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Featured Application The analysis of the transmission of Mueller matrices facilitates studies of optical activity in samples that also exhibit linear anisotropy and depolarization and may have a multilayered structure. Such studies are important for the development of applications in chiroptics. Optical chirality, in terms of circular birefringence and circular dichroism, is described by its electromagnetic and magnetoelectric material tensors, and the corresponding optical activity contributes to the Mueller matrix. Here, spectroscopic ellipsometry in the spectral range 210-1690 nm is used to address chiral phenomena by measuring Mueller matrices in transmission. Three approaches to determine chirality parameters are discussed. In the first approach, applicable in the absence of linear polarization effects, circular birefringence and circular dichroism are evaluated directly from elements of a Mueller matrix. In the second method, differential decomposition is employed, which allows for the unique separation of chirality parameters from linear anisotropic parameters as well as from depolarization provided that the sample is homogeneous along the optical path. Finally, electromagnetic modeling using the Tellegen constitutive relations is presented. The last method also allows structural effects to be included. The three methods to quantify optical chirality are demonstrated for selected materials, including sugar solutions, alpha-quartz, liquid crystals, beetle cuticle, and films of cellulose nanocrystals. ; Funding Agencies|Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linkoping University [SFO-Mat-LiU 2009-00971]