A Framework for Optimizing Lighting in Animal Shelters for Domestic Cats

In this project, we aim to enable designers to optimize lighting conditions for domestic cats in animal shelters. Specifically, we developed an optimization framework that controls the spectral power distribution (SPD) of light sources and returns the effect on feline visual perception. In our model, we used standard light source SPDs and predicted light reflected from different surfaces within an animal shelter. The reflected SPDs were combined with the known brightness sensitivity of domestic cats across the visible light spectrum to develop an understanding of cats’ visual experience in the shelter under different lighting conditions. The optimization framework then minimizes the difference between a desired lighting effect (here, daylight) and a modeled effect using a set of light source SPDs. Initial results demonstrate that by using slightly more advanced lighting design and control, shelters can potentially improve the visual experience for cats.


Introduction
Much work has been performed in designing favorable lighting conditions for humans.However, less attention has been given to how animals' wellbeing is affected by indoor lighting.The work that has been performed indicates that disruption of the light/dark cycle, specific light intensities, wavelength, and other light-related variables can have significant physiological impacts on animals, as discussed by Emmer et.al [1].Coupled with an environment such as a research laboratory or an animal shelter, these impacts can be compounded with many additional biological and psychological stressors.
Animal shelters are uniquely stressful environments for many animals.As noted in the 2022 Association of Shelter Veterinarians document The Guidelines for Standards of Care in Animal Shelters, "Facilities should be designed to offer as much natural light as possible…When natural lighting is not available and artificial light is used, it should approximate natural light in duration and intensity to support circadian rhythms" [2].While some work by Wilson [3] has studied the impact of indoor lighting on domestic dogs in animal shelters, the impact on domestic cats, who perceive light similarly but distinctly from dogs, is more underexplored.Domestic cat behavior is sensitive to environment; for example, behavior has been shown to change when indoor and outdoor cats were compared by Parker et.al [4], and cats in shelters face unique challenges to their wellbeing as discussed by Vojtkovská et.al [5].Stella et.al [6] show that failing lighting control timeclocks (in addition to other unusual external events; lighting effects were not isolated in the study) have the potential to cause gastrointestinal and urinary tract issues as well as skin and behavioral problems.It is well known that daylight and natural 1320 (2024) 012017 IOP Publishing doi:10.1088/1755-1315/1320/1/012017 2 light/dark cycles can have positive impacts on humans as well as animals, but unfortunately not all shelters can provide daylight to their residents.
To contribute to improving the wellbeing of cats in shelters, we developed an optimization framework specifically designed to optimize the spectral power distribution (SPD) (e.g., radiant power as a function of wavelength) of various light sources to mimic a standard description of daylight as experienced by cats inside an animal shelter.In contrast to existing works utilizing optimization frameworks for tuning lighting spectral outputs (e.g., for preserving artwork as discussed by Durmus et.al [7], or conserving energy as explained by Durmus et.al [8]), our work specifically focuses on domestic cats in an indoor environment and develops an optimization framework that does not use heuristic or genetic algorithms.Our framework is in the form of a mixed-integer linear program which can be solved to optimality and easily incorporate different input data (sensitivity curves, objectives, and various SPDs).Future work can include additional objectives such as enhancing color discrimination or targeting the appearance of the cats to potential adopters, whose perception of shelter animals can be improved by lighting adjustments as shown by Heemstra [9].

Background on Cats' Visual Perception
To analyze architectural lighting for cats, it was important to consider how each light fixture's radiant power would be perceived by cats.We identified a spectral sensitivity curve for cats from Crocker, et.al [10] to be used as a proxy for spectral brightness efficiency in setting up the optimization framework.For context, the proxy spectral brightness efficiency function for cats is plotted in Figure 1 alongside the CIE spectral luminous efficiency function for human photopic (daytime) vision.Both curves are unitless functions of wavelength that represent the relative ability for narrow bands of radiant power in the visible range to induce equal perception of brightness, as explained in the Lighting Handbook [11].As demonstrated by Figure 1 below, the proxy brightness efficiency function we used models cats as more sensitive to short wavelengths (can be considered as blue and violet light), while humans are more sensitive to medium wavelengths (green), and have more sensitivity to long wavelengths (red) than cats.

