Finite Acquisition Time Research Articles

Effects of solar evolution on finite acquisition time of Fabry–Perot interferometers in high resolution solar physics

Context. The Visible Tunable Filter (VTF) imaging spectropolarimeter will be operated at the Daniel K. Inouye Solar Telescope (DKIST) in Hawaii. Due to its capability in resolving dynamic fine structure of smaller than 0.05 arcsec, the finite acquisition time of typically 11 s affects the measurement process and potentially causes errors in deduced physical parameters. Aims. We estimate these errors and investigate ways of minimising them. Methods. We mimicked the solar surface using a magnetohydrodynamic simulation with a spatially averaged vertical field strength of 200 G. We simulated the measurement process scanning through successive wavelength points with a temporal cadence of 1 s. We synthesised Fe 1617.3 nm for corresponding snapshots. In addition to the classical composition of the line profile, we introduce a novel method where the intensity in each wavelength point is normalised using the simultaneous continuum intensity, and then multiplied by the temporal mean of the continuum intensity. Milne-Eddington inversions were used to infer the line-of-sight velocity, vlos, and the vertical (longitudinal) component of the magnetic field, Blos. Results. We quantify systematic errors, defining the temporal average of the simulation during the measurement as the truth. We find that with the classical composition of the line profiles, errors exceed the sensitivity for vlos, and in filigree regions also for Blos. The novel method that includes normalisation reduces the measurement errors in all cases. Spatial binning without reducing the acquisition time decreases the measurement error slightly. Conclusions. The evolutionary timescale in inter-granular lanes, in particular in areas with magnetic features (filigree), is shorter than the timescale within granules. Hence, depending on the science objective, fewer accumulations could be used for strong magnetic field in inter-granular lanes and more accumulations could be used for the weak granular magnetic fields. As a key result of this investigation, we suggest including the novel method of normalisation in corresponding data pipelines.

Quantification of fluctuations from fluorescence correlation spectroscopy experiments in reaction-diffusion systems.

Fluorescence correlation spectroscopy (FCS) is commonly used to estimate diffusion and reaction rates. In FCS the fluorescence coming from a small volume is recorded and the autocorrelation function (ACF) of the fluorescence fluctuations is computed. Scaling out the fluctuations due to the emission process, this ACF can be related to the ACF of the fluctuations in the number of observed fluorescent molecules. In this paper the ACF of the molecule number fluctuations is studied theoretically, with no approximations, for a reaction-diffusion system in which the fluorescence changes with binding and unbinding. Theoretical ACFs are usually derived assuming that fluctuations in the number of molecules of one species are instantaneously uncorrelated to those of the others and obey Poisson statistics. Under these assumptions, the ACF derived in this paper is characterized only by the diffusive timescale of the fluorescent species and its total weight is the inverse of the mean number of observed fluorescent molecules. The theory is then scrutinized in view of previous experimental results which, for a similar system, gave a different total weight and correct estimates of other diffusive timescales. The total weight mismatch is corrected by assuming that the variance of the number of fluorescent molecules depends on the variance of the particle numbers of the other species, as in the variance decomposition formula. Including the finite acquisition time in its computation, it is shown that the ACF depends on various timescales of the system and that its total weight coincides with the one obtained with the variance decomposition formula. This calculation implies that diffusion coefficients of nonobservable species can be estimated with FCS experiments performed in reaction-diffusion systems. Ways to proceed in future experiments are also discussed.

Speed measurement of spherical objects using an off-the-shelf digital camera

Motion blur is a result of finite acquisition time of practical cameras and the relative motion between the camera and moving objects. We present a method for speed measurement of spherical objects using motion blurred images captured by a digital camera. The object is assumed under a straight line uniform-velocity motion, and the speed is calculated according to the imaging geometry and blur extent estimates. We have established a link between the motion blur information of a 2-D image and the speed information of a moving object. Experimental results are presented for the real-scene images.

Monte-Carlo simulation of optical trap stiffness measurement

The high precision calibration of optical trap stiffness is the foundation of the weak force measurement in an optical tweezers system. And the accuracy of the trap stiffness measurement is limited by the bandwidth of the acquisition system. In this article, such an influence is analyzed and discussed. The stiffness measuring process using an acquisition system with a finite acquisition time is numerically simulated by using Monte-Carlo method. Then the simulated results are analyzed by thermal motion analysis method to deduce the trap stiffness for different trapping system and for measuring systems with different acquisition time. As a comparison the power spectrum analysis method is used to study the thermal motion of the bead and to compute the trap stiffness for the same acquisition system, from which it is concluded that the bandwidth of the acquisition system is determined by its acquisition time, not the sampling frequency. The influence of the finite acquisition time or the limited bandwidth on the trap stiffness measurement is discussed. The numerical simulation shows that the measured position, which is here the average position within the acquisition time, shifts to the trap center due to the trapping force, which gives an alternative interpretation for the deviation of the measured stiffness from the true trap stiffness.

Continuous radial data acquisition for dynamic MRI

Since image acquisition times in MRI have been reduced considerably over recent years, several new important application areas of MRI have appeared. In addition to pure static anatomic information, the evolution of a dynamic process may be visualized by a sequence of temporal snapshots of the process acquired within a short time period. This makes applications like interactive or interventional MRI as well as the acquisition of additional functional information feasible. For high temporal resolution, all these applications require a quasi real-time image acquisition during the time the interaction or dynamic process evolves. We present an approach to real-time imaging using a continuous radial acquisition scheme. The intrinsic advantages of radial or projection reconstruction (PR) techniques are used to minimize motion-related image distortions. Modifications of the acquisition scheme as well as dedicated reconstruction techniques are used to further reduce the temporal blurring due to the finite acquisition time of one entire data set in our approach. So far we have used this technique for the visualization of active joint motion.

Comparison of models for parameter estimation in broad-line NMR spectra

The effects of finite acquisition time, improperly chosen sampling time, and spectrometer dead time on broad-line NMR spectra are examined. A discrete Fourier-transform model equation for a nonlinear least-squares analysis that overcomes these limitations is derived. A nonlinear regression method is used to perform the nonlinear least-squares fit of the simulated and experimental data. The accuracy of the proposed model is compared with those of the conventional Lorentzian and the time-domain models. It is shown that the proposed discrete Fourier-transform model yields higher accuracy than the conventional Lorentzian line. The accuracy of the estimation of the proposed discrete Fourier-transform model is similar to that of time-domain model; however, its uncertainty level is lower.

Why carbon-13 FT NMR spectra cannot be phased

It is commonly observed that in spite of repeated cycles of applying zero- and firstorder phase corrections to absorption-mode carbon-13 FT NMR spectra, the spectra still possess what appears to be a residual dispersion-mode component at random places in the spectrum. This phenomenon is not due to any electronic circuit characteristics, but rather arises from a combination of the finite acquisition time of the NMR FID and the discrete nature of Fourier transform spectra. The existence of the phenomenon can be predicted from a knowledge of T/T 2 ∗, the ratio of the acquisition time to the relaxation time of the FID. The reason why the “residual dispersion component phenomenon” is common for FT NMR of nuclei with a wide range of chemical shifts, but not with proton FT NMR, is discussed. The “residual dispersion component phenomenon” can be obviated by exponential apodization, by extended zero filling or by magnitude-Lorentzian interpolation. For well-separated peaks, magnitude-Lorentzian interpolation is the method of choice.