A Reference-Free Calibration for Ultrafast Spatiotemporally Encoded 2-D NMR Spectroscopy

Spatiotemporal encoding (SPEN) is a state-of-the-art nuclear magnetic resonance (NMR) technique, utilized to acquire 2-D or even multidimensional ( $n$ -D) NMR spectra and/or images in a single (or a few) scans. Benefitting from special encoding and decoding schemes, SPEN can thus accelerate the classical 2-D NMR experiment by orders of magnitude. SPEN's decoding in particular is executed under the effects of oscillating magnetic field gradients; inevitable hardware imperfections may then give rise to inconsistencies between odd and even SPEN data lines, making only half (odd or even) of the acquired data available for processing. This halves the spectral bandwidth available in the direct dimension and decreases the spectral sensitivity, leading to the emergence of peak folding artifacts and/or a decline of the spectral quality. Past research has been carried out to correct these distortions induced by gradient imperfections, but requires an extra reference scan collected under identical experimental conditions. This work presents a detailed theoretical analysis of the impacts of various imperfections on the 2-D SPEN NMR spectrum and proposes a three-step reference-free calibration algorithm in accordance with theoretical analysis. Experimental data on single-shot 2-D correlation spectroscopy (COSY) and heteronuclear single-quantum correlation (HSQC) NMR spectra collected using SPEN were performed and processed, which demonstrate the feasibility and applicability of the proposed reference-free algorithm.