will mean that it is impossible to get into the desired direction when evaluating the
kernel of the equation. To solve this problem, we need another additional node that fixes the
intermediate point r of equation (
In contrast to direct modelling methods based on ray or photon tracing and counting, local estimates allow us to estimate the luminance at a given point in a given direction based on the probability of departure from the Markov chain walk path to the point under study described by the kernel of the equation [3].
Note that for the first time such a method in the phenomenological approach was formulated in the work [10].
The development of methods for solving the global illumination equation and the emergence of new methods for measuring luminance [5] allows lighting engineering to move away from the diffuse lighting model and find the luminance characteristic saw by the human eye. So, we can raise the question of a new stage in developing qualitative characteristics based on the LSAD analysis.
To date, when designing non-special lighting installations, such as office premises, public places, shops, shopping centres, etc., in fact, one single criterion describing the quality of the installation is used – UGR. In terms of the LSAD, visibility is affected as the absolute value of the observed luminance and the ratio of the source-background luminance difference to the background luminance (adaptation luminance) - contrast [13]. The ratio of contrast to threshold contrast can serve as a criterion for lighting quality.
In the case of a continuous LSAD over the lighting scene, the natural generalization of contrast is the ratio of the gradient of the luminance distribution over the observation field to the average luminance over the field [4]. As the gradient value increases, the boundary between the light source and the background will become more defined, and the lighting quality will decrease accordingly. The larger the source and the higher the luminance gradient around the bright source, the greater the contribution to the discomfort that source makes. Note that extended glare is both a source of discomfort in real life and contributes to the adaptation luminance. The generalized contrast at a point in the scene can be determined by: where
K (x, y) grad L(x, y) p(x, y)
L L 1
L(x, y) p(x, y)dxdy, A dxdy
A ( A) ( A)
(
Therefore, it is possible to formulate the criterion for the lighting quality Q as a weighted average contrast K(x,y), estimated by a certain threshold:
1 Q
Kth
K(x, y)dxdy ,
(
One can see from the expression that even a slight change in luminance can lead to a change in the luminance gradient, contributing to the quality criterion in the proposed form. Simultaneously, it is obvious that changes in contrast in luminance below a certain limit will not make a real contribution. For example, it is obvious that if there is a direct light source in the field of view or glare from it in the room, contrasts in a dark corner are likely to play a role in the feeling of lighting quality. But if one formally conducts the calculation, then they will also give a contribution. Thus, contrasts below some threshold Lth should not actually be considered.
In [1] conducted huge research work on setting up threshold contrasts in solving the detection problem. In this work, the relationship between threshold contrast and adaptation luminance at different target angular sizes was experimentally proved.
Following this work, it is possible to define Lth as a certain number of threshold values. Primarily, one needs to set the minimum element size to be detected in a given visual task. For example, it can be the size of a character when reading text or a character from a certain distance. Considering the adaptation luminance, for which one can take the average luminance over the field of view, it is possible to find from Blackwell's study the threshold changes in luminance L for solving this problem. For identification tasks, it is necessary to set a certain number of threshold exceedances, which allows determining the threshold luminance:
Lth N L
(
Therefore, we take a certain number of thresholds as the threshold luminance for cutting off contrasts that do not affect the quality criterion. Then the expression for contrast can be written as 0, L(x, y) Lth; K (x, y) (14)
K (x, y), L(x, y) Lth.
An experiment to study the proposed criterion for lighting quality was conducted in the Moscow metro [4]. One of the real visual tasks solved in the metro is reading signs with signs. It was this task that formed the basis of the experiment. Simultaneously, in lighting practice, an expert comparison of various lighting installations is often carried out among themselves, as a rule, having the same functional lighting. So, the lighting of one metro station can be compared with the lighting of another based on expert assessments – "better-worse." In this experiment, such a scale of relations was built, as the only one available in practice. Thus, the observers' task was to find on a 10-point scale how comfortable it is to perform the specified visual task when reading the sign with navigation signs. The station was photographed from the same angles with a Nikon D3100 digital camera in RAW format, and the absolute luminance values were measured with a Konika Minolta LS-100 luminance meter for subsequent normalization of photos.
The proposed quality criterion (
The required number exceeding the threshold N is unknown for performing the visual task in a real scene with the Moscow metro's existing lighting system and requires further clarification based on experimental data. For this purpose, the Department of Lighting Engineering plans a three-stage experiment to determine the Kth when performing a visual task in office and public spaces based on a standardized C-test [11], the NASA Task Load Index questionnaire (NASA-TLX) [7] and a multidimensional questionnaire developed by the Expert Forum on Indoor Lighting (EFI) [12], which should result in a table of Kth values for different levels of visual tasks.
