Analysis of optical systems with extended depth of field using the Wigner distribution function

We describe the use of a Wigner distribution function approach for exploring the problem of extending the depth of field in a hybrid imaging system. The Wigner distribution function, in connection with the phase-space curve that formulates a joint phase-space description of an optical field, is employed as a tool to display and characterize the evolving behavior of the amplitude point spread function as a wave propagating along the optical axis. It provides a comprehensive exhibition of the characteristics for the hybrid imaging system in extending the depth of field from both wave optics and geometrical optics. We use it to analyze several well-known optical designs in extending the depth of field from a new viewpoint. The relationships between this approach and the earlier ambiguity function approach are also briefly investigated. (c) 2006 Optical Society of America.

I. Efforts toward the synthesis of aliphatic iodonium salts. II. Flourine-19 nuclear magnetic resonance spectroscopy of cyclic and bicyclic systems

The synthesis of iodonium salts of the general formula [C₆H₅IR]⁺X^-, where R is an alkyl group and x- is a stabilizing anion, was attempted. For the choice of R three groups were selected, whose derivatives are known to be sluggish in S_N1 and S_N2 substitutions: cyclopropyl, 7, 7 -dimethyl-1-norbornyl, and 9 -triptycyl. The synthetic routes followed along classical lines which have been exploited in recent years by Beringer and students. Ultimately, the object of the present study was to study the reactions of the above salts with nucleophiles. In none of the three cases, however, was it possible to isolate a stable salt. A thermodynamic argument suggests that this must be due to kinetic instability rather than thermodynamic instability. Only iodocyclopropane and 1-iodoapocamphane formed isolable iododichlorides.

Several methylated 2, 2-difluoronorbornanes were prepared with the intent of correlating fluorine -19 chemical shifts with geometric features in a rigid system. The effect of a methyl group on the shielding of a β -fluorine is dependent upon the dihedral angle; the maximum effect (an upfield shift of the resonance) occurs at 0° and 180°, whereas almost no effect is felt at a dihedral angle of 120°. The effect of a methyl group on a γ -fluorine is to strongly shift the resonance downfield when fluorine and methyl group are in a 1, 3 - diaxial-like relationship. Molecular orbital calculations of fluorine shielding in a variety of molecules were carried out using the formalism developed by Pople; the results are, at best, in modest agreement with experiment.

Localization of sources of human evoked responses

The evoked response, a signal present in the electro-encephalogram when specific sense modalities are stimulated with brief sensory inputs, has not yet revealed as much about brain function as it apparently promised when first recorded in the late 1940's. One of the problems has been to record the responses at a large number of points on the surface of the head; thus in order to achieve greater spatial resolution than previously attained, a 50-channel recording system was designed to monitor experiments with human visually evoked responses.

Conventional voltage versus time plots of the responses were found inadequate as a means of making qualitative studies of such a large data space. This problem was solved by creating a graphical display of the responses in the form of equipotential maps of the activity at successive instants during the complete response. In order to ascertain the necessary complexity of any models of the responses, factor analytic procedures were used to show that models characterized by only five or six independent parameters could adequately represent the variability in all recording channels.

One type of equivalent source for the responses which meets these specifications is the electrostatic dipole. Two different dipole models were studied: the dipole in a homogeneous sphere and the dipole in a sphere comprised of two spherical shells (of different conductivities) concentric with and enclosing a homogeneous sphere of a third conductivity. These models were used to determine nonlinear least squares fits of dipole parameters to a given potential distribution on the surface of a spherical approximation to the head. Numerous tests of the procedures were conducted with problems having known solutions. After these theoretical studies demonstrated the applicability of the technique, the models were used to determine inverse solutions for the evoked response potentials at various times throughout the responses. It was found that reliable estimates of the location and strength of cortical activity were obtained, and that the two models differed only slightly in their inverse solutions. These techniques enabled information flow in the brain, as indicated by locations and strengths of active sites, to be followed throughout the evoked response.

