The Euler transformation is a linear sequence transformation to accelerate the convergence of an alternating series. The sequence of weights of the transformation is extended to a continuous weight function which can accelerate Fourier type integrals including Hankel transforms with a slowly convergent integrand. We show that the continuous weight function can also be used to compute the Fourie...

A Penning trap mass spectrometer is a well established instrument for the precise mass determination of both, stable and short-lived nuclides. For this purpose two different concepts are employed. Masses of stable species are mostly determined by the non-destructive detection of image currents induced in the trap electrodes and a subsequent Fourier transformation (FT). For short-lived nuclides ...

In our last work, we formulate a Fourier transformation on the infinitedimensional space of functionals. Here we first calculate the Fourier transformation of infinite-dimensional Gaussian distribution exp ( −πξ ∞ −∞ α 2(t)dt ) for ξ ∈ C with Re(ξ) > 0, α ∈ L2(R), using our formulated Feynman path integral. Secondly we develop the Poisson summation formula for the space of functionals, and defi...

We present a method of 3D automated shimming in high-resolution applications. This does not heavily rely on Pulsed Field Gradient (PFG) modules and can be used with any spectrometer equipped with shims and homospoil facilities at least. The method exploits Fourier imaging technique for mapping of static magnetic field inhomogeneity and field shapes generated by shim coils, which are used as inp...

Received Abstract. Fe II radiative lifetimes were measured applying the time-resolved nonlinear laser-induced fluoresence technique. We investigated 21 levels of up to 47000 cm −1. The uncertainties are typically 2 – 3 %. The lifetimes provide an improved absolute scale to our branching fractions which were measured with a Fourier transform spectrometer and a high–resolution grating spectromete...

A theoretical model is developed to interpret the output of the diffraction grating spectrometer used to analyze the channelled spectrum produced by a low coherence interferometer set-up. This model leads to an unique interpretation which covers both cases (i) of Talbot bands and (ii) of a Michelson interferometer used in most spectral interferometry set-ups for sensing as well as for Fourier d...

In view of in vivo surgical smoke studies a difference-frequency-generation (DFG) laser spectrometer (spectral range 2900-3144 cm(-1)) and a Fourier-transform infrared (FTIR) spectrometer were employed for infrared absorption spectroscopy. The chemical composition of smoke produced in vitro with an electroknife by cauterization of different animal tissues in different atmospheres was investigat...

We are developing a new type of miniature Fourier transform (FT) Raman spectrometer; the spatial heterodyne Raman spectrometer (SHRS), which provides high spectral resolution in a very small system with high light throughput. The resolution of the SHRS is not dependent on a slit, so miniature systems, <1 cm footprint, can be made with high spectral resolution. The ability to miniaturize the SHR...