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The basic principles of the ionosonde technique for ionospheric electron-density determination are reviewed, with special emphasis on the satellite version. It is shown that the lamination method of data reduction, developed initially for the analysis of ionograms obtained with ground-based ionosondes, can be used to calculate the electron density N versus true height h in the topside ionosphere provided a number of refinements are introduced. These refinements are required because the extraordinary wave data have to be used to obtain N(h) profiles from topside ionograms, and because these data are very sensitive to the magnetic field variation over the great altitude range of topside soundings. A complete procedure for analyzing topside ionograms, based upon a parabolic-in-log N lamination method is presented which incorporates the actual values of the earth's magnetic field at all heights, a change in variable which renders the group path integrand finite at the reflection point, and iteration until successive calculations agree to within 0.01 km. A procedure was also developed to insure and accelerate the convergence of the iteration process. The importance of each refinement is discussed and illustrated quantitatively. It is shown that this new N(h) reduction technique can, in theory, yield topside electron-density profiles with an altitude accuracy of a few kilometers over a 3000 to 400 km altitude range. This theoretical accuracy can be achieved using typically ten to twenty data points per ionogram. In practice, the errors in the N(h) profiles arise primarily from the limited resolution of the ionograms, calibration inaccuracies, and deviations from vertical propagation. The actual accuracy of topside N(h) profiles is discussed in a companion paper .