A new statistical approach to phase correction in NMR imaging is proposed. The proposed scheme consists of first-and zero-order phase corrections each by the inverse multiplication of estimated phase error. The first-order error is estimated by the phase of autocorrelation calculated from the complex valued phase distorted image while the zero-order correction factor is extracted from the histogram of phase distribution of the first-order corrected image. Since all the correction procedures are performed on the spatial domain after completion of data acquisition, no prior adjustments or additional measurements are required. The algorithm can be applicable to most of the phase-involved NMR imaging techniques including inversion recovery imaging, quadrature modulated imaging, spectroscopic imaging, and flow imaging, etc. Some experimental results with inversion recovery imaging as well as quadrature spectroscopic imaging are shown to demonstrate the usefulness of the algorithm.

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There has been remarkable progress in generating ultralow-noise microwaves from optical frequency combs in the last decade. While a combination of techniques has enabled tens to hundreds of attoseconds residual jitter in microwave extraction, so far most of research efforts have been focused on extracting single-tone microwaves from combs; there has been no study on the noise properties of photocurrent pulses directly extracted from the photodiode. Here, we reveal that the residual jitter between optical pulses and rising edges of photocurrent pulses can be in the tens of attoseconds regime. The rising-edge jitter is much lower than the falling-edge jitter, and further, this ultralow rising-edge jitter could be obtained by both p-i-n and (modified-)uni-travelling-carrier photodiodes. This finding can be directly used for various edge-sensitive timing applications, and further shows the potential for ultrahigh-precision timing using silicon-photonic-integrable on-chip p-i-n photodiodes.

We demonstrate optical-microwave timing synchronization by employing electro-optic sampling-based timing detector with residual phase noise (at 8-GHz carrier) of –174.5 dBc/Hz at 100 kHz offset frequency and 88-as integrated timing jitter (over 1-MHz bandwidth).