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Student Project: Raphael Frey
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Fitting of 3D-PSF models to fluorescent microbead stacks

Raphael FreyMaster project
Section Microtechnique, EPFLApril 2007



To understand cellular processes down to molecular scales, modern biological research depends on optical microscopy. However, in some cases, even advanced instrumentation as confocal microscopes may not provide sufficient resolution. In this case post acquisition image enhancement operations, such as image deconvolution can be applied. For an optimal deconvolution we need to know the image-forming properties of a microscope. These properties can be described with the point spread function (PSF). Such a PSF can be observed by regarding fluorescent microbeads through a microscope. An example of such an image is shown in Figure 1.

If it is possible to fit an analytical PSF to these 3D images, the properties of the optical system could be determined. A 3D PSF can be deduced from the Maxwell theory of electromagnetic waves. A minimum of the norm of the error between an analytical PSF and real images can then be found with an algorithm described by Newton-Raphson. The implementation of this algorithm provides the characteristic parameters of an optical system, such as the position of a bead, its amplitude, the numerical aperture and the spherical aberration of the objective. In the case shown in Figure 1, for example, the following parameters have been found: NA=1.477 and W=-363nm. The nominal value of NA was 1.45.

Figure 1: Image of a fluorescent microbead (left side) and a simulation of a PSF (right side), x-z sections.

While the main target group was the biological microscopy community, the plugin provides also a good framework for developing and testing new algorithms, making it a useful tool for the image processing community as well. A view of the plugin's GUI, as well as an example can be found in figures 1 to 4. • 30.05.2007