**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) [30–32] 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 [33–40] 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. 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

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

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]. 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 [18,49–51].

*Heritage* **2021**, *4* FOR PEER REVIEW 8

**Figure 6.** A damage appearance model (DAM) can be developed based on the research studies investigating the impact of different aspects of light on pigments. A computational model such as this can have inputs including spectral power distribution, intensity, exposure duration of the light source, action spectra of the light-receiving material, material (binder, pigment, dye) type, and choice of a reference illuminant (i.e., daylight, incandescent). The DAM outputs can be the color difference to quantify damage and the color appearance of the light-receiving material. **Figure 6.** A damage appearance model (DAM) can be developed based on the research studies investigating the impact of different aspects of light on pigments. A computational model such as this can have inputs including spectral power distribution, intensity, exposure duration of the light source, action spectra of the light-receiving material, material (binder, pigment, dye) type, and choice of a reference illuminant (i.e., daylight, incandescent). The DAM outputs can be the color difference to quantify damage and the color appearance of the light-receiving material.

> 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 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 [18,49–51].

### 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 **5. Conclusions**

**5. Conclusions** 

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] 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.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The author declares no conflict of interest.
