SigOpt hosted our first user conference, the SigOpt AI & HPC Summit, on Tuesday, November 16, 2021. It was virtual and free to attend, and you can access content from the event at sigopt.com/summit. For more than any other reason, we were excited to host this Summit to showcase the great work of some of SigOpt’s customers. Today, we share some lessons from Paul Leu at the University of Pittsburgh on how to improve the design process, learn more from exploration, and optimize multimetric performance for glass surface reflections. We will discuss Paul’s experience collaborating with the SigOpt team to accelerate the development of new fabrication strategies for glass to improve its performance in key properties, such as reducing glare, haze, and reflectance.

Background

One of the most serious problems facing modern consumer electronic devices such as smartphones and tablets is that of glare and reflections from the surface of the device display. Consumers usually enjoy polished screens with a glossy surface for a sharp, clear image. However, that glossy surface can create a mirror reflection of your own face under the right lighting conditions. These reflections from the sun or bright lights can be distracting, uncomfortable, and even make the glass display completely unreadable.

Research Scientists have been trying to minimize reflections and glare ever since the CRT was first introduced. One of the earliest solutions was to simply rough up the surface of the glass. This allowed the glass to minimize mirror reflection, and the light reflected by the screen surface became a hazy glow.

Recently, Paul Leu, Associate Professor in the Laboratory for Advanced Materials (LAMP) at the University of Pittsburgh, explored ways to minimize light reflection from the top glass sheet across a broad range of wavelengths and a large variety of reflection angles. They combined real-world experiments and numerical simulations to study single-layer films, nanowire arrays, and nanocone arrays to meet the antireflection (AR) needs of mobile phones, tablets, and many consumer devices. 

Experiment

In collaboration with SigOpt, the University of Pittsburgh looked at three different types of glass display structures. (i) The first glass structure they looked at is a thin film with a single index of refraction. (ii) The second structure they looked at are vertical arrays of nanowires, which are tiny cylinders that are also made out of glass. The nanowires are defined by the diameter and the height, in addition to the spacing between the nanowires and the square array.

(iii) The third structure they looked at are nano cones, which are cone frustums. Mathematically, they’re not just a point at the tip — there is a diameter at the top. So this is just an array of nano cones and they are arranged in a square lattice. The nano cones are defined by height, top diameter, bottom diameter, and the pitch (spacing between the nano cones).

For each of these three structures, they designed two objective functions that are trying to minimize reflection with Bayesian Multiobjective Optimization. The first objective function is the solar reflection at zero degrees incidence, and the second objective function is the solar reflection at 65 degrees incidence. These two objective functions aim to minimize reflection across a wide variety of wavelengths and different incidence angles. To do this, Paul’s team worked with SigOpt in using Bayesian Optimization and Multimetric Optimization to efficiently search for the pareto optimal set of these three structures based on these two objective functions. Together they reformulated the original optimization problem into a new form so that they could minimize reflection and explore different parts of the pareto efficient frontier:

Results

Intelligent experimentation with Multimetric Optimization resulted in 500 simulations of nanowires and nano cones. The top left chart shows the thin film varying the thickness, the top right chart shows results for the nanowires, the bottom left chart shows the results for the nano cones, and the bottom right chart shows composite results of the three structures plotted together. You can see the pareto efficient frontier is plotted in black. The thin film is in blue, the nanowire array is in green, and the nano cones are in red.

You can see in the composite results that the thin film (blue) and the nanowire array (green) are fairly comparable. However, bare glass (purple) had the worst results with a much higher reflection than the other structures. Finally, the nano cones (red) had the best results with the lowest 0 degree solar reflection and 65 degree solar reflection.

Conclusion

To learn more about how Multimetric Optimization improved the design process of glass materials, I encourage you to watch the talk. You can also read the full research paper. To see if SigOpt can drive similar results for you and your team, sign up to use it for free.