Self-coherent detection with interferometric field reconstruction aims at retrieving the complex-valued optical field (amplitude and phase) by digitally processing delay interferometer (DI) measurements, in order to realize a differential direct detection receiver with capabilities akin to that of a fully coherent receiver with polarization multiplexing, albeit without requiring a local oscillator laser in the receiver. Here we introduce a novel digital recursive algorithm capable of accurately reconstructing the optical complex field (both amplitude and phase) solely from the quadrature DI outputs, eliminating the AM photo-detector branch. We analyze a key impairment namely the accumulation of errors and fluctuations in the reconstructed amplitude and phase due to ADC quantization noise, recirculating in the recursion. We introduce signal processing measures to effectively mitigate this noise impairment leading to a potentially practical self-coherent receiver, demonstrated in this paper for a single polarization. We also investigate the range of applicability of self-coherent detection concluding that it is most suitable to relatively low baud-rate systems such as passive optical networks, for which application the self-coherent receiver outperforms the coherent homodyne receiver due to its improved laser noise tolerance, obtained due to the removal of the optical local oscillator.