Dynamic response of hysteretic systems with application to a system containing limited slip

A general class of single degree of freedom systems possessing rate-independent hysteresis is defined. The hysteretic behavior in a system belonging to this class is depicted as a sequence of single-valued functions; at any given time, the current function is determined by some set of mathematical rules concerning the entire previous response of the system. Existence and uniqueness of solutions are established and boundedness of solutions is examined.

An asymptotic solution procedure is used to derive an approximation to the response of viscously damped systems with a small hysteretic nonlinearity and trigonometric excitation. Two properties of the hysteresis loops associated with any given system completely determine this approximation to the response: the area enclosed by each loop, and the average of the ascending and descending branches of each loop.

The approximation, supplemented by numerical calculations, is applied to investigate the steady-state response of a system with limited slip. Such features as disconnected response curves and jumps in response exist for a certain range of system parameters for any finite amount of slip.

To further understand the response of this system, solutions of the initial-value problem are examined. The boundedness of solutions is investigated first. Then the relationship between initial conditions and resulting steady-state solution is examined when multiple steady-state solutions exist. Using the approximate analysis and numerical calculations, it is found that significant regions of initial conditions in the initial condition plane lead to the different asymptotically stable steady-state solutions.

The ecological impact of different mechanisms of chronic sub-lethal toxicity on feeding and respiratory physiology

Sub-lethal toxicity tests, such as the scope-for-growth test, reveal simple relationships between measures of contaminant concentration and effect on respiratory and feeding physiology. Simple models are presented to investigate the potential impact of different mechanisms of chronic sub-lethal toxicity on these physiological processes. Since environmental quality is variable, even in unimpacted environments, toxicants may have differentially greater impacts in poor compared to higher quality environments. The models illustrate the implications of different degrees and mechanisms of toxicity in response to variability in the quality of the feeding environment, and variability in standard metabolic rate. The models suggest that the relationships between measured degrees of toxic stress, and the maintenance ration required to maintain zero scope-for-growth, may be highly nonlinear. In addition it may be possible to define critical levels of sub-lethal toxic effect above which no environment is of sufficient quality to permit prolonged survival.

Molecular biomarkers and toxic consequences of impact by organic pollution in aquatic organisms

Organic contaminants are readily bioaccumulated by aquatic organisms. Exposure to and toxic effects of contaminants can be measured in terms of the biochemical responses of the organisms (i.e. molecular biomarkers). The hepatic biotransformation enzyme cytochrome P4501A (CYP1A) in vertebrates is specifically induced by organic contaminants such as aromatic hydrocarbons, PCBs and dioxins, and is involved in chemical carcinogenesis via catalysis of the covalent binding of organic contaminants to DNA (DNA-adducts). Hepatic CYP1A induction has been used extensively and successfully as a biomarker of organic contaminant exposure in fish. Fewer but equally encouraging studies in fish have used hepatic bulky, hydrophobic DNA-adducts as biomarkers of organic contaminant damage. Much less is known of the situation in marine invertebrates, but a CYPlA-like enzyme with limited inducibility and some potential for biomarker application is indicated. Stimulation of reactive oxygen species (ROS) production is another potential mechanism of organic contaminant-mediated DNA and other damage in aquatic organisms. A combination of antioxidant (enzymes, scavengers) and pro-oxidant (oxidised DNA bases, lipid peroxidation) measurements may have potential as a biomarker of organic contaminant exposure (particularly those chemicals which do not induce CYP1A) and/or oxidative stress, but more studies are required. Both CYP1A- and ROS-mediated toxicity are indicated to result in higher order deleterious effects, including cancer and other aspects of animal fitness.

