Revised analysis of the Zn VI spectrum

1994 ◽  
Vol 72 (5-6) ◽  
pp. 193-205 ◽  
Author(s):  
G. J. van het Hof ◽  
Y. N. Joshi ◽  
A. J. J. Raassen
Keyword(s):  
Least Squares ◽  
Wavelength Region ◽  
Grazing Incidence ◽  
Operator Technique ◽  
Least Squares Fitting ◽  
Extensive Data ◽  
Orthogonal Operator ◽  
Transition Array

The spectrum of zinc was photographed in the 100–300 Å (1 Å = 10−10 m) wavelength region on a 10.7 m grazing-incidence spectrograph. On the basis of these precise and extensive data the 3d7–3d64p transition array of Zn VI was reanalysed. All 19 levels of the ground configuration 3d7 were confirmed but the level values were revised. Out of the 161 levels of the 3d64p configuration reported earlier, 10 levels were rejected and 16 new levels were established thus totalling the known levels to 167. The number of the classified lines is 538, almost doubling the previous number. The least-squares-fitting parametric calculations adequately interpret the observed spectrum. The 3d7 configuration was also described by an orthogonal operator technique.

Analysis of the (5d8 + 5d76s)–5d76p transitions of seven-times-ionized bismuth: Bi VIII

1995 ◽  
Vol 73 (1-2) ◽  
pp. 63-73
Author(s):  
R. R. Kildiyarova ◽  
Y. N. Joshi ◽  
M. A. Lumsden ◽  
A. J. J. Raassen
Keyword(s):  
Least Squares ◽  
Wavelength Region ◽  
Normal Incidence ◽  
Isoelectronic Sequence ◽  
Scaling Factors ◽  
Energy Parameters ◽  
Transition Array

The spectrum of bismuth was photographed in the 400–1200 Å (1 Å = 10−1 m) wavelength region on a 3 m normal incidence spectrograph using a triggered spark source. The 5d8, 5d76s, and 5d76p configurations of Bi VIII were analysed. The missing 1S0 level of the 5d8 configuration, 27 of 38 levels of the 5d76s configuration, and 30 additional levels of the 5d76p configuration were established. One previously identified level at 338 016 cm−1 (J = 3) was revised to 338 701 cm−1. Two hundred and sixty-three lines were classified in the 5d76s–5d76p transition array, and 26 additional lines were classified in the 5d8–5d76p transition array. The least-squares-fitted parametric calculations interpret the observed spectrum satisfactorily. The scaling factors of the energy parameters were compared in the isoelectronic sequence from Au IV to Bi VIII.

The 5s25p4 – (5s5p5 + 5p36s) transitions in Ce VII and 5s25p3 4S – 5s5p4 4P transitions in Ce VIII

2008 ◽  
Vol 86 (5) ◽  
pp. 714-725
Author(s):  
A Tauheed ◽  
Y N Joshi
Keyword(s):  
Least Squares ◽  
Configuration Interaction ◽  
Wavelength Region ◽  
Normal Incidence ◽  
Grazing Incidence ◽  
Spectral Lines ◽  
Hartree Fock ◽  
Resonance Transitions

The spectrum of cerium was photographed in the 300–1230 Å wavelength region on a 3~m normal incidence spectrograph at the Antigonish laboratory and on a 3 m grazing incidence spectrograph at the Institute of Spectroscopy laboratory in Troitsk in the 250–350 Å region. The 5s25p4 – (5s5p5 + 5p36s) transitions of six-time ionized cerium (Ce~VII) were identified. All levels of these three configurations have been established. Forty spectral lines have been classified in the Ce VII spectrum. Configuration interaction Hartree–Fock calculations and least-squares-fitted parametric calculations were used to interpret the observed spectrum. In the Ce VIII spectrum, we have identified the 5s25p3S3/2 – 5s5p4P1/2, 3/2, 5/2 resonance transitions. PACS Nos.: 32.30.Jc, 32.30.–r

scholarly journals An Error-Reduction Method for Temporal Phase Unwrapping Based on Double Three-Step Phase-Shifting and Least-Squares Fitting

2012 ◽  
Vol 6-7 ◽  
pp. 76-81
Author(s):  
Yong Liu ◽  
Ding Fa Huang ◽  
Yong Jiang
Keyword(s):  
Least Squares ◽  
Reduction Method ◽  
Intermediate Phase ◽  
Error Reduction ◽  
Phase Unwrapping ◽  
Phase Shifting ◽  
Surface Measurement ◽  
Acquisition Time ◽  
Least Squares Fitting ◽  
Temporal Phase

Phase-shifting interferometry on structured light projection is widely used in 3-D surface measurement. An investigation shows that least-squares fitting can significantly decrease random error by incorporating data from the intermediate phase values, but it cannot completely eliminate nonlinear error. This paper proposes an error-reduction method based on double three-step phase-shifting algorithm and least-squares fitting, and applies it on the temporal phase unwrapping algorithm using three-frequency heterodyne principle. Theoretical analyses and experiment results show that this method can greatly save data acquisition time and improve the precision.

Fitting Weighted Total Least-Squares Planes and Parallel Planes to Support Tolerancing Standards

2012 ◽  
Author(s):  
Craig M. Shakarji ◽  
Vijay Srinivasan
Keyword(s):  
Least Squares ◽  
Point Contact ◽  
Coordinate Measuring Machine ◽  
Total Least Squares ◽  
Point Sampling ◽  
Least Squares Fitting ◽  
Weighted Total Least Squares ◽  
Measuring Machine ◽  
Fitting In ◽  
Value Decomposition

We present elegant algorithms for fitting a plane, two parallel planes (corresponding to a slot or a slab) or many parallel planes in a total (orthogonal) least-squares sense to coordinate data that is weighted. Each of these problems is reduced to a simple 3×3 matrix eigenvalue/eigenvector problem or an equivalent singular value decomposition problem, which can be solved using reliable and readily available commercial software. These methods were numerically verified by comparing them with brute-force minimization searches. We demonstrate the need for such weighted total least-squares fitting in coordinate metrology to support new and emerging tolerancing standards, for instance, ISO 14405-1:2010. The widespread practice of unweighted fitting works well enough when point sampling is controlled and can be made uniform (e.g., using a discrete point contact Coordinate Measuring Machine). However, we demonstrate that nonuniformly sampled points (arising from many new measurement technologies) coupled with unweighted least-squares fitting can lead to erroneous results. When needed, the algorithms presented also solve the unweighted cases simply by assigning the value one to each weight. We additionally prove convergence from the discrete to continuous cases of least-squares fitting as the point sampling becomes dense.

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