Optimization Framework
The optimization framework was developed in Python and utilized the GUROBI solver within the CVXPY interface [12] to optimize various chosen objectives subject to constraints on the lighting source capabilities.We considered different light sources that a shelter may have access to and their impact on the appearance of light within a space relative to daylight.Specifically, we consider a combination of narrow band (colored) LEDs and white-light sources, including phosphor-based LED and fluorescent, to determine which combination would produce a visual signal in cats closest to that as experienced under a daylight spectrum.We identified a typical SPD for each source from Cree [13] and the Illuminating Engineering Society of North America [14], and through measurements using a Konica Minolta CL-500 illuminance spectrophotometer of each color channel of an ETC Desire D22 fixture.We then scaled the source SPDs to get the same radiant watts for each source at maximum brightness, as can be seen in Figure 2 below.Also, in our optimization, we allowed each source to dim, which required modifier variables.We used the CIE standard illuminant D65 for the daylight spectrum and assumed that the relative SPD was not affected by its transmittance through glazing, as we did not account for the effect of windows on the daylight curve.The SPDs of the sources were modeled with the variables and their modifiers listed below.daylight Reference daylight source SPD blue1, b1 First blue LED source SPD, modifier green1, g1 First green LED source SPD, modifier yellow, y Yellow LED source SPD, modifier orange, o Orange LED source SPD, modifier red1, r1 First red LED source SPD, modifier dark_red, dr Dark red LED source SPD, modifier red2, r2 Second red LED source SPD, modifier white, w White LED source SPD, modifier amber, a Amber LED source SPD, modifier green2, g2 Second green LED source SPD, modifier cyan, c Cyan LED source SPD, modifier blue2, b2 Second blue LED source SPD, modifier indigo, i Indigo LED source SPD, modifier LED2700, led2 2700 K LED source SPD, modifier LED4000, led4 4000 K LED source SPD, modifier ϐluorescent2950, ϐlu2 2950 K fluorescent source SPD, modifier ϐluorescent4000, ϐlu4 4000 K fluorescent source SPD, modifier ϐluorescent6500, ϐlu6 6500 K fluorescent source SPD, modifier These variables were convolved with a brightness efficiency function representing human or cat vision, ‫,ݕݐ݅ݒ݅ݐ݅ݏ݊݁ݏ‬ and the spectral reflectance of a representative wall color, ‫,ݎ݈ܿ‬ which can vary, as indicated by Figure 3 below.The resulting values were modified from the initial variable by adding a subscript of c to each variable name.We used these convolved SPDs in our optimization.
We developed several constraints for our optimization problem.We assumed dimming of the light intensity was allowed, using fixed values between 0 and 255.Thus, to constrain our problem, we restricted the modifier variables to be integers from 0-255, as shown in Equation 1 below.Daylight was used as a reference across all objectives, and we assumed it was at its maximum value for all objectives, using a consistent multiplier of 255.

≤ ‫ݎ݂݁݅݅݀݉‬ ≤ 255 EquaƟon 1: Constraints
We also developed several optimization objectives for our problem.First, we compared several architectural white-light sources to daylight.Next, we iterated through a combination of sources, considering only colored LED sources, only white-light LED sources, and all sources.In our objectives, we considered the convolved SPDs over the wavelengths, ߣ, 380-730 nm.
In Objective 1, we considered the 2700K LED compared with daylight, attempting to minimize the difference between daylight and the LED source, as shown in Equation 2 below.We squared the difference to penalize higher differences as well as penalize both positive and negative differences between the two curves.Similarly, in Objective 2, we compared the 4000K LED source and daylight, as shown in Equation 3 In Objectives 6-8, we considered multiple sources.In Objective 6, we considered the colored LED sources compared with daylight.The colored sources consisted of blue1 and blue2, green1 and green2, yellow, orange, red1 and red2, dark_red, cyan, and indigo.In Objective 7, we compared all LED sources with daylight.Finally, in Objective 8, we compared all sources with daylight.These objectives can be seen in Equations 7-9 below.While we squared the objective values to consider absolute differences and penalize larger differences, we wanted to determine the resulting difference, difference, between daylight and the light IOP Publishing doi:10.1088/1755-1315/1320/1/0120176 sources for each objective, which we calculated by using the square root of the objective value, output, where n is the objective number, ranging from 1-8 as detailed above.

