The first crude pictures of the structure of Mira photospheres were derived from velocity analyses of emission and absorption lines appearing shifted, doubled and doppler-broadened in Mira spectra. Positions and shapes of profiles change with phase and often do not repeat in successive cycles. Non-repeating cycles are also found in colors (e.g., TiO bands in Fig. 9 of Spinrad & Wing 1969) and in light curves and present, of course, a problem in matching specific observed and modeled cycles. The large geometric extension of Mira photospheres was demonstrated by monochromatic radius observations of o Ceti and R Leo by Labeyrie et al. (1977) and Bonneau et al. (1982) which, however, did not systematically follow the stars through different phases and cycles.

The structure of a Mira photosphere is essentially determined by the propagation of shock fronts. A shock front enters the bottom of the photosphere once each cycle and travels outwards.