Mertz Apodization Function

$\begin{figure}\begin{center}\BoxedEPSF{MertzApodizationFunction.epsf scaled 700}\end{center}\end{figure}$

An asymmetrical Apodization Function defined by

$\begin{displaymath} M(x,b,d)=\cases{ 0 & for $x<-b$\cr (x-b)/(2b) & for $-b<x<b$\cr 1 & for $b<x<b+2d$\cr 0 & for $x<b+2d$,} \end{displaymath}$

where the two-sided portion is

long (total) and the one-sided portion is

long (Schnopper and Thompson 1974, p. 508). The Apparatus Function is

$\begin{displaymath} M_A(k,b,d)={\sin[2\pi k(b+2d)\over 2\pi k}+i\left\{{{\cos[2\pi k(b+2d)]\over 2\pi k}-{\sin(2b)\over 4\pi^2 k^2 b}}\right\}. \end{displaymath}$

References

Schnopper, H. W. and Thompson, R. I. ``Fourier Spectrometers.'' In Methods of Experimental Physics 12A. New York: Academic Press, pp. 491-529, 1974.