The Strehl ratio as a phase histogram.

It is shown that the Strehl ratio can always be written as an integral over an apodization-weighted phase histogram. The corresponding mathematical formalism, based on Federer's co-area formula, is enumerated, and a practical numerical method to quickly and accurately calculate apodization-weighted phase histograms is detailed and compared with similar methods. Conditions for expressing the Strehl ratio as a product = are investigated.

Zernike-like Laguerre-Gaussian orthonormal polynomials for optical field reconstruction.

Analytic closed form expressions for orthonormal polynomials exhibiting both rotational and Gaussian symmetries are derived for both circular and elliptical geometries. They exhibit a close correspondence to the Zernike polynomials but are of Gaussian shape and orthogonal over the (x,y) plane. Consequently, they may be expressed in terms of Laguerre polynomials.

Time-ordering in Heisenberg's equation of motion as related to spontaneous radiation.

Despite many years of research into Raman phenomena, the problem of how to include both spontaneous and stimulated Raman scattering into a unified set of partial differential equations persists. The issue is solved by formulating the quantum dynamics in the Heisenberg picture with a rigorous accounting for both time- and normal-ordering of the operators. It is shown how this can be done in a simple, straightforward way.

Raman Characterization of Fungal DHN and DOPA Melanin Biosynthesis Pathways.

Fungal melanins represent a resource for important breakthroughs in industry and medicine, but the characterization of their composition, synthesis, and structure is not well understood. Raman spectroscopy is a powerful tool for the elucidation of molecular composition and structure. In this work, we characterize the Raman spectra of wild-type and and their melanin biosynthetic mutants and provide a rough "map" of the DHN () and DOPA () melanin biosynthetic pathways.

Identification of toxic mold species through Raman spectroscopy of fungal conidia.

We use a 785 nm shifted excitation Raman difference (SERDS) technique to measure the Raman spectra of the conidia of 10 mold species of especial toxicological, medical, and industrial importance, including Stachybotrys chartarum, Penicillium chrysogenum, Aspergillus fumigatus, Aspergillus flavus, Aspergillus oryzae, Aspergillus niger, and others. We find that both the pure Raman and fluorescence signals support the hypothesis that for an excitation wavelength of 785 nm the Raman signal originates from the melanin pigments bound within the cell wall of the conidium. In addition, the major features of the pure Raman spectra group into profiles that we hypothesize may be due to differences in the complex melanin biosynthesis pathways.