The concept of coherence is fundamental and quite important in all fields dealing with fluctuating quantities. A new method for measuring coherence based on the cross correlations of the tones of a multi-component waveform has been developed. The correlation terms which comprise the measure are samples of the time-frequency correlation functions (TFCF) of scatterers and channels. The measure has been used to characterize the time-frequency spread associated with scatterers and channels and represents the signal coherence. This paper will provide a review of scattering function representations and aggregate coherence measures as derived from a correlation matrix. The new coherence measure termed correlation mass will be defined. It will be shown that this measure can be decomposed into correlated components resulting from interaction with a scatterer and a channel. In other words the composite correlation is obtained by sampling the product of the scatterer and channel TFCF's. Data from in-water experiments and digital sonar simulations will be presented which validates the linear systems model of the composite scattering process.