Characterizing Color Quality, Damage to Artwork, and Light Intensity of Multi-Primary LEDs for Museums

1. Introduction

Optical radiation is electromagnetic energy that dissipates through space. Light, the visible part of optical radiation, upon reaching the surface of an object is either reflected, transmitted (if the object is transparent or translucent), or absorbed. Reflected light initiates vision when it is detected by the human visual system. Light absorbed by the object turns into heat and is considered wasted for illumination purposes. The absorbed light (energy) may cause a chemical change in the molecules due to photochemical reactions, and if the object is light-sensitive, such as a painting, it may cause irreversible damage (e.g., color fading) [1,2]. The dilemma between visibility and damage is a crucial aspect of lighting design for museums and galleries.

Characterizing the properties of the absorbed light can enable estimating and preventing further damage to sensitive works of art. Past studies suggest that there are four primary parameters that influence the optical damage to artwork: light intensity, exposure duration, spectral power distribution (SPD) of the light source, and spectral sensitivity of light sources [2,3]. An increase in light intensity and exposure duration increases damage to artwork, although the relationship is likely not linear. The spectral power distribution and spectral sensitivity of the pigments interact in a more complex manner.

Early models of damage were based on the Einstein–Planck law, which states that energy in lower wavelengths (i.e., ultraviolet radiation) may cause more damage than energy in longer wavelengths [4]. However, several research studies showed that energy in long wavelengths, such as infrared radiation, and energy in the visible spectrum could also cause damage to artwork [5,6,7,8]. Another important factor is the selective influence of light source SPD on the magnitude of damage. Studies suggest that the spectral absorption of pigments may dictate the amount of damage to an artwork since only the light absorbed by a pigment causes photochemical action [9,10,11,12]. This understanding, coupled with the overall effect of lighting intensity, encouraged researchers to use spectral optimization algorithms to reduce damage caused by lighting [13,14,15,16,17,18,19]. Some of these optimization studies even considered the energy consumed by lighting to balance the end-users’ different needs [14,16,18,19]. Despite the increase in computational power and knowledge of materials’ response to light, there is still no universal damage model that can account for different types of pigments. Another unresolved issue is the holistic presentation of the trade-offs and complex relationships between the parameters, such as damage to artwork, the color appearance of the painting, illumination levels (both for damage and visibility), and energy consumption.

Although multi-primary LED (mpLED) systems can be optimized to generate tailor-made solutions for light-sensitive artwork, quantifying the complex relationships between target parameters using a single-dimensional model is not possible. Fortunately, the complex relationships between different aspects can be presented using a 3-D graph, and discretizing each continuous dimension of the graph (voxelating) can result in a discrete, measurable volume. The voxelization method has been previously applied to color rendition variability in mpLEDs [20]. Here, the voxelization method is applied to display the trade-offs between damage, the color appearance of artwork, illumination levels, and energy efficiency. The voxelization method is based on the idea that a large distribution of data points can be grouped into discrete packages or cubes called voxels, as shown in Figure 1. Converting a large dataset to voxels results in increased interpretability of the data, reduces visual cluster, and enables creating predictive models. The data points within each voxel are considered the “same” for classification purposes, and the “sameness” (uniqueness) of the data points within a voxel can be defined by identifying the borders of the voxel in each dimension. The voxelization in the context of museum lighting should contain the primary goals of illuminating artwork, such as preventing damage caused by lighting, optimizing the appearance of artwork (brightness and color), and improving the efficiency of the light sources.

2. Methods

Three-dimensional graphs are widely used in science communication to demonstrate the relationship between conflicting parameters. The proposed voxelization method goes a step further by discretizing the continuous data of each dimension to create unit voxels (analogous to pixels in 3-D shapes). The size of a voxel can be defined by identifying the acceptability or detectability of the minimum value for each dimension. The minimum identifiable value is often characterized as a just-noticeable difference (JND) in psychophysical studies. It is also possible to convert continuous data to discrete data by selecting arbitrary unit sizes when a JND cannot be identified. Once the dimensions of a unit voxel are identified, they can be plotted in a 3-D graph, as shown in Figure 1.

