Skip to main content

A New Nonlinear Least Square Algorithm for Voigt Spectral Lines

Buy Article:

$29.00 plus tax (Refund Policy)


In this paper a new fitting algorithm which works with Voigt functions is discussed. The fitting algorithm used is an extension of the rapidly convergent gradient method of Fletcher and Powell, who claim faster convergence than the Newton-Raph-son method which has been used by Chang and Shaw for fitting Lorentz line widths. The Fletcher and Powell algorithm involves the effects of second derivatives although second derivatives are not explicitly calculated. In our algorithm, first and second derivatives are computed not numerically, but analytically via a modification to Drayson's Voigt function subroutine. This algorithm provides rapid convergence even when there are few data points. Profiles have been fitted with as few as five data points. Our typical line fits involve 40 points. The run time of the algorithm has been compared with the shrinking cube algorithm of Hillman and found to be at least 10 times faster under identical starting conditions. Sample single line and single line plus background are shown illustrating the speed and efficiency of the new algorithm, as well as the importance of good zero-order estimates to start the iterations.

Keywords: Computer applications; Line fitting; Spectroscopic techniques

Document Type: Research Article


Affiliations: The Perkin-Elmer Corporation, Norwalk, Connecticut 06986

Publication date: May 1, 1980

More about this publication?

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more