A holographic technique for studying induced absorption in transmitting media using a scheme with an additional phase measuring grating is described. A matrix analysis is conducted, and expressions for the induced absorption are derived from the asymmetry of the transmitted beam intensity variation. The dynamics of the induced absorption in a photochromic glass is studied by the standard single-beam diffraction method and a new dual-beam interference method. The influence of a residual absorption grating resulting from the measuring phase grating on the induced absorption dynamics is analyzed. Measuring data obtained by the two methods are shown to be in good agreement