On lamps, walls, and eyes: The spectral radiance field and the evaluation of light pollution indoors

https://doi.org/10.1016/j.jqsrt.2017.09.022Get rights and content

Highlights

  • Human photoreceptoral inputs depend on the spectral radiance field.

  • The radiance field indoors is modulated by the spectral wall reflectances.

  • Effective filter functions are instrumental to quantify this effect.

  • Simple analytical models may be used to describe the walls modulating role.

  • Tayloring the wall reflectances allows to control the subject's light exposure.

Abstract

Light plays a key role in the regulation of different physiological processes, through several visual and non-visual retinal phototransduction channels whose basic features are being unveiled by recent research. The growing body of evidence on the significance of these effects has sparked a renewed interest in the determination of the light field at the entrance pupil of the eye in indoor spaces. Since photic interactions are strongly wavelength-dependent, a significant effort is being devoted to assess the relative merits of the spectra of the different types of light sources available for use at home and in the workplace. The spectral content of the light reaching the observer eyes in indoor spaces, however, does not depend exclusively on the sources: it is partially modulated by the spectral reflectance of the walls and surrounding surfaces, through the multiple reflections of the light beams along all possible paths from the source to the observer. This modulation can modify significantly the non-visual photic inputs that would be produced by the lamps alone, and opens the way for controlling—to a certain extent—the subject's exposure to different regions of the optical spectrum. In this work we evaluate the expected magnitude of this effect and we show that, for factorizable sources, the spectral modulation can be conveniently described in terms of a set of effective filter-like functions that provide useful insights for lighting design and light pollution assessment. The radiance field also provides a suitable bridge between indoor and outdoor light pollution studies.

Introduction

A growing body of research has underscored the role of light as a regulator of significant physiological processes, most notably the entrainment of the human circadian system [1], [2], [3], [4], [5], [6], [7], [8]. The discovery in 2002 of the intrinsically photosensitive retinal ganglion cells (ipRGC), and of their anatomical and functional connections with the brain centers responsible for circadian regulation [9], [10], [11], [12], [13], [14], [15], provided a sound mechanistic basis for understanding several of the photic responses previously observed in laboratory settings and in clinical practice. This has led to a renewed interest in the quantitative determination of the light field at the entrance of the eye, particularly in indoor settings.

Humans in modern societies spend a considerable amount of time inside buildings, subjected to illumination levels and spectral distributions noticeably different from the ones existing in the natural environment. The progressive extension of the human activity into nighttime, enabled by the availability of artificial light sources and the low energy prices, has been identified as a likely cause of disruption of the circadian patterns in wide sectors of the population, with potentially significant health consequences [7], [8]. Not surprisingly, there is a growing consensus about the need of evaluating the non visual effects of light when selecting light sources for indoor applications. Several physical magnitudes are of interest for assessing these effects: the absorbed dose, spectral composition, directionality, timing, previous photic history, and duration of the exposure are some of them. Particular atention has been given to the spectral content, since both the ipRGC excitation and the associated non-visual responses (measured, e.g., by the control-adjusted percentage of acute melatonin suppression after exposure to a light pulse at the central hours of the night) show a strong wavelength dependence, peaking at the short wavelength region of the visible spectrum [11], [12].

The most conspicuous recent changes in indoor lighting are precisely those related to the spectral composition of light. Whilst other lighting parameters tend to evolve relatively slowly in time (for instance, the recommended illumination levels, or the typical timespan of the urban nighttime activities), the spectrum of the light sources is undergoing nowadays a fast and deep transformation. The widespread introduction of solid-state lighting (SSL) devices, particularly those based on phosphor-converted light emitting diodes (pc-LED), is altering the spectral landscape to which we were used after decades of lighting based on gas-discharge, fluorescent, and thermal sources. This fact explains the intense research effort devoted to assess the relative merits of these new sources in terms of their potential side-effects on the environment and human health [16], [17], [18], [19], [20], [21], [22], [23], [24].