Key dimensions of the proposed demonstration method for museum studies are damage, light intensity, color quality, and energy efficiency. Damage to artwork can be quantified using the Berlin model [3] or the amount of light absorbed by the painting [19]. In the Berlin model, the damage caused by optical radiation is calculated as a function of effective radiant irradiance.

$$E_{dm}=\underset{\lambda }{{\displaystyle \int }}{E}_{e,\lambda }\times s{(\lambda )}_{dm,rel}\times d\lambda$$

(1)

where E_dm (unit: W/m²) is the effective irradiance that causes damage, E_e,λ is the spectral irradiance (unit: W/m²), s(λ)_dm,rel is the relative spectral responsivity of a material normalized at 300 nm, so that s(λ)_dm,rel = 1.0 for λ = 300 nm, and λ is wavelength (unit: nm) [3]. The alternative damage calculation method is the ratio of the light absorbed by the surfaces under a test light source to the light absorbed by the surfaces under a reference illuminant

$$A=\frac{\underset{\lambda }{{\displaystyle \int }}{E}_{e,\lambda ,test}(\lambda )\times (1-R(\lambda ))\times d\lambda }{\underset{\lambda }{{\displaystyle \int }}{E}_{e,\lambda ,ref}(\lambda )\times (1-R(\lambda ))\times d\lambda }$$

(2)

where A is a unitless relative absorption value reported as a percentage, E_e,λ,test(λ) is the test light source irradiance, E_e,λ,ref(λ) is the reference source irradiance, and R(λ) is the reflectance factor of a pigment. The test light source E_e,λ,test(λ) should be rescaled so that the light reflected from the painting under the test and reference light sources are equal. Equalizing the reflected light from the painting under the test and reference light source ensures the luminance is the same in both conditions so that the comparison is not affected by luminance related color appearance phenomena, such as the Hunt Effect [21] and Bezold–Brücke hue shift [22].

Both the Berlin Model and relative absorption calculation method account for the Grotthuss–Draper law, which states that only light that is absorbed can cause photochemical activation. The difference between the two methods is that the relative absorption A offers an easy-to-interpret measure for damage, but it does not account for the Planck–Einstein relation (lower wavelength radiation has higher energy potential). On the other hand, the Berlin Model uses a damage curve (action spectra) normalized to 300 nm, which may undermine the Grotthuss–Draper law and can be hard to interpret.

In the proposed voxelization method, the light intensity can also be quantified by using appropriate metrics, such as illuminance (unit: lx) or irradiance (unit: W/m²). Although illuminance is relevant for the human visual system, irradiance can be used to account for the difference between spectral sensitivity of the materials and the spectral luminous efficiency function (visual system’s response to light). The color quality of the painting can be quantified using colorimetric tools, such as color rendition metrics, or more precise tools, such as color difference, chroma, and hue shift formulae. Color shift formulae can provide detailed and specific information about the magnitude and direction of color shifts between two lighting conditions. In the following voxelization example, the two lighting conditions will be a reference white illuminant (i.e., daylight and incandescent lamps are considered ideal in museums for color quality purposes) and a test light source (SPDs generated by a mpLED).

Test SPDs were generated by the linear optimization of a seven-channel mpLED lighting system. The spectrum of each channel, shown in Figure 2, were combined by iteratively mixing each channel at 20% dimming intervals, resulting in 279,936 (6⁷) test SPD combinations. The color differences in the appearance of 24 Macbeth ColorChecker test samples [23] between each test SPD combination and reference incandescent halogen light source were calculated using CAM02-UCS [24]. The root mean square (RMS) of the 24 color difference values (ΔE’_RMS) were calculated to get an average score of the color shifts.

An incandescent halogen light source spectrum was used as a reference since they are still widely used in museums [25]. Macbeth ColorChecker samples include a range of saturated, desaturated, chromatic, and achromatic samples, which can be representative of a wide range of artwork, and it is widely used in color and museum lighting research [26,27]. The color quality of every nominal white light was quantified using an ANSI/IES TM-30 fidelity index R_f, a gamut index R_g, and a local chroma shift in hue bin 1 (R_cs,h1) [28]. In addition, relative absorption A (light absorbed by a pigment under the test light source divided by the light absorbed by a pigment under the reference halogen light source), illuminance (E_v), irradiance (E_e), the luminous efficacy of radiation (LER), correlation color temperature (CCT), and the distance from the Planckian locus (Duv) [29] were calculated for each test SPD.

3. Results

The data generated by the linear optimization method have been sorted and analyzed for metric correlation. Since most of the LED combinations (236,502 out of 279,936) were not nominally white, color quality metrics that require a test light source to be close to the Planckian locus (i.e., R_f, R_g, CCT, Duv) were not used in the analysis. However, it is possible to filter out the non-white SPD combinations to utilize color quality metrics that are developed for white lights, with a caveat of reduced damage reduction for individual pigments.

