Sum regression decomposition of spectral and angle-resolved Mueller-matrices from biological reflectors

In this report we present studies on beetles of the Scarabaeidae family. The selected beetles show brilliant colors and in addition interesting polarization features. Mueller matrices of such beetles are of large interest to explore for biomimetics and for the understanding of the biological relevance of the observed polarization phenomena. Several species of the Scarabaeidae family have been studied by Hodgkinson, Goldstein and our group to mention some. Ellipticity, degree of polarization and other derived parameters have been reported and Arwin et al. also did optical modeling to determine structural parameters of the scutellum part of the exoskeleton of Cetonia aurata. Mueller matrices are very rich in information about the sample properties and can also be analyzed by addressing depolarization. Cloude showed that a depolarizing Mueller matrix can be represented by a sum of up to four non-depolarizing Mueller matrices weighted by the eigenvalues of the covariance matrix of the Mueller matrix. These eigenvalues are all positive for a physically realizable Mueller matrix and this, so called sum decomposition can be used to filter matrices and obtain a measure of experimental fidelity. The result of the decomposition can also be used to describe a Mueller matrix as a set of basic optical elements having direct physical meaning, such as polarizers and retarders. Pioneering work on decomposition of Mueller-matrix images, including studies of beetles, was performed by Ossikovski et al. We have also previously demonstrated this with Cloude as well as regression decomposition of Mueller matrix spectra and images measured at near-normal incidence on C. aurata. Using Cloude decomposition we found that the experimentally determined Mueller matrix of C. aurata decomposes into a set of a mirror and a circular polarizer. Those results were then the basis for a more stable regression decomposition where the result was confirmed.Funding agencies: Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linkoping University (Faculty Grant SFO Mat LiU) [2009 00971]; Vetenskapsradet (VR) [621-2011-4283]; Knut och Alice Wallenbergs Stiftelse [2004.0233]; Carl TryggersVid tiden för disputation förelåg publikationen endast som manuskript