The radio-wave method for monitoring bronchopulmonary function is attractive due to its simplicity of implementation and safety for patients. The achieved results in imaging the lung air-filling process were encouraging; however, they also revealed several limitations that hinder the development of the method as a diagnostic tool. This paper describes an improved setup for radio-wave monitoring of the breathing process, enabling the measurement of not only amplitude but also phase pulmonograms. The setup is based on the USRP device PlutoSDR and the GNU Radio framework. Using the Helmholtz equations, it was possible to separate the contributions to amplitude and phase variations in the pulmonograms into those associated with changes in lung size during breathing and those related to changes in relative permittivity due to lung aeration. The values of relative permittivity at selected measurement points may serve as a basis for developing diagnostic indicators of various bronchopulmonary diseases. The problem of selecting these measurement points is discussed, drawing an analogy with auscultation points, but focusing on locations that provide information about the lung air filling process. The estimated measurement accuracy indicates that a single breathing cycle is sufficient to determine the relative permittivity at each measurement point.