The data generated by the optimization method were voxelated using the most important measures for museum lighting: damage to artwork, color appearance, and energy efficiency. For example, a 3-D voxelated volume (VV1) was calculated using the relative absorption for a test color sample (Macbeth ColorChecker sample #24), the RMS color difference of 24 Macbeth ColorChecker samples ΔE’_RMS, and the LER, as shown in Figure 3. Measures in each dimension were discretized by rounding values to a unit size of 1 (e.g., LER of 200.3 lm/W and 200.7 lm/W were rounded to 200 lm/W and 201 lm/W, respectively, and they fell into two different voxels). All the test SPD combinations that fell into the same voxel were considered identical. Therefore, the number of unique voxels (VV1 = 45,813) represents the number of unique SPD combinations that can be generated within the seven-channel mpLEDs. It is important to note that the uniqueness of each voxel depends on the voxel size criteria. For example, if the LER was voxelated using 5 lm/W as the unit voxel size, the number of voxels would drastically decrease. Therefore, the absolute magnitude of the volume does not have an inherent meaning.

The data departed from normality at the 0.05 significance level as tested by the Shapiro–Wilk test, and a non-parametric test (Spearman’s rank correlation coefficient) was used to analyze the correlation between the dimensions of the voxelated VV1 volume. While the correlation between absorption A and ΔE’_RMS were low (ρ = 0.111), the LER was inversely correlated to absorption (ρ = −0.757) and ΔE’_RMS (ρ = −0.427).

Figure 3 illustrates the relationship between color quality, damage, and energy efficiency, where the top far corner is the ideal condition (low absorption, small color shifts, and high efficacy). The visual illustration makes it clear that the ideal SPDs are increasingly scarce compared to other SPDs that perform worse in terms of either damage, color shifts, or energy efficiency. Since the relative absorption A > 100 denotes additional damage, and the large color differences are not desired, it is possible to zoom into the graph by limiting the x and y axes (relative absorption (A < 100) and color difference (ΔE’_RMS < 20), respectively), as shown in Figure 4.

A second example (VV2) was calculated using relative absorption A for a test color sample (Macbeth ColorChecker sample #24), the TM-30 fidelity index R_f, and the irradiance E_e, as shown in Figure 5. In the second volume, which is the graphical representation of the same data, there were VV2 = 2,265 unique voxels. While the absolute volume size does not have an inherent meaning, comparing two or more light sources—using identical voxel dimension metrics—can provide more information about the performance of the light sources for a specific set of pigments (or the overall color quality of a painting).

Voxelated 3-D volume VV2 also shows the relationship between competing target parameters. The fidelity index R_f was not correlated with either relative absorption A (ρ = 0.010) or irradiance E_e (ρ = 0.017). However, irradiance E_e and relative absorption A were highly correlated (ρ = 0.996), which is not surprising since absorption increases with light intensity.

It should be noted that the graphical distributions were applied to a single pigment using relative absorption and to multi-pigments (e.g., a painting with numerous colors) using color quality metrics to demonstrate the different use cases of the proposed method. The proposed model can provide a more analogous analysis if all the dimensions are chosen at the individual pigment scale (e.g., absorption for a single color and color difference in the pigment under reference and test light sources). On the other hand, the proposed model can also be used to gain a holistic understanding of a painting by using a high-level approach (e.g., average absorption ratio by the pigments used in a painting, the average color difference of pigments in the painting under reference and test light sources). While the provided examples do not include the exposure time—an important dimension of damage to artwork—it is possible to incorporate the total radiant exposure as a metric to the voxelization method. The total exposure can be calculated by multiplying exposure time t (unit: hr) with irradiance (E_e × t, unit: W h/m²) or illuminance (E_v × t, unit: lx h). Alternatively, the radiant exposure can be quantified using the Berlin model (H_dm, unit: W h/m²) [3].

4. Discussion

The proposed voxelization method can help analyze and compare the performance of multi-primary LED systems. Since each SPD is represented as a single dot in a 3-D graph, the proposed method cannot be used to analyze a single static SPD light source. However, it is possible to analyze large datasets that include commercially available light sources in the proposed 3-D volume. Such large datasets can provide museum curators, conservators, and lighting designers with an opportunity to compare the performance of different lighting technologies. Large datasets of different lighting technologies can also be used to analyze a set of reference test samples collected in a museum or a painting (similar to the color rendition approach) to attain an approximate idea of the performance in a given space. The caveat in such an approach would be the consideration of object surface reflectance characteristics since it may be challenging to identify the action spectra of the pigments and dyes in every painting in a museum or a gallery.

