Publisher Summary This chapter reviews conventional resolution definitions and criteria. An alternative definition and corresponding criterion have been proposed and explained in the chapter. Two overlapping component functions are said to be resolved from a given set of error disturbed observations if the estimates of their location parameters are distinct. The component functions are unresolved if the estimates of the location parameters exactly coincide. Although exactly coinciding solutions for parameters may seem highly improbable, they regularly occur and do so more often as the component functions increasingly overlap. Singularity theory has been used to explain the occurrence of coinciding solutions and to show that they are a result of systematic errors or nonsystematic errors in the observations. The chapter demonstrates the generality of the proposed definition and criterion. Different from conventional definitions, in the proposed definition, the number of observations need not be such that the use of asymptotic statistical results is justified.

Resolution reconsidered—Conventional approaches and an alternative

Dr. P.W. Verbeek heeft als toegevoegd promotor in belangrijke mate aan de tot-standkoming van het proefschrift bijgedragen. This work was carried out in graduate school ASCI. ASCI dissertation series number 49.

/pdf/the-psd-chip-high-speed-acquisition-of-range-images-3r100xnysy.pdf

The PSD chip - high speed acquisition of range images

Model-based image processing techniques have been proposed as a way to increase the resolution of optical microscopes. In this paper, a model based on the microscope's Point Spread Function (PSF) is analyzed and the resolution limits achieved with a proposed goodness-of-fit criterion are quantified. Several experiments have been performed to evaluate the possibilities and limitations of this method: a) experiments with an ideal (diffraction limited) microscope, b) experiments with simulated dots and a real microscope, c) experiments with real dots acquired with a real microscope. The results show that a threefold increase over classical resolution (e.g. Rayleigh) is possible. These results can be affected by model mis-specifications while model corruption, as seen in the effect of Poisson noise, seems to be unimportant. This work can be considered as preliminary with the final goal being the accurate measurement of various cytogenetic properties, such as gene distributions, in labeled preparations.

Applying the Theory in Quantitative Microscopy

Model-based image processing techniques have been proposed as a way
to increase the resolution of optical microscopes. Here a model
based on the microscope’s point-spread function is analyzed, and the
resolution limits achieved with a proposed goodness-of-fit criterion
are quantified. Several experiments were performed to evaluate the
possibilities and limitations of this method: (a) experiments
with an ideal (diffraction-limited) microscope, (b) experiments
with simulated dots and a real microscope, and (c) experiments with
real dots acquired with a real microscope. The results show that a
threefold increase over classical resolution (e.g., Rayleigh) is
possible. These results can be affected by model misspecifications,
whereas model corruption, as seen in the effect of Poisson noise, seems
to be unimportant. This research can be considered to be
preliminary with the final goal being the accurate measurement of
various cytogenetic properties, such as gene distributions, in labeled
preparations.

Model-based resolution: applying the theory in quantitative microscopy

/pdf/model-based-resolution-34udi91x9j.pdf

Model-based Resolution

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Model-based Resolution

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Resolution reconsidered—Conventional approaches and an alternative

The PSD chip - high speed acquisition of range images

Applying the Theory in Quantitative Microscopy

Model-based resolution: applying the theory in quantitative microscopy

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