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.

Molecular origin of the Raman signal from Aspergillus nidulans conidia and observation of fluorescence vibrational structure at room temperature.

Successful approaches to identification and/or biological characterization of fungal specimens through Raman spectroscopy may require the determination of the molecular origin of the Raman response as well as its separation from the background fluorescence. The presence of fluorescence can interfere with Raman detection and is virtually impossible to avoid. Fluorescence leads to a multiplicity of problems: one is noise, while another is "fake" spectral structure that can easily be confused for spontaneous Raman peaks.

Femtosecond Laser Filaments for Use in Sub-Diffraction-Limited Imaging and Remote Sensing.

Probing remote matter with laser light is a ubiquitous technique used in circumstances as diverse as laser-induced breakdown spectroscopy and barcode scanners. In classical optics, the intensity that can be brought to bear on a remote target is limited by the spot size of the laser at the distance of the target. This spot size has a lower bound determined by the diffraction limit of classical optics.

CARS spectroscopy of Aspergillus nidulans spores.

Coherent Anti-Stokes Raman Spectroscopy (CARS) is performed on single spores (conidia) of the fungus Aspergillus nidulans in order to establish a baseline measurement for fungal spores. Chemical maps of single spores are generated and spectral differentiation between the cell wall and the cytoplasm is achieved. Principal Component Analysis of the measured spectra is then completed as a means to quantify spore heterogeneity.

Remote sub-diffraction imaging with femtosecond laser filaments.

Achieving super-resolution has become a scientific imperative for remote imaging of objects and scenes needing increased detail and has motivated the development of various laser-based techniques. We demonstrate a scheme which achieves subdiffraction imaging of remote objects by using femtosecond laser filaments. The use of laser filaments for imaging is destined to have applications in many environments.

Shaper-assisted phase optimization of a broad "holey" spectrum.

We develop a technique for optimizing the phase of broad spectrally-separated frequency sidebands-a "holey" spectrum. We use a source of multiple-order coherent Raman sidebands, obtained by crossing femtosecond pump and Stokes beams in synthetic single-crystal diamond. We combine the sidebands into a single beam and show the phase coherence among the sidebands by investigating the interference between them in groups of three while varying one sideband phase by an acousto-optics pulse shaper.

Equivalent path lengths in an integrating cavity: comment.

The equivalent absorption path length in an integrating cavity is examined. In an otherwise excellent paper, Tranchart et al. [Appl.

Propagation of ultrashort laser pulses in water: linear absorption and onset of nonlinear spectral transformation.

We study propagation of short laser pulses through water and use a spectral hole filling technique to essentially perform a sensitive balanced comparison of absorption coefficients for pulses of different duration. This study is motivated by an alleged violation of the Bouguer-Lambert-Beer law at low light intensities, where the pulse propagation is expected to be linear, and by a possible observation of femtosecond optical precursors in water. We find that at low intensities, absorption of laser light is determined solely by its spectrum and does not directly depend on the pulse duration, in agreement with our earlier work and in contradiction to some work of others.

Propagation of femtosecond laser pulses through water in the linear absorption regime.

We investigate the controversy regarding violations of the Bouguer-Lambert-Beer (BLB) law for ultrashort laser pulses propagating through water. By working at sufficiently low incident laser intensities, we make sure that any nonlinear component in the response of the medium is negligible. We measure the transmitted power and spectrum as functions of water cell length in an effort to confirm or disprove alleged deviations from the BLB law.