At this stage, according to the absence of dependence of threshold contrasts on the background luminance in the Weber-Fechner law, we can assume that the required number of exceeding the thresholds will lie in the range from 30 to 70. Empirically, by selecting N, the highest value of the correlation coefficient 0.61 was obtained, which corresponds to a noticeable correlation on the Chaddock scale, with the number of thresholds N equal to 50. In the future, it is planned to test the obtained value in the laboratory as part of the experimental work on determining the Kth.
Figure 1 shows the scattering map of the observers' assessment and the proposed lighting quality criterion.
The question of constructing a scale of sensations of observers is not trivial. In this experiment, there was no possibility to adjust any parameters at metro stations. The time of the experiment was also extremely strictly limited. Therefore, the "order scale" was chosen. To test the selected scale's stability, the observers ' responses randomly varied within 0.25 of the nominal value. Simultaneously, the correlation coefficient was calculated for 10,000 different variations, and its deviation was no more than 5%.
The question of finding the threshold luminance and finding the number of Blackwell thresholds is
our next task, as well as finding the threshold contrast in equation (
The combined index is calculated using the formula (
Thus, the UGR was calculated for all metro stations participating in the experiment. The correlation coefficient UGR from the proposed lighting quality criterion was 0.73, and UGR from the observers ' assessment was 0.62, which is a noticeable correlation in both cases. Figure 4 shows the scattering map of the proposed UGR vs. lighting quality criterion.
Currently, the development of lighting technology is largely associated with the BIM technology (Building Information Model), based on the digital description of buildings and the equipment installed in them. This model is a method of network planning, execution, operation, and implementation of construction projects. One of the main conditions for using BIM is the collection of all the data necessary for a building project. In this case, the building project, once created, is then updated to the stage of its full implementation. Nobody can avoid design errors, but here it can be detected at an early stage of design. A single database makes the history of changes and corrections simple and understandable for all participants.
The description of lighting equipment is based on 3D models of luminaires with their photometric data. The calculation of lighting in the premises of buildings is carried out, considering the number and location of lamps in them. In the future, the association of customers, building designers, and equipment manufacturers on a single Internet platform. For most structures, the lighting of the main rooms is determined by standard schemes. Therefore, in principle, the platform can choose the database's equipment when determining the lighting quality criterion.
Currently, the development of lighting technology is largely associated with the BIM technology (Building Information Model), based on the digital description of buildings and the equipment installed in them. This model is a method of network planning, execution, operation, and implementation of construction projects. One of the main conditions for using BIM is the collection of all the data necessary for a building project. In this case, the building project, once created, is then updated to the stage of its full implementation. Nobody can avoid design errors, but here it can be detected at an early stage of design. A single database makes the history of changes and corrections simple and understandable for all participants.
The description of lighting equipment is based on 3D models of luminaires with their photometric data. The calculation of lighting in the premises of buildings is carried out, considering the number and location of lamps in them. In the future, the association of customers, building designers, and equipment manufacturers on a single Internet platform. For most structures, the lighting of the main rooms is determined by standard schemes. Therefore, in principle, the platform can choose the database's equipment when determining the lighting quality criterion.
The lighting quality criterion proposed in this paper can be the basis for optimizing the choice of equipment. There are a finite number of combinations from which the best option is selected. Today, along with direct search, some algorithms use some heuristic rules (for example, the genetic algorithm), which significantly accelerate convergence.
The revolution in computer graphics in the modeling of three-dimensional scenes is also reflected in lighting technology. The formulated method of double local estimates introduces the possibility of calculating the luminance spatial-angular distribution at an arbitrary point in the volume into the lighting engineering design of lighting installations. It is a true revolution of design based on assessing the integral characteristic of luminance – illumination at specified points on the surfaces of the scene. This path in lighting engineering took a practical century from the formulation in the Ferree work that the quality of lighting depends on the luminance distribution in the field of view to the actual possibility in lighting engineering to carry out such calculations.
The paper shows the possibility of using the new opportunities that have opened for practical application, particularly for calculating the generally accepted criterion of lighting quality – UGR. Moreover, the possibility of creating new quality criteria is shown based on the use of the LSAD.
The presence of various quality criteria will allow you to move on to solving the inverse problemdesigning for a given quality. At the first stage, of course, iterating from a set of solutions with minimizing the criteria functions. This will allow lighting engineering to find its place in BIM design.