‫݁ܿ݊݁ݎ݂݂݁݅݀‬ = ‫ݐݑݐݑ‪ඥ‬‬
The resulting objective function thus represents the difference between the sources and the convolved daylight curve, with a higher difference being penalized in our objective.A lower difference indicates the sources better match daylight.

Results
Through our optimization objectives, we were able to compare the different lighting scenarios and determine which best matched daylight.In Table 1, we detail the intensity of each light source and the difference between the light sources and daylight, summed across wavelengths.We show both cat and human results based on the corresponding brightness efficiency functions.Human results are included to provide an example of the potentially different lighting needs of cats and humans.In the table, fluorescent sources are denoted by fluor and objectives are denoted by obj.Moreover, Figure 4 shows plots with the resulting convolved SPDs based on source SPD, cat visual perception, wall color, and dimming of each source.The results below assume a white wall color, though spectral reflectance curves for more saturated room finish colors can be modeled.As demonstrated by Table 1, humans and cats have different optimal electric lighting scenarios for mimicking the perception of daylight with common light source technology, with humans needing higher values of dark red and cats needing higher values of indigo, for example.The optimization was better able to match daylight perception for the cats than humans, resulting in lower difference values.Of the single-source objectives, the modeled 4000 K LED source was best able to match the daylight perception as measured through the wavelength-by-wavelength comparison of the convolution of eyeincident SPDs and brightness efficiency functions.Additionally, the optimization with multiple light sources resulted in a lower difference than those with a single light source, with Objective 8 resulting in the lowest difference and Objective 1 resulting in the highest difference.Figure 4 shows the convolved SPDs of the sources in each objective with the proxy brightness sensitivity function for cats compared to the convolved D65 daylight spectrum.Objectives 1-5 had less overlap with the convolved daylight curve compared to Objectives 6-8, which utilized multiple sources.

Discussion and Future Work
In this paper, we developed an optimization framework that considers the capabilities of different lighting sources, the spectral sensitivity of cat eyes, the spectral reflectance of walls, and tunes the spectral power distribution of the overall setup to match daylight (as seen by an indoor domestic cat) as close as possible.Animal shelters were chosen as the application due to their potential impacts on cat wellbeing relative to the current practice of lighting for humans in the space.A daylight objective was focused on due to the reasonable assumption that it is an important spectrum for supporting cats' wellbeing.The results indicate that, out of the chosen set of lighting sources, a combination of sources better achieves daylight-matching.Specifically, we found a combination of a 2950 K fluorescent and narrow-band dark red, blue, and indigo LEDs resulted in the best daylight match.The results from this study could be extended to include dynamic light adjustments over time, more complex surface reflectance models, a standard brightness efficiency function for cats, or brightness efficiency functions for other animals, such as dogs.Different light sources could be added into the model, allowing customizable inputs.Daylight spectra beyond D65 could also be considered, incorporating various daylight conditions and considering the shift in the spectrum throughout the day.Additional objectives could be considered as well, such as improving color discrimination for cats perceiving toys, or making shelter cats appear more attractive to potential adopters.For shelters without advanced lighting controls, objectives such as optimizing light timers could also prove beneficial for cats' circadian rhythm, as discussed by Kuwabara et.al [15].To address circadian entrainment in our optimization, the framework could incorporate spectral sensitivities of the non-image-forming system such as melanopic sensitivity with an objective based on the metric of melanopic equivalent daylight illuminance.Lastly, the optimization framework can include additional decision variables that can improve wellbeing or shelter objectives further, such as temperature control, energy savings, and daylight integration.

Figure 3 :
Figure 3: Animal shelters uƟlize various light sources, including tubular daylighƟng devices (leŌ) to help bring in daylight.Most have fluorescent or LED lights (center).Different surface colors (right; all) moƟvate a dynamic, adjustable approach.

Table 1 :
Summarized Results for Cats and (Humans)