Problem:

In physical chemistry, medical research and other fields, fluorescence measurements are used to obtain information about the microscopic structure of a substance, e.g. the structure of its molecules. The setup of the experiment is as follows. A light flash hits the probe which in return sends out fluorescent light. Its intensity is measured as a function of time. The measurements are distorted by (white) noise, usually 1% to 10% of the intensity of the measured signal. The information desired can be extracted from the so called distribution of lifetimes. The aim of the project was to develop an algorithm that can calculate this distribution accurately from the fluorescence intensity. The effect of the shape of the light pulse, which is itself measured and thus known only approximately, should also be taken into account.

Solution:

The mathematical model for the measurement process leads to an integral equation of the first kind. Such equations are ill-posed, which means that measurement errors are amplified and may lead to meaningless solutions. An algorithm was developed based on regularization techniques, which can solve the problem in a stable way. The example shows that useless results are obtained with a standard algorithm (left) while the regularization algorithm produces results which are optimal for the given noise level (right). In both pictures the true solution (in this example, simulated data were used) is indicated by the dotted line.

Keywords:

Fluorescence Analysis, Regularization, Indirect measurements.

Transferable expertise:

Nearly all indirect measurement problems, where a signal is measured by an instrument which has a spread-out impulse response, lead to the same mathematical problems. Stabilizing via regularization algorithms may improve the measurement quality dramatically.

Contact person:

o.Univ.-Prof. Dr. Heinz Engl

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Today's date and time is 03/21/10 - 15:33 CET and this file ( /industry/examples/fluor.html ) was last modified on 10/21/04 - 17:29 CEST