A device for exploring the full angular excitation space - Can more angular projections improve determination of a molecules 3D-orientation in the presence of noise?

In the past, different methods have been presented to determine the 3D orientation of single molecules in a microscopic set-up by excitation polarization modulation. Using linearly polarized illumination from different directions and thereby measuring different 2D projections enables reconstructing the full 3D orientation. Theoretically, two projections suffice for a full 3D orientation determination if the intensities are properly calibrated. If they are not, a third projection will enable unambiguous orientation measurements. The question arises if three projections already contain the maximum information on the 3D orientation when also considering the limited number of available photons and shot noise in an experiment, or if detecting more projections or even continuously changing the projection direction during a measurement provides more information with an identical number of available photons. To answer this principle question, we constructed a simple device allowing for exploring any projection direction available with a particular microscope objective and tested several different excitation modulation schemes using simulated as well as experimental single molecule data. We found that three different projections in fact already do provide the maximum information also for noisy data. Our results do not indicate a significant improvement in angular precision in comparison to three projections, both when increasing the number of projections and when modulating the projection direction and polarization simultaneously during the measurement.In fluorescence microscopy polarized illumination from different directions enables the determination of the 3D orientation of single molecules by combining the 2D information of different projection directions. Ambiguities that emerge when using only two projections can be eliminated using a third projection. In a systematic study we show that – also considering the limited number of available photons and shot noise in an experiment – three projection directions already contain the maximum information on the 3D orientation. Our results do not indicate a significant improvement in angular precision in comparison to three projections, both when increasing the number of projections and when modulating the projection direction and polarization simultaneously during the measurement.

Remarks on small sets on the real line Remarks on small sets on the real line

We consider two kinds of small subsets of the real line: the sets of strong measure zero and the microscopic sets. There are investigated the properties of these sets. The example of a microscopic set, which is not a set of strong measure zero, is given.

Micro-Raman spectroscopy applied to polymers

Over the last years micro-Raman spectroscopy has developed to a mature subdiscipline within the field of Raman spectroscopy. Its potential power seems obvious: (a) fluorescence suppression, a major obstacle in many Raman spectra; (b) micro-analysis of samples down to 1 μm lateral resolution yielding molecular information; (c) when using a confocal arrangement with the microscope, in addition to lateral resolution the depth resolution can be enhanced up to the 1 μm level.We applied micro-Raman spectroscopy over the last few years and recently developed a confocal Raman microscopic set-up. Our main application being in the field of polymers, the first thing to worry about is to what happens to the polymer sample when it is irradiated locally with a high laser power density. One should be warned even long before melting in order to avoid morphological changes because, after all, Raman spectroscopy is a powerful tool to study polymer morphology in detail. We use the Stokes/Anti-Stokes intensity ratio for determining the sample temperature.

The Effect of Pigment Particle Size on Some Physical Properties of Rubber Compounds

The importance of flow in rubber on the reinforcing properties of pigmented systems has been emphasized by Park. He suggests that: (1) in the presence of a finely divided pigment, the flow which occurs when a piece of rubber is stretched takes place in the capillary spaces between the pigment particles; (2) some modification of the laws of liquid flow may govern the behavior of rubber with reference to pigments embedded in it, and (3) the forces causing increased stiffness in pigmented rubber compounds are similar to those causing increased resistance to flow of liquids iii tubes of capillary dimensions. Thus increasing fineness of subdivision and the resulting fineness of capillary spaces between the particles should be accompanied by an increase in reinforcing properties. It would be desirable to study the actual stresses around pigment particles in rubber under strain, but so far no suitable microscopic set-up has beem devised. A few years ago the writer, resorting to analogies, measured the strains and stresses around large particles with the assumption that the strains would be relatively the same with small particles. For this study, holes of the desired size and shape were cut in strips of calendered but uncured rubber and fitted with pieces of an uncured semihard rubber compound. After vulcanization squares were marked on the tensile sheets as shown in Fig. 1.