The Gaussian Function

The following is an example of a two-dimensional Gaussian function.

                                                   2
                                             -(X-Xo)
		f(X,Y) = Amplitude x exp( ------------ )
                                                 2
                                               Rx
                                                  
                                                   2
                                             -(Y-Yo)
		                   x exp( ------------ )
                                                 2
                                               Ry

X - horizontal location in space
Y - vertical location in space
Amplitude - Peak amplitude of Gaussian
Xo - horizontal midpoint in space
Yo - vertical midpoint in space
Rx - horizontal space constant
Ry - vertical space constant

Note: A Gaussian specified with a sigma (S or standard deviation) typically has an 2*S*S in the denominator of the exponent while a Gaussian specified with a time constant,a, typically has a a*a in the denominator of the exponent.
Click here for a table taken from the above text which describes the relationship between different measures of Gaussian width.

Click here for a table taken from the above text which describes the relationship between the width of a Gaussian function and the width of its Fourier transform

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