The information content of the optical signals collected with continuous-wave (CW) methods is restricted by the constant intensity. In non-scattering media, the optical properties are fully characterized by one parameter, the absorption coefficient, which can be determined by application of the Beer-Lambert law (Eqs. (2.8) and (10.11)). In scattering media, which are described by two optical coefficients (the absorption and scattering coefficients) and by the scattering phase function, the information content of CW methods (measured at a single location and a single wavelength) is insufficient for a full optical characterization of the material. Even in the diffusion-approximation regime, where the details of the scattering phase function are not relevant, since it is only the average cosine of the scattering angle (g = ⟨cos θ⟩) that matters, and where two parameters (the absorption and the reduced scattering coefficient) fully characterize the medium, a single measured quantity, the constant intensity, provides limited information content. Such information content may be enriched by measuring the continuous-wave intensity under different conditions (e.g., multiple angles in the non-diffusive regime, or multiple distances from a point source, or multiple wavelengths of light, or multiple spatial frequencies of structured illumination, etc.), and this may provide valuable additional information for a more complete optical characterization of the medium.

Time-resolved methods, however, in which the detected optical signal is not constant in time, provide additional information related to the distribution of the optical pathlengths in scattering media, which is not accessible to CW methods. Time-resolved methods are typically implemented either in the time domain, with a pulsed light source and time-resolved detection, or in the frequency domain, with an intensity-modulated light source and phase-sensitive detection. Theoretical and general concepts for time-domain methods are described in this chapter, whereas frequency-domain methods are described in Chapter 12. Experimental and instrumentation aspects of time-domain spectroscopy are presented in Chapter 13 (Section 13.4.1). The reader will note that the index of refraction (n) has not been mentioned above in the description of the optical quantities that characterize a scattering medium. The reason is that for light propagation in scattering media, the index of refraction only plays the role of scaling the speed of light in the medium, since cn = c/n.