Synthetic direct demodulation method and its applications in Insight-HXMT data analysis

Aims. A modulation equation relates the observed data to the object where the observation is approximated by a linear system. Reconstructing the object from the observed data is therefore equivalent to solving the modulation equation. In this work we present the synthetic direct demodulation (synDD) method to reduce the dimensionality of a general modulation equation and solve the equation in its sparse representation. Methods. A principal component analysis is used to reduce the dimensionality of the kernel matrix and k-means clustering is applied to its sparse representation in order to decompose the kernel matrix into a weighted sum of a series of circulant matrices. The matrix-vector and matrix-matrix multiplication complexities are therefore reduced from polynomial time to linear-logarithmic time. A general statistical solution of the modulation equation in sparse representation is derived. Several data-analysis pipelines are designed for the Hard X-ray modulation Telescope (Insight-HXMT) based on the synDD method. Results. In this approach, a large set of data originating from the same object but sampled irregularly and/or observed with different instruments in multiple epochs can be reduced simultaneously in a synthetic observation model. We suggest using the proposed synDD method in Insight-HXMT data analysis especially for the detection of X-ray transients and monitoring time-varying objects with scanning observations.

Kelvin probe force microscopy for local characterisation of active nanoelectronic devices

Frequency modulated Kelvin probe force microscopy (FM-KFM) is the method of choice for high resolution measurements of local surface potentials, yet on coarse topographic structures most researchers revert to amplitude modulated lift-mode techniques for better stability. This approach inevitably translates into lower lateral resolution and pronounced capacitive averaging of the locally measured contact potential difference. Furthermore, local changes in the strength of the electrostatic interaction between tip and surface easily lead to topography crosstalk seen in the surface potential. To take full advantage of the superior resolution of FM-KFM while maintaining robust topography feedback and minimal crosstalk, we introduce a novel FM-KFM controller based on a Kalman filter and direct demodulation of sidebands. We discuss the origin of sidebands in FM-KFM irrespective of the cantilever quality factor and how direct sideband demodulation enables robust amplitude modulated topography feedback. Finally, we demonstrate our single-scan FM-KFM technique on an active nanoelectronic device consisting of a 70 nm diameter InAs nanowire contacted by a pair of 120 nm thick electrodes.

Quantitative analysis of neutron-capture gamma-ray energy spectra using direct demodulation

Because of the effects of background and measurement environment and multiplet effects of different elements, high-precision analysis of mixed capture [Formula: see text]-ray energy spectra of complicated formations remains challenging for geochemical elemental logging. The direct demodulation (DD) method makes full use of the measured data information, enabling physical constraints to be rationally applied to the spectral analysis process, and can yield high-precision elemental content from poor-statistics, low signal-to-noise ratio, and disturbed data. We construct mixed formations of different sandstones and limestones, mixed formations of sandstone and anhydrite, and more complicated mixed formations of multiple lithologies and employ Monte Carlo numerical simulations to obtain the neutron-capture [Formula: see text]-ray energy spectra of these mixed formations. We then employ the DD method and the weighted-least-squares (WLS) method to analyze quantitatively such mixed spectra, respectively, and compare the results with the actual contents of formation elements. The results indicate that the DD method offers higher precision spectral analysis compared with the results of the WLS method. The results for the capture [Formula: see text]-ray energy spectra of the formation for two actual wells also indicate that the DD method can be useful for spectral analysis in actual application.