We compare frequency-and time-domain formulations of deep-tissue fluorescence imaging of turbid media. Simulations are used to show that time-domain fluorescence tomography, implemented via the asymptotic lifetime-based approach, offers a significantly better separability of multiple lifetime targets than a frequency-domain approach. We also demonstrate experimentally, using complex-shaped phantoms, the advantages of the asymptotic time-domain approach over a Fourier-based approach for analyzing time-domain fluorescence data.Optical technologies for noninvasive macroscopic fluorescence imaging in biological media utilize three main approaches: time domain (TD) using pulsed light sources [1][2][3][4][5], frequency domain (FD) using megahertz modulated sources [6][7][8], and continuous wave (CW) using steady state light sources [9][10][11]. Of these, the TD approach is the most comprehensive, since a short laser pulse (fs-ps) implicitly contains all the modulation frequencies, including the zero-frequency component. The tomographic analysis of TD data can, however, pose computational challenges. Several simplifications have been attempted, primarily using derived data types such as the fast Fourier transform (FFT) [5,7]. The FFT simplifies the TD forward problem but reduces it to a FD forward problem, identical to that for a genuine FD measurement. Alternatively, TD fluorescence data may also be analyzed by estimating lifetimes directly from the asymptotic region, followed by the separate inversion of the yield of each lifetime component [3,12]. The question arises as to how the FD forward problem compares with the asymptotic TD (ATD) approach, when lifetime sensitive targets are used. In this Letter, we address this question both with simulated and experimental TD data in the context of small animal imaging applications.Consider a diffuse imaging medium of finite support Ω, embedded with fluorophores characterized by yield and lifetime distributions, η (r) and τ(r). In the FD approach, the forward problem takes the form [6] (1) Here, G x and G m are the FD Green's functions at frequency ω for propagation from a source r s and a detector r d , respectively, to a medium point r. Equation (1) is first inverted to obtainThe lifetimes are then obtained from the phase Ø(r,ω) of F, as τ(r)=ø(r,ω)/ω. Finally, the yield reconstructions are given by . In the ATD approach, the decay amplitudes, a n (r s ,r d ), for each lifetime component, τ n =1/Γ n , take the place of the Fourier amplitude, , as the measurement data set [3]. The a n 's are related to the yield distribution, η n (r), for the lifetime component at τ n , through a linear forward problem:Note that in Eq. (2), the Green's functions are the same as that for the FD case in Eq. (1), but evaluated at an imaginary frequency of -iΓ n . (see [12] for details). The difference between Eq.(1) and Eq. (2) is clear if we express F(r,ω) in terms of discrete lifetimes rather than the continuous distributions τ(r). We then get F(r,ω)=∑ n τ n η n (r)/(1-iωτ n ). Thus ...