[en] The doublet neutron-deuteron (nd) scattering length b_2,d, which is at present only known with an accuracy of 5%, is particularly well suited to fix three-body forces in novel effective field theories at low energies. The understanding of such few-nucleon systems is essential, e.g. for predictions of element abundances in the big-bang and stellar fusion. b_2,d can be obtained via a linear combination of the spin-independent nd scattering length b_c,d and the spin-dependent one, b_i,d. The aim of this thesis was to perform a high-accuracy measurement of the latter to improve the relative accuracy of b_2,d below 1%. The experiment was performed at the fundamental neutron physics beam line FUNSPIN at the Paul Scherrer Institute in Switzerland. It utilises the effect that the spin of a neutron passing through a target with polarised nuclei performs a pseudomagnetic precession proportional to the spin-dependent scattering length of the nuclei. An ideal method to measure this precession angle very accurately is Ramsey's atomic beam technique, adapted to neutrons. The most crucial part of the experimental setup is the so-called frozen spin target, which consists of a specially designed dilution refrigerator and contains a sample with dynamically polarised nuclear spins. The polarisation of the sample is determined by nuclear magnetic resonance (NMR) techniques. It turned out that the relaxation of the nuclear spins during the necessary ''cross-calibration'' of the two employed NMR systems is ultimately limiting the achievable accuracy of b_i,d. During the extensive use of the Ramsey resonance method in the neutron-deuteron experiment, an idea emerged that the applied technique could be exploited in a completely different context, namely polarised neutron radiography. Hence, the second part of the thesis covers the development of a novel neutron radiography technique, based on the spin-dependent interaction of the neutron with ferromagnetic samples and magnetic fields. For the first time, quantitative imaging of such samples could be performed using a dedicated compact Ramsey apparatus. First results of this spin-off project as well as the principle idea of the imaging technique are presented. (orig.)