Current phototransduction models [25], [26], [27], [28], [29] quantify the non-visual photic inputs in terms of appropriately weighted integrals of the spectral irradiance at the eye cornea, or, to be more precise, on a plane tangent to the cornea and perpendicular to the line of sight. Although this approach involves a certain simplification of the problem, because it does not take into account the spatial distribution of the radiance entering the eye [30], it was instrumental for enabling the first proposals of physiologically-based magnitudes describing non-visual inputs [25], [26], [27], [28], [29], and quantitative models for predicting the expected outputs after exposure to a light pulse under certain well defined experimental conditions [27], [28], [29]. Most of the above quoted research was directly applied to evaluate the photic effects of different types of lamp spectra. In typical indoor settings, however, the spectral composition of the light that actually reaches the observer's eyes does not depend on the characteristics of the light sources alone, but also on the spectral reflectance of the surrounding environment. Since this spectral reflectance is generally space-variant, the corneal irradiance will additionally depend on the direction of gaze. Any meaningful description of the actual light exposure conditions in indoor spaces must take into acoount the contribution of the surrounding surfaces, through the multiple reflections of the light beams in their way from the source to the observer.

In this paper we show that the spectral radiance field is a useful tool for a comprehensive description of the light entering the eye. In its seven-dimensional version it provides spatial, angular, spectral and time-resolved radiance information within any region of interest. Other radiometric and photometric magnitudes can be computed by integrating this field over the appropriate (solid angle, surface, wavelength and/or time) domains. We describe how the radiance field can be applied to the study of light pollution in indoor spaces, and propose a set of effective filter-like funtions useful for indoor lighting design and light pollution assessment.

Section snippets

The spectral radiance field in indoor spaces

The basic physical entity for describing radiative transfer processes at optical frequencies is the spectral radiance field, also called plenoptic function [31], denoted by L=L(x,y,z;θ,ϕ;λ;t)=Lλ(x,ω,t)where Lλ(x,ω, t) is the spectral radiance [Wm−2 sr−1 nm−1] at point x = (x, y, z) and time t, in the direction of the unit vector ω(θ, ϕ), at wavelength λ.

Lλ(x,ω, t) is a scalar field defined on a seven-dimensional space. However, this space can be reduced to five dimensions in rooms of ordinary

Factorizable sources: effective filter functions

Let us now assume that the sources are factorizable, in the sense defined in [36], i.e. that their spectral signature is the same for all active emitting points and all emission directions. Most practical indoor sources are factorizable to a good degree of approximation. For factorizable sources we have: L˜λ(x,ω)=Φ(λ)B(x,ω)

Both factors in Eq. (16) can be arbitrarily scaled, as long as their product gives the correct value for the emitted radiance. A useful choice is to identify Φ(λ) with the

Experimental results

In order to determine experimentally the order of magnitude of the spectral modulation effects due to the surroundings, we conducted a series of measurements of the spectral irradiance at the entrance plane of the eye of an observer, using different lamps and different directions of gaze, in a meeting room located within the premises of the Terrassa School of Optics and Optometry of Universitat Politècnica de Catalunya.

A simple analytical model

Some insights on the role of the surrounding surfaces as modulators of the source spectrum, and, in particular, on the qualitative behavior of the EISF shown in Fig. 6, can be obtained using a simplified model for which an analytical solution of Eq. (10) exists. Note that this highly simplified model is developed mainly as a complementary thinking aid, and it is not intended to be a substitute for the precise measurements or the numerical evaluations of the EISF function.

Let us consider a

Discusion

The radiance field is a useful tool for analyzing the light exposure of human observers in indoor spaces. If the sources are factorizable, the surrounding surfaces (wall, ceiling, floor, and objects within the room) act as an effective filter that selectively enhances or attenuates different regions of the source spectrum. This filter-like behaviour can be formalized through an effective inverse surface solid angle function, that once mutiplied by the spectral flux of the source

Conclusions

The spectral radiance field is a basic tool for analyzing photic effects in indoor spaces. The general framework described in this paper enables addressing a wide range of problems related to the interactions between light souces, surrounding surfaces and human observers. For factorizable light sources, the modulating effects of the multiple wall reflections can be described in terms of a set of effective filter-like functions acting on the spectral flux distribution of the source. As expected,

Acknowledgments

This work was developed within the framework of the Spanish Network for Light Pollution Studies (AYA2015-71542-REDT).

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