**Tailorable truncated retroreflector array (TTRA) technology can be used to design reflective sheeting such as is used for roadway and business signage, where retroreflective and non-retroreflective characteristics of the reflective sheeting can be optimized so that the sheeting retroreflects much of the light to a light source while much of the remaining non-retroreflected light, which has typically been viewed as signal loss, is redirected to desired locations to better meet requirements of specific lighting visibility scenarios. **

**To demonstrate the ability to design reflective sheeting using the TTRA technology, ****Dr. Jason Sickler**** ****of Torchlight Solutions LLC was engaged to perform engineering trade studies that compared the lighting visibility performances of different reflective sheeting designs produced using the tailorable truncated retroreflector array technology and prior art designs in different lighting visibility scenarios. A lighting visibility scenario includes one or more light sources, one or more light observers, and signage having reflective sheeting designed using the TTRA technology. One or more parameters (e.g., the truncation rotation) corresponding to different tailorable truncated retroreflector arrays were systematically varied to produce different reflective sheeting designs, where the lighting visibility performance of each reflective design was modeled using the OpticStudio® optical design software and performance data was stored for post-processing. **

**Post-processing software developed to support the engineering trade studies uses a mask (or filter) that assigns weighting values to observation location(s) of a given scenario, where many different types of masks can be used. A given mask is applied to lighting visibility performance data to calculate a Figure of Merit (FOM) for each design for the scenario that can be used to rank and identify the designs having superior lighting visibility performance for the scenario. **

**As with masks, different FOM equations can be used. For the engineering trade studies, the FOM = power/1.0e-10 for a single observation location and the FOM = average power/(standard deviation+1.0e-10) for multiple single observer locations, where the 1.0e-10 constant is used to avoid a divide-by-zero error that can occur when the standard deviation is zero. For scenarios involving multiple observers results produced for single observer locations can be combined.**

**The scenarios depicted below were used as part of the engineering trade studies, which compared the performance of a subset of what are essentially an infinite number of possible designs. Included in the engineering trade study were designs using truncated retroreflector arrays produced using an equilateral truncating object (or cutter) for truncation rotations of 0°, 2°, 4°, 6°, 8°, 10°, 30°, and 60°, where a 0° truncation rotation corresponds to a conventional triangular trihedral corner reflector array. Also included were a conventional rectangular trihedral corner reflector (i.e., corner cube) array and designs using truncated retroreflector arrays produced using rectangular cutters having length-to-width ratios of 1.67:1 and 1.5:1 for truncation rotations between 0°, 2°, 4°, 5°, 6°, 8°, 10°, 30°, and 60°, where the 1.67:1 ratio cutter 0°, 30° and 60° degree truncation rotations correspond to a design used in existing signage. Performance data was produced for each array with ten different array rotations between 0° and 90° (at 10° increments), where each array rotation of each array was treated as a separate design for a total of compared 540 array designs. **

**Scenario #1, which is depicted in Figure 1, involves a first car approaching a ‘T’ intersection at night, where the first car’s headlights are a first light source and the location of a first light observer (i.e., the driver of the first car) is perpendicular to signage located at the intersection. **

** The scenario #1 mask used for post-processing is provided in Figure 2.**

**Figure 3 presents the top twenty-one reflective sheeting designs for Scenario #1. Thin colored lines represent prior art designs and wide colored lines represent new designs produced using the TTRA technology.**

**The FOMs of the top three (1.67:1) designs were each 2.88975e+05 and the FOMs of the fourth and fifth (1.67:1) designs were each 2.889699e+05. The FOMs of the next nine (1.5:1) designs were each 2.88958e-+05. The FOMS of the next six (CC) designs were each 2.88954e+05 and the FOM of the last (1.5:1) design shown was 2.88953e+05. As expected, the top seventy FOM scores were for the ten different array rotations of the 0°, 30°, and 60° truncation rotations of the 1.5:1 and 1.67.1 rectangular cutter without metal backing designs and the ten different array rotations of the corner cube without metal backing designs, where the FOMs of those designs were all within 0.15% of each other. The next 120 ranked designs were the ten different array rotations of the 2°, 4°, 6°, 8°, and 10° truncation rotations of the 1.5:1 and 1.67.1 rectangular cutter without metal backing designs, where the 71st and 190th ranked designs had FOMS that were 0.82% and 4.6% less than the FOMs of the top three ranked designs, respectively.**