Non-invasive scanning techniques, such as Fourier-transform infrared spectroscopy (FTIR), X-ray fluorescence (XRF), Raman imaging, hyperspectral imaging, scanning electron microscopy (SEM), and energy-dispersive X-ray spectroscopy (EDS) [30,31,32] are often used to obtain absorption spectra from materials. The analysis of organic and inorganic pigments can also lead to new horizons in tailor-made museum lighting. In the future, it may be possible to build a library of pigment and dye characteristics and their response to light spectra, which may ultimately lead to a universal damage calculation model.

Despite the challenges of facing a universal damage model today, studies investigating the sensitivity of different materials [33,34,35,36,37,38,39,40] can converge into a complex damage appearance model (DAM), similar to color appearance models (CAMs). Although the CIE 1976 L*a*b* (CIELAB) is the most widely used color space in conservation science, the proposed damage model is based on the CAM concept due to the multi-layered nature and better performance of CAMs. The CIELAB has well-documented limitations, such as abnormal hue angle shifts [41,42], poor performance in the [43], and blue regions (negative b* axis) [44]. Research suggests that color appearance models, such as CAM02-UCS [24], can outperform CIELAB, especially when color differences are small—which are crucial for conservation science [45,46]. In addition, conservation scientists often perform visual observations of the artwork under controlled environmental conditions (e.g., laboratory). Therefore, the additional input parameters required by CAMs (i.e., background and surround conditions, adapting luminance) can be accurately determined by the users. In short, the CAM provides a better basis both conceptually and mathematically for the proposed damage calculation models compared to a color space, such as CIELAB.

A DAM can have several inputs, such as light source spectrum, light intensity, exposure duration, pigment spectral reflectance/absorption, artwork type (e.g., oil, gauche, acrylic paint), and choice of a reference illuminant (i.e., daylight, incandescent). DAM would provide an output of damage caused by lighting and the color appearance of the resulting pigment under a specific light source, as shown in Figure 6. It should also be noted that color difference formulae are often used in conservation science as a proxy for damage, as illustrated by fading. However, not all types of chemical and structural damage are caused by lighting [47]. For example, viscometry and chromatography are used to measure the brittle effect (the breakdown of paper fibers) [48].

Although a rudimentary DAM can provide an estimation of damage to a single material at a given time, more advanced models can be built by integrating the results across different pigments and dyes (e.g., providing averages with standard deviation and error estimates, using multi-dimensional data analysis or machine learning algorithms). More complex DAMs can be used in adaptive lighting systems, where a sensor detects the spectral reflectance function of paintings, and a projection system emits spectrally and spatially optimized lighting to each colored part of the painting to reduce damage while maintaining the overall color quality of the painting, or even visually restore the faded colors of the artwork [18,49,50,51].

5. Conclusions

Museum conservators and curators often face the multi-faceted problem of identifying the optimal lighting conditions in museums. While light is needed to display art, it may also damage sensitive artwork over time. Museum conservators, curators, and lighting designers can use the properties of light sources (spectral distribution, intensity, and exposure duration) and materials (spectral absorption characteristics) to estimate the damage caused by optical radiation. Here, a three-dimensional representation of the conflicting parameters (e.g., color quality vs. damage) is provided to display the trade-offs between several measures. The continuous scale of each dimension of the 3-D graph is converted to discrete data using unit voxels. The discretization of continuous data can enable the quantification of the performance of multi-primary LEDs in the context of art conservation. Sample calculations demonstrated the use of the proposed method to highlight the most common trade-offs in museum lighting design: conflicts between the color quality of paintings (average color difference), damage caused by lighting (absorption percentage), illuminance, and luminous efficacy of the radiation. However, it is possible to adopt different metrics for each dimension, such as color discrimination or other color rendition metrics for color quality, the Berlin model [3] and irradiance for damage quantification, and CCT and Duv for color quality of the light source. In addition, new metrics that are relevant for museum lighting and perception of artwork (e.g., visual clarity [52,53] and visual complexity [54]) can be utilized in the proposed 3-D volume. Future work will investigate the quantification of the trade-offs between various damage, color quality, and visual perception metrics and validate their accuracy through visual evaluations.