Detection of cryptosporidium oocysts in water and environmental concentrates

Whilst current methods for the isolation and enumeration of Cryptosporidium spp. oocysts in water have provided some insight into their occurrence and significance, they are regarded as being inefficient, variable and time-consuming, with much of the interpretation being left to the expertise of the analyst. Two expectations of novel developments are to reduce the variability and subjectivity associated with the isolation and identification of oocysts. Flocculation, immunomagnetisable and flow cytometric techniques, for concentrating oocysts from water samples, should prove more reliable than current methods, whilst the development of more avid and specific monoclonal antibodies in conjunction with the use of nuclear fluorochromes will aid identification. Further insight into the viability, taxonomy, species identification, infectivity and virulence of the parasite should be forthcoming through the use of techniques such as the polymerase chain reaction, in situ hybridisation and non-uniform alternating current electrical fields. Such information is necessary in order to enable microbiologists, epidemiologists, engineers, utility operators and regulators to assess the safety of a water supply, with respect to Cryptosporidium contamination, more effectively.

Hypoxic and low pH water in the nearshore marine environments of Monterey Bay, California: characterizing a decade of oxygen and pH, and drivers of variability.

A decade-long time series recorded in southern Monterey Bay, California demonstrates that the shallow, near-shore environment (17 m depth) is regularly inundated with pulses of cold, hypoxic and low pH water. During these episodes, oxygen can drop to biologically threatening levels, and pH levels were lower than expected. Weekly water chemistry monitoring revealed that the saturation state of aragonite (the more soluble form of calcium carbonate) was often below saturation and had a moderate positive relationship with pH, however, analytical and human error could be high. Pulses of hypoxia and low pH water with the greatest intensity arise at the onset of the spring upwelling season, and fluctuations are strongly semidurnal (tidal) and diurnal. Arrival of cold, hypoxic water on the inner shelf typically occurs 3 days after the arrival of a strong upwelling event and appears to be driven by upwelling modulated by internal tidal fluctuations. I found no relationship between the timing of low-oxygen events and the diel solar cycle nor with terrestrial nutrient input. These observations are consistent with advection of hypoxic water from the deep, offshore environment where water masses experience a general decline of temperature, oxygen and pH with depth, and inconsistent with biochemical forcing. Comparisons with concurrent temperature and oxygen time series taken ~20 km away at the head of the Monterey Canyon show similar patterns but even more intense hypoxic events due to stronger semidiurnal forcing there. Analysis of the durations of exposure to low oxygen levels establishes a framework for assessing the ecological relevance of these events. Increasing oceanic hypoxia and acidification of both surface and deep waters may increase the number, intensity, duration and spatial extent of future intrusions along the Pacific coast. Evaluation of the resiliency of nearshore ecosystems such as kelp forests, rocky reefs and sandy habitats, will require consideration of these events.

Species compositions of elasmobranchs caught by three different commercial fishing methods off southwestern Australia, and biological data for four abundant bycatch species

Commercial catches taken in southwestern Australian waters by trawl fisheries targeting prawns and scallops and from gillnet and longline fisheries targeting sharks were sampled at different times of the year between 2002 and 2008. This sampling yielded 33 elasmobranch species representing 17 families. Multivariate statistics elucidated the ways in which the species compositions of elasmobranchs differed among fishing methods and provided benchmark data for detecting changes in the elasmobranch fauna in the future. Virtually all elasmobranchs caught by trawling, which consisted predominantly of rays, were discarded as bycatch, as were approximately a quarter of the elasmobranchs caught by both gillnetting and longlining. The maximum lengths and the lengths at maturity of four abundant bycatch species, Heterodontus portusjacksoni, Aptychotrema vincentiana, Squatina australis, and Myliobatis australis, were greater for females than males. The L50 determined for the males of these species at maturity by using full clasper calcification as the criterion of maturity did not differ significantly from the corresponding L50 derived by using gonadal data as the criterion for maturity. The proportions of the individuals of these species with lengths less than those at which 50% reach maturity were far greater in trawl samples than in gillnet and longline samples. This result was due to differences in gear selectivity and to trawling being undertaken in shallow inshore waters that act as nursery areas for these species. Sound quantitative data on the species compositions of elasmobranchs caught by commercial fisheries and the biological characteristics of the main elasmobranch bycatch species are crucial for developing strategies for conserving these important species and thus the marine ecosystems of which they are part.

