July 2015
Spotlight Summary by Brad Deutsch
Lycurgus Cup: inverse problem using photographs for characterization of matter
The Lycurgus Cup was made in 4th-century Rome, and has dichroic properties: its color depends on the direction of illumination. Lit in reflection, the glass looks green, while in transmission it ranges from purple to brilliant red-orange. That this effect comes from metallic nanoparticles embedded in the glass has been known for a long time, and several studies have tried to estimate its exact chemical composition. In this manuscript, the author makes a similar estimate using nothing more than a photograph of the cup. This is a challenging task, since it requires detailed knowledge about the underlying physics and the measurement system (camera), as well as a strategy for dealing with computational expense. Even more challenging is the fact that the problem is ill-posed, meaning that it has more than one solution. Different chemical compositions can result in similar or identical photographs.
Barchiesi approches the problem knowing how the camera responds to each wavelength of light to generate recorded colors. Coupled with an understanding of scattering from small particles of gold, silver, and copper, she can predict what colors would appear in photographs of glass with a given chemical composition and illumination angle. By taking a guess at the composition and comparing the predicted result with the colors in the photograph, the guess can be refined using an efficient algorithm called Particle Swarm Optimization, which mimics the behavior of a swarm of bees in search of pollen to converge on an answer quickly. A best guess at the chemical composition is made when a minimum in the cost function is found.
Still, there is a large amount of uncertainty. Sometimes the optimization procedure predicts non-physical results, like a negative density of silver particles. Barchiesi takes this as evidence that the starting assumptions were wrong. This happens, for example, when the glass is constrained to include no copper nanoparticles. The compositional estimate can be further refined by including results from previous studies to help narrow down the search. In analogy, suppose we were looking for a particular fish somewhere on Earth. We might spend a lot of time combing the deserts if we ignored previous studies that suggest that fish are aquatic animals. Similarly, previous chemical experiments have suggested that the index of refraction of the Cup's glass is around two, and that there is about twice as much silver as gold embedded in it. This information helps the optimization converge quickly and with a higher degree of confidence.
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Barchiesi approches the problem knowing how the camera responds to each wavelength of light to generate recorded colors. Coupled with an understanding of scattering from small particles of gold, silver, and copper, she can predict what colors would appear in photographs of glass with a given chemical composition and illumination angle. By taking a guess at the composition and comparing the predicted result with the colors in the photograph, the guess can be refined using an efficient algorithm called Particle Swarm Optimization, which mimics the behavior of a swarm of bees in search of pollen to converge on an answer quickly. A best guess at the chemical composition is made when a minimum in the cost function is found.
Still, there is a large amount of uncertainty. Sometimes the optimization procedure predicts non-physical results, like a negative density of silver particles. Barchiesi takes this as evidence that the starting assumptions were wrong. This happens, for example, when the glass is constrained to include no copper nanoparticles. The compositional estimate can be further refined by including results from previous studies to help narrow down the search. In analogy, suppose we were looking for a particular fish somewhere on Earth. We might spend a lot of time combing the deserts if we ignored previous studies that suggest that fish are aquatic animals. Similarly, previous chemical experiments have suggested that the index of refraction of the Cup's glass is around two, and that there is about twice as much silver as gold embedded in it. This information helps the optimization converge quickly and with a higher degree of confidence.
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Article Information
Lycurgus Cup: inverse problem using photographs for characterization of matter
Dominique Barchiesi
J. Opt. Soc. Am. A 32(8) 1544-1555 (2015) View: HTML | PDF