We developed an optical probe for cross-polarized reflected light measurements and investigated optical signals associated with electrophysiological activation in isolated lobster nerves. The cross-polarized baseline light intensity (structural signal) and the amplitude of the transient response to stimulation (functional signal) measured in reflected mode were dependent on the orientation of the nerve axis relative to the polarization plane of incident light. The maximum structural signal and functional response amplitude were observed at 45 degrees , and the ratio of functional to structural signals was approximately constant across orientations. Functional responses were measured in single trials in both transmitted and reflected geometries and responses had similar waveforms. Both structural and functional signals were an order of magnitude smaller in reflected than in transmitted light measurements, but functional responses had similar signal/noise ratios. We propose a theoretical model based on geometrical optics that is consistent with experimental results. In the model, the cross-polarized structural signal results from light reflection from axonal fibers and the transient functional response arises from axonal swelling associated with neural activation. Polarization-sensitive reflected light measurements could greatly enhance in vivo imaging of neural activation since cross-polarized responses are much larger than scattering signals now employed for dynamic functional neuroimaging.
We provide a rapid and accurate method for calculating the prolate and oblate spheroidal wave functions (PSWFs and OSWFs), S mn (c, η), and their eigenvalues, λ mn , for arbitrary complex size parameter c in the asymptotic regime of large |c|, m and n fixed. The ability to calculate these SWFs for large and complex size parameters is important for many applications in mathematics, engineering, and physics. For arbitrary arg(c), the PSWFs and their eigenvalues are accurately expressed by established prolate-type or oblate-type asymptotic expansions. However, determining the proper expansion type is dependent upon finding spheroidal branch points, c mn •;r , in the complex c-plane where the PSWF alternates expansion type due to analytic continuation. We implement a numerical search method for tabulating these branch points as a function of spheroidal parameters m, n, and arg(c). The resulting table allows rapid determination of the appropriate asymptotic expansion type of the SWFs. Normalizations, which are dependent on c, are derived for both the prolateand oblate-type asymptotic expansions and for both (n − m) even and odd. The ordering for these expansions is different from the original ordering of the SWFs and is dictated by the location of c mn •;r . We document this ordering for the specific case of arg(c) = π/4, which occurs for the diffusion equation in spheroidal coordinates. Some representative values of λ mn and S mn (c, η) for large, complex c are also given.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.