Attenuation correction for confocal laser scanning microscopy and its application in chromatography.

The applicability of confocal laser scanning microscopy is limited, e.g. by attenuation of the excitation and the fluorescence emission beam. As a prerequisite for further processing and analysis of the obtained microscopic images, a new method is presented for correcting this attenuation. The correction is based on beam modelling and on a differential form of the modified Beer-Lambert law. It turns out that the intensity decay can be modelled as a double convolution of the microscopic image with the intensities of the excitation semibeam and the emission beam. Under weak assumptions made for the intensities of the fluorescent radiation and the detected signal, formulas for the attenuation correction and the attenuation simulation are derived. The method traces back to that one published by Roerdink which is modified concerning a more realistic beam modelling, avoiding the so-called weak attenuation expansion and considering fluorescence excitation throughout the light cone of the excitation beam. The applicability of the method is demonstrated for synthetic examples as well as microscopic images of chromatographic beads. It is shown that the new method can be successfully applied for reconstructing the true fluorophore distribution in specimens even if the microscopic images are affected by strong attenuation. LAY DESCRIPTION: The applicability of confocal laser scanning microscopy is limited by attenuation of the excitation and the fluorescence emission beam. As a prerequisite for further processing and analysis of the obtained microscopic images, a new method is presented for correcting this attenuation. The correction is based on modeling the excitation as well as the emission beam and on a modified Beer-Lambert law for beam attenuation. The applicability of the method is demonstrated for synthetic examples as well as microscopic images of chromatographic beads. It is shown that the new method can be successfully applied for reconstructing the true fluorophore distribution in specimens even if the microscopic images are affected by strong attenuation.

Estimation of filler macro-dispersion in rubber matrix by radiometric stereo microscopy.

A new microscopic principle based on radiometric stereo microscopy is presented, which is designed for investigating macro-dispersion of filler in rubber. The image acquisition is combined with a stereological method of estimating the volume-weighted size distribution of the filler particles. Experimental results for carbon black filler in rubber obtained by radiometric stereo microscopy are compared with those from microtomography using synchrotron radiation, and, furthermore, a simulation study is used for evaluation. It turns out that using the new three-dimensional microscopic method, the size distribution of the filler particles can be estimated from fresh cuts of rubber with high accuracy, and thus it is an interesting alternative to well-established dark field microscopy. LAY DESCRIPTION: Macro-dispersion of globular filler particles in a rubber matrix is an important quantity that depends on manufacturing parameters and influences various rubber properties. Therefore, it must be carefully adjusted during the incorporation process and investigated by industrial quality control (ASTM D7723-18). Quality control is usually based on freshly made planar sections so-called fresh cuts through rubber specimen. After stress retention of the rubber one obtains a rough cutting surface in which the filler particles appear as imprints or bumps, called nodges. These nodges can be made visible by classical light microscopy under dark field (DFM) illumination. The systems disperGRADER+ or the disperGRADER Alpha View were specifically designed for rubber inspection. However, it has proved to be very difficult estimating the size distribution of the filler particles from the observed white spots in the DFM image. In any case it is still necessary to compute the size distribution of the filler particles from an estimated size distribution of the section profiles. The latter is numerically unstable, i.e. small errors of the estimated size distribution of the section profiles lead to large errors of the computed filler size distribution. Applying DFM combined with filler dispersion estimation as described in ASTM D7723-18 appears to be a fingerprint method only. For this reason, the new microscope nSPEC 3D was applied for rubber inspection. The principle used for surface imaging is based on radiometric stereo allowing for perfect three-dimensional reconstruction of curved surfaces of fresh cuts. From this reconstruction it is possible to measure the height of particle nodges as well as their volumes. Furthermore, we present a new stereological method for estimating the filler size distribution from samples of the height and the volume of the nodges. Finally, microtomography with synchrotron radiation and computer simulation are applied to evaluate accuracy of the presented method.

Torsion estimation of particle paths through porous media observed by in-situ time-resolved microtomography.

The torsion distribution of cell paths in two-phase flow of a cell suspension through a porous medium is an important quantity for chromatographic processes. It can be estimated from cell tracking in sequences of three-dimensional images of a suspension pumped through the medium, where the images are acquired by in-situ time-resolved microtomography using synchrotron radiation and inline phase contrast modus. This contribution presents a new method for estimating path torsion from discrete positions, where the estimation is based on an appropriate discretization of the differential-geometric formula of the torsion of a space curve. Investigations performed for an alcoholic suspension of silica gel particles pumped through a partially open polyurethane foam show that the shape of the inner surface of the foam has a considerable impact on the particle paths. It turns out that the variance of the torsion for slow particle moving close to the surface is a half order of magnitude smaller than that of fast particles, which underlines the importance of torsion for filter efficiency.

Analysis of spatial cross-correlations in multi-constituent volume data.

We investigate spatial cross-correlations between two constituents, both belonging to the same microstructure. These investigations are based on two approaches: one via the measurement of the cross-correlation function and the other uses the spatial distances between the constituents. The cross-correlation function can be measured using the fast Fourier transform, whereas the distances are determined via the Euclidean distance transform. The characteristics are derived from volume images obtained by synchrotron microtomography. As an example we consider pore formation in metallic foams, knowledge of which is important to control the foam production process. For this example, we discuss the spatial cross-correlation between the pore space and the blowing agent particles in detail.

The chord length transform and the segmentation of crossing fibres.

Segmentation of crossing fibres is a complex problem of image processing. In the present paper, various solutions are presented basing on tools of morphological image processing. Two new image transforms are introduced--the lineal distance transform and the chord length transform. Both transforms are applied to two-dimensional images and their results are three-dimensional images. Thus, the segmentation problem originally formulated for crossing fibres observed in a two-dimensional image can be reformulated as a segmentation problem in a three-dimensional image. This can be solved by a segmentation in the three-dimensional image. Algorithms for the lineal distance transform and the chord length transform are given and their use in image analysis is demonstrated. Furthermore, the chord length distribution function of the foreground of a binary image can efficiently be estimated via the chord length transform.

On the analysis of spatial binary images.

This paper deals with the analysis of spatial images taken from microscopically heterogeneous but macroscopically homogeneous microstructures. A new method is presented, which is strictly based on integral-geometric formulae such as Crofton's intersection formulae and Hadwiger's recursive definition of the Euler number. By means of this approach the quermassdensities can be expressed as the inner products of two vectors where the first vector carries the 'integrated local knowledge' about the microstructure and the second vector depends on the lateral resolution of the image as well as the quadrature rules used in the discretization of the integral-geometric formulae. As an example of application we consider the analysis of spatial microtomographic images obtained from natural sandstones.

An integral-geometric approach for the euler-Poincare characteristic of spatial images

The determination of the Euler-Poincare characteristic of a set can be based on observations of a digitized image of that set. In the present paper the correctness of the method is proved due to a strict integral-geometric approach. Our result also provides a link to the methods which are used in image analysis and are based on graph theory.