**Scenario #2a, which is depicted in Figure 4, involves a second car approaching the same intersection at night, where the second car’s headlights are a second light source and the location of a second light observer (i.e., the driver of the second car) varies from being 85° to 65° relative to the signage as the second car approaches the intersection. Parameters used to model movement of car 2 relative to the signage are provided in Table 1.**

**The mask used for the 65° angle observer location of scenario #2a is provided in Figure 5, which weights power highest at locations having a 65 angle relative to the normal of the sign that are to the left and right of the sign within a 1° cone. Similar masks were used for the 70° angle, 75° angle, 80° angle, and 85° angle observer locations.**

**Figure 6 presents the top twenty-one reflective sheeting designs for scenario #2a.**

**Table 2 presents performance data for the four designs ranked highest for scenarios** **#1 and #2a, where example engineering trade comparisons are described below. Generally, various algorithms can be used that automatically compare performance data for some number of designs for multiple scenarios against established performance criteria such that a composite ranking of the best overall designs can be produced.**

**Figure 7 depicts the percentage decrease in FOM #1 and percentage increase in FOM #2a when using one of seven designs other than the 1.67:1, 0° TR, 90° AR design, where the CC, 0° TR, 50° AR design appears to have the best overall visibility performance for Scenarios #1 and #2a. **

**An engineering trade decision for the engineering trade comparisons described above could be based on whether a design meets other established performance criteria such as a minimum power threshold for Car 2. **

**It can be noted that other common scenarios have similar light visibility requirements as scenario 2a. For example, Figure 8 depicts a scenario 2b involving a car approaching a rural railroad crossing and Figure 9 depicts a scenario 2c involving a boat approaching an entrance to a harbor, where the additional power at glancing angles provided by signage with reflective sheeting having the 1.5:1, 8° TR, 90° AR design could be of particular importance. **

**Scenario #3, which is depicted in Figure 10, involves a first person (i.e., a first observer) walking down a sidewalk in front of a store at night, where a first light source above signage on the store front has an 80° angle relative to the normal of the signage.**

**The masks used for scenario #3 were the same masks used for scenario #2a. Figure 11 presents the top twenty-one reflective sheeting designs for scenario #3.**

**Scenario #4, which is depicted in Figure 12, involves a second person (i.e., a second observer) walking down a second sidewalk across the street from the store of Scenario #3.**

**The mask used for scenario #4 was the same mask used for scenario #1. Figure 13 presents the top twenty-one reflective sheeting designs for scenario #4.**

**Table 3 presents performance data for the top four designs for scenarios #3 and #4 and the designs shown in Table 2 relating to scenarios #1 and #2a. **

**The performance data in Table 3 indicates that the top four designs for scenario #3 have very low performance for scenario #4. Overall, the M, Tris, 30 TR, 90 AR design appears to be the best overall design candidate for signage for providing visibility to both person #1 and person #2 in scenarios #3 and #4. The 1.67:1, 30 TR, 0, AR design performed best overall for scenarios #3 and #4 out of those designs that performed best overall for scenarios #1 and #2a.**

**Generally, the engineering trade studies indicated that it can be highly beneficial to tailor a truncated retroreflector array to produce reflective sheeting that best meets lighting visibility requirements of a given situation.**

**Below are pictures of large scale prototypes of four different array designs taken with overhead lighting on and then with overhead lighting off using a camera flash. Prototypes were produced using a resin 3D printer and spray painted with metallic silver paint.**