Multigrid algorithm for least-squares wavefront reconstruction.

Multigrid (MG) methods are presented for fast, efficient, flexible, and robust least-squares wavefront reconstruction in extremely high-resolution conventional adaptive optics, or ExAO. We demonstrate that MG can robustly handle a variety of sensor-actuator geometries, and it can accommodate deformable mirror influence function models that are more realistic than the common piecewise bilinear model. With MG one can also easily incorporate additional penalty, or regularization, terms to damp out the waffle mode in Fried geometry and to damp out instabilities due to actuators near the pupil boundary with poorly sensed influence. We present closed-loop simulation results that suggest that only one or two MG iterations per time step are needed to control an ExAO system.

Fast, robust total variation-based reconstruction of noisy, blurred images.

Tikhonov regularization with a modified total variation regularization functional is used to recover an image from noisy, blurred data. This approach is appropriate for image processing in that it does not place a priori smoothness conditions on the solution image. An efficient algorithm is presented for the discretized problem that combines a fixed point iteration to handle nonlinearity with a new, effective preconditioned conjugate gradient iteration for large linear systems. Reconstructions, convergence results, and a direct comparison with a fast linear solver are presented for a satellite image reconstruction application.

Diffusion and reaction within porous packing media: a phenomenological model.

A phenomenological model has been developed to describe biomass distribution and substrate depletion in porous diatomaceous earth (DE) pellets colonized by Pseudomonas aeruginosa. The essential features of the model are diffusion, attachment and detachment to/from pore walls of the biomass, diffusion of substrate within the pellet, and external mass transfer of both substrate and biomass in the bulk fluid of a packed bed containing the pellets. A bench-scale reactor filled with DE pellets was inoculated with P. aeruginosa and operated in plug flow without recycle using a feed containing glucose as the limiting nutrient. Steady-state effluent glucose concentrations were measured at various residence times, and biomass distribution within the pellet was measured at the lowest residence time. In the model, microorganism/substrate kinetics and mass transfer characteristics were predicted from the literature. Only the attachment and detachment parameters were treated as unknowns, and were determined by fitting biomass distribution data within the pellets to the mathematical model. The rate-limiting step in substrate conversion was determined to be internal mass transfer resistance; external mass transfer resistance and microbial kinetic limitations were found to be nearly negligible. Only the outer 5% of the pellets contributed to substrate conversion.

Space-charge-dominated mass spectrometry ion sources: Modeling and sensitivity.

The factors determining the sensitivity of space-charge-dominated (SCD) unipolar ion sources, such as electrospray (ESP) and corona atmospheric pressure ionization (API) have been studied theoretically. The most important parameters are the ion density and ion drift time in the vicinity of the sampling orifice. These are obtained by solving a system of differential equations, "the space-charge problem." For some simple geometries, analytical solutions are known. For a more realistic "needle-in-can" geometry, a solution to the space-charge problem was obtained using a finite-element method. The results illustrate some general characteristics of SCD ion sources. It is shown that for typical operating conditions the minimum voltage required to overcome the space-charge effect in corona API or ESP ion sources constitutes a dominant or significant fraction of total applied voltage. Further, the electric field and the ion density in the region of the ion-sampling orifice as well as the ion residence time in the source are determined mainly by the space charge. Finally, absolute sensitivities of corona API ion sources were calculated by using a geometry-independent treatment of space charge.