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Unlike the previous revisions, Filter 2 was optimized using a more rigorous method compared to the brute force method used above. A constrained optimization by linear approximation (COBYLA) method was implemented in a stochastic basin-hopping algorithm to optimize the position of the cut-on/cut-off wavelengths, transmission of the pass and stop-bands, and slope of the transition regions. The transition regions of the filterβs short-wavelength band-stop region was constrained within +/- 10 nm of their previous values; this was done to maintain the overall shape of the previous design while allowing some room for color balance optimization. The transmittance was constrained between 5 and 15% in the stopbands, and between 80 and 95% in the passbands, to allow for high throughput and relative ease of manufacturing. The error function proportionality constant was constrained between 0.25 and 1. The long-wavelength stopband region was constrained between 600 β 700 nm, but the band-stop width was not constrained; this was done to prevent attenuation of the M and L cones at their peak sensitivities (~550nm, ~580 nm respectively), while also preventing needless optimization beyond the visible wavelengths (> 700 nm). With these constraints in place, Filter 2 was optimized in order to minimize the modified merit function: ΞπΈβππππ‘hπππππ π‘ππ , where ΞπΈ is the color difference between Filter 1 and Filter 2 when transmitting D65 white light and Widthbandstop is the spectral width of the short-wavelength band-stop region of Filter 2. This procedure yielded an optimized response for Filter 2 with stopbands at 450 - 500 nm and 630 - 680 nm, and stopband/passband transmittance of 10% and 90%, respectively (Figure S3(a)). The rendered color of transmitted D65 white light through the filters is given in Figure S3(b), with a ΞπΈ color difference of 5.21. (a) (b) Filter 1 ΞE = 5.21 Filter 2 (i) (ii) (ii) (ii) Figure S3: (a) Optimized transmission response for filters 1 and 2 after the third design revision, with band-stop regions between 450 β 500 nm (i) and 630 β 680 nm (ii). Region (i) splits the short- wavelength cone, region (ii) improves the white-balance of the filter pair (b) Rendered colors for CIE D65 white light transmitted through each filter from (a), with a ΞE color difference of 5.21. 4PDF Image | Enhancing color vision by breaking binocular redundancy
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