Linear regression, combined with search over nonlinear parameters, is useful in fitting Sellmeier formulas to dispersion data. A special advantage accrues in fitting several sets of data to one formula: linear regression permits systematic normalization to a common absolute value. Rational procedures are discussed also for weighting of data sets of unequal precision. The fitting of common formulas to six sets of data on helium, for wavelengths from 0.09 to 2 μm, illustrates the various procedures.
© 1983 Optical Society of America
Original Manuscript: April 18, 1983
Published: September 15, 1983
Edson R. Peck, "Sellmeier fits with linear regression; multiple data sets; dispersion formulas for helium," Appl. Opt. 22, 2906-2913 (1983)