Velocity distributions calculated from the Fourier transforms of Ramsey lineshapes

A computerized method for finding velocity distributions from the Fourier transforms of Ramsey lineshapes has been developed. Experimental and numerical tests of the method show that it works very well for broad distributions and lineshapes where the drift time is much longer than the excitation time. The method is routinely used to find velocity distributions for the primary frequency standard NIST-7. The second-order Doppler shift is calculated from these distributions with an uncertainty of a few tenths of 1 percent.