An apparatus was constructed to experimentally quantify the field-free alignment of diatomic molecules irradiated by strong femtosecond laser pulses. In this apparatus, both homodyne and pure heterodyne detections were realized. The alignment signal is proportional to [<cos(2)theta> - 1/3](2) for homodyne detection and (<cos(2)theta> - 1/3) for pure heterodyne detection, where theta is the polar angle between the molecular axis and the laser polarization direction. Fourier transform spectra of the homodyne signal and the pure heterodyne signal were also studied. By comparing the alignment signal and its Fourier transform spectrum with the numerical calculation of the time-dependent Schrödinger equation, we demonstrated that the pure heterodyne signal directly reproduced the alignment parameter <cos(2)theta>, and its Fourier transform spectrum provided information regarding the populations of different J states in the rotational wavepacket.