
3.1.9 Wavelength Calibration
Jack C.M. Wang Statistical Engineering Division, ITL
Sarah L. Gilbert
William Swann Optoelectronics Division, EEEL Many new high capacity systems use several laser transmitters, operating at slightly different wavelengths, to increase the transmission capacity of a single fiber, a technique known as wavelength division multiplexing (WDM). This requires that the wavelengths of the individual lasers be well known and controlled. A NISTdeveloped SRM is a fiberconnected gas absorption cell that permits quick wavelength calibration of instruments, such as optical spectrum analyzers, used in the development of WDM systems. The measurements used in the calibration consist of wavelength and corresponding absorption power. The calibration is carried out by fitting a model, called Voigt, to the data.
A Voigt density is obtained by convolving a Gaussian density with
a Lorentzian (Cauchy) density.
Specifically, if U is a Gaussian random variable with parameters
and ,
and V is a Lorentzian random variable with
parameters
and
and is independent of U,
then
W = (U+V)/2 is distributed as a Voigt with density
function given by
For datafitting purpose, a Voigt model must be general enough to allow for an arbitrary translation of the data. The Voigt model, relating absorption power (y) and wavelength (x), is given by where are parameters of the model. The parameters of interest are the wavelength that attains the maximum absorption power (), and the relative height and width of the absorption power spectrum (functions of and ). Since both power and wavelength are subject to measurement errors, a Fortran program, utilizing a nonlinear errorsinvariables regression procedure, has been developed to estimate the parameters and their standard errors.
Figure 9: The top figure displays the density functions of Gaussian, Lorentzian and Voigt (, , and ). It shows that a Voigt possesses the peak feature of a Gaussian and the tail profile of a Lorentzian. The bottom plots the scatterplot of wavelength vs. power and the Voigt (solid curve) model fitted by the errorsinvariables regression. The ``'' points were used to fit the model and ``'' points were not used.
Date created: 7/20/2001 