Use of stereo camera systems for assessment of rockfish abundance in untrawlable areas and for recording pollock behavior during midwater trawls

We describe the application of two types of stereo camera systems in fisheries research, including the design, calibration, analysis techniques, and precision of the data obtained with these systems. The first is a stereo video system deployed by using a quick-responding winch with a live feed to provide species- and size- composition data adequate to produce acoustically based biomass estimates of rockfish. This system was tested on the eastern Bering Sea slope where rockfish were measured. Rockfish sizes were similar to those sampled with a bottom trawl and the relative error in multiple measurements of the same rockfish in multiple still-frame images was small. Measurement errors of up to 5.5% were found on a calibration target of known size. The second system consisted of a pair of still-image digital cameras mounted inside a midwater trawl. Processing of the stereo images allowed fish length, fish orientation in relation to the camera platform, and relative distance of the fish to the trawl netting to be determined. The video system was useful for surveying fish in Alaska, but it could also be used broadly in other situations where it is difficult to obtain species-composition or size-composition information. Likewise, the still-image system could be used for fisheries research to obtain data on size, position, and orientation of fish.

On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

Simulation of Tail Weight Distributions in Biological Year 1986–2006 Landings of Brown Shrimp, Farfantepenaeus aztecus, from the Northern Gulf of Mexico Fishery

Size distribution within re- ported landings is an important aspect of northern Gulf of Mexico penaeid shrimp stock assessments. It reflects shrimp population characteristics such as numerical abundance of various sizes, age structure, and vital rates (e.g. recruitment, growth, and mortality), as well as effects of fishing, fishing power, fishing practices, sampling, size-grading, etc. The usual measure of shrimp size in archived landings data is count (C) the number of shrimp tails (abdomen or edible portion) per pound (0.4536 kg). Shrimp are marketed and landings reported in pounds within tail count categories. Statistically, these count categories are count class intervals or bins with upper and lower limits expressed in C. Count categories vary in width, overlap, and frequency of occurrence within the landings. The upper and lower limits of most count class intervals can be transformed to lower and upper limits (respectively) of class intervals expressed in pounds per shrimp tail, w, the reciprocal of C (i.e. w = 1/C). Age based stock assessments have relied on various algorithms to estimate numbers of shrimp from pounds landed within count categories. These algorithms required un- derlying explicit or implicit assumptions about the distribution of C or w. However, no attempts were made to assess the actual distribution of C or w. Therefore, validity of the algorithms and assumptions could not be determined. When different algorithms were applied to landings within the same size categories, they produced different estimates of numbers of shrimp. This paper demonstrates a method of simulating the distribution of w in reported biological year landings of shrimp. We used, as examples, landings of brown shrimp, Farfantepenaeus aztecus, from the northern Gulf of Mexico fishery in biological years 1986–2006. Brown shrimp biological year, Ti, is defined as beginning on 1 May of the same calendar year as Ti and ending on 30 April of the next calendar year, where subscript i is the place marker for biological year. Biological year landings encompass most if not all of the brown shrimp life cycle and life span. Simulated distributions of w reflect all factors influencing sizes of brown shrimp in the landings within a given biological year. Our method does not require a priori assumptions about the parent distributions of w or C, and it takes into account the variability in width, overlap, and frequency of occurrence of count categories within the landings. Simulated biological year distributions of w can be transformed to equivalent distributions of C. Our method may be useful in future testing of previously applied algorithms and development of new estimators based on statistical estimation theory and the underlying distribution of w or C. We also examine some applications of biological year distributions of w, and additional variables derived from them.