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Methods Color calculations and CIE color differences. The International Commission on Illumination (CIE) standard was used for color calculations, represented by the equation2,18: 𝜆2 ̅ 𝜆2 Θ = ∫ 𝜃(𝜆)𝑇(𝜆)𝐼(𝜆)𝑑𝜆⁄∫ 𝑦̅(𝜆)𝐼(𝜆)𝑑𝜆 𝜆1 𝜆1 where Θ = [X; Y; Z] are the XYZ tristimulus values, 𝜃̅(𝜆) = [𝑥̅(𝜆), 𝑦̅(𝜆), 𝑧(̅ 𝜆)] are the 1931 CIE 2° standard observer matching functions, 𝑇(𝜆) is the transmission spectrum of the filter, and 𝐼(𝜆) is the spectral irradiance of light passing through the filter. The XYZ tristimulus values can be transformed to a different color space (e.g., RGB); here, we use the CIELAB color space because it is more perceptually uniform and allows for straightforward calculations of perceived color differences. The XYZ to LAB transformation is given by19: 𝐿1 =116𝑓(𝑌)−16,𝑎1 =500[𝑓(𝑋)−𝑓(𝑌)],𝑏1 =200[𝑓(𝑌)−𝑓(𝑍)], 𝑌𝑋𝑌𝑌𝑍 where 𝑛𝑛𝑛𝑛𝑛 and 𝑋 , 𝑌 , 𝑍 𝑛𝑛𝑛 1/3 63 𝑓(𝑡) = 𝑡 , 𝑡 > (29) 162 4 {3(29) 𝑡+29, 𝑜𝑡h𝑒𝑟𝑤𝑖𝑠𝑒 are the tristimulus values of the reference white point. Here, white light is defined by the CIE D65 standard illuminant, which roughly corresponds to average mid-day solar illuminance. The white point of D65 is (95.047, 100.000, 108.883)20. Filter Design An iterative optimization approach was used to design the transmission of Filter 1 and Filter 2, where the filter responses became more complex as our intuition grew between iterations. This approach was used to meet the primary design goal, splitting the spectral response of the S cone between eyes, while 14PDF Image | Enhancing color vision by breaking binocular redundancy
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