Fast Fourier Transform

Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: an approach to in vivo brain iron metabolism?

Toward in vivo histology: a comparison of quantitative susceptibility mapping (QSM) with magnitude-, phase-, and R2*-imaging at ultra-high magnetic field strength.

Problem Given the number of times in which an unknown event has happened and failed: Required the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named. SECTION 1 Definition 1. Several events are inconsistent, when if one of them happens, none of the rest can. 2. Two events are contrary when one, or other of them must; and both together cannot happen. 3. An event is said to fail, when it cannot happen; or, which comes to the same thing, when its contrary has happened. 4. An event is said to be determined when it has either happened or failed. 5. The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon it’s 2 happening.

An essay towards solving a problem in the doctrine of chances. [Facsimil]

Metrology of freeform shaped parts

The well-known problem of fitting a straight line to data with uncertainties in both coordinates is revisited An algorithm is developed which treats x- and y-data in a symmetrical way The problem is reduced to a one-dimensional search for a minimum Global convergence and stability are assured by determining the angle of the straight line with respect to the abscissa instead of the slope As opposed to previous publications on the subject, the complete uncertainty matrix is calculated, ie variances and covariance of the fitting parameters The algorithm is tested using Pearson's data with York's weights Although the algorithm is implemented in MATLAB, implementation in a different programming language is straightforward using the formulae presented An application example is given, a calibration line for dosimetry based on electron spin resonance of alanine is investigated

https://iopscience.iop.org/article/10.1088/0957-0233/18/11/025/pdf

A weighted total least-squares algorithm for fitting a straight line

Form filtering by splines

The Guide to the Expression of Uncertainty in Measurement (GUM) is the de facto standard for the evaluation of measurement uncertainty in metrology. Recently, evaluation of measurement uncertainty has been proposed on the basis of probability density functions (PDFs) using a Monte Carlo method. The relation between this PDF approach and the standard method described in the GUM is outlined. The Monte Carlo method required for the numerical calculation of the PDF approach is described and illustrated by its application to two examples. The results obtained by the Monte Carlo method for the two examples are compared to the corresponding results when applying the GUM.

https://iopscience.iop.org/article/10.1088/0957-0233/19/8/084009/pdf

Evaluation of measurement uncertainty and its numerical calculation by a Monte Carlo method

Within the scope of the efforts concerning the redefinition of the SI base unit 'kilogram' the final results of the international research project aiming at the redetermination of the Avogadro constant are ready to be announced. Among other quantities the volume of two spheres which are made of a highly enriched 28Si single crystal had to be determined. For this purpose a special Fizeau interferometer for the measurement of the spheres' diameters has been developed at PTB. This paper reports the final results of the volumes, the uncertainties and also the latest findings regarding systematic corrections including the effects of surface layers on the pure silicon core. The results are confirmed by density comparison measurements.

https://iopscience.iop.org/article/10.1088/0026-1394/48/2/S12/pdf

Volume determination of the Avogadro spheres of highly enriched 28Si with a spherical Fizeau interferometer

A fast and reliable convolution algorithm to calculate the mean line of a roughness profile using the Gaussian filter according to ISO 11562 has been derived. The algorithm is based on a recurrence relation for the weighting function. This greatly speeds up the calculation, making the algorithm nearly comparable to algorithms using the fast Fourier transform (FFT) in a usual way. The algorithm has been implemented as a short C function to be used with any evaluation program. The application of this function to a measured profile is given for demonstration and compared with the results obtained by the ordinary FFT filter algorithm.

Michael Krystek

Papers

A weighted total least-squares algorithm for fitting a straight line

Form filtering by splines

Evaluation of measurement uncertainty and its numerical calculation by a Monte Carlo method

Volume determination of the Avogadro spheres of highly enriched 28Si with a spherical Fizeau interferometer

A fast gauss filtering algorithm for roughness measurements