Phase control and measurement in digital microscopy

The ongoing merger of the digital and optical components of the modern microscope is creating opportunities for new measurement techniques, along with new challenges for optical modelling. This thesis investigates several such opportunities and challenges which are particularly relevant to biomedical imaging. Fourier optics is used throughout the thesis as the underlying conceptual model, with a particular emphasis on three--dimensional Fourier optics. A new challenge for optical modelling provided by digital microscopy is the relaxation of traditional symmetry constraints on optical design. An extension of optical transfer function theory to deal with arbitrary lens pupil functions is presented in this thesis. This is used to chart the 3D vectorial structure of the spatial frequency spectrum of the intensity in the focal region of a high aperture lens when illuminated by linearly polarised beam. Wavefront coding has been used successfully in paraxial imaging systems to extend the depth of field. This is achieved by controlling the pupil phase with a cubic phase mask, and thereby balancing optical behaviour with digital processing. In this thesis I present a high aperture vectorial model for focusing with a cubic phase mask, and compare it with results calculated using the paraxial approximation. The effect of a refractive index change is also explored. High aperture measurements of the point spread function are reported, along with experimental confirmation of high aperture extended depth of field imaging of a biological specimen. Differential interference contrast is a popular method for imaging phase changes in otherwise transparent biological specimens. In this thesis I report on a new isotropic algorithm for retrieving the phase from differential interference contrast images of the phase gradient, using phase shifting, two directions of shear, and non--iterative Fourier phase integration incorporating a modified spiral phase transform. This method does not assume that the specimen has a constant amplitude. A simulation is presented which demonstrates good agreement between the retrieved phase and the phase of the simulated object, with excellent immunity to imaging noise

How validity travelled to economic experimenting

Validity was first given a more specifically scientific meaning by psychologists in the early twentieth century in the contexts of psychological tests. Following the classification of different validity-types in the American Psychological Association's Technical Recommendations (1954), validity travelled from psychological tests to psychological experiments through the work of Donald Campbell. Thus the idea was introduced that also experiments could be more or less valid. In addition, a distinction was made between the internal and the external validity of an experiment. Of the two domains in which validity was employed in psychology, only the internal and external validity of experimental methodology travelled to economics. The initial implementation of validity in economic experimentation was reluctant, and focused upon showing how external validity in particular was not problematic in economic experiments. However, the gradual adoption of validity by economists working with experiments eventually led to the clear, analytical definition of internal validity by Francesco Guala, a definition that was subsequently taken over by other economists. In its travels from psychological tests to psychological experiments to economic experiments the concept of validity generally retained its meaning as the accuracy of a scientific procedure. At the same time, however, it was put to use in dissimilar ways and elicited different discussions in the scientific realms in which it was applied.validity, tests, experiments,

Kahneman and Tversky and the Origin of Behavioral Economics

Kahneman and Tversky and their behavioral economics stand in a long tradition of applying mathematics to human behavior. In the seventeenth century, attempts to describe rational behavior in mathematical terms run into problems with the formulation of the St. Petersburg paradox. Bernoulli’s celebrated solution to use utility instead of money marks the beginning of expected utility theory (EUT). Bernoulli’s work is taken up by psychophysics which in turn plays an important role in the making of modern economics. In the 1940s von Neumann and Morgenstern throw away Bernoulli and psychophysics, and redefine utility in monetary terms. Relying on this utility definition and on von Neumann and Morgenstern’s axiomatic constraints of the individual’s preferences, Friedman and Savage attempt to continue Bernoulli’s research. After this fails economics and psychology go separate ways. Economics employs Friedman’s positive-normative distinction; psychology uses Savage’s normative-descriptive distinction. Using psychophysics Kahneman and Tversky broaden the normative-descriptive distinction and argue with increasing strength for a descriptive theory of rational behavior. A prominent part of contemporary behavioral economics is founded upon the export of Tversky and Kahneman’s program to economics. Within this research, two different branches of research can be observed. One branch continues Kahneman and Tversky’s search for a descriptive theory of rational behavior and extends the normative-descriptive distinction with a prescriptive part. A second branch takes Tversky and Kahneman’s work as a falsification of positive economics. It argues that economics should take account of the psychological critique but stick to rigorous mathematical model building and Friedman’s positive-normative distinction.Kahneman and Tversky; behavioral economics; expected utility theory; normative economics

Who are the Behavioral Economists and what do they say?

The most important financial source for behavioral economics is the Russell Sage Foundation (RSF). The most prominent behavioral economists among the RSF’s twenty-six member Behavioral Economics Roundtable (BER) are Kahneman, Tversky, Thaler, Camerer, Loewenstein, Rabin, and Laibson. The theoretical core of behavioral economics made up of the work of these seven researchers is positioned in opposition to Adam Smith/Hayek type of economics, as exemplified by experimental economists Vernon Smith and Plott; and what is referred to as ‘mainstream’ or ‘traditional’ economics, meaning the neoclassical economics that roughly builds on Samuelson. On the basis of an overview of the work of these seven behavioral economists, a theoretical division can be observed within behavioral economics. The first branch considers human decision-making to be a problem of exogenous uncertainty, which can be analyzed with decision theory. It employs traditional economics as a nor! mative benchmark and favors a normative-descriptive(-prescriptive) distinction for economics. The second branch considers human decision-making to be a problem of strategic interaction, in which the uncertainty is endogenous. Its main tool is game theory. It rejects traditional economics both positively and normatively.Behavioral economics; Russell Sage Foundation; experimental economics; Kahneman; Tversky; Thaler; Laibson; Loewenstein; Rabin; Camerer

Gigerenzer the Decided: A Tale of Difficult Distinctions

This paper provides an overview of the work of Gigerenzer, thereby focusing on his criticisms of the Heuristics and Biases theory of Kahneman and Tversky. It is proposed that Gigerenzer's work can be both thematically and chronologically organized as: historical research on statistics => criticism on Kahneman and Tversky => the bounded rationality research program. That is, Gigerenzer' attacks on the Heuristics and Biases program derive from his historical work on Brunswik and Thurstone. In turn, these attacks functioned as the driving force behind the development of the bounded rationality research program. Behind the debate, it is argued, lies a fundamental different idea of how human decision-making is to be understood and investigated.Gigerenzer; Kahneman and Tversky; Cognitive Psychology; Bounded rationality; decision-making

What Simon says

This paper provides an overview of the work of Herbert Simon and his ideas about rational decision making. By his own standards, Simon is an economist who works in the tradition of Adam Smith and Alfred Marshall. The central theme in Simon’s research is how human beings organize themselves in different structures of distributed decision making in order to achieve a degree of rationality that is higher than which can be attained by the individual. In this realm his main preoccupation are hierarchic organizations such as the business firm and the computer. Simon sharply contrasts his views with the EUT, the dominant view on rational decision making in economics and other social sciences.Herbert Simon; decision making; Expected Utility Theory; hierarchic organizations

The Origin of Prospect Theory, or Testing the Intuitive Statistician

The origin of prospect theory is the desire to test the intuitive statistician in the real world. The development of this theory by the cognitive psychologists Kahneman and Tversky can be traced to the formers work in cognitive psychophysics, in which deviations from average behavior are termed (statistical) errors; and the latters work on decision theory, with its normative vs. descriptive framework. The combination of these two types of probabilistic psychology culminated in a new descriptive theory of human decision making in the real world, coined Heuristics and Biases. The 1979 Econometrica article applies this new descriptive theory to economists EUT. It equates the intuitive statistician with the rational economic man and shows how it descriptively fails.Kahneman and Tversky; Prospect Theory; Intuitive Statistician; Heuristics and Biases